http://hps.phil.pku.edu.cn/bbs/read.php?tid=882
Time: Friday, December 26, 2008, 3:00–5:00 p.m.
Place: Academic Lecture Hall, Center for Science and Society, Chengze Garden
Speaker: Bai Tongdong, Assistant Professor, Department of Philosophy, Xavier University, USA
Topic: How to Solve the Underdetermination Problem—Using Cushing’s Defense of Hidden Variables as an Example
Commentator: Liu Huajie
Although I couldn’t really raise any questions, and Monday’s report can’t really continue along this line, today’s lecture was quite interesting.
What I found interesting was not the topic itself, but rather the many inspirations that Professor Bai mentioned in passing during his talk. As for the topic, my reaction was rather like that of the journal office supporting orthodox quantum mechanics—although the argument was all well and good, why go to such lengths to criticize a doctrine that was already going nowhere?
It came as something of a surprise to me that there should be such a large contingent in the philosophy of physics supporting hidden-variable theories. Although I had previously read works such as Bunge’s Philosophy of Physics, which also opposed the orthodox interpretation of quantum mechanics, those were very old books, and I still lack a proper grasp of the latest debates in the West. If the arguments are still being tangled up in hidden variables… how should I put it… although one could excuse it by saying that academia is often conservative and that philosophy is often more willing to speak up for the underprivileged, still it is somewhat regrettable.
Professor Bai mentioned that one could conduct an SSK study of the interests of philosophers of science, analyzing why the proportion of supporters of hidden variables among philosophers of science is so much higher than among scientists, and examining what social, cultural, and historical roots lie behind this. I think that is indeed very interesting. Of course, this relationship can be studied as external history or internal history; in particular, one could examine whether there is any intrinsic connection between the philosophical tradition of logical empiricism and the tendency to support hidden-variable theories. Professor Wu and Professor Liu also mentioned how the philosophical ideas of logical empiricism might be related to the constitutional systems established in the West since Locke, and thereby mutually reinforce one another. These are all very interesting questions.
I think philosophers influenced by the tradition of logical empiricism are more likely to feel close to hidden-variable theories because of certain intrinsic factors. First of course is an obsession with “determinism,” but that is by no means the whole story. More important, perhaps, is “realism”—that is, the kind of “scientific realism” I will be reporting on next Monday. Although this form of realism is a relatively recent formulation, it is rooted in the tradition of logicism (that is, a certain Platonic realism). This line of thought insists that a theoretical term must have a referent, and that the object of reference is something determinate, independent of human beings, autonomous, and real. Thus “electron” refers to the object electron; this object is objectively real, and whether or not human beings observe it, it and its state certainly exist.
Quantum mechanics, however, has shattered this kind of naive realism based on everyday experience—“electron” and “atom” are theoretical tools; as theoretical terms, they are meaningful only when operated with within the entire theoretical system. And as explanations of objective reality, they can speak of some sort of truth only within the whole context that includes the operator and the operation itself; to speak independently about the reality of any single electron is utterly meaningless.
Once one genuinely accepts such an anti-realist way of thinking, the paradoxes of quantum mechanics disappear without a trace. The reason quantum mechanics seems so baffling is that the language used in our everyday thought is ultimately a realist language. Quantum mechanics is not absurd, nor is it necessarily non-deterministic; the key is not to seek another scientific alternative, but rather to reflect on the limits of our language.
I may also touch on related topics a little in Monday’s report.
Finally, let me add one point. When we say “hidden variables,” there are at least two layers of meaning: first, “hidden-variable interpretation”; second, further on, “hidden-variable theory,” or the so-called “Bohmian mechanics.” Likewise, “orthodox quantum mechanics” also has two layers: one refers to the orthodox mechanical theoretical system, and the other to its “interpretation,” that is, the Copenhagen probabilistic interpretation.
By the level of the theoretical system, I mean an entire mathematical system used to measure, calculate, and predict empirical phenomena. The same phenomenon can be described with different concepts, calculated with different equations; but if the different methods of calculation are mathematically equivalent in the end, then their distinction can only appeal to their “physical meaning.” And if they are not mathematically equivalent, then in principle one may be able to find some decisive experiments to determine which is right and which is wrong. We know that quantum mechanics has three theoretical systems that have been proven mathematically equivalent: Heisenberg’s matrix mechanics, Schrödinger’s wave mechanics, and Feynman’s path integrals. These three theoretical systems are completely equivalent mathematically, so of course in principle they cannot be distinguished empirically. But their interpretations of events are utterly different: one takes the electron to be an uncertain particle, one takes the electron to be a wave function, and one takes the path of the electron to be the sum of all possible paths. In other words, their descriptions of “reality” “look” vastly different. This is what the strictest sense of underdetermination is.
So what does “hidden variables” advocate? On the basis of remaining mathematically equivalent to the orthodox theory, does it offer a different interpretation? Or does the set of theories it provides fail to be mathematically equivalent to the orthodox theory, meaning that in principle some decisive experiments could be designed? We see that supporters of hidden variables once actively proposed a decisive experiment—namely the EPR-Bell experiment. But even if that experiment did not bring about the downfall of hidden variables, it was still greatly unfavorable to them. Thereafter, hidden-variable theories could no longer claim any decisive experiment; instead, they seemed to be striving to claim empirical equivalence with the orthodox theory. But they also failed to produce a new mathematical system and prove it to be mathematically equivalent to orthodox quantum mechanics; that is to say, they were not aiming to provide the existing theoretical system with a different interpretation. So what else can hidden-variable theories do? In the end, it seems they can at most keep insisting: the current mainstream theory may be flawed. But that is a triviality.
In fact, it is not only supporters of hidden variables who are dissatisfied with the Copenhagen interpretation. We can see that by the end of the twentieth century, many new interpretations had already emerged, seeking to replace the Copenhagen probabilistic interpretation. The most influential is the “many-worlds interpretation,” which in some surveys of scientists even enjoys a support rate far higher than that of the Copenhagen interpretation; there are also “many histories,” “decoherence,” “spontaneous localization theories,” and so on. Among these, the many-worlds interpretation was also ignored when first proposed, but later it still won the broadest support. This shows that the disadvantaged position of hidden variables probably cannot be explained simply as the hegemony of Copenhagen.
December 26, 2008
Translated from the Chinese original with AI assistance. The original text is authoritative.
Leave a Reply