It appears that I haven’t had a good rant on this blog for some time, but I have been stimulated into doing so by some of the discussion following the Quantum Pontiff‘s recent post about Bohmian Mechanics. I don’t want to talk about Bohm theory in particular, but to answer the following general question:

- Just what is the goal of studying the foundations of quantum mechanics?

Before answering this question, note that its answer depends on whether you are approaching it as a physicist, mathematician, philosopher, or religious crank trying to seek justification for your outlandish worldview. I’m approaching the question as a physicist and to a lesser extent as a mathematician, but philosophers may have legitimate alternative answers. Since the current increase of interest in foundations is primarily amongst physicists and mathematicians, this seems like a natural viewpoint to take.

Let me begin by stating some common answers to the question:

1. To provide an interpretation of quantum theory, consistent with all its possible predictions, but free of the conceptual problems associated with orthodox and Copenhagen interpretations.

2. To discover a successor to quantum theory, consistent with the empirical facts known to date, but making new predictions in untested regimes as well as resolving the conceptual difficulties.

Now, let me give my proposed answer:

- To provide a clear path for the future development of physics, and possibly to take a few steps along that path.

To me, this statement applies to the study of the foundations of any physical theory, not just quantum mechanics, and the success of the strategy has been born out in practice. For example, consider thermodynamics. The earliest complete statements of the principles of thermodynamics were in terms of heat engines. If you wanted to apply the theory to some physical system, you first had to work out how to think of it as a kind of heat engine before you started. This was often possible, but a rather unnatural thing to do in many cases. The introduction of the concept of entropy eliminated the need to talk about heat engines and allowed the theory to be applied to virtually any macroscopic system. Further, it facilitated the discovery of statistical mechanics. The formulation in terms of entropy is formally mathematically equivalent to the earlier formulations, and thus it might be thought superfluous to requirements, but in hindsight it is abundantly clear that it was the best way of looking at things for the progress of physics.

Let’s accept my answer to the foundational question for now and examine what becomes of the earlier answers. I think it is clear that answer 2 is consistent with my proposal, and is a legitimate task for a physicist to undertake. For those who wish to take that road, I wish you the best of luck. On the other hand, answer 1 is problematic.

Earlier, I wrote a post about criteria that a good interpretation should satisfy. Now I would like to take a step back from that and urge the banishment of the word interpretation entirely. The problem with 1 is that it ring-fences the experimental predictions of quantum theory, so that the foundational debate has no impact on them at all. This is the antithesis of the approach I advocate, since on my view foundational studies are supposed to feed back into improved practice of the theory. I think that the separation of foundations and practice did serve a useful role in the historical development of quantum theory, since rapid progress required focussing attention on practical matters, and the time was not ripe for detailed foundational investigations. For one thing, experiments that probe the weirder aspects of quantum theory were not possible until the last couple of decades. It can also serve a useful role for a subsection of the philosophy community, who may wish to focus on interpretation without having to keep track of modern developments in the physics. However, the view is simply a hangover from an earlier age, and should be abandoned as quickly as possible. It is a debate that can never be resolved, since how can physicists be convinced to adopt one interpretation over another if it makes no difference at all to how they understand the phenomenology of the theory?

On the other hand, if one looks closely it is evident that many “interpretations” that are supposedly of this type are not mere interpretations at all. For example, although Bohmian Mechanics is equivalent to standard quantum theory in its predictions, it immediately suggests a generalization to a “nonequilibrium” hidden variable theory, which would make new predictions not possible within the standard theory. Similar remarks can be made about other interpretations. For example, many-worlds, despite not being a favorite of mine, does suggest that it is perfectly fine to apply standard quantum theory to the entire universe. In Copenhagen this is not possible in any straightforward way, since there is always supposed to be a “classical” world out there at some level, which the state of the quantum system is referred to. In short, the distinction between “the physics” and “the interpretation” often disappears on close inspection, so we are better off abandoning the word “interpretation” and instead viewing the project as providing alternatives frameworks for the future progress of physics.

Finally, the more observant amongst you will have noticed that I did not include “solving the measurement problem” as a possible major goal of quantum foundations, despite its frequent appearance in this context. Deconstructing the measurement problem requires it’s own special rant, so I’m saving it for a future occasion.

Copyright © 2006 Matthew Leifer. All Rights Reserved.

Hi, like to comment on this issue.

I think there’s no understanding of a physical theory without interpretation. Beyond the basic meanings of the mathematical terms, what we demand of a physical theory is how it connects with the world, and this is what an interpretation do.

An interpretational framework that has not much influence on practical advance can still be important, provided it is able to make certain aspects of the basic meanings of the theory more natural and intelligible. But I do believe that a good interpretation will not only transform how we view a theory, but also suggest previously hidden ways to improve on (or go beyond) the theory.

However I agree with you on one point, that in our generation the word “interpretation” (and “philosophy”) has a bad name. This may be forgivable for those who engage in the more practical aspects of the theory, but for those who is serious about understanding and meaning, such ignorance is perilous.

You are really mixing up things, Matt. One question is whether this or that theory is correct, ultimate, fundamental, or what have you, and an altogether different question is how this or that theory —

assumedto be correct, ultimate, fundamental, or what have you — fits in with this or that story that addresses issues that are beyond the ken of physics altogether. Fuchs and Peres have tried before you to argue that “Quantum theory needs no interpretation”. Every mathematical formalism that is supposed to be part of physics needs an interpretation that relates it to the universe, period.I don’t think I’m mixing things up. I’m just trying to change the question and move the debate on. It seems to me that the traditional “pure interpretation” debate is a dead end. We have several answers and none of them recommend themselves as the unique solution. Therefore, I ask myself whether any “pure interpretation” question has been posed and answered successfully for any other theory in the history of physics. The answer seems to be no – although people have always thought about the foundations of physical theories, the goals of “getting the right picture” and “moving physics forward” have always been closely tied together and never achieved completely independently.

The bottom line is that even if you can come up with an interpretation of quantum mechanics that you believe to be fully consistent and satisfactory, but you do not simultaneously move physics forward, then NO ONE NEED EVER HAVE ANY REASON TO BELIEVE YOU! (and Ulrich, I know you know this from experience.) I can’t emphasize this point enough, so here are a few more exclamation marks!!!!!!!

I do not agree with Fuchs and Peres, although I do share some of the pragmatist convictions that are behind their argument, as is probably apparent from my comments. The bottom line is that these issues ARE mixed up, or more accurately that they OUGHT to be.

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