Why Quantum Mechanics Makes Sense

Conrad Dale Johnson

conraddjohnson@gmail.com

Draft August 11, 2020

Abstract

We take it for granted that our physical environment communicates information, making

things observable and measurable. But this is possible only under very special conditions,

essentially because information is contextual. Measuring or communicating any kind of

information requires an appropriate interactive context, and these contexts are complex,

always involving other kinds of information determined in different contexts. This makes

measurement hard to grasp theoretically, since every measurement involves other kinds of

measurements. But this also places very strong constraints on the fundamental physics of

any universe in which anything is measurable. Observable facts can only exist in a highly

specialized environment where different kinds of interaction provide contexts for each other.

This essay explores the functional requirements for a universe like ours, where new facts are

constantly being defined in local contexts, and then used to set up contexts for other kinds

of facts, in a self-sustaining process. These requirements explain the strange dual dynamics

of quantum theory, with its superpositions and mysterious “collapse of the wave function.”

They also explain why the randomness and indeterminacy of quantum physics nonetheless

support a very different, deterministic dynamics on the scale of classical physics, since both

types of physics are needed to make any measurement possible. Moreover, because the

fundamental physics has to be able to define itself in the web of communications between

local contexts, its background space and time has to be structured on relativistic principles.

Finally, I propose a way of investigating how the amazingly complex and finely-tuned physics

of our universe could have emerged from more primitive systems of contextual information.

Table of Contents

Chapter 1 Introduction 1

1.1 What Does it Take to Make Things Observable? 1

1.2 Why There’s a Measurement Problem 3

1.3 The Genesis of a Self-Defining Universe 5

1.4 The Organization of This Essay 7

Chapter 2 Quantum Measurement as Natural Selection 10

2.1 The Dual Dynamics 10

2.2 The Physics of Possibility 11

2.3 The Collapse 14

2.4 The Born Rule 16

2.5 Natural Selection 18

Chapter 3 Your Present Moment in Spacetime 22

3.1 The World from Inside 22

3.2 Two Versions of Spacetime 23

3.3 Asynchronous Spacetime – EPR and Schrödinger’s Clock 25

3.4 The Equivalence Principal and the Gravitational Metric 30

3.5 Cosmological Questions 32

Chapter 4 On the Origins of Determinate Information 35

4.1 Toward an Archaeology of Physics 35

4.2 Stage I – Interaction 37

4.3 Stage IIA – Recurrence 38

4.4 Stage IIB – Pre-Metric Spacetime 39

4.5 Stage IIIA – Local Gauge Symmetries 43

4.6 Stage IIIB – Locality and Gravitational Spacetime 46

4.7 Summary – The Physics of Possibility 49

Conclusion – What It Takes to be Fundamental 53

End Notes 56

1

Chapter 1 Introduction

1.1 What Does i t Take to Make Things Observable?

Classical physics describes a world that makes sense to us. There are always precisely definite facts about

things and their relationships in space and time, whether or not these facts happen to be observed. Then

given these facts, all interaction between things is exactly determined by a few simple mathematical laws.

This gives us a very clear idea of how the physical world works, and it’s verifiably correct to a very close

approximation. So why should physics be so radically different at a more fundamental level, and vastly

more complicated?

The precise determinism of classical physics is the statistical result of a deeper -level physics that’s largely

indeterminate and random, yet at the same time so complex that we need quantum field theory and the

Standard Model to describe it. Here measurement plays an important role that hasn’t been understood:

in general, there are definite facts about quantum systems just to the extent that the context in which we

observe them makes those specific facts determinable. If a particle’s momentum can’t be measured, for

example, in a given interactive context, then quantum theory tells us it has no definite momentum. But

the theory doesn’t tell us what counts as a measurement; in fact, the linearity of its equations should

prohibit any “collapse of the wave function” under any circumstances.

The goal of this essay is show why all this makes sense – why a universe like ours needs to be based on

this strangely complex and seemingly incomplete kind of physics. The key is to clarify what’s required to

support an interactive environment that makes things observable by defining and communicating facts.

Though we take it for granted that interaction conveys information about things, I’ll argue that it takes a

highly specialized system involving many kinds of interactions to make this possible. The same argument

explains why the concept of measurement is so obscure at the quantum level, and why the pervasive

randomness and indeterminacy of the quantum realm can nonetheless give rise to the simple, clearly

defined and deterministic world of classical physics. In short, I’ll show that both quantum and classical

physics are needed to make any information observable, or even meaningfully definable.

Before proceeding with the argument, I want to point out that we have strong prima facie evidence for

this thesis. Our universe is incredibly rich in observable phenomena, and gives us many ways of measuring

them. But any measurement is possible only because there are things that serve as reliable clocks and

rulers and detectors, etc. – and such things only exist because of the great stability and exact uniformity

of atomic structure. If there were no atoms, or if each atom had slightly different properties, or if atoms

didn’t connect in complex ways to build quasi-rigid molecules, there would be no higher-level structure in

the universe. There could then be no way to determine distances in space or time, or any other kind of

information.

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Now it was already clear to Bohr that the precise determinacy of the classical domain is needed to make

any kind of measurement possible.[1] But we also need the quantum physics that stabilizes atomic nuclei

and their electron-shells – physics that’s not only very complex, but also finely-tuned in many respects.

According to well-established theory, a universe could be based on exactly the same physics as ours, with

only minor changes in a few basic constants, and never be able to produce any stable atoms.[2] In such a

universe, particles could have no determinable properties; neither space nor time nor any of the laws of

physics would be observable, or even definable.

Of course such a universe would have no observers either – so why would it matter if there’s nothing to

observe? Can’t particles actually be there, having certain properties and obeying certain laws, whether

or not there’s any way to measure them? Yes, that’s how we think about reality in classical physics, where

well-defined information is just assumed to exist in the things themselves, whether or not there’s any

context that can actually define it. But quantum theory is telling us something else, which is what we’re

trying to elucidate here. The first step is to see that there’s something quite remarkable about a physical

environment like the one we live in, where many different kinds of facts are constantly being determined

and communicated, over and over again in every moment, from countless different points of view.

I’m not saying that a universe has to have atoms just like ours, in order to define observable facts. There

might well be many other ways for a system of interactions to measure and communicate information. In

the only universe we know about, though, it takes a lot of very complex and counter-intuitive physics to

accomplish this. So it surely makes sense to consider what’s needed, in principle, to make information

observable and measurable. What does it tell us about our universe that it can do this?

Recently it’s become normal for theorists to contemplate a vast landscape of universes with different

values for their basic constants, or with entirely different mathematical foundations. But if observable

information can only exist in our universe because of the finely-tuned combination of many kinds of

interaction, it seems likely that few of these alternate universes would be able to produce discernible

facts, or make any of their structural parameters physically definable.[3] And if most of these worlds are

empirically indistinguishable from each other, then they really differ only on paper. The concepts we use

to describe them mathematically make sense in the context of our observable universe, but would have

no definable meaning within the worlds they supposedly describe.

In our universe, on the other hand, all kinds of phenomena are empirically definable in the context of

other observable phenomena. And it seems that most of what we know about quantum physics and

cosmology is in some way involved in making this information-defining system work. So if we can clarify

what’s needed to support such a functional communicative environment, that could take us a long way

toward explaining not only the strangeness of quantum mechanics, but all the peculiarities of the Standard

Model plus gravity, including its finely-tuned constants.

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1.2 Why There’s a Measurement Problem

The main obstacle to such a program is obvious: at a fundamental level, we don’t even know what a

measurement is. Quantum mechanics seems perversely designed to make this question as obscure as

possible.[1] What I want to show, however, is that QM isn’t to blame for our difficulties in understanding

measurement. It’s the other way around: what’s made quantum physics seem so incomprehensible is

our reluctance to deal with some basic facts about how things get measured.

These facts are easily summarized. The observable world consists of many kinds of information, and they

all get measured in different ways. There’s no one way of interacting with things that’s basic to all

measurements. Moreover, setting up a context in which one kind of information can be measured always

involves making other kinds of measurements. Just to make a distance in space observable, something

other than space also has to be observable. So I’m taking this as a fundamental principle, which will be

the basis of my argument: no kind of information can ever be observed or measured except in the context

of certain other kinds of information that are also observed and measured.

Physicists generally treat information as an abstract quantity – as a number of bits or qubits. Yet any

information that can be defined or used in any way is always information of some particular kind, in the

context of other related kinds of information. Even in pure mathematics, for example, to define a number

you also need to define another kind of information, i.e. the operations to be performed on numbers.[2]

A logical bit can only hold usable information if we can also specify its location in a string or storage -unit.

In short, information is inherently contextual: it can only exist where different kinds of information

provide contexts for each other.

The physical world clearly bears this out. It’s structured by a remarkably diverse array of measurable

parameters: there are intervals in space and time, velocity and acceleration, mass and charge, energy and

momentum, electromagnetic potentials, the speed of light, the gravitational constant and many more,

including all the variables and constants of the Standard Model. None of these quantities is determinable

by itself, or has any definable meaning apart from the others.[3]

As we’ll see, this contextual interdependence is at the root of the quantum measurement problem. That

problem doesn’t stem from anything peculiar to the quantum realm, but from the nature of information

itself. The main reason measurement is hard to conceptualize, at a fundamental level, is that any context

in which one parameter can be measured always involves other parameters, that need to be measured in

other kinds of contexts.[4] Since every measurement depends on information provided by other kinds of

measurements, nearly all of physics could ultimately be required to make any measurement possible. In

any case, contexts can have no clear boundaries. Measurement can never be adequately conceived as a

specific set of events in isolation, or as a chain of interactions that transfers data from an object to an

observer. Such descriptions radically oversimplify the situation, by taking the existence of measurement-

contexts for granted.

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Now physicists are well aware of the deep complexity and “messiness” of any actual measurement-

context, at a fundamental level. Unfortunately this makes the notion of context seem ill-defined, or at

any rate too difficult to approach theoretically.[5] We’re used to conceiving the world in terms of discrete

entities or fields with clearly defined, context-independent characteristics – reasonably enough, since this

way of thinking is highly effective everywhere except in the quantum domain. In classica l physics and in

all the other sciences we expect our theories to describe objective reality, i.e. what things actually are in

and of themselves.[6] It seems bizarre that quantum theory makes the factual reality of things depend

on the existence of complicated measurement-contexts.

Of course these contexts also exist at the level of classical physics – but there we can afford to take them

for granted. At that scale the web of interactions is extremely dense; it constantly communicates highly

redundant information about things through many different channels at once. Because there are always

adequate contexts, at this level, we can always find ways of measuring things as closely as we like. The

specific contexts don’t matter at all, so long as they all produce consistent information about things. We

only have to concern ourselves about them at a practical level, when special arrangements are needed to

measure something, or when we have to resolve discrepancies between measurements. So in classical

physics we do very well without any theoretical conception of context. It never becomes an issue that

contexts always depend on the existence of other kinds of contexts.

In quantum physics, on the other hand, we’re right at the edge of what’s measurable. Observations of

quantum systems typically depend on a single interaction, like a particle hitting a detector. And here it

turns out that the contexts are crucial – determinate information only exists when and where the context

actually determines it. If there’s any way to tell which path a particle takes, in a dual-slit experiment, then

it takes a particular path; otherwise not. This seems to make no sense because in daily life, and in all the

rest of science, we take the objective reality of things for granted, along with the interactive environment

that defines that reality.

At a fundamental level, though, this can’t work: no inherently determinate objective reality can function

as the basis for an observable world. Here’s why: even if there were some definite factual reality at the

bottom of things, only what’s observable can contribute to the contexts in which other information is

observable. Only information that gets communicated through interaction can play any role in defining

and communicating other information. This means that the ultimate reality of things in themselves is in

principle irrelevant to the structure of interdependent contexts that make things measurable. Whether

or not there’s any underlying reality, the world of communicated information has to be able to define

itself entirely in terms of itself.[7]

Any fundamental physical theory, then, has to be concerned with the complex structure of different kinds

of contexts. The basic issue is not what the world ultimately is, but what it does, to maintain a functionally

self-determining informational environment. It’s true that the concept of context is not currently well-

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defined, but we need to remedy that, if we want to understand why the deepest levels of physics we can

reach are also the most complicated, or why this physics has to be so finely-tuned.

The good news here is that our current theories, based on quantum mechanics and relativity, provide a

remarkably detailed set of blueprints for the system that produces measurable facts, in our universe.

Complex as this system is, we have nearly complete specifications for its many components. If we still

don’t seem close to a truly fundamental theory today, despite this amazing depth of knowledge, it’s

because we’ve had no clear idea of what it means to be physically fundamental. We haven’t tried to

imagine the physical world as a functional system, where all these diverse types of informational structure

work together to make each other determinable.

As to our two foundational theories, quantum mechanics and relativity, the main reason it’s been so hard

to clarify what they’re telling us about the world, or how they’re related to each other, is the taken-for-

granted assumption that they describe objective reality – as classical physics and all the other sciences do.

When we approach them that way, these two theories seem to give completely different pictures of the

underlying reality, based on nearly incompatible mathematical frameworks. And both these pictures

seem so different from the world we actually experience, in daily life, that we hardly expect either one to

make any sense to us, except as mathematical structures.

But the problem we face is really just the opposite. The reason these two theories are so di fficult to

comprehend is that what they’re describing is the world we experience – the world of communicated

information – and we haven’t yet learned how to think about physics from this point of view. Trying to

incorporate “the observer” into our theories can’t help, so long as we haven’t clarified what obser ving

means. And that can’t be done unless we focus on the structure of mutually-supporting contexts that

makes any kind of observation possible.

1.3 The Genesis of a Self-Defining Universe

We usually think of defining, observing and measuring as human activities, not as functional capacities of

the physical world. And as human activities they seem deceptively easy. All I have to do is open my eyes

and a huge quantity of information comes flooding in – so observing seems effortless. Measurement too

seems simple and elementary, just a matter of comparing things with each other and recording the data.

I can check how big something is by putting a ruler next to it; I tell time by glancing at a clock; I can see

how much something weighs just by setting it on a balance-scale.

At a deeper level, though, none of this is simple at all. Our visual perception of things turns out to depend

on the coordinated activity of many highly-evolved neural processing systems in our brains. Clocks and

rulers and even gravity are profoundly complex, at bottom. There are no fundamental processes in

physics that just copy information from one system to another, or compare one bit of data with another.

A photon conveys information in its linear and angular momentum, but only if it’s absorbed by an electron

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or some other charged particle, shifting the state of the particle in ways that make a difference in some

other context – by changing the energy-levels of an atom, for example, which changes the configuration

of a molecule, and so on. Every physical interaction makes a difference to some other type of interaction,

which then makes a different kind of difference to something else.

Moreover, our mathematical description of interactions, at the quantum level, treats them as complex

superpositions of many possible events. All basic processes in quantum physics are both complicated and

largely unpredictable. At the level of individual quantum systems and interactions there are structures of

potential information, as represented in wave-functions, but actual facts about their position, momentum

etc. only emerge at a higher level, where different kinds of interaction-contexts support each other in

making specific facts determinable.

In the next chapter we’ll consider at length how this happens. We’ll conceive the physical world as a self -

sustaining system of measurement-contexts, defining and communicating the many kinds of information

needed to keep on setting up more such contexts.[1] As a step toward understanding how such a system

works, Chapter 2 explains why the base-level physics needs to be described in terms of superpositions of

possibilities, why definite facts nonetheless appear wherever some context can define and communicate

them, and why the probabilities of specific outcomes are given by the Born rule.

Here I want to open up some broader questions about this approach, which will also be addressed in

subsequent chapters. First and foremost, if it really takes all the finely-tuned complexity of our known

physics to make anything observable, why should such a system come to exist, and how did it arise? And

how can atomic structure play any fundamental role in this, when we know there were no atoms for the

first 300,000 years of cosmic history?

The current concordance model of cosmology gives a detailed, well-substantiated sequence of events

going nearly all the way back to the beginning of the universe, assuming that the basic laws of physics

were already established in the first nanoseconds. And since nothing could have been measurable in the

high-energy chaos of the early universe, doesn’t this prove that a very complex system of physics can be

well-defined independently of the contexts that make its components determinable?

I don’t think so, but we’ll consider this question further in Chapter 4. I don’t doubt the validity of the

established cosmic history, which explains so much about the composition of the universe we see today.

But the question is how to interpret this story from a quantum mechanical standpoint. When we look

back toward the origin of the universe, empirical evidence made available by our current environment

lets us reconstruct the long and complex sequence of events that eventually resulted in the emergence of

atoms, molecules and higher levels of material structure. But before all that happened, no such evidence

could exist. Early on, our finely-tuned system of particles and interactions – the system of physics that

turned out to support atomic structure – wouldn’t have been distinguishable in any way from countless

other possibilities.

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What quantum mechanics suggests is that all these possibilities need to be taken into account when we

consider the state of the pre-atomic universe.[2] Only as there gradually emerged a structure of contexts

that could define and communicate facts, did it also become possible to define the specific sequence of

historical events that resulted in this particular system. At that point all other possible histories became

irrelevant. The only prior events that could leave any definite trace in the newly emerging universe of

atomic interaction were those that conformed to the changeless laws and principles of this new world.

This doesn’t mean that the entire structure of our current physics suddenly appeared all at once, out of a

chaos of indefinite possibilities. It’s true that before there were atoms there could have been no way to

define a spacetime metric, or to make any kind of quantitative measurement. But there are important

features of our current physics that can be defined without reference to any metric – for example, the

basic underlying structure of electromagnetism, or the many types of symmetry we find in the structure s

of spacetime and the Standard Model. As I’ll propose in Chapter 4, we can consider these diverse types

of pre-metric structure as evidence for a sequence of “prehistoric” stages through which our self-defining

universe emerged. That is, certain basic kinds of information may already have been definable in terms

of each other, before there were physical contexts that could determine intervals in space and time, or

define trajectories for individual particles, or make other quantitative parameters physically measurable.

In any case, I have no doubt that something like the current theory of the early universe is essential to

understanding the world as we see it today. But this theory doesn’t tell us anything about how or why

this particular complicated, multi-layered system of broken and unbroken symmetries came to exist. It

doesn’t attempt to explain why the physical world should be based on this particular set of observable

parameters, or why it’s so finely-tuned to support the emergence of many levels of stable higher-level

structure. Within the framework of current theory it hardly seems possible to ask such questions. But

my aim here is to show that our established theories are telling us much more than we’ve so far been able

to recognize about why our world is built the way it is.

1.4 The Organization of This Essay

The underlying question I’m raising here is this: how and why does our physical environment convey

information? The key point I’ve made is that no kind of interaction does this by itself. Observing any

parameter requires a context in which other parameters are also observable, and those require other

kinds of interaction-contexts. This means that the base-level structures that support a self-defining

universe are necessarily diverse and complicated. However, to a great extent we know what these

structures are, in our own universe. So the task we face is essentially a matter of reverse engineering. If

we can be clear about what this system of physics does, we can figure out how it works.

In Chapter 2 we take up the key issue: how do quantum measurements actually happen, and why does

the theory seem to be silent about this? The vast literature on this question has helped clarify some

features of the quantum domain, but it’s never focused on the system of mutually supporting contexts

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that makes measurement possible. I’ll argue that by taking this into account, we can make sense of

quantum mechanics just as it stands, without any specific mechanism to “collapse” the wave-function.

Measurement is understood here as a type of random natural selection, analogous to – but also very

different from – the Darwinian selection that drives biological evolution.

Chapter 3 brings relativity into the picture. Based on the argument of section 1.2 above, I’ll explain why

the absolute space and time of Newtonian physics can’t function as the framework for an observable

world. On the other hand, the peculiar way in which space and time are connected in Special Relativity

provides just the kind of framework needed for the parallel distributed processing system of a self -

defining universe, where local measurement-contexts constantly define new facts and pass them on to

set up more such contexts elsewhere. We’ll see that the flexible spacetime metric of General Relativity

has several important functions in supporting the emergence of atomic structure, and that the parameters

defining gravity and the cosmic expansion need to be especially finely-tuned for the system to work.

This chapter also clarifies the connection between quantum theory and relativity, in that both these

theories describe the physical world “from inside” – from particular points of view in local contexts –

rather than from the universal “God’s eye” viewpoint that’s implied in the notion of objective reality.

While both theories support the objective reality of classical physics, at a higher level, the underlying

structure of the world is that of communication between local contexts. Understanding this functional

requirement helps clarify the meaning of locality and non-locality in physics, and lets us make sense of

strange situations like the EPR correlations and Schrödinger’s cat.

Chapter 4 suggests a way of understanding how a complex self-defining system like our universe could

have emerged through a sequence of stages. It involves no new physics, but aims at sorting out distinct

layers of structure in our established theories, to identify simpler precursors of our current observable

world. The starting-point is a more radical version of the quantum vacuum – an environment of entirely

unconstrained and structureless interaction. The idea is that very primitive contextual structures could

have emerged in this environment by defining their own constraints, providing a foundation for higher-

level self-defining systems. The assumption is that all these levels of structure should still be evident in

the physics of our universe today.

Traditionally, the ultimate goal of physics is to explain all the complexities of the universe on the basis of

a simple and unified mathematical foundation. This ambition proved very useful up to the advent of the

Standard Model, but since then its prospects have dimmed, since it hardly seems possible that a more

unified theory will be in any sense simple. But even if such a theory could be found, how much can we

expect it to tell us? If all the basic interactions derive by spontaneous symmetry-breaking from some

underlying structure, that still gives no way of explaining why that structure should exist to begin with;

nor would it help us understand the remarkable diversity, complexity and fine-tuning of the physics that

operates our universe today. Whether or not all these interactions are ultimately the same, what’s more

important are the profoundly different roles they play in sustaining a communicative environment.

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My proposal is that we should embrace the messiness and diversity of our empirically established physics,

and of measurement-processes in particular. The goal shouldn’t just be a more elegant and unified formal

theory, but a way of understanding why these many kinds and levels of complex structure are needed for

a universe like ours to work. I want to show there’s a clear path toward explaining the basic features of

quantum mechanics, relativity and classical physics by considering the functional requirements of a world

of determinable facts. If this kind of approach can succeed, we have at our disposal a vast resource of

knowledge to draw on in investigating why this system needs to operate with such a wealth of complex

structure, and how such an astonishingly productive system could have come to exist.

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Chapter 2 Quantum Measurement as Natural Selection

2.1 The Dual Dynamics

The previous chapter presented a conception of the physical world as a web of measurement-contexts,

where new facts are constantly being defined and communicated in order to set up more such contexts.

These measurement-contexts are profoundly complex, always consisting of many kinds of interactions,

and since they’re neither discrete entities nor fields, it’s not clear how to approach them theoretically.

Nonetheless, we know a great deal about them, in that we understand the kinds of situations we need to

set up to be able to measure any physical parameter. Moreover, my goal in this chapter is to show that

quantum mechanics already gives us a highly-developed theoretical description of just this kind of

foundational structure, though it hasn’t been conceived in these terms.

What I want to focus on here is the dual aspect of quantum dynamics. On the one side we have the

continuous evolution of quantum systems represented by the wave-function; on the other, there’s the

seemingly unaccountable, discontinuous “collapse” that happens when measurements are made. The

whole content of the theory lies in the equations, which are mathematically deterministic, like those of

classical physics. However the equations don’t describe any definite, factual reality. They represent

systems as superpositions of possible states and interactions – more precisely, as superpositions of

possible measurement results, in some specified context. They provide no mechanism for selecting a

particular outcome when a measurement is made, “collapsing” the superposition and updating it with

new information. The equations say that when quantum systems interact, their superpositions become

entangled in more complex superpositions, preserving unitarity. No collapse should ever occur.

Nonetheless, measurements give results. As soon as there’s a context that makes something about a

system determinable, a particular fact appears. What’s strange about this is not just that there’s no

physics to account for it; it’s also that these contexts are non-local in space and time. They can include

arbitrarily distant events, and may not even involve any interaction with the system itself, as in the EPR

scenario, where we determine the spin-orientation of a particle by interacting with another entangled

particle far away. In delayed-choice experiments, we don’t decide what the measurement-context will be

until after the interaction we’re concerned with has already taken place; even so, what happened in that

interaction still turns out to depend on the context we choose later on. Or in the quantum eraser version

of the dual-path experiment, the context is set up to determine which path each particle takes, which

should collapse the superposition. If the which-path information becomes inaccessible, though, the result

is just as if no collapse had occurred. So in every case, there get to be definite facts about quantum

systems just insofar as the overall context makes those facts physically knowable.

This is true even where no actual measurement is involved. Wherever the physical context makes it

possible to infer something about a system indirectly, the effect is the same as if that information had

been observed. For example, there’s no need to measure the momentum of an atomic electron to know

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that it lies within a limited range, since if its momentum were any greater, it wouldn’t stay bound to the

nucleus. Since the context determines the electron’s momentum to that extent, the uncertainty principle

requires its position to be indeterminate within a corresponding range, just as if its momentum had been

measured. And this indeterminacy has important physical consequences. The fact that atomic electrons

can’t have exact locations plays a primary role in stabilizing atomic electron-shells against the Coulomb

force, which would pull the electrons into the nucleus if they could be that precisely localized.

The point is that the determinacy of facts about a quantum system doesn’t necessarily depend on the

presence of an observer, or even a measuring device. But it does depend on the ability of the interactive

environment to determine those facts, and make them relevant to other contexts where other kinds of

information are determined. This only makes sense if we think of facts as existing in the informational

environment, not in quantum systems by themselves.[1]

As argued in the Introduction, a universe needs to support this kind of self-determining environment to

have any definable structure. This doesn’t necessarily involve observers who exchange information with

each other, but it does require a system of interactions that makes measurement and communication

possible. Since all observable information must always be definable in the context of other observable

information, the fundamental structure has to be one in which contexts can determine facts and pass

them on to set up other such contexts. The existence of any intrinsically determinate underlying reality

is in principle irrelevant to the functioning of such a system.

How can we describe the dynamics of this kind of environment, where facts are not just given in reality

but have to be constantly defined and communicated? The answer is quantum mechanics, with its dual

dynamics of superposition and collapse. To demonstrate this, I first want to explain why a fundamental

theory has to represent systems as superpositions of possible measurement-results. I’ll then show why

quantum theory provides no mechanism for collapsing these superpositions – why no additional physics

is needed for the selection of particular outcomes, once a measurement-context is set up – and why the

probabilities of the various possible outcomes are given by the Born rule.

2.2 The Physics of Possibility

The long debate over the meaning of the wave-function has essentially two alternatives in view. The

“ontic” position takes this function as describing a strange kind of objective reality, where systems exist

in a superposition of their possible states. In the “epistemic” approach it only represents our knowledge

of these systems. But this dichotomy is misleading. I don’t doubt that quantum theory tells us about

what’s out there in the physical world, not what’s in our minds. But quantum systems have no definable

reality in themselves, apart from the web of contexts that define and communicate their states. The base-

level structure of the world is indeed the structure of what’s knowable, i.e. what’s physically determined

about a system in a specific context. But it doesn’t depend on what anyone actually knows.

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The wave-function represents a certain kind of situation, in which a certain set outcomes are possible,

and where the particular outcome that actually occurs makes a difference to what’s possible in other such

situations. If instead we take the equations as describing quantum systems by themselves, it seems

bizarre that a system can be in many different states at once, or follow many different paths. But there’s

nothing strange in considering a situation as a superposition of possibilities, some of them more likely

than others. In fact this is just how we ordinarily describe situations, in terms of the various things that

can happen in them. Of course quantum superpositions are different from the kinds of situations we

generally encounter, in that they manifest cyclical patterns of interference between their possibilities.

That’s an issue we’ll take up later on, in Chapter 4.[1]

Now one reason for our difficulty in conceptualizing quantum physics is that our traditional notions of

possibility and probability are inadequate. Because we’ve taken it for granted that facts about reality are

fundamental, we’ve given possibility no significant role to play in the physical world. We generally

describe possibilities just the same way we describe facts, except that possibilities may not actual ly be the

case.[2] For example, the walls in my study are green, but they could be painted blue – that’s the sort of

possibility we usually have in mind. In the deterministic world of classical physics, possibilities are just

facts that happen to lie in the future, but will certainly occur. And probabilities only exist in our minds,

due to our limited ability to predict future events.

In quantum theory, however, possibility comes first. The equations describe the world entirely as a

structure of more and less probable possibilities. In any particular situation, the possibilities for what

might happen are strongly constrained, both by the laws of physics and by the context of previously

determined facts. These constraints, reflected in the wave-function, shape the situation by making many

outcomes impossible, and making some possible outcomes more likely than others – the more likely ones

being those that can come about in many different ways.[3] But only rarely do the laws and prior facts

together determine a unique result. Even when they do – where the context requires some parameter of

a system to have a specific value – this only makes all the system’s conjugate variables less determinate,

per Heisenberg’s principle.

To make sense of this we need to conceive possibility as a category in its own right, not as a secondary,

provisional mode of factuality. Possibility means the same as indeterminacy – i.e. freedom, subject to

constraint. Without constraints, possibility can have no shape – it can’t be the possibility of anything in

particular. Possibility evolves by being restricted, narrowed down – possibilities become more specific

the more tightly they’re constrained. What quantum theory describes is a world of possibilities limited

by a complicated set of mathematical rules. These operate to support a process in which new factual

constraints are constantly being defined, so as to set up new situations that can keep this process going.

This way of conceiving the world as an evolving structure of possibilities is unfamiliar, but it’s not at all in

conflict with our ordinary experience.[4] At any moment in our daily lives we’re in some situation where

many things might happen, some of them much more likely than others. When something does happen,

13

that changes the possibilities and probabilities for what can happen next, and what can happen elsewhere

later on. We’re used to thinking of this in terms of classical causality, where precisely determinate facts

exactly determine what happens, so that possibility and probability have no role to play. But the picture

I’m sketching here is really much closer to our experience of the world, where nothing is ever perfectly

predictable. Our minds and even our sensory systems operate by anticipating what might be helpful or

dangerous or interesting in the current situation. We perceive the world mainly in terms of what might

happen and how our situation might change; only secondarily do we step back and observe objective facts

about things.

Likewise any measuring device must be set up to define a certain range of possible results. Every system

of communication involves a set of possible signals and meanings from which actual messages can be

selected. Any context in which information can be determined is essentially a structure of possibilities.

Measurement results and meaningful messages narrow down the scope of subsequent possibilities,

constraining them so that new possibilities arise in new situations.[5]

At the level of classical physics, the combination of laws and facts is so constraining that it seems to

eliminate possibility altogether, forcing things to happen exactly according to mathematical laws. Yet if

we want to imagine such exact determinism working at a fundamental level, we have to overlook some

fairly obvious problems. It’s not just that it would take an infinite amount of information to define the

position and momentum of each and every particle in the universe. Even if that were possible, the

equations of classical dynamics couldn’t actually determine trajectories for these particles. We know

there’s no analytic solution to Newton’s equations for the motion of just three gravitating point-like

masses, even if they could be isolated from any other influence. The more accurate equations of General

Relativity have no known solution for just two bodies, unless we ignore the mass of one of them. So to

suppose that physical dynamics is mathematically determined is just a fantasy: in general, mathematics

can only define trajectories perturbatively, by a process of successive approximation. Yet the physical

world itself can obviously define trajectories for huge numbers of particles, interacting in many different

ways at once, and it does so in real time.

Quantum theory shows us how this is accomplished. This physics doesn’t operate with infinitely exact

information about things, and it doesn’t compute trajectories. Instead it applies constraints to set up

complex structures of possibility, represented by wave-functions, and then lets the actual outcomes be

selected by chance. This is the dual dynamics at work. The very precise synchronization of countless

trajectories, at the level of classical physics, isn’t achieved by making things obey mathematical laws, but

by quantum statistics applied to huge numbers of aggregated events. And fortunately, because physicists

can imitate this procedure with remarkable accuracy, using perturbation methods, they’ve been able to

gain a very clear and detailed understanding of the many kinds of constraints that make this process work.

Unfortunately, in the absence of any insight into the reason these constraints exist, theorists still tend to

imagine the world as built on purely mathematical foundations. So despite the remarkable success of

14

perturbative theories in predicting the results of experiment, it seems wrong to them that this needs to

be done by summing up terms in an infinite series of possibilities. They feel that exact, non-perturbative

equations ought to be fundamental – which is one motivation for the long, so far unsuccessful quest for

a deeper, more elegant mathematical basis that would underlie and unify all our current theories.

Here, on the other hand, the issue is not formal elegance or unification but functionality. The constraints

represented by the very diverse laws and principles of our currently-known physics are what keep this

information-defining system going. Whether or not there’s any deeper common ground for the known

types of interaction, the differences between them are crucial to the functioning of the communicative

environment. They work together to ensure that certain special kinds of situations arise over and over

again, where specific outcomes are selected from a range of possibilities, creating new facts that create

new measurement-contexts. The key question, to which we turn next, is how this selection happens.

2.3 The Collapse

Every measurement requires an adequate context. The point of this section is to show that wherever a

context exists that can randomly pick out a specific outcome and communicate it to other contexts,

nothing more is needed to bring about such a selection, to whatever degree of precision the situation

allows. My goal here is to explain why there’s no physical mechanism for wave-function collapse, and

why this part of the dual dynamics doesn’t show up in the equations.

To begin with, it makes sense that no particular type of interaction is responsible for the collapse. Any

measurement-context involves many kinds of interactions, and depends on facts defined in other kinds of

contexts, so that every measurement involves many different aspects of physics. A single interaction may

be able to convey information, in the right context, but no interaction communicates anything by itself.

Not only do measurements involve many interactions, but as Von Neumann demonstrated long ago, the

linearity of the equations means that it makes no difference to the statistical predictions of the theory

which interaction we consider as bringing about the collapse. The probabilities for the outcomes of a

measurement depend on the context as a whole. If it seems baffling that the collapse can sometimes

depend on something that happens far away, or on changes made to the measurement-context after a

particle has already passed through a beam-splitter, it’s because we mistakenly imagine measurement as

a localized physical event. Measurements can never be strictly local in space or time, because their

contexts always depend on other previous contexts, and a definite result appears only insofar as it gets

registered, i.e. makes a difference in some other context.

In short, measurement can’t be defined at the level of individual quantum systems and interaction-events.

Definite outcomes occur only in higher-level situations, where contexts define and communicate facts.

When we talk about quantum particles, states and fields, we’re not describing any definite reality that

exists beneath the web of communicated information. The wave-function doesn’t represent the micro-

15

structure of reality, it represents the structure of constraints on what’s possible , in any given situation,

determining probabilities for what will be observed when the situation changes so that a particular fact

about the system becomes empirically definable. The collapse isn’t something that objectively happens

to a quantum system by itself. It’s just a change in the situation that sets up a context where a specific

outcome can be distinguished, and made relevant to other such contexts.

Why should this happen? If any of the possible outcomes included in the wave-function would satisfy all

the relevant constraints of a given situation, why should one of them be randomly selected as the actua l

measurement result, while all the others become irrelevant? The short answer is that this is required by

the laws of physics – specifically, the conservation laws. If we shoot a particle at a screen, for example,

these laws require it to show up at some particular spot: the particle’s charge, energy and momentum

aren’t allowed just to disappear, or get spread out over the entire screen. The deeper answer is that the

laws of physics are set up this way because they’re part of a self-sustaining process. The selection of a

particular fact is needed, wherever the context allows this to happen, because that makes it possible to

set up more such contexts in which other specific facts can be determined. We can think of it as a kind of

spontaneous symmetry-breaking, in which the unitarity of the equations gets superseded by the random

choice of particular outcomes, updating the equations. This is the fundamental process that sustains the

observable world.

If this seems hard to grasp, it’s because we’re used to thinking in terms of classical physics, where all

events are transitions from one definite state to another definite state, occurring through specific types

of interaction. We often use this same sort of language to describe quantum events as well, but here it

can’t be taken literally. Quantum states are complex structures of constraints on the information that’s

potentially available in the interactive environment. When the environment changes, so do the states.

And the changes that constitute any measurement necessarily involve many kinds of interaction, most of

which don’t directly engage the system being measured.

The bottom line is that at a fundamental level, observing and measuring aren’t physical events, in the

usual sense. As noted above, it’s an illusion to suppose that a world of interaction as complex as the one

we live in could actually operate according to mathematical laws applied to exact, intrinsically definite

states. In quantum theory the laws of physics don’t work like this – they don’t force things to happen in

a predetermined way. Ultimately, everything happens at random – but only those random events that

happen to “obey” all the relevant laws and factual constraints can be observed, or have any determinate

character. Facts only become observable in the context of prior facts, insofar as they help set up new

contexts that make other facts observable. The laws of physics are just de facto constraints that happen

to keep this system going. Nothing enforces them, nor are they given a priori, based on mathematical

principles. They merely reflect the conditions that let interacting systems keep on creating the contexts

that define those systems.

16

What quantum physics shows us is that the solid, stable and precisely reliable world of classical physics is

the statistical result of a great many random interactions, subject to the condition that only observable

events contribute to the contexts that make other events observable. The collapse happens just because

it can happen, in certain very special kinds of situations, and insofar as it does, it makes it possible for

more such situations to arise.

This explains the seeming paradox that the fundamental laws of physics are merely statistical. Taken

individually, quantum events are random; aggregated at a higher level, they fall into mathematically

predictable patterns. That’s because the higher-level structure is what’s needed for the communicative

environment to function. It’s the uniform structure of atoms and molecules and the regularity of their

interactions that provides the basis for our world of definable information. The deeper level of individual

particles and interactions can’t be defined so precisely, and doesn’t need to be.

Likewise, the fine-tuning of many aspects of fundamental physics is unproblematic, in this picture. There’s

no reason to assume that the values of all physical constants should reflect deep mathematical patterns.

These values too are randomly selected, subject to the basic constraint that they support the ongoing self-

definition of the communicative environment. Among other things, that requires all observable events to

happen according to laws that are reliably the same in every context, so that facts can be communicated

between different points of view throughout the observable world.

It also requires that the environment keeps on communicating a coherent body of facts that are reliably

the same from all points of view. It has to maintain a common and consistent historical background for

defining current events – that is, a shared objective reality into which all newly determined facts must fit,

so that further facts can continue to appear. At the quantum level, the specific outcomes of any situation

are left to chance, but there always has to be a specific outcome, to the extent the current context can

define one. And that outcome has to be consistent not only with the laws of physics but with all relevant

facts defined in other associated contexts.

2.4 The Born Rule

To confirm this picture, let’s think about the Born rule. The wave-function assigns a probability to each

possible outcome of a measurement, but we call it a “probability amplitude,” since according to the rule,

the actual probability of a particular outcome is essentially its amplitude squared.[1]

This way of computing probabilities would seem peculiar if we imagined the wave-function as describing

the actual state of a quantum system in itself, and the collapse as an actual physical event in which that

state changes. In that case there’s no clear reason why we should use squared amplitudes instead of

normal probabilities for predicting measurement outcomes. But at the quantum level, there are no facts

about things apart from the contexts that determine them. The wave-function describes the structure of

information that’s potentially determinable in a given situation, and a measurement is any change in the

17

situation that lets a particular outcome be communicated to other contexts. So what the Born rule gives

is not the probability of a change in the system by itself. Rather, it’s the probability that a certain fact

about the system will be consistently observed in all other contexts to which that information becomes

relevant, even though there’s no given underlying reality to which that information refers.

How should we compute such a probability? We begin with the amplitude given by the wave-function,

reflecting the initial probability of one specific outcome being randomly selected in a measurement.[2]

For this to become an objective fact, it has to be confirmed by some other observation – which could be

a second measurement of the same system, or a measurement made on another entangled system, or

any other observation that can independently verify this fact. In the absence of any underlying reality,

the results of both measurements are random, and the probability that both of them will happen to

produce the same outcome is the amplitude for that outcome squared. Hence the Born rule. It merely

reflects the fact that one particular outcome has to be agreed upon, to maintain the functionality of the

environment – but that agreement has to be achieved by a random selection in both observations.

Why do we consider only two measurements? Because no matter how many other observations might

be made that reflect this outcome, they all need to give consistent results for it to function as objective

fact. We don’t keep on multiplying by the amplitude again and again for every new measurement, as if

each one might have a different outcome. But it doesn’t matter which two measurements we consider

as the initial ones, that happen to get the same result independently, just by chance. The Born rule reflects

an agreement that arises within the entire environment to which the result is relevant – but again, an

agreement that’s achieved through mutually random selection.[3]

At the level of classical physics, every observable event involves huge numbers of such agreements, all

constrained to agree with each other in various ways. This great redundancy gives us a world in which

the properties of things can seem intrinsically well-defined, independent of any context. Rules that are

merely statistical, at a fundamental level, seem absolutely precise and deterministic. Even so, physicists

have found ways to demonstrate on a macroscopic scale the very different character of the underlying

physics – for example, in the EPR scenario. Here measurements are made of the spin-orientations of two

entangled particles, which have been separated so there can’t be any causal connection between the

measurements made on each particle.[4] Each measurement involves the random selection of a specific

outcome, and yet the two outcomes are found to be correlated by the usual quantum rules.

This simply confirms what is also shown in many other experiments, that the collapse is never a strictly

local event. Facts are only determinable in the context of other facts, defined in other contexts, so the

selection of any outcome always requires coordination with many other outcomes to maintain the

consistency of the environment. Almost always, though, such non-local coordination is apparent only in

the sub-microscopic quantum domain; it takes much ingenuity and effort to demonstrate it on the scale

of direct experience, as in the EPR situation. Ultimately though, this coordination has to come about by

chance. As noted above, no mathematical system can define precise trajectories for countless particles,

18

interacting in many ways at once. Our physical world accomplishes this by letting everything happen at

random, while the only combinations of events that can be observable are those that happen to sustain

a self-consistent environment of objective facts, operating according to universal rules that continually

create new measurement-contexts.

This picture seems strange to us, perhaps even unbelievable, since this kind of dynamics is the opposite

of the precise determinism that prevails on the scale of human experience. If it were not for the abundant

evidence of quantum physics, no one would ever have imagined that a world could function like this, or

that all the complex phenomena that constitute our universe could arise from entirely random processes.

But the evidence is there. Moreover, we know of a completely different kind of natural process that’s

also able to maintain astonishing levels of functional complexity on the basis of random events, to be

discussed in the following section.

The key point here is that the collapse – the random choice of a particular outcome – is based on the

statistical weighting of amplitudes for each possible result, but the actual probability of an outcome

doesn’t refer to the result of any measurement by itself. It refers to the emergence of a spontaneous

agreement that arises between many random outcomes in many other contexts. And while the result of

any observation taken by itself is simply random, the selection of an outcome by such an agreement is

doubly random – as evidenced by the Born rule. Yet this kind of agreement is what’s needed to support

an objective reality that can keep on producing new facts. A random selection made in any one context

can only participate in our observable universe if it happens to be consistent with all other relevant facts

that appear in other contexts, even though there’s no causal connection underlying such correlations.

2.5 Natural Selection

I’ve been describing measurement as a recursively self-sustaining process, in which random events are

constrained in order to keep on making new measurements possible. Events that don’t help sustain the

world of observable phenomena don’t need to be prevented or suppressed – they just don’t matter, since

they can’t be observed or make any definite difference to what’s observed.[1]

This invites comparison with another recursive process that’s much better known and much easier to

envision – the process of biological reproduction that’s responsible for the evolution of life on Earth. That

process operates very differently from the measurement process, but there are many significant analogies

between the two, beginning with the fact that they both make use of random selection to support the

existence of amazingly complex and finely-tuned functional systems. To help support and clarify the

picture I’m developing of the physical process, I want to outline briefly both how it differs and how it’s

similar to the biological one.

Biology is, of course, based on physics. Life is possible because molecular structure is precisely uniform,

so that even extremely complex molecules interact in reliably repeatable ways. Before the emergence of

19

living organisms, though, only very simple molecules could exist, because complex systems are always

much easier to break than they are to build. For this reason molecules containing more than a dozen or

so atoms are rare in the non-living universe. But there is one way, in nature, to overcome this physical

limitation. If some kind of system can reliably make copies of all its component molecules and replicate

itself in multiple versions before it gets broken up by the environment, then there are almost no limits to

the level of ordered complexity such systems can achieve.

The problem is, physics and chemistry don’t provide any easy way for this to happen. As a result, self-

replicating systems are also very rare in this universe. On the other hand, if by chance such a system

comes to exist, in some unusual physical environment, then so long as it keeps on making copies of itself

it will automatically evolve. Random events will selectively promote the proliferation of those variants

that happen to be best at reproducing themselves, and eventually adapting to other environments, while

the less successful variants will disappear. Over a few billion years, this process was able to produce the

astonishing diversity of living organisms on this planet, every one of them radically more complex than

any other kind of physical system.

Now selection in quantum physics works very differently from Darwinian natural selection, because the

underlying functionalities are so different. Biology depends on the well -defined and exactly uniform

information built into the structure of molecules: its key functionality is the copying of such information

through chemical interactions that catalyze the building of new molecules. On the other hand, as noted

earlier, there are no basic processes in physics that simply replicate given information. The underlying

functionality in physics is more basic: it’s not a matter of copying information to preserve it over time;

it’s about making information definable in the first place.

In both cases, though, what makes these processes special is that to the extent they succeed, they pass

on the information that’s needed to keep the same process going. This is obvious in biology, but less so

in physics, because measurement-contexts are not discrete identifiable objects, like organisms, and they

never replicate themselves: contexts contribute information to other kinds of contexts. Moreover, the

self-sustaining process in which contexts determine and communicate facts doesn’t result in a gradual,

incremental development of more and more complex systems, as happens with the evolution of life. In

fact it does just the opposite. Physical information can only be reliably defined and communicated if the

same basic structures of interaction apply everywhere, throughout all space and time. Since this radical

consistency is crucial to sustaining the process, the result of random selection in measurement is to keep

on redefining the same changeless system of physical laws and objective historical facts.

Nonetheless there’s a similar kind of dual dynamics at work, in both measurement and reproduction. They

both depend on a very complex, tightly-controlled system involving many kinds of interactions – defined

on the one hand by the universal laws of physics, and on the other by the particular genetically-encoded

operating instructions that get passed down from one generation to the next, in each biological species.

And in both cases, the other side of the dynamics – natural selection – is not only random, but has no

20

definite character at all. In biology, natural selection refers to any kind of event that in any way affects

the reproductive success of an organism – and that could be anything from a random mutation in a single

molecule to a global geological disaster. In physics, the collapse that selects a specific measurement result

can be brought about by any kind of change in the environment that makes some parameter of a system

determinable, whether directly or indirectly.

What makes both these processes work is that the tightly-controlled side of the dynamics is a structure

of variant possibilities. A species can evolve because it consists of many individual organisms, each one

carrying a particular version of the species genome that can potentially be reproduced. At the level of

individual organisms, it’s mainly a matter of luck which ones happen to succeed in reproducing their

genes, so over short time-periods and in small populations, genetic change from one generation to the

next is largely random. At a higher level, though, the cumulative result of random selection over time is

to promote each species’ adaptation to its environment, favoring the species that evolve most rapidly.

This involves changes to thousands of genes in response to countless different environmental factors. But

since evolution happens through random selection, the tremendous complexity of interrelated changes it

responds to doesn’t present any obstacle to the process.

In physics, the controlled side of the dynamics is described by the wave-function, which represents a

situation as a superposition of all the possible facts that could be passed on to other contexts, if and when

a measurement occurs. At the level of individual measurements, the outcomes are essentially random,

but because of phase-interference between possibilities, and because many different possibilities can lead

to the same outcome, the aggregate results of many measurements give a highly predictable statistical

distribution of outcomes. On the scale of our ordinary experience, this gives us the precise dynamics of

classical physics. And again, since the underlying selection is random, the tremendous complexity of all

higher-level situations doesn’t present any problem. Trajectories determined by this process of natural

selection can take account of many different kinds of interaction with countless other systems all going

on at once.

In both biology and physics there’s a basic functional unit – the living cell and the atom. Everything in

biology depends on the self-replication of individual cells, the basic building-blocks for all forms of life,

which also perform a great variety of subsidiary functions. Atoms too are not only building-blocks for

every kind of material structure, but also function as tiny measuring-rods and clocks, providing universal

standards of distance and frequency. They detect photons with specific energies, store information over

time in the energy-levels of their electron-shells, and communicate with other atoms, both nearby and

very far away. The observable world is at bottom a world of signals exchanged between atoms, just as

the living world is made of interacting cells.

Both atoms and cells are complicated, finely-tuned systems, with many functional components that all

need to operate in precisely reliable ways. Yet the deepest levels of interaction in each case are largely

random. The interaction of molecules in a cell, as between sub-atomic particles, is essentially chaotic.

21

The system works nevertheless, because all this uncontrolled interaction averages out statistically to keep

the process going. This happens not because of any preordained law, but just because where it doesn’t

happen, the system ceases to contribute to the ongoing process. A cell that fails to reproduce itself makes

no difference to the further evolution of life. Physical events that don’t support the exact reliability of

atomic interaction can’t be observed, or contribute to making other things observable.

Every organism on earth descends from a very long line of ancestors, back to the beginning of life, every

one of which succeeded in reproducing itself. In physics, only information that’s successfully defined in

some local context and passed on to other contexts can make any difference to anything. So here too,

everything that happens in the observable world is the result of a long history of accidents, back to the

beginning, each one of which made some definite difference to the context in which other events could

make a difference. All the regularities of physics come about because only things that help make other

things measurable can make any contribution to this history.

Because both these self-sustaining processes are so profoundly complex, what’s hardest to understand

about them is how they came to exist in the first place. In biology, at least we have a fossil record of an

evolutionary process that gradually produced more and more complicated forms of life – although the

earliest cells for which we have evidence were already far more advanced than the first self -replicating

systems could have been. In physics, the historical record shows us no such process of gradual change in

the finely-tuned system of laws and principles that makes measurement possible – so we face a much

greater conceptual challenge in envisioning how this system could have emerged from simpler kinds of

self-defining systems. This is the question we’ll take up in Chapter 4. To prepare that discussion, I want

to turn first to our other foundational theory – relativity – and think about how its peculiar conception of

spacetime helps support the physics of measurement.

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Chapter 3 Your Present Moment in Spacetime

3.1 The World from Inside

As compared with quantum mechanics, relativity is a classical theory. It takes for granted that there are

always objective facts about things, and that the facts are also observable. It assumes the existence of

accurate clocks and rigid measuring-rods, and doesn’t consider what underlying physics might be needed

for this. Like quantum theory, however, it makes the values of many observables depend on the context

in which they’re measured. And while it deals only with one aspect of these contexts – the observer’s

local frame of reference in space and time – it defines these strictly on the basis of local measurements,

without relying on any objectively given global geometry.

My goal here is to show that like the dual dynamics of quantum theory, the peculiar four -dimensional

geometry of relativistic spacetime reflects the functional requirements of an observable universe. As

noted in the previous chapter, information determined in one local context can only be communicated to

other contexts if it can be treated as objective, context-independent fact. And even so, these facts must

always be definable in local contexts. Though we’re used to conceiving the physical world from a “God’s

eye” viewpoint, as if we could stand outside of space and time and see things as they are in themselves,

the structure of an observable world has to be definable from inside, from particular points of view in

spacetime, communicating with other local viewpoints.

I’ll argue that this requirement is the basic rationale for relativity. To support a physics that continually

creates new measurement-contexts, there needs to be a universal structure of spacetime relationships

that’s everywhere the same; even so, this geometry must be definable by local observers in local frames

of reference. A global structure is needed, but just as in quantum physics, it can’t just be given in an

underlying objective reality. It has to be determined empirically, through the real-time communication of

locally measured information.

I also noted in the previous chapter, in discussing the EPR scenario and delayed-choice experiments, that

measurement-contexts can never be strictly local in space and time, because every context depends on

facts determined in other contexts, which depend on still other contexts. This nonlocality is basic to the

quantum domain, where the wave-function represents the possibilities of a situation prior to an actual

measurement. Here, on the other hand, we’re dealing with the larger-scale spacetime structure of facts

that are actually observed. At this level, measurement-contexts are necessarily local, in that the context

in which any fact is determined must always consist of other facts that are also available in that same time

and place. Even in the EPR scenario, where the quantum wave-function correlates the spin-states of two

entangled particles in widely-separated locations, these correlations only become observable when both

measurement results are available in the same local context. We’ll come back to this scenario later on, in

considering how relativity and quantum theory are related.

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3.2 Two Versions of Spacetime

We’re conceiving the basic process of physics as one in which new facts are defined in contexts set up by

the communication of previously determined facts. In effect, the physical world is a parallel distributed

processing system, in which a single objective reality is constantly being woven out of facts determined

separately in countless local situations. This constantly evolving web of communicated information is just

what we, along with all our measuring instruments and recording devices, actually experience in present

time.

Unfortunately this picture doesn’t match the way relativity is commonly understood today, though it’s

close to the picture presented in Einstein’s initial theory. In essence, Special Relativity is a method for

translating between the inertial reference-frames of different observers. Its key innovation was to insist

on defining space and time in terms of local measurements, coordinated with each other not by locating

them within a global framework, like Newton’s absolute space and time, but by means of the light-speed

postulate, relating to the dynamics of communication.

Early on, however, Minkowski recast the theory as describing the intrinsic geometry of four -dimensional

spacetime, once again conceived as a global background-framework. When this opened up the path to

General Relativity and the new theory of gravity, the viewpoints of particular observers seemed to be

superseded by this deeper conception of objective reality. And in fact, since space and time were now

understood as inseparable parts of a single geometry, relativity came to be seen as proof that our view of

the world from inside is profoundly wrong. While from the standpoint of any observer there’s a basic and

obvious difference between space and time, relativity seemed to make them fundamentally the same.

This gave rise to the notion that our experience of living moment-to-moment in present time is some kind

of illusion. In truth we’re actually four-dimensional beings in a static “block universe” where past, present

and future events all co-exist, in a body of changelessly given fact.[1]

Now I have no problem with the theory of four-dimensional spacetime, but this way of interpreting it is

badly misleading. Relativity certainly does not treat time as another dimension of space , as the “block”

idea implies. I’m going to argue that the original view of the meaning of relativity still makes sense, and

the peculiar way that space and time are connected, in Minkowski’s geometry, perfectly corresponds to

our present-time experience of the world. In fact, this rather odd way of structuring spacetime is just

what’s needed to support the real-time distributed processing system we’re envisioning here. If the world

were just a static pattern of events laid out in four (or more) dimensions, there would be no reason why

it should have this special type of spacetime geometry.

I’m going to contrast two versions of spacetime, both of them conveniently illustrated in the familiar

diagram below.

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The layout of the diagram itself, with time and space on orthogonal axes, represents an observer’s local

region in a four-dimensional block universe. It depicts spacetime as if we were standing outside of it,

seeing the past, present and future as different regions within a

static geometry. Here the observer’s present moment is pictured

as a three-dimensional hypersurface containing all the events

throughout the universe that are happening simultaneously, at

this particular point on the time-line.

The basic argument made by proponents of the “block universe”

is that according to relativity, this present moment is frame-

dependent; it has no objective physical reality. Observers who are

moving in relation to each other will define different sets of

events as simultaneous – in the diagram, each observer’s present-

time hypersurface will be tilted with respect to the other’s. This

means there’s no objective reality to what we experience as

“now”– there’s no physical borderline that distinguishes past

events from those in the future. And since past events are obviously factual, then future events must be

factual too – hence the block universe. This gives rise to the bizarre idea that our experience of living in

present time is an illusion somehow generated in our minds, without any basis in physical reality.

The problem with this argument is that it has nothing to do with the present moment that anyone or

anything can experience. It’s true that there’s no physical reality to this universe-wide “hypersurface of

the present.” But none of the events on this hypersurface – or anywhere else outside the observer’s past

light-cone – can actually be observed, or even have any physical relevance to what can be seen from the

observer’s present-time viewpoint. In the diagram, it’s the lower light-cone that represents the three-

dimensional space of the observable world – the web of communicated information as seen from inside.

For any observer, this is the boundary that effectively separates the given facts of past history from events

that may or may not happen, and will only become determinable sometime in the observer’s future.

So what relativity tells us is not that there’s no such thing as the physical present moment, but that this

“now” in which each of us exists is essentially local.[2] “Real time” experience always takes place in some

specific context in which new facts are being determined, here and now. Again, these contexts are not

“strictly local” – measurements don’t happen at any precise point in space or time. Like the present-time

world of our subjective awareness, physical contexts have no specific boundaries, but are always extended

in space and time. In fact, we share our physical “now” with everyone and everything that’s immediately

present to us – that is, close enough that we can exchange information back and forth with no appreciable

time-lag, so that we’re all participating in the same situation.

Since this communication can happen nearly at light-speed, which is extremely fast on the scale of human

perception, this ongoing “now” in which we live is essentially common to everyone on the planet. Here

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on Earth we do effectively inhabit a “hypersurface of the present.” If we drew the above diagram on the

time-scale of human experience, both the past and future light-cones would flatten out, essentially

coinciding with the horizontal axes. And so, based on our experience, we naturally take it for granted that

everything “moves through time” together, simultaneously. If we were to imagine a basic physical process

that constantly defines new facts in present time, we would tend to imagine it as happening everywhere

in the universe at once, as an objective process, not tied to the viewpoints of particular observers.

But here we’re considering an alternate conception of spacetime, where “now” is represented by the past

light-cone. This is harder to envision, even though it’s what we actually experience. In this view, time is

always the “proper time” measured in some local context, and the border line between past and future is

not the same for distant observers. Nonetheless, Minkowski spacetime is structured so that the web of

light-speed communication effectively separates the factual past from the possible future, for any set of

communicating observers. When two observers are in communication, events in the past light-cone of

one of them can never be in the future of the other. What’s only a future possibility for one can never

already be a decided fact for the other. Distant observers do share a common past history, where their

past light-cones overlap, and they likewise have a common, unknowable future to which they can both

contribute. But they don’t share a common “now” in which possibilities become facts. The contexts in

which facts get determined are always local, on the lower light-cone horizon of the local present time. So

the global real-time physics of our universe doesn’t happen on any “hypersurface” – it consists in the

weaving together of new facts determined independently in countless local situations, communicating

with each other through the light-cone web. So while we can represent spacetime structure as a global

background-geometry, it’s more accurately pictured as an evolving web of communicated information.

3.3 Asynchronous Spacetime – EPR and Schrödinger’s Clock

Before exploring the implications of this notion, I want first to make it clear that this second version of

spacetime is the one that corresponds to the geometry of Minkowski and Einstein. In the global block

geometry of the diagram, where time is essentially a fourth dimension of space, the spacetime distance

between any two events would be given by the square root of S2 + T2, where S is the spatial distance

between two events on the horizontal plane, and T is the distance between them on the time-axis. This

means that when two events are distant from each other both in space and in time, then they’re even

farther apart in spacetime. But relativity tells us the opposite: the invariant spacetime interval between

two events is given by the square root of S2 – T2. The minus sign means that space and time are stitched

together backwards, in effect, so that spatial and temporal distances cancel each other. Events that are

equally far apart in space and in time – that is, in the diagram, events that are on each other’s light-cones

– have zero separation between them in spacetime.

This is well-known to all physics students, but the meaning of these “null intervals” is rarely clarified. We

often hear, in fact, that the spacetime interval “lacks physical significance” and is only a convenient aid to

calculation. That lets us hang on to our common-sense notion of space and time as an objective universal

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framework – the view from outside, as shown in the diagram. Mathematically, we conceive spacetime

first of all as a four-dimensional manifold, and then note that it happens to have a particular “signature”

– a minor complication that’s easily handled in the equations. We then forget about the signature and go

on to describe the structure of spacetime by means of “foliations” – constructs like the “hypersurface of

the present” that have no relation to how things interact or what’s observable from any point of view, but

are easy to visualize as slices of a block spacetime.

But the signature is crucial to the way spacetime works, and null intervals are certainly not meaningless.

It’s true that the objective view of the diagram gives no clue as to what it could mean for time and space

to cancel each other. But this cancellation perfectly describes the structure of spacetime we experience

from inside – for example, when I look up at night and see the stars. The light I’m seeing here and now

was emitted from events on the surface of those stars – events that are very distant from me both in

space and in time. Yet because these distances cancel each other, this light is immediately present to me

now. From any point of view, all events on the past light-cone are experienced as happening in local

present time.

This isn’t how we usually imagine this situation. Usually we take the objective view: if a star is five light-

years away, then objectively I’m seeing the star as it was five years ago. That corresponds to the block

geometry of the diagram, where my “now” is a spacelike hypersurface of simultaneous events, and “five

years ago” is another parallel hypersurface, when the light I’m seeing now was emitted from the star. In

this view, that light has been travelling along through space for five years, from the time it was emitted

to the time it finally reaches my eye.

That’s a reasonable description, and easy to understand, but we know it’s not fundamentally correct.

Relativity tells us that as velocities approach light-speed, clocks run slow and lengths contract. At the

limiting velocity of light, time stops and length vanishes – so it takes no time at all for a photon to cross

any distance in empty space. Of course this doesn’t mean that the photon’s emission from the star and

its absorption in my eye happen simultaneously. Simultaneity is a two-way relationship, and light-speed

connections across null intervals go only in one direction, from the star to me. And there’s still a real

distance in space and in time between these two events, although these distances will be measured

differently in different frames of reference. But in every frame of reference, these spatial and temporal

distances will be equal, offsetting each other.

This kind of geometry is difficult to envision, though it’s entirely consistent with our real -time experience.

In the diagram it would look something like a web of light-cones connecting the local present moments of

distant observers as they communicate back and forth – but that objective view from outside spatializes

time, and so misses the immediacy of these one-way connections. For every observer there’s a unique,

ongoing local “now” that’s effectively shared with other nearby observers, and is also directly connected

with a specific moment on the time-lines of any distant observer, where their respective light-cones

overlap. But if I’m on a videocall with a friend on Mars, for example, it’ll be obvious that we don’t share

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the same present time. If I make a joke, I have to wait maybe twenty minutes before I see her laugh. Our

respective present moments don’t fall within each other’s past light-cones, so her “now” is always a few

minutes in my future, and vice-versa.

This real-time separation between our local contexts isn’t due to the slowness of light, but to the way

space and time are cross-connected. The so-called velocity of light isn’t really a speed at which anything

moves; it’s just a conversion constant between our units of measurement for space and time, reflecting

the fact that a certain distance in space is canceled out by an equivalent distance in time. This is why light

always has the same velocity in all inertial reference frames, and it’s also why nothing can ever move or

be communicated faster than light. In Minkowski’s geometry there is no “faster than light,” because a

spacetime interval can never be less than zero.

Why should a universe be structured in such a peculiar way? Because, in order to support the ongoing

process that creates new facts in the context of prior facts, there needs to be one common framework of

spacetime relationships everywhere, along with the changeless structure of the laws of physics and a

consistent background of historical facts. Specifically, there needs to be a universally consistent time-

orientation for all events, from the factual past into the undecided future. But this ordering of events in

space and time can’t just be given in an underlying, absolute geometry. It can’t be built, for example, on

the basis of mathematical “foliations” of spacetime that are unrelated to anything observable. It has to

be defined in and through the web of communicated information.

This is what’s accomplished by the invariant structure of null intervals, physically instantiated in the

electromagnetic field. It provides a kind of rigid skeleton for an otherwise asynchronous system of parallel

distributed processing. Every measurement-context is set up by facts communicated on or within its past

light-cone. All newly defined facts get communicated out to other possible contexts on or within its future

light-cone. And though all measurements of spatial and temporal distances are relative to the observer’s

local reference-frame, these light-cone connections are absolute. Null intervals are null in any frame, and

the speed of light has the same velocity however spatial and temporal intervals are measured. So the

web of null intervals connects arbitrarily distant real-time contexts in a way that maintains a universally

consistent distinction between past and future for all communicating observers, relying only on local

observables.

This allows a consistent “direction in time” to be maintained for all local measurement-contexts and all

communications between contexts. But the consistent time-ordering of events is only definable within

the web of communicated information; it does not apply to “spacelike separated” events that lie outside

each other’s light-cones. In fact, the entire spacelike sector of the diagram – the part outside the dual

light-cone – is missing from relativistic geometry. Unlike null intervals, spacelike intervals are merely

mathematical constructs that “lack physical significance.”

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And nonetheless, like quantum physics, relativity supports our objective view of reality, as pictured in the

diagram. Nearby observers do inhabit a shared space and time that’s well modeled by the block diagram.

Any set of communicating observers do share a common factual history, and anything that’s factually

determinate for one observer can eventually become a fact for any other. But this objective reality has

to be accomplished over time, by weaving together the separate strands of fact defined asynchronously

in separate local contexts.

So even though the objective view of the world “from outside” is not fundamentally correct, there are

very few situations in which it causes any problem. One such situation, however, is well known – the EPR

scenario, as realized in experimental tests of the Bell inequality. Here the spin-orientations of two

entangled particles are measured by Alice and Bob in spacelike-separate regions, and they find their

results are correlated, per the usual quantum rules. Objectively, it seems that measuring one of the

particles must somehow have affected the state of the other one, though relativity rules out any such

faster-than-light connection. In fact, it tells us that there’s no objective fact as to which of the two

measurements happened first.

What this scenario illustrates, though, is not “spooky action at a distance.” Rather it’s just the thesis of

this essay – that at bottom the world is not an objectively factual reality, but a web of communicated

information – the world that’s actually experienced, always from a particular point of view in some local

context. From Alice’s point of view, Bob’s measurement hasn’t happened until it falls within her past

light-cone. Until then it remains in a superposition of possible outcomes. Likewise from Bob’s point of

view, Alice’s measurement doesn’t have any definite result, when he makes his measurement. Only later,

when both their results eventually become available in the same location, does there arise a physical

context in which the correlation between the two results can be determined. Only then can the overall

situation described by the entangled wave-function “collapse” to select out a definite set of results, which

turn out to be correlated according to quantum rules.

This seems paradoxical, because we naturally think in terms of a global objective reality. We want to

locate both Bob and Alice within a common framework of space and time, where both measurements had

already taken place long before either of them could know about the other one’s result. If Alice’s result

was already factually determined in her context, and Bob’s in his, then the two results must obviously

have been correlated long before they could be compared, even though in spacelike separate regions.

This seems incontrovertible, because it seems self-evident that there’s one overall space and time for the

universe, just as there is, effectively, here on Earth.

However, both Relativity and Quantum Mechanics show us this is not the case. Within the asynchronous

spacetime structured by light-speed communication, Alice’s time and Bob’s are not synchronized. So it’s

true that when Alice makes her measurement, Bob’s result remains undetermined, and vice-versa. For

either Bob or for Alice the “collapse” has already occurred in one measurement, giving a particular random

result. But only later, when both results can be compared, can these separate threads of existence get

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woven together into a shared objective reality. Until then there’s no physical situation to which the

quantum correlation rules can apply.

This is an extremely unusual situation – it takes a lot of careful effort to set up an arrangement in which

quantum superpositions are spread out over such distances. But what this scenario demonstrates is no

different from what we see in delayed-choice or quantum eraser experiments: the laws of physics can

only apply to what’s observable – to the structure of measured and communicated information – not to

any underlying reality. The spacetime geometry in which things happen is likewise the structure of a

communications web, where distant regions evolve independently – where Bob’s measurement is still

physically in Alice’s future when she makes her measurement, and vice-versa. This doesn’t mean that Bob

or Alice or both remain in a superposition of states, until their results are compared. But in this kind of

spacetime geometry, there’s no definable “actuality” that encompasses spacelike-separate regions.

Consider another scenario, that of Schrödinger’s Clock. To avoid mistreating animals, we replace the cat

in the box with a clock, which is set up so that will stop when and if a particle decays. So long as the box

remains closed, we represent the situation inside as a superposition of possible states, in some of which

the clock is still ticking, while in others it’s been stopped. When we open the box, the superposition

collapses, and we find the clock had in fact stopped just half an hour earlier.

The point is the same as with Bob and Alice: the time going on inside the box is not the same as the time

outside. For an observer inside the box, the “collapse” has occurred and the clock has stopped, but for us

outside, the collapse occurs only when the box is opened. Here the clock and the world outside are

separated by a box that’s assumed to be able to block all signals, which may not be realistic. In the EPR

scenario, the separation is definitely real, due to the structure of spacetime itself. But in any case, in both

scenarios the objective view of the situation makes sense, after the fact. Once the box is open, we can all

agree that the clock had in fact stopped half an hour ago; once Bob and Alice compare results, it makes

sense to say that they’re correlated with each other. But the physical world does not operate after the

fact: it exists in real time, in the web of communications between local contexts. And while eventually

all observers can agree about past facts, they don’t all share a single present time in which the facts g et

determined.

Whether or not it seems paradoxical to us, the laws of physics governing an observable world have to

operate in and through the web of communicated information. Laws that apply to objective reality are

obviously important, at the level of classical physics and our everyday experience, but they can’t be the

fundamental laws. On the other hand, all the fundamental laws work together to achieve the objective

reality of classical physics, to the greatest extent possible. It takes a great deal of careful effort to make

quantum effects manifest on a large scale – as in tests of the Bell inequality over spacelike distances.

Relativistic effects only appear when we’re dealing with astronomical distances or velocities near the

speed of light. So there’s a very broad range of scales over which there are always clear and causally

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deterministic relationships between factual events, set within in a common objective framework of space

and time.

But we know that the underlying physics is strange and complicated in many different ways. My task here

is simply to suggest a reason for that.

3.4 The Equivalence Principal and the Gravitational Metric

So far we’ve discussed only one aspect of spacetime geometry – the invariant skeleton of null intervals, a

structure that’s independent of the metric as defined by measurements with local clocks and rulers. This

independence is reflected in the fact that the basic structure of the electromagnetic field can be expressed

mathematically without reference to the spacetime metric.[1] In the following chapter we’ll take up the

suggestion that this skeleton-structure of intersecting light-cones represents a primitive stage in the pre-

history of our self-defining universe, prior to the emergence of measurable space and time in the world

defined by interactions between atoms.

Here I want to focus on the metric given by local measurements, and consider how General Relativity fits

into the picture we’re developing. That theory arose from the question, why is there an exact equivalence

between gravitational and inertial mass? Einstein pointed out that measurements made inside an

elevator – which, like Schrödinger’s box, is assumed to block all signals from outside – can’t tell us whether

we’re in a gravitational field or are being accelerated uniformly by a rocket. Objectively, of course, there’s

a great difference between these two situations. If the elevator had windows, we could see whether

there’s a massive planet below us or something pulling us upward. But in the local context of the elevator,

the two situations are physically the same.

I’ve argued that fundamental physics has to be definable entirely in terms of local measurements. So if

it’s true that local measurements can’t distinguish between gravity and inertia, then those two must be

fundamentally the same, even though they’re objectively very different. This was the gist of Einstein’s

theory, although he didn’t base it on this kind of argument – he always maintained an objective view of

spacetime structure. Yet both Special and General Relativity do define spacetime geometry strictly on the

basis of what’s locally measurable.

For Einstein the Equivalence Principle was just an empirically established fact. His theory explains it by

assuming that gravity and inertia are physically the same: in the absence of other forces, things move

inertially along geodesic paths, through a spacetime metric shaped by the distribution of mass-energy.

General Relativity doesn’t consider how or why this happens, but it gives us a mathematical law that

accurately predicts a wide range of observed phenomena. But we can understand why the universe

operates this way if we can show what Einstein’s equations for spacetime curvature contribute to the

structure of an observable world.

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It’s clear that gravity played a key role in the emergence of our world of solid material objects, in which

intervals in space and time are physically measurable over a vast range of scales. Without gravity, atoms

would never have been drawn together to form galaxies and stars, and there would be no heavy nuclei

with which to build molecular structure. But the law expressed in Einstein’s field equations does much

more than that. For example, it makes the curvature of spacetime flatten out, locally, and the smallness

of the gravitational constant makes its geometry essentially Euclidean on a local scale. The way space,

time and gravity are defined by General Relativity gives a very close approximation to the Newtonian

framework at the level of local measurements, and the curvature of the metric is entirely negligible at the

quantum level. This is why quantum physics can be formulated mathematically on a background of flat

spacetime.

Even where gravitational curvature is not at all negligible, the relativistic structure of spacetime still

provides a basis for defining inertial frames of reference anywhere in the universe: where other forces

are absent, the local rest-frame of any object in “free fall” is always inertial. And where things are not in

free fall, as on the surface of the Earth, local measurements can always determine the magnitude and

direction of their acceleration, whether due to gravity or other forces, and this acceleration will be found

to have the same value in any inertial frame.

Moreover, Einstein’s equations include a cosmological constant governing the rate of expansion of the

universe. In the early universe this expansion brought about the gradual cooling that allowed for the

eventual emergence of atomic structure, through a complex series of stages. To open up enough time for

an observable world to evolve, however, the expansion rate had to be extremely finely-tuned to balance

the pull of gravity, taking into account the contribution of quantum fluctuations to the energy-density of

the vacuum. If the value of this constant had been slightly different, the universe would either have

recollapsed on itself long before any atoms could emerge, or else have blown itself apart so quickly that

no galaxies and stars could form. So this one basic law of physics given in Einstein’s theory accomplishes

a remarkable variety of important tasks in creating our observable universe.

The bottom line is that relativity, like quantum theory, supports the world of classical physics, where

stable material structures have precisely determinate properties, and interact according to simple laws in

an objective framework of Euclidean space and time. But this framework is not just given in reality, as it

is in Newton’s conception. All of this gets accomplished strictly on the basis of information defined in

local measurement-contexts and communicated between such contexts.

Relativity shows us that this is done through a combination of two distinct systems. The metric of General

Relativity defines a universal system of local inertial reference-frames, where things can be measured in

a locally flat Euclidean space and time. Then the rules of Special Relativity allow for the consistent

translation between measurements made in different inertial frames. The result is that in principle, any

two observers in communication with each other can reconcile their respective local observations to

achieve a shared objective knowledge of the facts, no matter how different their local situations may be.

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This may seem an exceedingly complex and roundabout way to accomplish something very simple. Why

not just start out with an objectively given factual world, organized by Euclidean geometry and the laws

of classical physics? But such a world is a fantasy. It tacitly assumes the existence of contexts in which

facts can be determined and the laws can be defined, without considering what’s needed to make such

contexts work. In the real world we need highly functional atoms to build material structure, and the

interactive environment needs to determine many kinds of information – including the laws of physics

and spacetime geometry. The clear and simple classical physics of the world we experience can only

operate because our universe provides all the complex informational technology that underlies it.

3.5 Cosmological Questions

To conclude this chapter, I want to mention several outstanding issues in cosmology that only seem to be

problematic because it’s taken for granted that the universe should be described “from outside,” as an

objectively factual reality, rather than as a functional web of communicated information. For example,

there’s the question why gravity is so much weaker than all the other basic forces, and why the energy-

density of the vacuum is so much smaller than expected, given all the virtual -particle contributions to

vacuum energy given in the Standard Model. The approach sketched out above explains these apparent

anomalies: if the gravitational and cosmological constants in Einstein’s equations were not very small,

flattening out the spacetime geometry of our universe, none of the technology of measurement could

have come to exist.

In general, fine-tuning seems problematic because physics is understood as essentially a mathematical

structure. It’s bad enough that the deep-level physics is mathematically subtle and complex, without

having to include many unexplained parameters whose values seem “unnatural.” But if the mathematical

structures of our theories are explained by the functional requirements for defining and communicating

information, their finely-tuned parameters can be understood the same way.

A different sort of explanation is possible for the “horizon problem” – why the background radiation left

over from the early universe is so nearly homogenous in all directions, given that no interaction can ever

have occurred between widely-separated regions in our sky. A similar question asks why the interactive

environment of the early universe had such extremely low entropy that it’s still rather low today, after

billions of years in which entropy has steadily increased. Such questions conceive the world as body of

well-defined objective fact, and the problem is to understand why the universe began in an extremely

special state. For example, the notion of inflation is invoked to account for the uniformity of the early

universe by tracing it back to an earlier factual state that seems more general and “natural.”

In the context of my argument here, I would turn these questions around. If we’d found that there were

major differences in the temperature of background radiation from distant regions of the universe, how

could we explain those differences? If those regions were always spacelike separated, in what physical

context could differences between them have been defined? I’m not supposing there were well-defined

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factual states throughout the universe, to begin with, that were all highly correlated with each other. The

assumption is rather that there were no meaningfully definable differences between unconnected parts

of the universe, since all facts must be defined in some context of local interaction. When we look at the

sky in different directions, on Earth today, our local contexts let us measure and compare radiation from

widely separated regions of the early universe. But since there were no such contexts to begin with that

could encompass these distant regions, there can’t have been determinate factual differences between

them. Necessarily, however, in order for them to be observable here and now, the physics of all these

regions has to be consistent with the universal requirements of our observable world.

As a matter of fact, we do find small deviations in the temperature of the CMB from different parts of the

sky. These are understood as reflecting quantum fluctuations in the energy-density of the early universe,

which happen to be the right order of magnitude to seed the emergence of galaxies. These differences

would not have been measurable from any local viewpoint, in the early universe, but they have a clear

and important functional role. Like the weakness of gravity and the quietness of the quantum vacuum,

they can be explained as necessary to the emergence of a world of measurable information.

Finally, what seems today to be the main outstanding issue in fundamental physics is the relationship

between quantum physics and gravity. A great deal of effort has gone into the project of unifying these

theories, on the assumption that there must be some ultimate reality at the bottom of things, and some

unified mathematical structure that describes it. Despite the near-complete lack of empirical evidence

for any physics beyond the scope of our current theories, it’s certainly possible that a deeper unifying

theory may eventually be found. But if what’s fundamental in physics is not the mathematical structure

of an underlying reality, but rather the functionality of the communicative environment, then there may

be no reason why any deeper unifying theory should exist.

General relativity and quantum field theory address very different aspects of the interactive system that

supports measurement, and there are hardly any observed phenomena to which both these theories are

relevant. As noted above, the very small constants in Einstein’s field equations give an effectively flat

spacetime environment in the quantum domain, so that gravity plays no direct role in determining facts

at the level of atoms and molecules. And it seems that quantum contributions to the vacuum-energy of

spacetime are precisely cancelled out, leaving only the tiny fluctuations needed to support the historical

emergence of galaxies and stars. So relativity and quantum physics work remarkably well together,

complementing each other, but it’s not obvious, from a functional standpoint, that there has to be any

reconciliation between their very dissimilar mathematical foundations. Nor does it seem sensible, from

the point of view taken here, to speculate about physics at the Planck scale, so far beyond the range of

any conceivable measurement.

There may still be important questions to be resolved, once we’ve found observable phenomena that

involve both quantum physics and gravity. But the answers may not lie in the formal unification of these

two types of theory. So at least as a working premise, it may make sense to assume that our current well-

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established theories already give us what’s needed to understand the workings of our self-defining

universe. Outstanding issues like the mystery of dark matter may be more approachable once we have a

well-developed framework that focuses on the contextuality of information. After all, dark matter also

plays a significant role in creating the galaxies, stars and heavy nuclei needed for the emergence of stable

material structure.

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Chapter 4 On the Origins of Determinate Information

4.1 Toward an Archaeology of Physics

How could a self-determining system as deeply complicated as our universe have come to exist? This

system is made of many kinds of interaction that continually set up new situations that let certain kinds

of facts be determined, which are then passed on to set up other such situations, in a self -sustaining

process. The goal of this chapter is to sketch out a possible approach to understanding how this kind of

system could have emerged through a sequence of stages, from more primitive self-defining systems that

involved fewer and simpler kinds of information.

The idea is that the structures that emerged in each of these stages should all still be evident in the

complex foundations of our current theory. This means that we don’t need to guess at the nature of these

earlier systems. We should be able to sort out the corresponding layers of organization in our current

physics, through a kind of archaeological analysis.

I want to be clear that what I’m sketching here is not meant to replace our current cosmological history,

which gives a detailed account of the formation of atoms, galaxies, stars etc. Apart from aspects of this

story that are speculative (e.g. inflation) or not yet understood (dark matter), I assume this account is

essentially correct. The Standard Model lets us trace this history back to the first billionths of a second

after the beginning, on the premise that the basic structures of physics were well-defined almost from

the start, and haven’t altered since.

As argued in Chapter 1, however, none of the evidence for this history could have been definable in the

chaotic conditions of the early universe. This doesn’t mean the history is wrong. As I’ve argued above.

any observable world has to base itself on a changeless system of universal laws that apply throughout all

space and time. Beyond that, it needs to define and maintain a historical background of commonly-shared

objective fact, to support communication between local contexts. So the origin of our universe involved

not only selecting out a specific system of physics from all other possibilities, but also choosing a specific

past history based on those laws that could result in the emergence of atoms and molecules, as the basis

for stable material structure. So it’s not surprising that the empirical evidence available today lets us trace

the history of our current physics as far back as spacetime itself can be defined, by this physics. [1] Even

so, we should keep in mind that before the emergence of atoms, spacetime structure would not have

been definable, nor would the system of the Standard Model have been distinguishable from any other

possible physics.

In any case, while our current cosmology explains a great deal about our universe, no history based on

changeless laws and principles can address the question of how or why this system of physics came to

exist. The question of origins requires a different kind of answer, which is what we’re trying to imagine

36

here. Since cosmology takes the context-structure of the observable world for granted, it needs to be

supplemented by a theoretical account of how that kind of structure could have emerged.

Evidently such a theory can’t assume any well-defined factual state of affairs, to begin with. But as

proposed in Chapter 2 above, what’s fundamental in the physical world are not facts but possibilities.

Essentially our world is made of situations in which various things can happen, given the constraints

imposed by past history and the laws of physics. And situations are more specific and more complex as

their possibilities are more tightly constrained. Definite facts arise only in very complex situations – i.e.

measurement-contexts – that can select one specific outcome from all other possibilities, and then use

that outcome to constrain new possibilities in other contexts.

To start with, then, we assume a situation with no given facts, nor any other kind of constraint on what

was possible – since in the beginning there would be no context in which facts or laws could have any

meaning. We imagine the original environment as a more radical version of our quantum vacuum – as a

chaos of entirely free possibility, where anything at all can happen.[2] Here there’s no way to distinguish

what happens from what doesn’t, or to define where or when anything happens in relation to anything

else. Even so, any more structured system of events could exist in this environment, so long as it could

define all its own constraints in terms of each other – as, for example, our own observable universe does.

I proposed in section 2.3 that at a fundamental level, the laws of physics don’t force things to happen the

way they do. At bottom, all events are random – but the only events that can be observed, or have any

definite character, are those that satisfy the conditions for maintaining a communicative environment.

Unlawful events don’t need to be suppressed, since they can’t make any determinate difference to what

happens in the observable world. So this world we experience is just a tiny subset of all the possible

events in an underlying unconstrained and indeterminate chaos. It’s an ongoing random selection of

events that happen to provide contexts that keep on making things measurable.

Now our current universe operates with so many complex constraints, involving so many different kinds

of information, that it’s hard to imagine this entire system coming to define itself all at once. So instead

we’ll assume that this physics emerged in stages, beginning with very primitive self-defining systems of

constraints.[3] At each stage the environment was able to delimit a certain subset of possibilities, ruling

out those that didn’t happen to meet this system’s requirements. Then within this self-selected subset,

new kinds of contexts could emerge, defined by more complicated systems of constraints. Eventually this

gave rise to the many-leveled system of many kinds of mutually-defining constraints that constitutes our

observable universe.

At each stage, most of the possibilities allowed in the previous stage were ruled out by new constraints.

So as this process went on, the indeterminacy of the original chaos was gradually used up. In the final

stage, with the emergence of our current system of physics, situations constantly arise that are so tightly

constrained that events seem strictly determined by exact mathematical laws. But even at this stage, at

37

the quantum level, what happens is still essentially random. Yet the complex constraints of quantum

physics produce a statistical weighting of probabilities that maintains our higher-level environment of

precisely measurable facts.

What’s appealing about this idea is that each stage inherits and incorporates all the constraints defined

by prior stages. This should make possible an empirically grounded reconstruction of the sequence of

stages through which our current physics emerged. Here I attempt a very rough and incomplete outline

of such an analysis. The goal is not to develop an actual theory, but only to make it plausible that a

functional analysis of our current well-established theories can potentially explain where our universe

came from and why it works the way it does.

4.2 Stage I – Interaction

What kind of constraint could be the starting-point for this process? In quantum theory, everything that

happens in the world ultimately consists of one particular kind of event, i.e. quantized interaction – tiny

discrete moments of connection between things, involving a minimal quantum of action. In our current

universe this is a measurable quantity – Planck’s constant – and there are many different ways in which

different types of particles interact. But none of this could have been definable in the original chaos of

unconstrained happening. To begin with, then, we need a more general concept of interaction.

Usually we think of interactions as distinct from the things that interact. But quantum physics blurs this

distinction, since interactions are described as particles, and particles are defined by their interactions.

And in our initial environment of free, indefinite possibility, there’s no context for defining “things” of any

kind. So we start by conceiving interaction just as a momentary connection between other interactions,

in a web of interlinking events that are otherwise undefinable. At this stage we’ll imagine the physical

environment as a superposition of all possible connections between events, in a network with no definite

topology. We can’t yet distinguish different types of connection, or specify which events are connected

to which others. The fact that all interaction is quantized, in our current physics, just means that these

connections are the simple basic elements from which all observable phenomena are built. To begin with

there’s no context in which any deeper structure could appear within these primitive events.

The initial constraint, then, selects out events that connect at least two other such events, within a web

of momentary happening. There’s no context to determine which possible events satisfy this constraint,

but events that don’t connect to other events are in any case irrelevant – they can make no difference to

anything that happens within this network, and can’t contribute to any higher -level order.[1] So this is a

self-defining system in the most primitive sense, where the only events that matter are those that connect

to events that connect to other events. Neither space nor time have any meaning here – but as we’ll see,

even this minimal level of structure provides a basis for defining higher-level contexts.

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4.3 Stage IIA – Recurrence

That first constraint is easy to justify, since it’s clear that any observable event needs a context of other

events it’s connected with. And if we imagine the primitive environment as a superposition of all possible

one-to-one connections between events, we can also treat it as a superposition of all possible sequences

of events, where one interaction leads to the next. We have no context yet for relating these possible

chains of events to each other, or for orienting them in space or time. But we can distinguish two different

types of possible sequences – those that loop back on themselves and those that don’t.

In a web of all possible connections, there are countless different paths between any two events. All such

paths are essentially equivalent, since there’s no way to differentiate direct from indirect connections, or

to count the number of events along any path. Likewise there are countless equivalent paths from any

momentary event that loop back again to that same moment, in a recurring sequence. And we can also

imagine possible sequences that never loop back on themselves – that always keep on connecting new

moments of connection without ever reconnecting to prior ones.

This gives us a second primitive selection rule, where each recurring sequence of events provides its own

context, selecting its own events. There’s still no broader context that could determine which sequences

satisfy this rule. There’s no way in which this repeated recycling of events could make any difference to

anything else. Nonetheless, the distinction between recurrent and non-recurrent event-sequences does

play a fundamental role in the physics of our current universe. In our world, every observable sequence

of connected events has a definite order in time, and these sequences never loop back on themselves. All

observable happening goes from the past into the future, never the other way. And as we’ve seen in the

last chapter, the four-dimensional spacetime of our universe is specifically structured so as to maintain a

consistent distinction between the factual past and the possible future for all communicating observers.

So in our current physics, this second selection rule operates negatively: it eliminates all the recurrent

event-sequences, to enable a universally consistent time-ordering for all observable events.[1] On the

other hand, at the deeper level of quantum superpositions, these recycling sequences are ubiquitous;

they constitute the entire structure of the quantum domain. As described by wave-functions, quantum

systems aren’t things that just persist through time, maintaining a static identity, as things do in classical

physics. These systems exist by continually recycling through sequences of all their possible states and

interactions. Probability amplitudes are largely determined by phase-relationships between all these

cyclical sequences.

In the path-integral picture, for example, if a photon is emitted by particle A and absorbed by particle B,

its wave-function includes amplitudes for all conceivable paths between A and B – including paths that

are disallowed by the laws of classical physics. Each of these paths contributes to the total amplitude for

the interaction – but almost all paths are cancelled out by nearly identical paths that have opposite phase.

The only trajectories whose amplitudes aren’t cancelled out are those close to the photon’s classically

39

defined trajectory; only these possibilities end up with a significant probability of being observed in an

actual measurement.

This is essentially how quantum physics achieves the precise determinism of the classical realm, on the

basis of random events. Phase-relationships between cyclical quantum systems shape the statistics of

interaction so that classical outcomes become overwhelmingly probable. Of course all these phases and

amplitudes are defined by the physics of our current universe, where quantum systems have measurable

frequencies, and wave-functions represent a cyclical process that takes place in space and time. But we

can see this recycling as reflecting a more primitive stage in the emergence of our current physics, where

the only sequences of events that could have any definable character at all were those that defined

themselves by continually reselecting a sequence of events.

At that stage there was no external context to define any relationships between these cyclical sequences,

while all the other, non-looping sequences were entirely unconstrained. There’s so little structure here

that it’s not clear how any higher-level system could emerge from it. Fortunately, it’s not our task here

to invent new levels of self-defining structure a priori. Rather, within the complex physics of our current

universe, we’re looking for some simple system of selection rules that provides a context for relationships

between different event-sequences. This system needs to be able to define itself without reference to

the spacetime metric, and yet serve as a framework on which our world of measurable space and time

could be built.

4.4 Stage IIB – Pre-Metric Spacetime

As noted above, a basic feature of our observable universe is the ordering of all events in time, which

means excluding any event-sequences that loop back on themselves (or rather, restricting all these self-

recycling sequences to the subliminal domain of quantum superpositions). But there also needs to be

some way of relating all the non-looping sequences to each other so they all proceed in parallel, so to

speak, lined up along a common time-axis. The events along one sequence need to be connected with

events on other sequences in a way that maintains a universally consistent temporal order.

As noted in Chapter 3, our universe has a way of ensuring the consistent time-ordering of all connected

events, based solely on the local frames of communicating observers. Rather than assuming any relations

of simultaneity between distant events, as in Newtonian physics, it orders events through the structure

of light-speed communication. We noted that this “skeleton” of null intervals is independent of the

spacetime metric, since null intervals are null in any reference frame. If we take this skeleton to represent

a primitive level of structure underpinning our measurable space and time, this indicates clearly enough

where we can look for the next stage in the series of emergent self-defining systems – in the structure of

the electromagnetic field.

40

Usually we describe this field in terms of measurable quantities – potentials with specific values at each

point in the spacetime metric. But there are peculiar features of electromagnetism that point to a more

primitive underlying structure. The field is gauge invariant: its local potentials are defined in relation to

each other, and have no absolute values at particular points in space and time. The magnetic fie ld is

determined by variances in the electric field and vice versa, so these two components of the combined

field provide contexts for each other. Accordingly, Maxwell’s equations can be cast in a form that has no

reference to measurable intervals in space or time.[1]

While the two previous stages were each defined by a single selection rule, in this primitive, pre-metric

version of electromagnetism we have a system of several rules, each defined in the context of the others.

The first of these constraints selects out a specific subset of all possible non-looping event-sequences, as

the set of sequences on which all the other rules of the system operate. This initial rule corresponds, in

the physics of our current universe, to the conservation law for electric charge. It selects sequences that

always keep on adding new events, never terminating or looping back on themselves. It also requires that

selected sequences remain distinct from each other, never branching into multiple paths or merging with

other paths. That is, it selects event-sequences corresponding to the paths of charged particles in classical

electrodynamics.[2]

To begin with, these continuous charge-sequences have no definite relationship with each other. The

function of all the other rules is to define such relationships, setting up a structure of cross-connections

between charge-sequences corresponding to the field of photon-interactions across null intervals. The

resulting system selects out sets of possible charge-sequences that are everywhere consistently aligned

with each other, on a common time-axis.

In this primitive pre-metric system, though, charges don’t have definite positions or trajectories, and its

parameters have no quantitative magnitudes. All parameters of this system represent simple binary

choices between symmetrically opposite possibilities. Each of its rules determines whether a charge goes

in one direction, relative to some axis, or in the opposite direction.

For example, the initial parameter – the conserved electric charge of each sequence – can either be

positive or negative. These represent the two opposite directions along the time-axis defined by the

system – that is, positively-charged sequences are those that go one way in time, negatively-charged

sequences go the opposite way. The time-axis is symmetrical, having no preferred direction; however,

the charge conservation rule requires positive charges to remain positive and negative charges negative;

they’re never allowed to turn around in time. Of course in the physics of our current universe, there’s

only one direction of time, defined by the irreversible processes of measurement at the quantum level,

and by classical thermodynamics. But even here, electromagnetism has no “arrow of time” – all its rules

are time-reversible, and negatively-charged particles act just like their oppositely-charged antiparticles

going the other way in time.

41

The other rules of this system define the two related fields, electric and magnetic, that connect charge-

sequences with each other. Each of these rules determines a binary choice between opposite directions

in space, so that positive charges go one way, negative charges the other. These can either be opposite

directions along a spatial axis, or opposite directions of cyclical rotation around a spatial axis. This is a

feature peculiar to electromagnetism – that its rules relate these two types of direction to each other,

linear and cyclical (recalling the difference between looping and non-looping sequences in the previous

stage). The electric and magnetic fields are symmetrically connected, with a linear direction in one field

determining a rotational direction in the other.

These fields are defined by two other conserved parameters – linear momentum and intrinsic angular

momentum (spin). These properties are carried both by the charge-sequences and by the photon-field

that cross-connects them. These momenta have no magnitude, since this system doesn’t yet define any

distances, angles, velocities or accelerations. Here momentum is just another binary choice between

opposite directions, either along some spatial axis (for linear momentum) or around a spatial axis (in the

case of spin). Because the system’s rules relate linear directions on a spatial axis to rotational directions

in a plane orthogonal to that axis, the system as a whole defines a pre-metric space of possible directions

that’s inherently three-dimensional.

Conservation of momentum serves two functions. This rule maintains the continuity of each charge-

sequence, by requiring that the direction of a charge’s linear momentum and the direction of its spin get

passed on from one interaction to the next along each charge-sequence. But these directions can also

change as the charges interact, exchanging momentum with each other through the combined fields. So

the rule of momentum conservation also ensures that any change in the momentum of one charge is

balanced by an opposite change in another charge’s momentum, along the same spatial axis.

I won’t try to detail all the rules for electric and magnetic interaction between charges, in which both

types of momentum are involved. These are familiar, corresponding to Maxwell’s equations: for example

when two charges interact, the linear momentum of each charge is redirected along the spatial axis

between them: if the two charges are different they go toward each other, or the opposite way if the

charges are the same. Every change in a charge’s linear momentum also generates a change in the local

magnetic field, which affects both the linear momentum and the spin of other charges. In the space and

time of our current universe, the combined effect of these several interaction rules defines remarkably

complex trajectories when charged particles interact. But in the primitive system I’m sketching here,

there are no positions or trajectories in space and time, only a simple self-defining system of rules and

parameters determining symmetrical changes of direction along arbitrary sets of orthogonal axes.

These rules operate on a web of null-interval connections between charge-sequences, a web that has no

definite structure to begin with. Any event on any sequence can be connected with any other, giving a

superposition of possible cross-connections. But from this superposition, the system of rules selects out

sets of connections that maintain a rigidly determinate structure. Every interaction along a charge-

42

sequence inherits its directions of linear momentum and spin from the prior interaction in the sequence,

and those directions change, in each interaction, according to a rule that connects it with an opposite

change on another sequence. All the rules are temporally symmetrical, applying the same way in either

direction on the time-axis. But in each interaction there’s a binary choice between opposite directions,

and a rule that strictly determines which direction must be chosen. And the system as a whole operates

to select out sets of possible sequences that are all consistently aligned with each other on the universal

axis of time, in a three-dimensional space of possible directions.

This rigid determinism doesn’t carry over to the physics of our current universe, where there are many

more degrees of freedom and many more interaction-rules. As noted in Chapter 2, the dynamics of our

current world is far too complex to be mathematically determined – instead, the trajectories of particles

are defined statistically, by a combination of mathematical laws and random selection. At this primitive,

pre-metric stage, however, the rules need to be simple and unequivocal, because there’s so little pre-

established structure to build on. Only interactions that happen strictly according to this set of universal

laws can have any definite character at all. The rigidity of this system is what enables it to maintain a

consistent set of spatial and temporal orientations among all its selected sequences.

While each of its rules and parameters are quite simple, though, this system as a whole is fairly complex.

Couldn’t there be a much simpler set of mutually-defining constraints that could organize relations among

sequences of events? Yes, very likely – but it’s not hard to see why this system in particular became the

basis for our observable world. The metric version of electromagnetism is incredibly versatile, playing a

key role in every interaction except gravity. It underlies the structure of atomic electron-shells and their

ability to make molecules, and it determines the higher-level properties of all forms of matter. Its twin

fields sustain oscillations that not only distribute stellar energy over vast distances, but provide a medium

of communication that carries essentially all the empirical information we have about our universe. The

functionality of this system is unparalleled, and it may well be that no simpler system could have filled

these many roles.

So we can imagine that in the superposition of all possible sequences of events, there was some set of

interconnected sequences that happened to satisfy this complicated system of constraints. Since several

different kinds of rules are involved, such a constellation would be extremely unusual – but if it did arise

anywhere, its structure of mutually-defining fields would provide a context in which more and more

events could be selected, conforming to the same rules. Just as light propagates out into space, in our

current physics, we can imagine such a system spreading out into the space of possibilities, propagating

its structured superposition of relationships across null intervals, in both directions along its self -defined

axis of time, continually replicating the same pattern in new sets of interactions.

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4.5 Stage IIIA – Local Gauge Symmetries

In the physics of our current universe, electromagnetism is one of three very different systems of rules

that reproduce themselves this way – each interaction according one rule setting up a context in which

another rule applies. The other two are the systems of weak and strong nuclear interaction, which inherit

many of the features of pre-metric electromagnetism. They both define certain subsets of non-looping

sequences as particles that carry new conserved parameters – weak and strong versions of hypercharge

and isospin – as well as electric charge, linear momentum and spin. Like electromagnetism, they both

connect fermions with each other through local gauge-invariant boson fields.

But neither of the nuclear forces is anything like a straightforward extension of electromagnetism. Both

are remarkably complex, and in distinctly different ways. So the Standard Model actually gives us three

quite disparate theories that are unified only in being described by similar mathematics. That similarity is

important, pointing to some kind of common origin for the three Standard Model forces. But the usual

way of conceiving this – imagining them as originating from an initially unified force through spontaneous

symmetry breaking – doesn’t tell us very much. It can’t explain why the initial unified force should have

such complicated symmetry to begin with, or why random breakage should result in three so peculiarly

different systems of interaction.

On the other hand, it’s clear that each of these systems plays a significant functional role in creating our

observable world of atoms and molecules. The strong force confines huge quantities of energy in tiny

atomic nuclei, giving them enough mass that they’re precisely localized in space, with enough inertia to

serve as stable, point-like central charges for the Coulomb field in which electron-shells are organized.

The weak force plays the key role in nucleosynthesis, supporting the emergence of many types of atoms

and molecules; it also regulates the distribution of matter and energy out into the universe when stars

collapse and explode.

Here we imagine the relationship between these three systems of interaction in the following way. We’ll

suppose that the pre-metric structure of electromagnetism provided a context in which a great variety of

higher-level systems could define themselves, by adding new sets of selection rules to those already

established. Just as we imagined Stage IIA as a superposition of all possible event-sequences, here we

imagine a superposition of all possible systems that could define themselves on this same pre-metric

pattern of conserved charges interacting through local gauge fields. But out of all these possible

configurations, only two very complicated ones turned out to be useful in the foundation of our world.

Along with electromagnetism, they provided a framework of universal rules that could support atomic

structure and measurable spacetime. And in the newly emergent environment of interacting atoms, all

the other possible pre-metric structures became irrelevant, leaving no trace in the physics of our current

universe, where even virtual interactions in the quantum vacuum follow the Standard Model.

44

Each of these three systems has its own mutually-defining parameters and fields, its own set of rules

operating in its own space of possible directional orientations. The pre-metric space of electromagnetism

discussed above is a primitive version of the four-dimensional spacetime in which we live, whereas the

spaces of the nuclear forces are unrelated to spacetime, being structured by different symmetry groups.

And since these spaces define themselves separately from spacetime, we can interpret them as distinct

self-defining systems arising in the pre-metric universe.

Now symmetry in general can be conceived as a relation between different kinds of information, where

one parameter has a definite fixed value while other related parameters remain in a superposition of all

their possible values. In archeological physics, symmetries can be seen as reflecting the different stages

at which certain parameters become definable. For example, if electromagnetism defines a universal

time-axis before there’s any context that can determine a preferred “arrow” of time, then the rules of

that system will be symmetrical with respect to the direction of time. A symmetry arises by default,

whenever the values of one parameter are defined before those of other related parameters.

The local gauge symmetries of all three Standard Model systems can be understood this way. If these

systems of mutually-defining selection rules emerged before the establishment of the spacetime metric,

then their potentials could not be defined in terms of relative locations in space and time; they could be

defined only relative to the gauge fields. So, in our current universe, these potentials can be assigned

arbitrary values at any spacetime point without changing the underlying field-structure.

I won’t attempt to describe the many complex selection rules of the nuclear interactions. I will only point

out some of the ways these systems differ from primitive electromagnetism, since these set the stage for

the emergence of our measurable space and time.

In the first place, it’s clearly important that both the weak and strong forces have limited range, acting

mainly on the scale of nuclei. But since these are originally pre-metric systems, the range of these two

forces isn’t defined directly in terms of distances in space. Instead, quite complicated mechanisms are

involved. In the case of the weak force, the three bosons that carry weak hypercharge and isospin also

interact with the Higgs field. In the metric spacetime of our current physics, this gives these particles large

masses, drastically limiting the range over which they can transfer energy and momentum. As to the

strong force, quark confinement is accomplished by an entirely different mechanism that’s not yet well

understood, although the strength of interaction between quarks is thought to be independent of the

distance between them, consistent with the pre-metric character of this system.

Both nuclear forces thus contribute to the extreme localization of nuclear interaction, though at this stage

there’s no continuous scale of measurable distances. We don’t yet have a space and time in which

particles with mass move at sub-light speeds. Here there’s only the electromagnetic “skeleton” of null

intervals, supplemented by new selection rules with larger symmetry-groups, defining interactions in their

separate possibility-spaces. Before the actual emergence of atomic structure, these nuclear forces

45

wouldn’t yet have been distinguishable from any other conceivable system of pre-metric, locally gauge-

invariant interaction.

The nuclear forces depart from the pattern of electromagnetism in another way. Electric charge never

varies – any charged particle is permanently either positive or negative. Charge-sequences exchange

linear and angular momentum through the photon-field, but photons don’t carry electric charge. The

situation is different with the two nuclear forces, whose boson-fields do carry charge. The strong force

operates with a three-fold color charge, so the charges of quarks constantly change through gluon-

interaction with other quarks. Only the total color charge of nuclear particles is conserved – and in fact,

selection rules require that any stable combination of quarks has to have a net zero color charge.

I noted above that the basic pre-metric system of electromagnetism is fully deterministic, and needs to

be so in order to define itself. That’s because in Stage IIB there was no given external context that could

define relationships between charge-sequences. So for there to be any definable relationship between

charge-sequences, all the rules of the system had to be strictly followed. If a positive charge could at any

point become negative, for example, there would no longer be any definable axis of time.

Stage IIIA, on the other hand, already has the established context of electromagnetism as a basis. This

means that the gauge-field structure of relations between sequences can be much more permissive. So

long as the total color-charge of every nuclear particle is zero, the color of their constituent quarks can be

indeterminate, always cycling through a superposition of possible color-states. Likewise in the weak force

interaction, the protons and neutrons in a nucleus are constantly exchanging identities with each other,

though in stable nuclei the total number of protons and neutrons remains constant.

To take another example, the electromagnetic system is symmetrical not only with respect to time and

charge, but also parity. If magnetic interaction follows the left-hand rule for a negative charge, it has to

follow an identical right-hand rule for positive charges – again, because there’s no external context to

define any difference between one direction and the other on the time-axis. But the larger symmetry-

groups of the nuclear forces do allow for differences between right-handed and left-handed particles,

though it appears that parity symmetry is actually broken only in weak interactions. This also implies that

weak interactions break time-symmetry, though this is can only be observed in a few rare types of particle

decay. It has no clear connection with the emergence of a radical difference between the past and future

in our current world – to be discussed in the following section. But this illustrates the much greater

freedom of operation that local gauge-field systems can have, being built on top of the stringent selection

rules of primitive electromagnetism.

Since many aspects of the weak-force system are still mysterious, it’s not clear whether its breaking of

parity-symmetry plays a significant role in supporting our observable world. It’s possible that some of the

peculiar complications of the Standard Model have no functional role, being merely epiphenomenal – for

example, it’s not obvious that the three generations of quarks and leptons are required to make our sel f-

46

defining universe work. So while we should expect to find a functional explanation for all the primary

features of our currently-known physics, there’s no reason to assume that this should apply to every

peripheral detail.

4.6 Stage IIIB – Locality and Gravitational Spacetime

So far we’ve been dealing only with superpositions of possibilities, constrained by selection rules. The

self-defining systems described above are only possible patterns of connected events, within an ocean of

other possibilities. What distinguishes them is only that these particular patterns were incorporated as

fundamental supporting structures in the architecture of our observable universe. And this universe is

based on an entirely new way of defining constraints on what’s possible. In addition to universal laws of

physics, we now have “initial conditions” to which those laws apply – that is, specific local situations

shaped by specific facts determined in other local contexts. Here the world not only defines patterns of

possibilities, but also determines which patterns are actually instantiated in observed phenomena.

Our task now is to try to imagine how this kind of physical existence could have emerged. I’ve argued that

the key event was the formation of stable atoms, connecting and communicating with each other via the

electromagnetic field. But this was neither the beginning nor the end of the process. Atoms do have a

fundamental role in physics, much as self-replicating cells have in biology. They define basic universal

standards for distance and frequency; they operate as primitive measuring instruments by absorbing and

emitting photons of specific energies, and they’re able to store this energy-data over time by reconfiguring

their electron-shells. And of course, they also serve as building-blocks for every kind of stable material

structure. Nothing in the subatomic domain even approaches this level of finely-tuned functionality.

Nonetheless, the formation of atoms depended on a long and varied pre-history, as discussed above, that

produced the array of subatomic particles early on, and eventually gave rise to an environment in which

stable atoms could exist. Moreover, even once the web of interacting atoms began to operate, it could

at first define very little higher-level information, since it consisted mainly of hydrogen and helium atoms

widely scattered through space. The emergence of a world of observable phenomena happened very

gradually over an extended period of time, as the cosmic environment underwent great changes.

Similarly, the “collapse” that happens in quantum measurement is not a specific event at a specific point

in time. Measurement occurs insofar as a context makes it possible to define certain aspects of a factual

situation, to a certain extent, and such situations arise only over a certain space and time. Likewise the

origin of our observable universe happened just insofar as the evolving interactive environment began

creating contexts that made the various aspects of our physical reality empirically determinable.

That’s the historical picture, of a world gradually evolving over time. This is the picture we construct

retrospectively from presently available evidence, assuming that the basic underlying physics hasn’t

changed since the beginning. In the other complementary picture – the one we’re trying to develop here

– time and space and the laws of physics weren’t just given from the start; they came into being in a series

47

of distinctly different stages. In this picture, the emergence of our world of measurable facts was not at

all gradual; it required a tremendous leap to a new level of self-determining organization. We saw another

leap like this above, in Stage IIB, where the origin of pre-metric electromagnetism involved the co-

emergence of a complicated set of rules and parameters. The case with Stage IIIB is far more radical: it

could only happen because two remarkably different and profoundly complicated systems could

somehow emerge together, providing contexts for each other.

One of these was the quantum physics we describe in the Standard Model. It inherits many rules and

parameters from the previous stages, but redefines them all as a system of quantitative relationships. All

its interactions, from Stage I, now involve specific quantities of action, based on the minimal unit of

Planck’s constant. The self-recycling sequences of Stage IIA show up in the superpositions described by

quantum wave-functions, which now have definite frequencies and wavelengths. The parameters of

Stage IIB electromagnetism – electric charge, the field-potentials, spin and linear momentum – all get

redefined as scalar and vector quantities related by Maxwell’s equations. Likewise all the parameters of

the nuclear forces, from Stage IIIA, acquire specific values that serve to support the existence of stable

complex nuclei.

Now all these parameters – even those of the nuclear forces – are empirically measurable through their

effects on the motion of things in space and time. This depends on the other newly emergent system –

the spacetime metric, built upon the IIB skeleton of null-intervals. This metric is structurally complex in a

completely different way from quantum physics. Where the latter defines many kinds of interaction, each

defined by many kinds of rules, here there are only the rules of gravitation and inertia. But gravity not

only pulls distant things together; it also determines the specific distances between them. It defines an

environment of continuously changing spatial relationships between pairs of local entities, operating over

a tremendous range of scales. The formal structure of its rules, expressed in Einstein’s equations, is

remarkably simple and elegant, in stark contrast to the mathematics of the Standard Model. But the

actual patterns of interaction it determines – the trajectories of particles and larger bodies, all affecting

each other’s motion – are far too complex to be mathematically computable.

Because every kind of quantitative measurement depends on this geometry of relative distances and

velocities, it provides a common ground for translating between different kinds of physical information.

This is a key requirement in a world where different systems of observable parameters provide contexts

for each other. But spacetime geometry doesn’t accomplish this by itself. Space and time themselves are

only observable because there are locally situated entities that follow continuous trajectories, which the

electromagnetic field makes it possible to track. To define such entities, Stage IIIB introduces a new kind

of conserved parameter, one that ties together all the various types of interaction. This is energy –

including the energy that’s localized in the form of mass.

Like other conservation rules, the conservation of energy has multiple functions. It preserves the constant

rest-mass of individual entities along their trajectories, and regulates the sharing of energy between them

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when they interact, whether through gravity and electromagnetism or through the nuclear forces involved

in particle collisions and decays. Unlike all the other conserved parameters, though, energy takes many

different forms, including the potential energy of all the various fields, and even vacuum energy. Since

every interaction involves a transformation of energy, this parameter plays a key role in making facts

defined in different contexts relevant to each other.

Energy conservation also plays a key role in the “collapse” that creates new facts by random selection, in

quantum measurement. Only one outcome can be observed, in a measurement, because this selection

rule requires that the total energy involved in the situation must remain constant. While many kinds of

interaction are needed to set up any measurement-context, the factual input that constitutes a situation

has always a specific total energy, and the same total energy has to appear in the facts that constitute the

outcome. All other possible outcomes included in the situation’s wave-function just vanish without

consequence, since there’s only energy enough to realize one of them. So both the transformations of

energy and the conservation of total energy have vital functions in maintaining a determinate reality

constituted by different kinds of information.

What essentially distinguishes the physics of our observable world from the previous stages are these two

new parameters: distance in space and time, and the energy carried by fields and particles. There’s a

basic relationship between these two parameters, given in Einstein’s field equations, which relate the

geometry of spacetime to the distribution of local energy-densities.

To unpack this, let’s consider first how energy gets localized. This happens in many different ways, but

primarily by giving mass to atomic matter. Atoms localize energy mainly in their nuclei, where several

complicated mechanisms are involved. First, elementary particles acquire mass through interaction with

the Higgs field, which operates differently for quarks and leptons. But particle masses make up only a

small part of the total nuclear mass, most of which comes from the huge confined energy of strong -force

interaction among quarks and gluons. A much smaller contribution to atomic mass comes from the mass

of electrons, which includes the energy of their self-interaction via the electromagnetic field; and there’s

also localized energy in the binding of electrons to the nucleus. Then too, all higher -level dynamics, from

the chemical interactions of molecules to the gravitational interactions of planets, stars and galaxies, also

contribute to the localized energy-densities that appear on one side of Einstein’s equations.

On the other side is the curvature of spacetime – gravity – which plays an indispensable part in evolving

our observable universe by pulling atoms together into galaxies and stars, which eventually produce the

heavy nuclei needed to make stable material structure in dust, rocks and planets. But there are other

aspects of this geometry that are equally important. As noted in Chapter 3, locally and at low velocities it

very closely approximates a flat Euclidean geometry, with space and time as independent variables. And

since gravity is so weak, compared with all the other forces, the curvature of spacetime has no effect on

the scale of quantum physics, which can therefore define itself within an essentially classical framework

of space and time. Further, Einstein’s geometry makes inertial reference-frames definable even where

49

the curvature is very strong. This means that unlike position or velocity, acceleration and related

parameters have objectively measurable values that are the same for all observers. So together with

quantum mechanics, general relativity supports the simple deterministic framework of Newtonian physics

over a very broad range of scales.

Finally, besides the small gravitational constant, two other parameters play key roles in this spacetime

structure. One is the cosmological constant in Einstein’s equation, which is related to the anomalously

small vacuum energy coming from virtual interaction in the quantum domain. The other is the initial rate

of the expansion of the universe. All three of these parameters need to be very finely-tuned to each other,

to provide enough time for stable material structure to emerge in the universe. If their values had been

slightly different, either the expansion of space would have ended very quickly in a gravitational collapse,

or it would have accelerated so rapidly that no higher levels of structure could ever have evolved.

The bottom line here is that the origin of our observable world involved the co-emergence of two

complementary kinds of information. On the one hand, there came to be measurable facts about

individual local entities with mass, which eventually included everything from particles to clusters of

galaxies. On the other, it became possible to determine facts about the interrelated trajectories of all

these entities in space and time. At a fundamental level, both the existence of localized entities and the

coordination of their relative motion depend on exceedingly complicated functional arrangements, as

described respectively in quantum physics and general relativity.

To complete this picture, however, we need to consider one other basic feature of our IIIB universe, which

is equally essential to making this system work. In different ways, based on different structural

foundations, quantum physics and gravitational spacetime both support the clear and simple objective

reality described by classical physics. Over a very wide range of scales, all the underlying complexity of our

fundamental theories can be ignored; the world operates as a vast body of precisely determinate, context -

independent fact, subject to a simple set of mathematical laws.

It’s hard to imagine how any kind of measurement could be possible without the perfect dependability of

this higher-level physics, or the simple, exact mathematical relationships between all its parameters

within a transparent framework of Euclidean space and time. Neither relativity nor quantum theory could

make sense without the existence of reliable clocks and rulers that define local intervals in time and space

exactly the same way everywhere. So there are really three foundations needed to support the

functionality of an observable world: quantum physics, spacetime physics and the classical physics they

create between them.

4.7 Summary – The Physics of Possibility

We come back to the question at the beginning of this Chapter: how could a self-determining system as

deeply complicated as our universe have come to exist? The aim of this “archaeological” analysis was to

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break the problem down into a series of stages, in each of which a new dimension of physical structure

could plausibly emerge. Yet the transition to this final stage involves so many new kinds of quantitative

information, related to each other in so many different ways, that it may hardly seem reasonable to

suppose it could all become definable at once.

In the earlier stages we could sort out most of the structural components of our known physics into a

more or less plausible sequence, with increasingly dramatic advances in complexity from each stage to

the next. Stage I has only the basic notion of interaction. In Stage II we consider all possible sequences

of interactions – IIA involving sequences that define themselves by recycling through a series of events.

These sequences are special, but arise naturally in a superposition of all possible sequences. In contrast,

Stage IIB requires a leap to a new level of structure, one that defines reciprocal relationships between

distinct charge-sequences. To accomplish this a number of different selection-rules have to emerge

together, along with the new conserved parameters of charge and momentum.

The same pattern is repeated in Stage III, which considers higher-level systems based on the skeleton-

structure of pre-metric electromagnetism. In IIIA, again we imagine a superposition of possible systems

of this kind – those that define themselves by adding new selection rules to the IIB structure, with new

types of charges and gauge fields. The two Standard Model systems of nuclear interaction can be seen as

arising naturally within this superposition, along with many other complex systems as well as simpler ones.

When we come to Stage IIIB, however, we see another leap to an entirely new level. This requires two

very different kinds of complex systems to emerge together – the quantum structure of atoms, and the

gravitational metric of spacetime. Between them they define a self-sustaining process of setting up

measurement-contexts, in which all the parameters of the prior stages become determinable quantities.

Now as already noted in the previous section, this last transition – from a superposition of possibilities to

a world of objective, measurable facts – didn’t take place all at once. It happened over a long period of

time, as contexts arose in which new kinds of facts were defined, that could keep on setting up these

contexts. This process first began in the environment of communications between stable atoms; the key

facts that kept on being redefined were about the uniform structure and behavior of atoms and their

nuclei – quantitative facts about the properties of sub-atomic particles and the kinds of interaction that

make those properties determinable. But for a long time, the kinds of facts that are most familiar to us

today wouldn’t have been definable – for example, the properties of bulk matter, or the trajectories of

massive bodies. At the beginning of the atomic universe, the only higher-level facts that could make any

difference were the gradually declining energy-density of the environment and the gradually increasing

differences in energy-density over vast regions of space.

So what slowly emerged over the first few billion years was our environment of deterministic interaction

at intermediate scales of distance, velocity and energy – the world of macroscopic objects, where classical

physics and chemistry give rise to the amazingly diverse array of phenomena we can observe today. But

it’s hard to see how the physical foundations of this universe could have developed gradually over time.

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The relational geometry of spacetime couldn’t define itself apart from the context of communications set

up by nuclear and atomic physics, or vice-versa. The basic premise of this essay is that all observable

information needs the support of other kinds of observable information, and that most of what we know

about the deep-level structure of physics is needed for there to be any observable phenomena at all. And

if that’s so, then the transition to a world that’s able to define specific facts necessarily involved the co-

emergence of many different kinds of measurement-contexts.

That may well seem miraculous.[1] Yet given the wealth of possible systems of interaction defined in the

previous stages, it must have been possible for one particularly complex set of mutually defining systems

to begin this self-sustaining process of determining quantitative facts. Some combination of selection

rules must have been able to knit the nuclear forces together with electromagnetism to support the

appearance of stable atoms and molecules, in the context of an expanding and gravitating spacetime.

Though we’ve so far given little thought to the question of how all these systems work together to define

a local metric of distances and frequencies, it seems that our existing theories must have a great deal to

teach us about this. And if we can gain some clarity about the functioning of our current physics, that

should offer insight into the question of how the creation of measurement-contexts first began.

At any event, the “collapse” that occurs in every measurement-event recapitulates this same sort of

miracle. As argued in Chapter 2, whenever a context makes it possible for a fact to be determined and

communicated, the laws of physics require that a specific fact be selected at random; nothing more is

needed to bring this about. Even though any such context depends on many kinds of facts determined in

many other contexts involving different interactions, this tremendous complexity presents no obstacle to

the process, since it operates by random selection. The laws of physics function to ensure that these

contexts continually arise, and that there are always possibilities that will satisfy all relevant constraints .

But the laws don’t need to determine the specific outcomes of measurements. Outcomes just happen

because they can happen, and insofar as they do they make further outcomes possible.

The origin of this self-perpetuating physics of measurement can be conceived in a similar way. In the

underlying chaos of indeterminate happening, there were possible sets of related events that happened

to satisfy the special combination of mutually-defining selection rules that constitutes our current physics.

Insofar as they could keep on setting up contexts to select other such events, nothing more was needed

to begin a self-sustaining process of defining new facts. No specific mechanism could accomplish this, just

as no specific mechanism could achieve what the random “collapse” accomplishes. But if it was possible

for a system of mutually-supporting measurement-contexts to get underway, it was in the nature of the

process itself – like self-replication in biology – to keep on making itself possible again in new situations.

This means that our so-called laws of physics are entirely de facto. Nothing established them, nothing

enforces them; they’re just a set of constraints that reflect the way random events can keep on defining

the same system. At bottom anything can happen, but only insofar as things happen according to these

laws can they be observed or have any definite character, or contribute to contexts in which other kinds

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of things become definable and observable. It doesn’t matter if the laws are complicated, or require a lot

of fine-tuning, so long as they work. It doesn’t matter if several different mathematical frameworks are

needed to represent them, or if the math is only computable in very simple situations, or even if the math

is only self-consistent within certain limits. Physical laws don’t control the world; they only express its

particular ways of defining itself.

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Conclusion – What It Takes to be Fundamental

It’s usually taken for granted, in physics, that the objective view of the world has to be the fundamental

one. That is, we assume it makes sense to theorize about a block universe, or a multiverse, or physics at

the Planck scale, or some other sort of fundamental reality that just is what it is in itself, even though

there’s no conceivable context that could make it observable. Against this, there are interpretations of

QM, like QBism[1] and Relational Quantum Mechanics[2], that take an explicitly subjective or observer-

dependent view of the world at a fundamental level.

Now there’s no doubt that the macroscopic world is objectively factual – but I’ve argued that this can’t be

the case at a fundamental level. In quantum mechanics, determinate information can exist only to the

extent that the interactive context actually determines it and passes it on to other contexts. But this

doesn’t necessarily involve an observer. The point is rather that no unobservable, context-independent

reality can be relevant to the base-level operating system of an observable universe. The fundamental

physics has to be a structure of mutually-supporting contexts that makes different kinds of information

definable and measurable in terms of each other.

Nonetheless, our most important theories do extrapolate beyond the scope of what’s observable. All of

quantum theory describes a world of quantum superpositions that are never directly observed. General

Relativity describes spacetime as a geometry of infinitesimal intervals on a continuous manifold, though

there can never be infinitely precise measurements. And cosmology gives us a detailed prehistory of

particle interaction in the early stages of the cosmos, long before the emergence of atoms and molecules.

But as I’ve tried to show, these theories don’t really represent a foundational reality that exists in and of

itself, beyond the limits of measurement. Rather, they articulate in objective language the many kinds of

complex structure needed to create and sustain an environment of communicated information. What’s

really fundamental is the functionality of this environment. It’s the ability of our universe to support

measurable information that ultimately explains all the underlying physics.

This contrasts with the traditional “reductive” way of explaining things, in physics. The goal there is to

show how many diverse and complex phenomena can arise from a single relatively simple basis, and of

course this approach was extremely successful, down to the level of atoms. But atomic structure is well

explained by a theory that’s far from simple, and even in the Standard Model far from unified. So to say

that classical physics “reduces” to quantum physics sounds a bit odd. Yet the traditional goal still holds

sway. The quantum field theory of the Standard Model is now understood as an “effective” theory that

applies in the low-energy limit of some unknown, more fundamental physics that may not be in any sense

simple, but will at least incorporate gravity. Unfortunately, we have virtually no empirical evidence for

any such theory.

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Here we’ve pursued a different idea of what it means to be fundamental. The question is what it takes to

be a basis for anything – what kinds of functional supports are needed for there to be any observable

phenomena at all. This is in line with the growing understanding that in general, reductive explanation

tells only part of the story. This “bottom-up” approach ignores “top-down” factors that are also at work

in the emergence of new levels of structure.[3] These factors are contextual – for example, in the context

of self-replicating systems, evolving through natural selection, exactly the same physics that produces

simple inorganic molecules becomes capable of building all the hugely complicated molecules needed to

support life. To say that biology “reduces” to chemistry and molecular physics is correct, in a way; but it

doesn’t explain the profound difference that gradually opened up between living beings and the rest of

the universe. That has to be understood in terms of a basic shift in the functional context.

So being fundamental is complicated. What explains things – what makes it possible for them to be what

they are – includes the lower-level structures on which they depend, but also the higher-level contexts in

which they come to exist. In physics, nothing could be measurable without the underlying structures of

quantum physics and relativity. But it’s equally true that measurement depends on the context of other

measurable phenomena, in the deterministic context of the world described by classical physics. The

deeper-level theories are indeed “effective,” but in a different sense – not in that they need to be reduced

to some still deeper theory, but in that they’re able to support the higher-level environment of observable

information.

In the previous chapter I tried to imagine how our world of multi-leveled interactive contexts could have

come about. Obviously this sketch bears no resemblance to an actual physical theory. But I want to show

that it should be possible to construct an empirically grounded theory to explain why our universe needs

so many layers of complex and counter-intuitive structure. The basic message of this essay is that we can

reasonably ask why our universe operates the way it does, and that this question is important for the

development of a truly fundamental theory. If we can clarify what all this physics is doing – what it takes

to be a basis for a self-defining, self-communicating universe – then we have at our disposal a vast body

of knowledge detailing how this system works. To a great extent the answers are there, once we learn

how to ask the right questions.

That doesn’t mean everything is explainable, though. Our world is the product of historical accident, even

at a fundamental level; there’s no reason to think that a universe has to be built exactly like this in order

to support communicable information. There might well be other ways to define a Stage IIB system of

relationships between event-sequences, for example, or a IIIB web of communication among localized

contexts. Even in the physics of our own universe there seems to be a lot of leeway – many of the basic

constants could have had somewhat different values, without undercutting the basic functionality of

measurement. Like everything else, the foundations of this physics were ultimately selected at random,

subject to the constraint that they sustain an environment of definable and communicable information.

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But being accidental doesn’t make things meaningless; on the contrary. If our universe did after all turn

out to instantiate some perfect mathematical pattern, that would be great for the theorists who discover

it, but what would it mean, beyond that? Ultimately things are meaningful insofar as they happen in a

context where they make a difference, making it possible for something else to have meaning in some

future context. As I’ve tried to demonstrate, that’s what physics is all about.

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End Notes

To return to the main text after clicking on a [note] use Alt-Left Arrow.

Notes to Chapter 1 – Introduction

1.1 What Does It Take to Make Things Observable?

1. It was a basic principle of the Copenhagen school that both measurement arrangements and the

results of measurements are necessarily described in terms of classical physics. For a recent analysis

of specific aspects of classical physics required in measurement processes, see Barbara Drossel and

George Ellis, “Contextual Wavefunction Collapse: An integrated theory of quantum measurement,”

2018 New J. Phys. 20 113025, iopscience.iop.org/article/10.1088/1367-2630/aaecec/pdf, section 5.4.

2. Fine-tuning shows up in many seemingly unrelated aspects of atomic physics and cosmology – see

Luke Barnes, “The Fine-Tuning of the Universe for Intelligent Life”, arxiv.org/abs/1112.4647. But the

idea that our universe might be finely-tuned for the sake of intelligent life – or any form of life – is

peculiar. For one thing, the mechanisms of biology are also finely-tuned in many ways, but the reason

for this is clear in biology itself: without the complex mutual adjustment of many different molecular

cycles and higher-level processes, self-replicating organisms could not exist. Few biologists believe

that the evolution of life was directed toward producing the kind of intelligence that only one species

has. But there’s just as little reason to believe that the complexities of the physical world were

directed toward creating life – since there are so many other things that physics supports, nearly all

of which are far more prevalent in the universe than living beings.

The goal here is to investigate a specifically physical reason why physics needs to be complex and

finely-tuned: if it were not, nothing would be measurable or in any way determinable. But I’m not

suggesting that the laws of physics have to be exactly as they are in order to support observable

information. Not everything in physics seems to be finely-tuned; there’s evidently some leeway in

the construction of our universe. And it’s possible that universes structured very differently from ours

might be able to define and communicate a different set of measurable parameters.

3. See e.g. Matt Strassler, “Naturalness and the Standard Model”, profmattstrassler.com/articles-and-

posts/particle-physics-basics/the-hierarchy-problem/naturalness/. This makes a rough attempt to

quantify the percentage of possible worlds that operate more or less like ours, dealing with only one

finely-tuned parameter affecting the possibility of measurement – the smallness of the Higgs mass.

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1.2 Why There’s a Measurement Problem

1. As already noted, the unitarity of the quantum equations seems to allow no way for the “collapse of

the wave-function” to occur. Moreover, all the theory gives us is a statistical structure of more and

less probable outcomes for any particular measurement, and the linearity of the equations makes

these statistics independent of any assumption about how and when the “collapse” happens. It’s

therefore difficult to find empirical evidence to support any theory of how the “collapse” occurs.

Various approaches to this question are discussed in the Appendix on Quantum Interpretations. The

view to be developed in Chapter 2 is that the collapse certainly does occur, but can’t be ascribed to

any specific physical event.

2. Mathematics aims at rigorous proofs, and for this reason any system of axioms refers to certain

primitive notions (e.g. point, line, set) that remain undefined. These generally have meanings that

can be taken for granted on the basis of our common experience of the physical world, and so seem

self-evident. But if all mathematical terms had to be defined in terms of each other, then any proof

would be circular. In the physics of an observable world, however, this circularity is unavoidable.

When we consider any one parameter, we can take the others for granted – for example, when we

define acceleration we take it for granted that we can measure intervals in space and time. But this

disguises the fact that at a fundamental level, giving a complete description of any measurement-

context would require describing many other kinds of measurements as well.

3. See the Appendix on Physics as a Mathematical Language, discussing the radical “semantic closure”

of this language, in that all the observable parameters in physics are necessarily defined in terms of

other observable parameters.

4. This isn’t obviously true for all measurements. Simple measurements can seem to involve only one

parameter, as when we measure length of a pencil against lengths marked out on a ruler, or when we

determine the mass of an object by weighing it against another object on a balance scale. But the

existence of measuring rods, clocks and balance scales involves all the parameters of atomic physics.

Measurements can seem simple only because the background of mutually-supporting contexts can

be taken for granted.

5. There are however some recent efforts to develop a theory of contexts – see Barbara Drossel and

George Ellis, “Contextual Wavefunction Collapse: An integrated theory of quantum measurement,”

2018 New J. Phys. 20 113025, iopscience.iop.org/article/10.1088/1367-2630/aaecec/pdf. This paper

presents mathematical models for the various levels of interaction involved in typical measurement

arrangements, arguing that the unitarity of the quantum equations necessarily breaks down when a

quantum system is in contact with higher-level systems that must be described in classical terms.

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For another interesting approach see Alexia Auffèves and Phillipe Grangier, “A Generic Model for

Quantum Measurements,” 2019 Entropy 21(9):904, arxiv.org/abs/1907.11261, “Contexts, Systems

and Modalities: a new ontology for quantum mechanics” (2014) arxiv.org/abs/1409.2120 and P.

Grangier, “Completing the quantum formalism: why and how?” 2020, arxiv.org/abs/2003.03121.

These argue that quantum states must be attributed to the combination of the measured system and

its context, defining these contexts operationally as classical systems.

Both these approaches complement the present essay – in the first case by clarifying the physics of

actual measurement processes, and in the second by clarifying the role of contexts in interpreting the

quantum formalism.

6. I use the term “objective” in this specific sense, relating to facts intrinsic to the objects themselves,

independent of any context. In this sense contexts are not objective – the same things and events

can be seen in different contexts, from different perspectives. When a successful measurement is

made, the result is objective factual, the same from any point of view. But there’s no objective fact

about exactly which background-interactions constituted the context for this measurement, or exactly

when and where the “collapse of the wave function” occurred – as illustrated in the scenario of

“Wigner’s friend.”

However, “objective” can also have another meaning, referring to observer-independence rather than

context-independence. See for example Phillipe Grangier (2001), “Contextual objectivity: a realistic

interpretation of quantum mechanics,” arxiv.org/abs/quant-ph/0012122. The work of Affèves and

Grangier referenced in note 5 above aims at vindicating the objective reality of the quantum domain

by defining its basic entities as quantum systems in specific measurement-contexts. This is compatible

with the approach taken here, though the terminology reflects our different aims: my interest is not

in rescuing the concept of objective reality but highlighting its specific limitations in connection with

quantum physics. I treat the context-structure of the physical world as essentially distinct from the

structure of objective facts, even though its made up of those same facts. For me, “objective reality”

refers to the factual information content that’s defined and communicated by interaction; the system

that does the defining and communicating is an essentially different aspect of the same physical

world. See the Appendix on The Subject/Object Dichotomy.

7. I’m not saying it’s invalid to base a theory on hypotheses about an unobservable reality. In general

it’s quite reasonable to explain what we observe based on plausible assumptions about things that

aren’t directly observable. But fundamental physics is not just a matter of explaining observed

phenomena; we’re trying to understand how anything gets to be observable. This depends entirely

on the ability of different kinds of observable information to provide contexts for each other.

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1.3 The Genesis of a Self-Defining Universe

1. Throughout this essay he term “measurement” refers to the physical determination of information

that takes place everywhere, to the extent that adequate contexts exist. The assumption is that when

we observers set up measurements, we’re taking advantage of the same physical processes that also

happen when we and our devices are not present.

The “observer” came to play a role in quantum measurement – from Von Neumann and Wigner to

Wheeler et al. – only by default, because quantum mechanics doesn’t provide any specific physical

mechanism to “collapse” the wave-function. Von Neumann envisioned a chain of events linking a

quantum system to an observer, and showed that it was arbitrary where in that chain we consider the

“collapse” to occur. To some it seemed that this must somehow come about through the intervention

of consciousness, because no other solution seemed to be available – see the Appendix on Quantum

Interpretations. In the picture developed here the “chain” concept is replaced by the notion of

interdependent contexts, which certainly exist although they’re difficult to describe. The issue here

is not how information that exists in quantum systems gets transferred into the brain of an observer,

but how the physical environment is able to define and communicate specific information.

2. A somewhat similar approach is presented in the context of string theory by S. W. Hawking and

Thomas Hertog, “Populating the Landscape: A Top Down Approach”, arxiv.org/abs/hep-th/0602091:

“Here we put forward a different approach to cosmology in the string landscape, based not on

the classical idea of a single history for the universe but on the quantum sum over histories. We

argue that the quantum origin of the universe naturally leads to a framework for cosmology where

amplitudes for alternative histories of the universe are computed with boundary conditions at

late times only.”

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Notes to Chapter 2 – Quantum Measurement as Natural Selection

2.1 The Dual Dynamics

1. We generally conceive measurement as a transfer of information from an observed system to an

observer or recording device – so there seems to be a definite starting-point and end-point for the

measurement. But I’m arguing that quantum systems don’t contain in themselves the information

that appears when they’re measured, nor is there any particular point at which the superposition

“collapses” to create a factual result, as discussed in this chapter. The “Wigner’s friend” scenario

shows that a measurement may have been completed from one observer’s standpoint, but not from

that of other observers. So at a fundamental level, measurements don’t have definite starting or end-

points. Measurement needs be defined recursively – that is, a measurement has taken place insofar

as a specific result appears in the context set up by prior measurements, that then contributes to the

contexts of further measurements.

Measurements are possible only in such an ongoing, self-sustaining process. Facts only exist in the

communicative environment as long as they’re relevant, contributing to the historical background in

which new facts can be defined. See the Appendix on Quantum Interpretations for a comparison of

this idea with other approaches to the question of measurement.

2.2 The Physics of Possibility

1. The cyclical character of the wave-function and the phase-relationships that produce interference

patterns are the most general of many kinds of “virtual” structure – structures that aren’t directly

observable, but appear in the equations that determine probabilities for measurement outcomes.

Chapter 4 discusses the origin of our the complex physical foundations of our universe, treating these

“subliminal” aspects of quantum structure as evidence for earlier stages in the emergence of self -

determining systems.

2. An extreme example of this is the “modal realism” of philosopher David Lewis, who argues that all

possibilities are in fact actualized in other versions of the world. The notion that possibilities are

physically real is central to the “possibilist transactional interpretation” of Ruth E. Kastner, The

Transactional Interpretation of Quantum Mechanics, Cambridge University Press (2013) – see the

Appendix on Quantum Interpretations. Kastner’s website, transactionalinterpretation.org, offers a

wealth of material on this approach. Here also I treat possibility as physical, but I emphasize the

difference between the contextual structure of possibility and the structure of factual reality. Free

and open possibility is basic, and there get to be definite facts only insofar as the possibilities of a

situation are constrained to the point that a specific fact becomes determinable.

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3. I have in mind here Feynmann’s path integral formulation of quantum mechanics, where at bottom

all possible paths are equally likely. The difference in probability for different outcomes arises first

from the phase-relationships between possible paths, such that most of them are cancelled out by

paths with opposite phase, eliminating most outcomes. The probabilities of the various remaining

outcomes are determined by destructive and constructive interference between the many possible

paths leading to each outcome.

This contrasts with Heisenberg’s suggestion reviving the Aristotelian notion of potentia – tendencies

for things to happen in a certain way, built into the nature of things in themselves. This is another

way of conceiving possibility in terms of reality, as an objective proclivity toward a particular actual

outcome. It seems to me that Feynmann’s approach makes such a notion unnecessary.

4. Philosophically, the source for this conception of possibility is Martin Heidegger’s Being and Time,

which develops a notion of fundamental (“authentic”) temporality in which possibility plays the

primary role. The notion that awareness is essentially anticipatory has been developed by many

authors in psychology – see for example John McCrone (2000) Going Inside: A Tour Round a Single

Moment of Consciousness, Faber and Faber. Heidegger’s aim was a deeper understanding of time in

fundamental ontology, but so far as I know this approach has not been pursued in physics.

5. This conception of information as selection from a space of possibilities was originally developed in C.

E. Shannon’s quantitative information theory, which originally brought the concept of information

within the scope of physics.

2.3 The Collapse

There are currently no notes for this section. Various approaches to the “collapse” will be discussed

in an Appendix on Quantum Interpretations.

2.4 The Born Rule

1. Since quantum amplitudes are complex numbers, the probability is actually calculated as the square

of the absolute value of the amplitude, or equivalently as the amplitude multiplied by its complex

conjugate. This always give a non-negative real number for the probability

2. Because the amplitude is a complex number it can’t be taken literally as a probability, but it is directly

related to the relative probability of a particular outcome.

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3. A somewhat similar understanding of the Born rule is presented in a “realist” form by Ruth E. Kastner

in The Transactional Interpretation of Quantum Mechanics (2013), Cambridge University Press. See

her website at transactionalinterpretation.org for extensive discussion of this approach to quantum

theory, originally due to John Cramer. It envisions the collapse as taking place through a reciprocal

relationship between two events, e.g. the emission and subsequent absorption of a particle. This is

not a popular interpretation among physicists, since it envisions a time-reversed action from the

absorber back to the emitter, happening in a level of reality underlying our empirical spacetime.

Nonetheless, if we assume that quantum mechanics should be understood as describing some kind

of objectively factual reality, this seems to me the only reasonable interpretation.

Here I’ve argued the opposite: that in principle, no objectively factual reality can be the basis for an

observable universe, and that the reality we experience must have foundations that are relational and

contextual. Even so there are many points of similarity between this conception of quantum theory

and the Transactional approach, especially in that they both treat measurement as a matter of

agreement between two parties, explaining the Born rule on this basis. See section 4.3 of this essay

on the notion of a pre-metric, time-reversible structure of interactions that underlies our measurable

spacetime.

4. The measurements are made in “spacelike separate” locations so that any connection between them

would have to be faster than light. See Chapter 3 for the meaning of “locality” and “non-locality” in

physics, and section 3.3 for discussion of the EPR scenario.

2.5 Natural Selection

1. The situation is actually more complex than this, since quantum theory describes many kinds of

“virtual” particles and interactions that obey some but not all the laws that apply to observable

phenomena. Though these are not directly observable and not fully determinate, they play an

important part in defining quantum statistics. I suggest in Chapter 4 that this virtual realm reflects

deeper, more primitive layers of self-defining structure on which our observable world is built.

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Notes to Chapter 3 – Your Present Moment in Spacetime

3.1 The World from Inside

There are no notes to this introductory section.

3.2 Two Versions of Spacetime

1. The argument about whether relativity proves this notion has gone on for many decades in hundreds

of papers, and there’s still no sign that one side might convince the other. In my view the clearest

picture is that of the “Evolving Block Universe” developed by George F. R. Ellis – see for example “The

Evolving Block Universe and the Meshing Together of Times,” Ann N Y Acad Sci. (2014) Oct;1326:26-

41, arxiv.org/abs/1407.7243. This comes close to the view presented here, though based on different

arguments.

2. This is consonant with the Evolving Block Universe picture in Note 1 above. The notion that the past

light-cone represents the space of the local “now” is developed at length by Hanoch Ben-Yami (2007),

“Apparent Simultaneity,” philsci-archive.pitt.edu/3260/1/Apparent_Simultaneity.pdf. A recent paper

summarizing the debate over the block universe criticizes both the “Presentist” and “Eternalist”

standpoints, proposing the “local present” as a preferable third option: Carlo Rovelli (2020), “Neither

Presentism nor Eternalism,” arxiv.org/abs/1910.02474.

The view proposed here rejects the “Eternalist” position that there’s no physical distinction between

past, present and future events. But the “Presentist” position – that only what exists in the present

time is real – makes no sense to me. Its proponents are generally thinking of a universal present

moment, which has no basis either in physics or in any possible experience. But it’s not clear to me

what kind of “reality” can be ascribed to events without reference to anything in the past or future.

The determination of any fact always depends on the communication of prior facts and the context-

structure of possibilities that these prior facts set up; moreover, facts have meaning only insofar as

they make a difference to what can happen in the future.

3.3 Asynchronous Spacetime – EPR and Schrödinger’s Clock

There are currently no notes to this section.

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3.4 The Equivalence Principal and the Gravitational Metric

1. See for example David H. Delphenich (2014) “On the electromagnetic constitutive laws that are

equivalent to spacetime metrics,” arxiv.org/abs/1409.5107, David Delphenich (2015) “Pre-metric

electromagnetism as a path to unification,” arxiv.org/abs/1512.05183. Delphenich also has a two-

volume exposition available on his website: Pre-Metric Electromagnetism, Neo-classical Press, 2009,

neo-classical-physics.info/electromagnetism.html.

3.5 Cosmological Questions

There are currently no notes to this section.

Notes to Chapter 4 – The Origins of Determinate Information

4.1 Toward an Archaeology of Physics

1. The fact that our current theories break down and become inconsistent as we approach the “Planck

scale” is generally taken as evidence that a deeper theory is required. This assumes there must be

some set of facts and principles that were definable even at the very origin of the universe. Here we

don’t ask what really happened at the beginning, because no aspect of our current physical reality

could have been definable then. Our cosmological history of the early universe is a retrospective

projection of the emergence of the world of communicating atoms, and this projection only makes

sense in terms of atomic physics.

2. In contrast, the quantum vacuum of our current universe is a highly structured combination of many

kinds of quantum fields. It consists of “virtual” events that satisfy most of the constraints that apply

to actually observable interactions, as described by the first four stages presented in this chapter, but

not the constraints of the final stage that defines our observed reality. This quantum vacuum is

“empty” in the sense that its events can have no determinate effect on anything observable, but it

plays an important role in structuring the statistics of the quantum realm.

3. For an explanation of the schema of five stages developed in this chapter see the Appendix on The

Concept of Context and the Stages.

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4.2 Stage I – Interaction

1. Clearly events that connect with no other events can’t play any role in an observable world, but the

same is true of events that connect to only one other event in the network. Such dangling loose ends

aren’t interactions, in the sense of this section – they can’t participate in any higher-level contexts

that might give them definable characteristics.

4.3 Stage IIA – Recurrence

1. Of course spacelike separated events are not connected and do not have a definite order in time. But

the light-cone geometry of relativity still disallows any looping back in time – assuming that certain

“pathological” solutions to the equations of General Relativity don’t apply to our universe.

4.4 Stage IIB – Pre-Metric Spacetime

1. See David H. Delphenich, Pre-Metric Electromagnetism (2009), Neo-classical Press, neo-classical-

physics.info/electromagnetism.html, “On the electromagnetic constitutive laws that are equivalent

to spacetime metrics,” arxiv.org/abs/1409.5107, “Pre-metric electromagnetism as a path to

unification,” arxiv.org/abs/1512.05183, “A pre-metric generalization of the Lorentz transformation,”

arxiv.org/abs/2002.09500,

The following is from the Introduction to “Complex Geometry and Pre-Metric Electromagnetism,”

arxiv.org/abs/gr-qc/0412048:

Since the early days of Einstein’s theory of gravitation, it had been suspected by some

researchers… that the introduction of a metric into the geometrical structure of the spacetime

manifold, although fundamental to the theory of the gravitational interaction, was not only

mathematically unnecessary in the theory of the electromagnetic interaction, but from a

physical standpoint it was also naïve. This is because the metric structure of spacetime is so

intimately related to the electromagnetic structure by way of the propagation of

electromagnetic waves that one rather suspects that the metric structure might plausibly follow

as a consequence of the electromagnetic structure, rather than represent a basic component of

that structure… This also has the effect of saying that gravitation is not entirely independent of

electromagnetism since gravitational waves are governed by the same light cones that are

defined by the demands of electromagnetic wave propagation.

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2. This section considers only the pre-metric structure of classical electrodynamics; it ignores not only

quantum electrodynamics, but also the unified electroweak theory and the fractional charges of

quarks in the Standard Model, all of which are relevant to the complex combination of roles played

by electromagnetism in the physics of our current universe. The assumption here is that none of this

complexity was definable in the earliest stages of the emergence of self-defining structure, but that

the simple electromagnetism of Maxwell’s equations does reflect the most primitive skeleton-

structure of spacetime, as described in this section.

4.5 Stage IIIA – Local Gauge Symmetries

There are currently no notes to this section.

4.6 Stage IIIB – Locality and Gravitational Spacetime

There are currently no notes to this section.

4.7 Summary – The Physics of Possibility

1. The origin of the earliest forms of life on Earth could also seem miraculous, since it must have required

a very unusual combination of conditions on a quite unusual planet. Even once self-replicating

systems became established, it certainly took a great deal of luck for them to survive major geological

changes during the early stages of their evolution. But the situation is similar to that proposed here

in physics: evidently it was possible for a process of self-replication to begin somewhere, and once it

happened it kept on making itself possible. No matter how improbable it was that life could begin

and continue to survive, that doesn’t make the theory of biological evolution any less explanatory.

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Notes to Conclusion

1. See Christopher A. Fuchs, N. David Mermin and Ruediger Schack (2013) “An Introduction to QBism

with an Application to the Locality of Quantum Mechanics,” arxiv.org/abs/1311.5253, N. David

Mermin (2018) “Making better sense of Quantum Mechanics,” arxiv.org/abs/1809.01639v1.

2. See Carlo Rovelli (1996) “Relational Quantum Mechanics,” arxiv.org/abs/quant-ph/9609002. Like

the present essay, RQM begins from the premise that there are no determinate facts about physical

systems in themselves. But rather than distinguishing a special category of measurement-contexts,

Rovelli goes to the extreme of considering any physical interaction as a measurement. So facts exist

only for particular observers, as in QBism, though in RQM any system that interacts with another

system counts as an observer. See the Appendix on Quantum Interpretations.

3. This is a primary theme in the work of George F.R. Ellis. See for example (2012) “Top-down

causation and emergence,” https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3262299/, Robert C.

Bishop and George F. R. Ellis (2020) “Contextual Emergence of Physical Properties,”

https://rdcu.be/b1TEW.