Archive for the ‘Philosophy’ category

Why is many-worlds winning the foundations debate?

11th April 2007

Almost every time the foundations of quantum theory are mentioned in another science blog, the comments contain a lot of debate about many-worlds. I find it kind of depressing the extent to which many people are happy to jump on board with this interpretation without asking too many questions. In fact, it is almost as depressing as the fact that Copenhagen has been the dominant interpretation for so long, despite the fact that most of Bohr’s writings on the subject are pretty much incoherent.

Well, this year is the 50th anniversary of Everett’s paper, so perhaps it is appropriate to lay out exactly why I find the claims of many-worlds so unbelievable.

WARNING: The following rant contains Philosophy!

Traditionally, philosophers have made a distinction between analytic and synthetic truths. Analytic truths are those things that you can prove to be true by deduction alone. They are necessary truths and essentially they are just the tautologies of classical logic, e.g. either this is a blog post or this is not a blog post. On the other hand, synthetic truths are things we could imagine to have been another way, or things that we need to make some observation of the world in order to confirm or deny, e.g. Matt Leifer has never written a blog post about his pet cat.

Perhaps the central problem of the philosophy of science is whether the correctness of the scientific method is an analytic or a synthetic truth. Of course this depends a lot on how exactly you decide to define the scientific method, which is a topic of considerable controversy in itself. However, it’s pretty clear that the principle of induction is not an analytic truth, and even if you are a falsificationist you have to admit that it has some role in science, i.e. if a single experiment contradicts the predictions of a dominant theory then you call it an anomaly rather than a falsification. Of the other alternatives, if you’re a radical Kuhnian then you’re probably not reading this blog, since you are busy writing incoherent postmodern junk to write for a sociology journal. If you are a follower of Feyerabend then you are a conflicted soul and I sympathize. Anyway, back to the plot for people who do believe that induction has some role to play in science.

Kant’s resolution to this dilemma was to divide the synthetic truths into two categories, the a priori truths and the rest (I don’t know a good name for non-a priori synthetic truths). The a priori synthetic truths are things that cannot be directly deduced, but are nevertheless so basic to our functioning as beings living in this world that we must assume them to be true, i.e. it would be impossible to make any sense of the world without them. For example, we might decide that the fact that the universe is regular enough to perform approximately repeatable scientific experiments and to draw reliable inferences from them should be in the category of a priori truths. This seems reasonable because it is pretty hard to imagine that any kind of intelligent life could exist in a universe where the laws of physics were in continual flux.

One problem with this notion is that we can’t know a priori exactly what the a priori truths are. We can write down a list of what we currently believe to be a priori truths – our assumed a priori truths – but this is open to revision if we find that we can in fact still make sense of the world when we discard some of these assumed truths. The most famous example of this comes from Kant himself, who assumed that the way our senses are hooked up meant that we must describe the world in terms of events happening in space and time, implicitly assuming a Euclidean geometry. As we now know, the world still makes sense if we drop the Euclidean assumption, unifying space and time and working with much more general geometries. Still, even in relativity we have the concept of events occurring at spacetime locations as a fundamental primitive. If you like, you can modify Kant’s position to take this as the fundamental a priori truth, and explain that he was simply misled by the synthetic fact that our spacetime is approximately flat on ordinary length scales.

At this point, it is useful to introduce Quine’s pudding-bowl analogy for the structure of knowledge (I can’t remember what kind of bowl Quine actually used, but he’s making pudding as far as we are concerned). If you make a small chip at the top of a pudding bowl, then you won’t have any problem making pudding with it and the chip can easily be fixed up. On the other hand, if you make a hole near the bottom then you will have a sticky mess in the oven. It will take some considerable surgery to fix up the bowl and you are likely to consider just throwing out the bowl and sitting down at the pottery wheel to build a new one. The moral of the story is that we should be more skeptical of changes in the structure of our knowledge that seem to undermine assumptions that we think are fundamental. We need to have very good reasons to make such changes, because it is clear that there is a lot of work to be done in order to reconstruct all the dependent knowledge further up the bowl that we rely on every day. The point is not that we should never make such changes – just that we should be careful to ensure that there isn’t an equally good explanation that doesn’t require making such as drastic change.

Aside: Although Quine has in mind a hierarchical structure for knowledge – the parts of the pudding bowl near the bottom are the foundation that supports the rest of the bowl – I don’t think this is strictly necessary. We just need to believe that some areas of knowledge have higher connectivity than others, i.e. more other important things that depend on them. It would work equally well if you think knowledge is stuctured like a power-law graph for example.

The Quinian argument is often levelled against proposed interpretations of quantum theory, e.g. the idea that quantum theory should be understood as requiring a fundamental revision of logic or probability theory rather than these being convenient mathematical formalisms that can coexist happily with their classical counterparts. The point here is that it is bordering on the paradoxical for a scientific theory to entail changes to things on which the scientific method itself seems to depend, and we did use logical and statistical arguments to confirm quantum theory in the first place. Thus, if we revise logic or probability then the theory seems to be “eating its own tail”. This is not to say that this is an actual paradox, because it could be the case that when we reconstruct the entire edifice of knowledge according to the new logic or probability theory we will still find that we were right to believe quantum theory, but just mistaken about the reasons why we should believe it. However, the whole exercise is question begging because if we allow changes to such basic things then why not make a more radical change and consider the whole space of possible logics or probability theories. There are clearly some possible alternatives under which all hell breaks loose and we are seriously deluded about the validity of all our knowledge. In other words, we’ve taken a sledgehammer to our pudding bowl and we can’t even make jelly (jello for North Ameican readers) any more.

At this point, you might be wondering whether a Quinian argument can be levelled against the revision of geometry implied by general relativity as well. The difference is that we do have a good handle of what the space of possible alternative geometries looks like. We can imagine writing down countless alternative theories in the language of differential geometry and figuring out what the world looks like according to them. We can adopt the assumed a priori truth that the world is describable in terms of events in asome spacetime geometry and then we find the synthetic fact that general relativity is in accordance with our observations, while most of the other theories are not. We did some significant damage close to the bottom of the bowl, but it turned out that we could fix it relatively easily. There are still some fancy puddings – like the theory of quantum gravity (baked Alaska) – that we haven’t figured out how to make in the repaired bowl, but we can live without them most of the time.

Now, is there a Quinian argument to be made against the many-worlds interpretation? I think so. The idea is that when we apply the scientific method we assume we can do experiments which have actual definite outcomes. These are the basic data from which we build a confirmation or refutation our theories. Many-worlds says that this assumption is wrong, there are no fundamental definite outcomes – it just appears that way to us because we are all entangled up in the wavefunction of the universe. This is a pretty dramatic assertion and it does seem to be bordering on the “theory eating its own tail” type of assertion. We need to be pretty sure that there isn’t an equally good alternative explanation in which experiments really do have definite outcomes before accepting it. Also, as with the case of revising logic or probability, we don’t have a good understanding of the space of possible theories in which experiments do not have definite outcomes. I can think of one other theory of this type, namely a bizarre interpretation of classical probability theory in which all outcomes that are assigned nonzero probability occur in different universes, but two possible theories does not amount to much in the grand scheme of things. The problem is that on dropping the assumption of definite outcomes, we have not replaced it with an adequate new assumed a priori truth. That the world is describable by vectors in Hilbert space that evolve unitarily seems much to specific to be considered as a potential candidate. Until we do come up with such an assumption, I can’t see why many-worlds is any less radical than proposing a revision of logic or probability theory. Until then, I won’t be making any custard tarts in that particular pudding bowl myself.

Temperamental Physicists

29th August 2006

The other day I was surfing on Chris Fuchs’ website, looking for a journal reference to one of his papers. I noticed that there is a new addition to his compendia of emails about the foundations of quantum mechanics. Now, depending on your temperament, you either love or hate reading such things. Certainly, the ideas are not as carefully formulated as they would be in a scientific paper, and some might find this annoying. Also, if you get annoyed by reading things that you don’t agree with, and you are bound to find at least something you don’t agree with unless your name is Chris Fuchs, then this is not for you. On the other hand, it does give some insight into how a fellow thinker about foundations formulates, develops and changes his ideas, which is something that most scientists go to great lengths to hide from public view. It also gives you an idea of his influences, and it is the reactions of other people to the emails and the quotes from philosophers that I will never be motivated to read myself, that really bring the thing to life. Speaking of the latter, I liked this quotation from William James – if anyone knows the source then please let me know:

The history of philosophy is to a great extent that of a certain clash of human
temperaments. Undignified as such a treatment may seem to some of my colleagues,
I shall have to take account of this clash and explain a good many of the divergencies
of philosophies by it. Of whatever temperament a professional philosopher is, he tries,
when philosophizing, to sink the fact of his temperament. Temperament is no conventionally
recognized reason, so he urges impersonal reasons only for his conclusions. Yet
his temperament really gives him a stronger bias than any of his more strictly objective
premises. It loads the evidence for him one way or the other, making a more sentimental
or more hard-hearted view of the universe, just as this fact or that principle would. He
trusts his temperament. Wanting a universe that suits it, he believes in any representation
of the universe that does suit it. He feels men of opposite temper to be out of key
with the world’s character, and in his heart considers them incompetent and ‘not in it,’
in the philosophic business, even though they may far excel him in dialectical ability.
Yet in the forum he can make no claim, on the bare ground of his temperament,
to superior discernment or authority. There arises thus a certain insincerity in our
philosophic discussions: the potentest of all our premises is never mentioned. I am
sure it would contribute to clearness if in these lectures we should break this rule and
mention it, and I accordingly feel free to do so.

It seems to me that the quote would still make sense if one replaced “philosophy” by “theoretical physics”. Now, before I get accused of being on the loony left of postmodernism and sociology of science, let me clarify that I do believe that the role of experiment is a big difference between the two subjects, and it is capable of resolving issues much more conclusively than argument alone. However, each physicist has to choose what topic to work on and which ideas and methods are most likely to lead to success. Despite the successes of the great edifice of modern theoretical physics, there are still dozens of possible views on which aspects of it are the most important and on why it all works in the first place. The temperament of the physicist plays a large role in coloring her/his attitude to such issues. For example, something as simple as the level of respect for authority can play an enormous role. This is evident in the currently ongoing debate about the success/failure of string theory (which I don’t claim to have enough expertise to say anything sensible about by the way) and in differing attitudes to whether the foundations of quantum mechanics is an important subject for a physicist to understand, or a load of metaphysical hogwash.

It takes all types to make the subject go forward, and it would be a boring life if we all agreed exactly what needed doing and how to go about doin it. However, I do think that if we paid greater attention to the fact that there need not be entirely scientific reasoning behind our differing points of view, and that this is OK – even normal – then that would help to diffuse some of the great controversies of modern science.


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