J. Baggott Beyond Measure: Modern Physics, Philosophy and the Meaning of Quantum Theory

Jim Baggott tells us in 'Beyond Measure', his latest book on the philosophy of quantum mechanics, that (p287),

'...no matter where we start from, we always return to the central philosophical arguments of the anti-realist versus the realist'

The realist, we are told, is the loser in this argument because (p287),

'...any final plea for an independent reality is really an appeal to faith, in the sense that the realist must ultimately accept the logic of the anti-realists' argument but will not be persuaded.'

Baggott describes himself as a realist and so his use of the word 'faith' is not disparaging. He subsequently writes (p288),

'Like all acts of faith, the search for an independent reality involves striving for a goal that can never be reached. This does not mean that the effort is any less worthwhile. On the contrary, when free of the straitjacket of dogma, it is through this process of striving for the unachievable that real progress in science is made.'

He seems to be affirming unshakeable, irrational realism. Yet, by contrast, he speaks strongly against 'dogma' and 'unquestioning acceptance' with respect to the Copenhagen interpretation of quantum mechanics.

Baggott also tells us (p203),

'It is in the nature of theoretical science that there can be no such thing as certainty. A theory is only 'true' for as long as the majority of the scientific community maintain a consensus view that the theory is the one best able to explain the observations.'

This remark does not bear close scrutiny but we get the gist i.e. we cannot be absolutely certain that a scientific theory is true.

Baggott adopts the posture of a tour-guide. He tells us, belatedly, that he has tried to argue (p287),

'...for all the different positions described in this book with something approaching equal force.'

This makes his discussions on the relationship of quantum theory to god theory and consciousness theory and free-will theory seem undiscriminating and out of character with the general quality of the book.

The quotes I have given above do, I think, represent the author's own voice. They are very similar to Einstein's as presented on p115. Nevertheless, we may conclude that Baggott is very confused: he is both dogmatic and anti-dogmatic; he appears to be more certain of his own notion of realism than he is of powerful scientific theories; and although he describes his realism as an essential inspiration for science he pessimistically tells us it is unrealisable.

It is my view that Baggott's realism is representative of the twentieth century. We can find in it, I think, the reason why twentieth century scientists and philosophers found quantum mechanics so incomprehensible and hence why Feynman wrote in 1965 (quoted p287),

'I think I can safely say that nobody understands quantum mechanics...'

The central question, therefore, is what is realism? The most precise definition of reality given by Baggott is that of Einstein, Podolsky and Rosen 1935 (quoted p131).

'If, without in any way disturbing a system, we can predict with certainty (i.e. with a probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity.'

This definition is not intended for philosophical application as it only progresses us from 'physical quantity' to 'physical reality', and 'physical' itself presumably implies reality. Apart from the issue of knowing about systems without disturbing them, which Baggott discusses, there is also a problem with the requirement of absolute certainty because such certainty is generally not claimed in scientific theory or measurement.

The aim of definition is to reach a secure understanding. In the case of 'reality' there seems no basis for much refinement for it is both widely used and philosophically murky. We say something is real in contrast to saying it is illusory or imaginary. The world around us is real. Solid objects are real. Liquids and gases may seem decreasingly real and light may seem miraculous. We understand that we apprehend the real by virtue of phenomena that mediates from objects to the object that is ourself, light for vision, sound for hearing etc. We understand that this apprehension has no effect on what is observed except that we, the observer, are also an object and real. Consequently we understand that the real persists regardless of whether it is observed or not. (Here is not the place to discuss arguments to the contrary.)

It follows that because our apprehension of the real is mediated it cannot be ideal — perception cannot be perfectly or completely informative of objects. Perception is less effective to the extent that the mediating phenomenon disturbs what is observed or damages the observer. Vision is our most powerful sense for recognising objects. When we imagine objects we do so visually. Vision is so powerful that we use a word from vision for imagining and we hardly notice when we say we can imagine hearing, feeling, smelling or tasting something.

It is my view that the world of seen objects, complemented by touch, is what most powerfully informs Baggott's (and almost everybody's) notion of the real. Consequently, although we understand that objects exist regardless of whether we see them or not, such an understanding requires us to imagine these unseen objects. This we do, quite literally, by producing an image (or 'ghost-image' perhaps). This is a philosophical argument about how we conceive of the real and it is, I think, a critical point of difference. Baggott would, I think, distinguish objects as we experience them from the objects themselves whereas I would emphasise that we have no notion of objects except as we experience them. Baggott would argue that the real is independent of our experience of the real whereas I would argue that our notion of a real independent of our experience is nevertheless conceived in terms of our experience.

I understand Baggott to be separating the real from our experience of the real. This is the reason his realism is unrealisable and is inaccessible except to faith. And to him, the real underlying our experience is the same real that underlies quantum mechanics. The apparent inconsistency of quantum mechanics with our experience, therefore, is for him a serious problem and any accommodation of that inconsistency is to him anti-realist.

I would argue that we conceive of the real underlying our experience in terms of our experience. When we analyse the real we are also delving into the mechanism of our own perception, a mechanism that we have no means of perceiving. (We might write 'mechanism' to mark that this is a metaphor from our experience of objects.) For example, we see objects because of light. The seeing of light itself is impossible in principle. Light is not see-able and so trying to imagine it involves an inconsistency in principle. As it is there is no coherent way of visualising light in practice and this is what we would expect.

I would argue, therefore, that when we analyse the real to arrive at quantum mechanics we go beyond our experience in principle and hence beyond our notion of the real. There is no reason to suppose that our concept of reality should be mirrored in quantum mechanics i.e. that the analysis should lead us back to where we started from (or according to Baggott's conception, to never depart from it). We do not look through a microscope to discover a world where microscopic microscopes can be made; and look through these to discover a world where micro-micro-microscopes can be made. This is the equivalent in physics of the regressive homunculus in reproductive biology.

Baggott, of course, does not support the view that the quantum world should somehow be a microscopic version of our own. Rather, we may understand him as wanting to include quantum mechanics into the diversity we find in the world that we experience so that quantum mechanics conforms to the principles of that diversity — the notions of space and time perhaps. He understands the world of quantum mechanics to be part of the real rather than arising from the analysis of the real. He is seeking, in effect, some features of the world, as we experience it, that persist under analysis.

The failure of quantum mechanics to fit into this scheme leads him to regard the current interpretation of quantum mechanics as anti-realist and he promotes the idea that we should fix this problem by finding better principles. We have suggested that Baggott falsely tries to conceive (i.e. imagine) a real without reference to experience. We now suggest that he abstracts the real into principles but finds these principles to be inadequate. We may characterise his real as the desire to find principles that unify our understanding of the world around us with the 'world' we find under analysis. It is a quest, in effect, for a regressive explanation and it is for this reason that his realism is probably best termed 'regressive realism'.

Baggott describes his realism as unachievable and requiring faith. I, also, would describe it as unachievable, but I reject the notion of unaccountable knowing suggested by the word 'faith'. Our recognition of the real is not unaccountable — it is conceived in terms of our experience. Baggott thinks his realism is an ideal to which we should aspire. I would argue that the 'world' of quantum mechanics cannot be understood as real and attempts to do so are regressive and futile. I would argue that Baggott's realism fails to respect the means by which we comprehend the real and I would assert, therefore, that it cannot guide us toward a deeper comprehension of the real.

If quantum mechanics is consistent with our experience of the world, which it appears to be to a profound degree, then it should be regarded as a realist theory for this reason. It cannot have a realist interpretation of its entities in the sense that these entities can be visualised or otherwise conceived of as objects because such entities are beyond our experience in principle — they are unperceivable by us and cannot contribute to our notion of the real. We may analyse a rock and find it is made up of smaller pieces of rock. It is only when we find something different in this process of splitting that any explanation becomes available to us. We ought not to be surprised that light cannot be visualised. We ought not to be surprised that our analysis of the real leads to the unreal. This does not mean the quantum 'world' is inaccessible to reason and it need not see quantum mechanics degenerating into 'senseless empiricism', as Einstein feared (quoted p115).

The reasonable approach to adopt is to abandon the futile quest for a regressive explanation of the real and instead to recognise that the real is our only tool for analysing the real, obviously in an experimental sense but also conceptually. The development of quantum mechanics from combining particle mathematics (from solids) with wave mechanics (from fluids) and interpreting it in terms of the mathematics of probability illustrates this process at work. Vision, in providing us with our concept of the real, naturally enough, is a powerful tool for analysing the real. If it were not such a powerful tool it is doubtful we could analyse the real at all. But just as we should not over-emphasise vision and expect the quantum world to be visually real nor should we under-estimate it.

There is not a sharp transition from the world as we experience it to the quantum world. (As I understand it, quantum mechanics comprehends this transition very well.) We can indeed see smaller and smaller pieces of rock, in principle at least, and there is not a point at which seeing is no longer possible, rather the picture becomes less coherent as we reach to the atomic scale. Atoms cannot be seen in principle but it may be satisfactory to argue that their closeness to the scale of visible objects is the reason visualisation in chemistry is so effective. Whatever the case, if visualisation leads to effective exploration then this is justification enough.

This philosophical look at quantum mechanics has not returned us to the debate between the 'anti-realist versus the realist'. Rather, we have argued that Baggott's realism, the realist view of the twentieth century, is poorly conceived. We have argued that quantum mechanics cannot be understood in terms of this realism, which is to say that quantum mechanics has been incomprehensible because we have tried to comprehend it in the wrong way. I have argued that the way forward is to deliberately and creatively use the real as a resource for analysing the real without concern for the unreality that may result. The twentieth century development of quantum mechanics is an example of this process at work. One may optimistically suggest, therefore, that a generalised understanding of this process may lead to as yet undreamt of comprehension of the real, progress that is not driven by unrealisable faith but by confident understanding. It is amusing to think that humanity may still be in its conceptual childhood, or, in the language of biology, that humanity has only just begun to explore the conceptual niche.

Postscript

This is the conclusion of this review except for a very brief discussion on Baggott's notion of truth, which I would argue is also representative of the twentieth century. This is an issue that is not specific to quantum mechanics but concerns science generally.

Baggott distinguishes between true and 'true'. He tells us scientific theories are 'true' because we cannot be absolutely certain they are true. We may understand him to be saying that it is useful to regard scientific theories as true but that they might nevertheless be false. Baggott does not deal with this issue explicitly and he takes it for granted that we understand what he means by true. I would expect him to regard mathematics as the model of true statements and would expect him to say mathematical statements are either true or false but never 'true' or 'false'. He would say, I think, that 1+1=2 is true within the traditional system of numbers and when applying this mathematics to counting apples would say 1 apple + 1 apple = 2 apples is 'true' (because the scientific theory that might say, 'Taking one object and then another object means we have two objects' is only 'true').

In mathematics, however, statements are evaluated according to the mathematical system in which they appear and we may use the terms consistent and inconsistent in place of true and false. (These systems are generally so precise that they can be mechanised!) The mathematical system itself is not true or false as such. It is just a system. Our evaluation of a mathematical system is likely to be in terms of its usefulness. This means that the issue of truth can be removed from mathematics entirely. If mathematics is the model of Baggott's truth, and I think it is, then we may assert that there is no truth, only 'truth'.

Baggott might not quite agree for he writes of Godel's 'incompleteness theorem' (p112),

'Such undecidable propositions can, however, be proved 'informally' through so-called meta-mathematical arguments outside the axiomatic structure.'

This suggests he sees the possibility of mathematical proofs outside axiomatic structures, which is odd given the trouble mathematicians take to embed proofs in axiomatic structures. His use of 'informally' and 'so-called', however, does not suggest much confidence and he is much less assertive than Godel himself:

'From the remark that [R(q);q] assets its own unprovability, it follows at once that [R(q);q] is correct, since [R(q);q] is certainly unprovable (because undecidable). So the proposition which is undecidable in the system PM yet turns out to be decided by metamathematical considerations.'

Perhaps, at last, there is declining confidence in Godel's 'incompleteness theorem'.

I would argue that 'true' is the only type of truth and that it can be understood as both objective and relativist (i.e. it is neither arbitrary nor absolute). This view of truth means that we regard statements as evaluated as true rather than intrinsically true, evaluation that does not of itself imply or require a final or absolute evaluation. Accordingly, we may say scientific theories are true. (It seems extraordinary, given their power, to suppose that they are not!) We may say experiments can and do prove theories (meaning 'prove' both in the sense of 'test' and 'verify' but obviously not in the mathematical sense). True theories may nevertheless become obsolete and may come to be regarded as in some way false.

The relationship between mathematics and science, according to this viewpoint, does not involve an interaction between true and 'true' — between ideal truth and contingent truth. I would argue that just as our notion of the real is founded on our experience so too is mathematics: number is a mathematical system abstracted from counting (and reflexly counting is an application of that system); geometry is a mathematical system abstracted from measuring space. These mathematical systems are reflexly applicable to the real because they have been conceived in terms of the real.

This completes this review of Baggott's 'Beyond Measure'. I have argued that he has mistaken notions of both realism and truth, confusions that are typical of the twentieth century. It is an interesting book and probably an excellent guide to the past. I have argued that it is no guide to the future.

© Lawrence Trevanion 2005

E-mail: Ltrev@pcug.org.au