relational events, an extended present and the conflict between relativity and the collapse thomas...

Relational events, an extended present and the conflict between relativity and the collapse

Thomas FilkDepartment for Theoretical Physics, Univ. of Freiburg

Parmenides Center for the Study of Thinking, Munich

Pullach, May 1st 2010

Physikalisches InstitutAlbert-Ludwigs-Universität Freiburg

• Two simple questions

• The meaning of “is”

• E+F scheme

• Relational events

• A “temporal extension” operator

• The non-locality problem from a relational perspective

• Where is the present?

Overview

Two Simple Questions

Which is which? Where is something?



E={a,b,c,d,e,f}



E={a,b,c,d,e,f} Without any additional structure both questions are ill defined.

In mathematics the “identifiability” of elements in a set is part of the axiomatic formulation of set theory.

In physics we associate mathematical structures to physical entities and the identification is far from trivial.

Possible solutions


E={a,b,c,d,e,f}

1. We define “properties” for the elements

2. We define relations among the elements

Relations

E={a,b,c,d,e,f} For some graphs these questions have no answer at all.

And for some graphs the intrinsic identifiability is unique.

For some graphs these questions have partial answers.


Relations

E={a,b,c,d,e,f}


a

b

c d

e

f

a – degree one, next to degree threeb – degree three, next to degree onec – degree three, next to degree twod – degree twoe – degree fourf – degree one, next to degree four

For graphs without symmetry a unique identification is possible by intrinsically referring to the structure.

Relations

E={a,b,c,d,e,f}


a

b

c d

e

f

a – distance 2 from c and eb – distance 1 from c, 3 from ec – the red elementd – distance 1 from c and ee – the green elementf – distance 1 from e, 3 from c

In some cases certain elements have to be “marked” arbitrarily in order to break the symmetry, making a unique identification possible.

The problem of identification

The problem of “identification” (the “which is which?”-question) of the elements of space-time (events) is relevant for a relational formulation of General Relativity.

Intrinsic properties are:

- the curvature (components) at a point

- the distance to other points with characteristic curvatures

- correlations of such distances.



• E+F scheme





Overview

The problem of localization

The problem of “localization” (the “where is something?”-question) assumes that the identification is given.

a

b e

f

c dLet “p” be a red dot ( ) and “R” be a (relational) structure where the concept of “location” is to be defined.

What could be the meaning of the following questions?

-Where is “p” in “R”?

-What is the position/location of “p” in “R”?


-Where is “p”in “R”?-What is the position/location of “p” in “R”?

The usual way to answer this question is to say: “p is at c”.

a

b

c d

e

f

“position” is defined as a mapping from the set of objects into the set of “possible positions”.

Position: {p} {a,b,c,d,e,f}

Position(p) = c


a

b

c d

e

f

However, intrinsically the “position” of an element of the underlying structure is defined by the relations of this element to the other elements.

Position: {c} {(c,d),(c,e),(c,b)}


a

b

c d

e

f

However, intrinsically the “position” of an element of the underlying structure is defined by the relations of this element to the other elements.

Position: {c} {(c,d),(c,e),(c,b)}

Notice that the underlying structure itself is defined as a set with a relational structure.

I define “location” of an object with respect to such an underlying structure. Other approaches try to get rid of the underlying structure altogether and define “location” as a relation among the objects alone. In my approach the underlying structure is part of reality.


a

b

c d

e

f

Why not consider “position” as a relation between an object (“p”) and the underlying structure?

Position: R(p) {p}×{a,b,c,d,e,f}

p

“position” of a single object is a subset of E (R(p)={c,d,f}) and can be represented as a mapping from the underlying structure E into the set {0,1}.

Descartes: “Location” denotes ... the position of a body among other bodies. In order to determine the location of a body, we have to consider these other bodies, which we assume to be at rest.


a

b

c d

e

f

Instead of the classical

- “ p” is at “c” or “d” or “f”

or the quantum mechanical

- “p” is at “c” AND “d” AND “f”

we can say:

- “p” has relations to “c” and “d” and “f”.

p


a

b

c d

e

f

Instead of the classical

- “ p” is at “c” or “d” or “f”

or the quantum mechanical

- “p” is at “c” AND “d” AND “f”

we can say:

- “p” has relations to “c” and “d” and “f”.

p

More general, the “position” of a single object becomes a field:

Position p ~ R(p)R ~ ψp(x) (xR)

and the “position” of two objects is represented as two fields.

Feynman‘s sum over histories

• Standard interpretation of the double slit experiment:

A particle propagates along path 1 AND path 2

• Relational interpretation:

Relation 1 (between a particle and a spatial point) propagates along path 1AND relation 2 propagates along path 2

path 1

path 2

Advantages of a relational concept of position

A relational object can “be” at two places at the same time

Advantages of a relational concept of position

In a relational picture, two objects which seem to be “miles apart” can actually be nearest neighbors

What is distance?

1033 ?

1 ?

The “relational distance” may not be the same as the “observed distance”.

Flow of energy or information may require different types of relations as “quantum correlations”.

T.F. (2006) Int. J. Theor. Physics 45, p.1166

What is distance?

The same network may allow for different “distance structures” (metrical structures)

For a society of people we can define “distance” according to: • physical distance• friendship distance• communication distance (two people making a phone call are “close” to each other with respect to this distance, even though they are far away physically), etc.

There is a dynamic in a society related to each of these distance concepts, and these dynamics are partially coupled.

“Microrelational” Quantum Theory

In a minimalistic version, this type of “microrelational” quantum theory just replaces the concept of “probability amplitude” by “relation”, with the additional postulate that “the absolute value of the relation is equal to the probability of measuring an object at a certain location”.

T.F. (2006) in Quantum Theory: Reconsideration of Foundations - 3,

T.F. (2006) Int. Journ. Theor. Phys. 45, p.1166

An “everyday” example

A relevant document (e.g., a boarding pass) may be stored (virtually) in the main server (the unit entity).

Every computer or printer has immediate access to the document (the relation to the network).

As soon as the document is transferred to one of the computers, e.g. for print-out (the “measurement”),

the access from the other computers is blocked (the collapse).

An “everyday” example

The document exists as a virtual entity. It is not “spread” over the network but remains a unity.

The document becomes “reality” upon entering the e-code and making a printout.

One never observes “half of a boarding card” at one printer and the other half at a different printer.

One never gets two boarding cards with the same e-code.



• E+F scheme





Overview

E + F and relational quantum theory

F-scheme

(refers to facts)

-boolean predication

-causal closure

-sequential time

-dichotomy of observer and observed

T.F. and A.v. Müller (2009) Mind and Matter 7, p.59T.F. and A.v. Müller (2010), submitted

E-scheme

(refers to the “statu nascendi” of facts = events)

-paratactic predication

-autogeneity

-extended present

-non-separability of observer and observed

E + F and relational quantum theory

E-scheme

-paratactic predication

-autogeneity

-Extended present

-Non-separability of observer and observed

Relational interpretation

-propositions as relations

-“collapse” as an autogenetic selection of relations

-Relational network of events (see next section)

- “relational quantum theory” in the sense of Carlo Rovelli



• E+F scheme





Overview

Relational network of events

Events to not happen at a certain point of space-time, but the network of events is the canvas of space-time.


However, the grid of events has a causal structure.

This implies that there are three possible types of relations:

• in-coming causal• out-going causal, and • non-causal.

If the (causal) Green’s functions of quantum field theory are a phenomenological expression for these relations, this distinction may be due to the different roles of the real and imaginary parts.

Particles in an accelerated system

A static test particle in the field of a charged particle “sees” an electric field.

E



If the probe moves with constant velocity it “sees” an electric and a magnetic field.

E,B

v




If the probe accelerates in the field of the charge it “sees” a time-dependend electric and magnetic field – i.e. radiation.

E(t),B(t)

a




If the probe accelerates in the field of the charge it “sees” a time-dependend electric and magnetic field – i.e. radiation.

E(t),B(t)

a

If the probe carries a detector, it measures photons. Where do the photons come from?

Feynman graphs as “summation over relations”

In a Feynman diagram the relations of events x and y are expressed by causal propagators. The integration over all “internal” locations of the events (emission of exchange particle; absorption of exchange particle) expresses the summation over all relations.

x y

x1 x2

x3 x4

),(),(),(),(),(),,,( 43214321 yxGyxSxxSyxSxxSdydxNxxxxA


If the location of an event is defined by its relations to other events, then an event does not happen at a sharp instant.

„time“


For two events, even if they are related to the same process, the propositions “a before b” and “b before a” are not exclusive.

For quantum processes, event a can have an influence on event b AND event b has an influence onto a.

Sequentiality of events – even along the same world line – may be lost.

„time“



• E+F scheme





Overview

There is no time operator

The uncertainty relations between energy and time cannot be derived from a time operator but follow from the properties of Fourier transforms of waves.

[H,T]=iħ exp(-iεT)|E~|E–ε

(but H should be bounded from below)

There is no time operator

The uncertainty relations between energy and time cannot be derived from a time operator but follow from the properties of Fourier transforms of waves.

But:

Measurements of T do not refer to objects (particles) but to events.

In contrast to position measurements which (in principle) can be performed everywhere, temporal measurements can only be performed in “the present”.

Measurements of T can only be planned for the future.

[H,T]=iħ exp(-iεT)|E~|E–ε

(but H should be bounded from below)

Temporal extension of events

If events have temporal relations to other events, we can define a measure for this temporal extension.

„time“

If it is not possible to define a time operator, may be one can define a “temporal extension” operator which measures for each event its temporal extension. It should be complementary to the energy operator measuring the energy transfer in this event.

A “temporal extension operator”

A “temporal extension operator” measures ΔTi (without measuring T). It should have a positive spectrum (by definition).

“time”

The operator is applied to an event i. A “dual” operator Hi may not refer to “energy” in general, but to the “energy transfer” involved in this event (or even to the “information transfer”) involved in this event.

Δt

i



• E+F scheme





Overview

The conflict between relativity and the collapse

How fast is the collapse?

A measurement – interaction between two systems – can lead to a reduction (collapse) of the quantum state.

It is generally assumed that this reduction happens “instantaneously”.

If the quantum state as the property of “non-locality”, this instantaneous reduction seems to be in conflict with relativity.


How fast is the collapse?

A measurement – interaction between two systems – can lead to a reduction (collapse) of the quantum state.

It is generally assumed that this reduction happens “instantaneously”.

If the quantum state as the property of “non-locality”, this instantaneous reduction seems to be in conflict with relativity.

The problem of non-local reduction is not restricted to “entangled states”. The quantum state of a single particle can be non-local (a photon in a Mach-Zehnder interferometer).

It is reminiscent of the conflict between relativity and the rigid body.


There is no conflict, if

- one assumes that the quantum state has no ontological counterpart (e.g., is related to my knowledge about a system),




- one has a “relative frequency” interpretation of quantum theory





- one restricts “relativistic locality” to the transfer of energy or information






- one assumes a “hyper-deterministic” world in which the future decisions about experiments are included in the initial conditions.






- one assumes a “hyper-deterministic” world in which the future decisions about experiments are included in the initial conditions.

There is a conflict in the many-worlds interpretation, even though there is no collapse. The “splitting” of the wave function happens simultaneously at separate points.


If we assume an ontological collapse, there seems to be a distinguished spatial hypersurface indicating an observer independent notion of simultaneity.

This would be a prerequisite for the concept of a universal “present”.


In a relational picture one can keep “locality” without violating the predictions of quantum theory and without giving up an ontology for quantum states.

The “spatial” relations determine the distance, however, the quantum relations determine the reduction.

For an EPR-state, the spatial relations may already exist for the charge and the mass of the particle, but not yet for the spin. The spin is still related to its partner particle.



• E+F scheme





Overview

Where “is” the present?Napoleon: “Where is God in your model?”Laplace: “There was no need for that particular hypothesis”.

We should distinguish between “the present of an event” and “the present” (in the sense of “now”).

Most of the statements about the non-sequentiality of time-space or the extension of the present can be formulated within the framework of the first meaning.

The second is up to pure speculations.

Where “is” the present?

Conscious systems (IGUSs?) are the probes for time and a present. But: no probe - no present?



There is no hint in Newton‘s laws indicating a distinguished “present”. Maybe there are hints in quantum theory.




The “present” marks the transition from possibilities (potentialities) to facts, and facts are traces in the canvas of the space-time network of events indicating that certain events have happened.




The “present” marks the transition from possibilities (potentialities) to facts, and facts are traces in the canvas of the space-time network of events indicating that certain events have happened.

The most direct hint to a present may be the collapse – i.e. the non-deterministic change of relations with respect to a single event.

The present as “relating events to history”

Lets imagine a set of events without any further structure.

The present may mark the layer of events which become related to a history.

The “dual” interpretation

Lets imagine a network of events, in which every event is related to almost every other event.

At his stage almost any “history” is possible.

The present as the “interface” of reduction

The “present” now marks the layer of events where the collapse leads from possibilities to facts.

Conclusion

-The solution to the paradoxical aspects of quantum theory may require new concepts of space, time, location, distance, ...

-It may also require to reintroduce a concept of the present into our physical models

-Two candidates:

-relational space + time as an expression of a change of relations

-relational space-time (+an extra dimension of time in which “the present” propagates)

relational events, an extended present and the conflict between relativity and the collapse thomas...

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