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In this paper, Testing quantum mechanics, S. Weinberg states that

The problem is to know what to test. Usually we can get guidance on how to test a theory like general relativity or the standard model of elementary particle interac- tions, by first inventing some generalized theory as a foil, such as general relativity with extra massless scalars, or the standard model with extra gauge bosons. By a “generalized” theory, I mean one that differs from the theory we want to test, but reduces to it when some parameters become very small. (In this sense, the local hidden variable theories do not qualify as generalizations of quantum mechanics.) We can set upper bounds on these parameters by doing experiments to look for new effects that could arise in the generalized theory, and in this way we get a sense of how accurate is the theory we want to test.

However, I cannot understand what does he mean by this paragraph? For example, why do we need a "generalized theory" to test the actual theory that we want to test?, and if we have one, how do we use it to test the actual theory? Is there any other way to test it [the actual theory]?

David Z
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Our
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  • Our convention is to link to a canonical page for a paper, such as the publisher's page, an arXiv page, or a DOI link. It looks like the link started out as pointing to the publisher's page (which is fine), got changed to a DOI link (which is also fine), and then got changed to a Google Drive link, which is not fine given that a more canonical source exists. The point of linking it here is to help identify the paper, not necessarily to show people where to get a copy of it; the DOI does that but the Drive link does not. So (TL;DR) don't change it back. – David Z Feb 15 '19 at 08:06
  • Incidentally, the INSPIRE page for the paper does link to a preprint. The INSPIRE page would be another perfectly fine option to use as a canonical link, if desired, since it fully identifies the paper. – David Z Feb 15 '19 at 08:09
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    @DavidZ Well I couldn't find any any way to let the Ben to access to paper; I know it is appropriate to share the paper in such a way, but science comes before the law, at least for me. – Our Feb 15 '19 at 14:50

1 Answers1

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The paper sounds interesting. Is it available somewhere without a paywall?

He's talking about testing a theory that has already been tested many times in a whole bunch of different contexts and has passed all those tests. Therefore the theory can't just be wrong, like Freudian psychology or Marxism. The only possibility is that it's a special case of some broader theory. This is called the correspondence principle: new theories have to be backward-compatible with old ones. Because of the correspondence principle, my freshman students are not going to disprove quantum mechanics by measuring the spectrum of hydrogen. You have to have some framework to guide you in constructing tests so that you can quantify which conditions are the ones that have not yet been tested, and or what upper limit has already been placed on violations.

It can also be a waste of time to try tests if it's logically impossible for the test to falsify the theory. For instance, suppose I want to test whether probability is conserved, as predicted by standard quantum mechanics. How the heck would I test that? I do the experiment, and something happens. If the total probability of the outcomes was 0.9, then what would that mean? Would the whole universe cease to exist for me with probability 0.1? Or what if the theory says that a certain probability is negative -- how do I test that theory?

Quantum mechanics turns out to be extremely fragile in this sense: it's very difficult to get any viable and different theory by making small perturbations to quantum mechanics. A good paper on this is Aaronson, "Is Quantum Mechanics An Island In Theoryspace?," http://arxiv.org/abs/quant-ph/0401062

  • "He's talking about testing a theory that has already been tested many times in a whole bunch of different contexts and has passed all those tests."; however, if you read the paper, the author argues, for example, that if you measure the spectrum of a harmonic oscillator, and it agrees with the prediction, it only verifies the Hamiltonian, and not directly the theory itself. This doesn't make sense to physicists, I agree, because there is no "really" theory, there is only models, so in that sense, as long as the predictions of the theory agree with the experiment, the theory is "true" ... – Our Feb 14 '19 at 04:05
  • because that is the only thing that I can verify, but I still gave the benefit of doubt to this argument that there might be something that I'm not understanding. – Our Feb 14 '19 at 04:07
  • @onurcanbektas: I haven't read the paper, because it's paywalled, so it's possible that I'm missing Weinberg's point completely. I would be interested in seeing the paper if you can locate a non-paywalled version or are willing to post it somewhere. What I'm describing in this answer is just a set of more general ideas about how we go about testing theories in physics. For example, this is the philosophy underlying the use of the PPN formalism as a test theory for tests of general relativity. I think that's all Weinberg is talking about in the paragraph you quoted. –  Feb 14 '19 at 15:01