Pergamon Stud. Hist. Phil. Mod. Phys., Vol. 28, No. 1, pp. 137-143, 1997 Published by Elsevier Science Ltd. Printed in Great Britain

1355-2198/97 $17.00+0.00

ESSAY REVIEW

What Theories of Everything

Thomas Breuer*

Don’t Tell

Jan Hilgevoord (ed.), Physics and Our View of the World (Cambridge: Cambridge University Press, 1994), 304 pp. ISBN 0-521-45372-O Hardback, U.SS35.00; 0-5214-7680-l Paperback, U.S.$14.95.

This is the volume of the proceedings of the Erasmus Ascension Symposium held in May 1992 in Leiden and Oosterbeek, The Netherlands. It contains contributions by John Barrow, Paul Davies, Dennis Dieks, Willem Drees, Paul Feyerabend, Bas van Fraassen, Mary Hesse, Gerard ‘t Hooft and Ernan McMullin.

The basic question of the symposium was ‘What do we know when we know physics?’ Three sections addressed different aspects of this question: (1) what do the results of modern physics tell us about reality? (2) does the scientific view of the world have a special status compared to other views? (3) physics and theology. Jan Hilgevoord wrote a beautiful introduction; Barrow, ‘t Hooft and McMullin were in the first section; Dieks, Feyerabend and Van Fraassen in the second; Drees, Davies and Hesse in the third. The book also contains selected parts of the discussion.

The contributions are very diverse indeed, partly because the basic question of the symposium is all-embracing, partly because of the diverse backgrounds of the contributors. I do not mean to complain about this diversity; admittedly, it makes it difficult for the newcomer to find a coherent way to tackle the basic question; one is partly overwhelmed by the multitude of fascinating approaches, partly puzzled that, in spite of their individual attractiveness, most of the approaches exclude one another. While one wonders how the different contributions fit into a unified picture, one can enjoy the direct confrontation of their authors reported in the discussion. Perhaps this is the way philosophy ought to be: you can have anything but not everything.

*&terreichische Akademie der Wissenschaften, lgnaz Seipel-Platz 2, 1010 Wien, Austria

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I will discuss the positions of some of the contributors on one of the central topics: the possibility and relevance of a theory of everything (TOE). This is related to questions of realism, determinism, reductionism and cosmology. Then I will contrast this with an argument of my own not against the possibility, but against the relevance of a theory of everything.

1. Toes and Isms

1.1. What is a TOE?

‘t Hooft takes a TOE to be an ‘ultimate law for basic dynamics’ (pp. 17, 20); for Barrow it is ‘a law unifying all the laws governing the fundamental forces’ (p. 44), according to Davies it ‘combines all physical laws and principles into a single, unified mathematical scheme, hopefully captured by a single, simple mathematical formula that you might be able to wear on your T-shirt’ (p. 226). These definitions seem to suggest that a TOE unifies physical theories which today are still unrelated or at odds with each other.

Actually, what a TOE would have to achieve is more than unification: at present it is not clear whether successful theories such as quantum mechanics and classical chemistry contradict each other or not. If they are to be unified one has to show that the threatening contradictions do not arise, or one of the theories has to be improved; only afterwards can they be welded together. What a TOE promises is thus a consistent description of material reality, as opposed to the collection of possibly mutually exclusive theories we have today. As an improvement of our present miserable state, the striving for a TOE is highly laudable. A TOE is the best physics can ever achieve, if indeed it can.

Would a TOE be able to explain everything? Most of the contributors seem to agree that it cannot: ‘t Hooft thinks that ‘complexity may very quickly reach the very limits even of the most powerful computers, and so, even if we have the full equations there would be uncertainty when we try to apply them’ (p. 30). Barrow argues that due to symmetry breaking a TOE need not account for the outcomes: it may well be that the laws possess a symmetry which the solutions do not possess. So there must be something left undetermined by the laws.1 According to Davies, such a theory would make no claim to explain the nature of human consciousness and it need not include an explanation for the origin of the universe (p. 227). Furthermore, Barrow (p. 56) considers as highly suspicious claims that a TOE can determine the value of constants of nature. So most contributors agree that one must not take literally the label ‘Theory of Everything’. For them, a TOE does not explain everything; however, this does not prevent such a theory being true of everything.

‘Primas (1981, pp. 1899192) explains in a non-technical way how in large quantum systems classical properties emerge through symmetry breaking. Which values these emergent properties take cannot be explained by the laws of quantum mechanics. Stiiltzner and Thirring (1994) also use this as an argument against the claim that Theories of Everything can explain everything.

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1.2. TOE and Reductionism

At first sight it seems that a TOE embodies a strong reductionist claim: what can be explained by other theories can also be explained by the TOE. In this sense explanations by other theories can be ‘reduced’ to explanations by the TOE. (Perhaps this is a replacement rather than a reduction.)

Historically, unification of different theories has often been thought of as reducing them to some ‘deeper’ theory. According to Dieks (p. 62) ‘this is motivated by the monistic conception that in the final analysis there is only one kind of “stuff ‘, which can be described completely by physics’. If we know how this stuff behaves we supposedly know everything. So often the main moti- vation for searching for a TOE is the reductionist belief that there is a most fundamental theory which explains everything. Therefore belief in the existence of a TOE is widespread among physicists of reductionist inclinations.

But the existence of a TOE is not necessarily linked to reductionism, not even if the TOE could indeed explain everything. A TOE might well be the conjunction of other theories with restricted non-intersecting domains of validity. In this case the explanation given by the TOE is exactly the one given by one of the partial theories. It would not be fair to say that the explanation of the TOE ‘reduces’ that of the partial theory.

1.3. Reductionism and Realism

Reductionist beliefs in a TOE are often held by realists: if, ultimately, the world consists of elementary particles, elementary particle physics is the most fundamental theory explaining everything.

To empiricists the possibility of a TOE is much less attractive. I paraphrase an argument from the discussion (p. 268): for an empiricist there is not One True Story of the world; all there is are the phenomena. But the One True Story of the world is exactly what the TOE provides. Arguing contrapositively: if, as the empiricist claims, there is no One True Story, there is no TOE.

But the connection between reductionism and realism is not necessary. As a counter-example, Dieks (p. 66) points to the logical empiricists of the early 20th century. They were empiricists-and therefore far from any sort of realism- but still analysed reduction relations between theories, for example between thermodynamics and statistical mechanics. What is involved here are interre- lations between theories, as opposed to an ordering of different levels of realitv.

So reductionism makes sense not only from a realist point of view. There is another way of being a realist without being a reductionist. From an

ontological point of view physics may be fundamental; but this does not mean that theories like biology can be reduced to physics. Perhaps biological terms are meaningful only within biology and cannot be defined in physical terms. If this is the case, then a biological description of a process cannot be replaced by a physical description, although biological processes are physical. Thus Dieks

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(p. 75): ‘The various scientific disciplines are considered as looking at the world from different angles; the resulting pictures complement each other, and are not in mutual conflict’.

1.4. Realism and Monism There are important relations between realism and monism. In one direction:

a monist believing that there is only one kind of substance characteristically has a realist outlook on the world; to him it makes sense to speak of an outside world existing even when we do not observe it. In the other direction: Dieks (p. 70) points out that, if one is a realist, one would probably take the fact that theories like chemistry and physics overlap in their range of applicability as strong evidence that these theories are actually about the same stuff.2 One can go on: if there is one chain of pairwise overlapping theories, and if every theory is part of this chain, then Dieks’ argument leads to the monistic conclusion that there is only one kind of stuff.

But a realist interpretation of science is not necessarily tied to the monistic idea that the world consists of only one kind of substance. It might equally well be that the real world consists of several non-interacting kinds of substances. A TOE describing this would be the conjunction of several independent partial theories.

1.5. Realism and Determinism Throughout the book the opinion is frequently expressed that realism

requires determinism. For ‘t Hooft (p. 20) a TOE is a deterministic dynamical law. According to McMullin (p. 91) and Van Fraassen (p. 117), Aristotle and Aquinas take science to be of the necessary. The laws of nature discovered by science describe necessities and are deterministic.

In his argument for empiricism Van Fraassen (pp. 120-124) starts by questioning the distinction between necessities and regularities. In the spirit of Ockham (McMullin, p. 92; Van Fraassen, p. 120) he argues: if we stick just to the phenomena, we may discover regularities but there is no way we can know that what actually happened happened necessarily. I agree with this but not with the conclusion Van Fraassen draws from this: he thinks realism is untenable because determinism is out of reach. This conclusion is only warranted if one takes determinism as a precondition for interpreting a theory realistically. But why should not nature be stochastic?

By the way, many arguments claiming that it is impossible to interpret quantum mechanics realistically seem to rest on the irreducible stochasticity of

‘The force of this argument is a bit impaired by the fact that contradictions between chemistry and physics cannot easily be excluded at the moment. For example, the existence of a molecule’s nuclear frame is not permitted by the standard quantum mechanics of finite systems, ‘Must a Molecule have a Shape?’ is the title of papers by Woolley (1978) and Amann (1992).

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quantum mechanics. I think stochasticity alone is not sufficient to prevent a

realistic interpretation of quantum mechanics.

2. Experimental Relevance of a TOE

So far I reported the positions of some of the contributors on the possibility and relevance of a theory of everything (TOE) and on how the issue is related to questions of realism, determinism and reductionism. Now I will give an argument of my own on how problems of self-reference impair the relevance of a TOE. Apart from the reasons mentioned above, this is an additional argument why a TOE cannot live up to the claims made by its name.

2.1. Self-Reference of TOES

Physical theories which can describe measurements-and a TOE should be able to do that-give rise to self-reference. This can happen in the following way. After the experiment the state of the apparatus refers to the state of the observed system; self-reference arises if the state of the observed system somehow refers back to the apparatus. This is for example the case if the observed system contains the apparatus; then the state of the observed system determines the state of its subsystems and thus also of the apparatus. Measurements by internal observers are self-referential.

Self-reference is not a problem as long as it is consistent. In the case of measurements by internal observers paradoxical self-reference can be avoided if one imposes a consistency condition: any apparatus state after the measure- ment should refer only to such states of the observed system whose restriction to the apparatus is the original apparatus state.

Using this consistency condition one can prove the following theorem (Breuer, 1995): No observer can distinguish all states of a system in which he is

contained. He cannot distinguish those states of the observed system whose

restrictions to the apparatus coincide. I will now discuss some consequences of this theorem for what we can expect from a TOE.

2.2. Determinism without Predictability

Above I have mentioned the widespread expectation that a TOE should be deterministic and that determinism is a precondition for interpreting a theory realistically. A deterministic TOE could be used for predicting with certainty everything from precise initial data. Given the initial data a TOE provides the One True Story of the world.

For the time being, define determinism in the following way: a physical theory is deterministic if the state of the world at one time determines uniquely the state at any later time. The difficulties this definition meets and how it has to be adapted for different theories are described in the book by Earman (1986).

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A classical concept of time figures prominently in this definition and a unification of quantum theory and gravitation will probably require radical changes in our concept of time and therefore in this definition. Nevertheless the definition is sufficient for my purposes.

Is predictability a consequence of, and perhaps an experimental criterion for, determinism? Predictability with a certain degree of precision-perhaps depending on how precisely we know the initial state or on how long the prediction has to be valid-is not good enough: such criteria are easily violated by chaotic or ergodic dynamical systems although such systems are determin- istic in the sense of the definition above. But is predictability from hypotheti- cally precise initial data an experimental criterion for determinism?

It is not; at least not if we take precise initial data to mean data which can be gathered by an ideal observer who is not bound by technological restrictions. The theorem above implies that no observer-not even an ideal one-can measure exactly the initial state of a system in which he is contained. These restrictions on the measurability are a matter of principle and not due to technological restrictions. They are not related to the quantum mechanical uncertainty relation; even the state of a classical system cannot be measured exactly by an internal observer. Therefore even in the case of a deterministic time evolution it is impossible to predict the state of a system in which one is contained.’

Can one hope to predict at least the state of a system in which one is not contained? After all, at least in principle it would be possible to know exactly the state of such a system. Even this modest hope is doomed to fail. The system in question has to be in interaction with its environment because without interaction measurement of its initial state is impossible. But if the system is not isolated, then to make precise predictions, one needs to know not only the state of the system, but also the state of its environment. The environment, however, contains the observer who according to the theorem will not be able to know exactly the state of the environment. Predictability fails for internal observers and for external ones, and irrespective of whether the time evolution is deterministic or stochastic.

2.3. The Experimental Relevance oj’a TOE

The biggest system a TOE supposedly can describe is a system without an external observer, namely the universe. Applying the theorem above we conclude: (1) no observer can distinguish all states of the universe; and (2) all observers together cannot achieve that.

Point (1) is an obvious consequence of the theorem, (2) is not quite so obvious. Perhaps two observers could cooperate to measure the state of the

‘A similar result was proved under stronger assumptions by Popper (1950); no matter how precise the knowledge of an observer about his past or present state, there will always be questions about his own future which he will not be able to answer.

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universe. Each might be able to measure the state of his outside world exactly, and the union of the two outside worlds is the whole universe. So it seems that together they can measure exactly the state of the universe. But this does not work. The knowledge of the two observers has to be brought together somewhere. The system where the knowledge is brought together is again a part of the universe. So the theorem applies: this system again cannot distinguish all states of the universe. Here is the physical reason why this attempt fails: bringing together the knowledge in one system changes the state of the system and thus the state of the universe. So the information provided by the two observers will always be outdated.

I conclude: problems of self-reference prohibit any exact measurement of the state of the universe. A TOE is thus experimentally not fully accessible. However, this does not imply that a TOE does not exist or that we cannot find it by chance. But even if we had it, we would not be able to say for sure that we had found the One True Story of the world.

References

Amann, A. (1992) ‘Must a Molecule Have a Shape?‘, South African Journal qf Chrmistr~~ 45, 29-38.

Breuer, T. (1995) ‘The Impossibility of Accurate State Self-Measurement’, Philosophy of Science 62, 1977214.

Earman, J. (1986) A Primer on Determinism (Reidel: North-Holland). Popper, K. R. (1950) ‘Indeterminism in Quantum Physics and in Classical Physics, Part

II’, British Journal for the Philosophy of Science 1, 1733195. Primas, H. (1981) Quantum Mechanics, Chemistry, and Reductionism (Berlin: Springer,

2nd edn, 1983). Stoltzner, M. and Thirring, W. (1994) ‘Entstehen neuer Gesetze in der Evolution der

Welt’, Naturwissenschaften 81, 243-249. Woolley, R. (1978) ‘Must a Molecule Have a Shape?‘, Journal of the Amrricun Chemica/

Society 100, 1073-1078.