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For example, the prefix term 'micro-' in 'microfinance' has a different purpose from the 'micro-' in 'microeconomics'.

I heard all 'interpretations' of quantum mechanics give exactly the same answer to every measurement so they are all equally correct. Is that the same use of the term 'interpretations' as in 'interpretations' of probability?

Context:

  1. In 2011, learned mathematical (frequentist) statistics in 2011 as a quant undergrad.

  2. In 2014, I encountered the aforementioned.

Sheldon: Okay. Um, what is the correct interpretation of quantum mechanics?

Howard: Since every interpretation gives exactly the same answer to every measurement, they are all equally correct. However, I know you believe in the Many Worlds Interpretation, so I’ll say that. Now do you think I’m smart enough?

  1. In 2015, I discovered the Bayesian interpretation of probability as a quant grad eg Bayesian logit model - intuitive explanation? and that 99% of my statistics were frequentist.

So Bayesians and frequentists interpret probability differently leading to the things like Lindley's parardox, but they both follow Kolmogorov's axioms and Bayes' theorem so they will never differ on $\mathbb P(A)$ where $A$ is an event in $(\Omega, \mathscr F, \mathbb P)$

Is that the same idea as the use of the term 'interpretation' in quantum mechanics?

If no, why exactly?

If so, elaborate if you want.

BCLC
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  • Every interpretation comes with its own small print that will make it identical when ti comes to predicting the outcome of conventional experiments. E.g. in case of Bohm theory the small print is quantum equilibrium. – Count Iblis Dec 07 '16 at 22:26
  • @BCLC I think there is an interesting connection but making it requires reifying the concepts in the various probability interpretations. – G. Bergeron Dec 08 '16 at 12:39
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    This seems like more of a philosophy question than a physics one to me. – By Symmetry Dec 08 '16 at 17:22
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    Not all interpretations of quantum mechanics are experimentally equivalent. For example the objective collapse theory predicts that we should not be able to prepare coherent quantum states of certain size. What's more, some interpretations have nothing to say for certain domains of physics, for example Bohmian mechanics can not describe quantum field theory (at least as far as I understand). Finally, we have not exhausted the consequences of our interpretations, so we may be surprised to learn that different interpretations make different predictions about nature that we did not anticipate. – Joel Klassen Dec 08 '16 at 18:34
  • @BySymmetry Well i would ask this on english se, but it's not necessarily that they're familiar with probability or physics. Anyway, edited to be clearer. – BCLC Aug 26 '20 at 11:40
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    Whether interpretations of quantum mechanics are really just interpretations of probability depends on the interpretation, actually! – knzhou Sep 01 '20 at 00:10
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    Why do you mention the "Big Bang Theory" (2014)? Because of the word "chance"? – Deschele Schilder Sep 01 '20 at 00:46
  • @JoelKlassen Why isn't Bohmian mechanics capable of describing QFT? – Deschele Schilder Sep 01 '20 at 00:47
  • @descheleschilder quote from episode: 'Um, what is the correct interpretation of quantum mechanics?' Editing post. see old revisions. the question was closed or downvoted previously because i mentioned a lot of TBBT lol – BCLC Sep 01 '20 at 23:15
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    Aha! I understand. Too bad the other questions were closed! Great fun, TBBT ;-) – Deschele Schilder Sep 01 '20 at 23:20
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    It's funny! Especially the first part concerning Stalin's plan to create a super-soldier. LOL! – Deschele Schilder Sep 01 '20 at 23:25

5 Answers5

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There are similarities and differences.

In probability, both interpretations give the same $P(A)$ for an event. But the interpretation of the even is the same: the event is absolute, i.e. it really happened.

In quantum mechanics, all interpretations give the same probabilities for a measurement outcome but the interpretation of the measurement outcome itself may vary.

In collapse theories, the measurement outcome is absolute and really happens, but causality is violated.

In many worlds, there is no single measurement outcome. The world becomes a superposition two worlds, each with its own outcome, and the observer in each world seeing (subjectively) a single outcome.

In Quantum Bayesianism, the probabilities and the measurement outcomes are completely subjective. This is actually a reformulation of probability theory where probabilities can interfere like waves. (This is because, in QM, the probability for a measurement $a$ is given by the square of the probability amplitude, $p=|\psi(a)|^2$. Since $\psi$ is, in general, a complex number, we can get interference between different classical processes by taking superpositions $\psi = \psi_1+\psi_2$.)

A recent paper (referred to in the following article) makes some of these ideas rigorous: https://www.sciencemag.org/news/2020/08/quantum-paradox-points-shaky-foundations-reality

But the point here is that the different interpretations of QM predict a different final state of the world and of the system after a measurement is made. However, how that measurement outcome is perceived by the observer making the measurement will be the same in all interpretations. So there are no observable differences between the different interpretations, only inobservable differences.

Deschele Schilder
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Eric David Kramer
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    I think you make a very good point. It is however not the probabilities, but the probability amplitudes that interfere - I mention it only because it seems that quite a few users here are not sure about the difference between probability theory and quantum mechanics, and whether the former is the same in quantum and classical physics. – Roger V. Aug 25 '20 at 12:04
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    That's a good point. I just added your point to my answer. I was in a hurry before and it seemed complicated to discuss so I left it out. Please tell me if you agree with my explanation. – Eric David Kramer Aug 25 '20 at 12:45
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    Your "recent paper" was published in 1939. How old are you? :) – D. Halsey Aug 25 '20 at 13:27
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    Oops wrong paper! Changing the link right now. I'm 33. – Eric David Kramer Aug 25 '20 at 13:35
  • Edited to be clearer. My question is about the use of the term 'interpretation'. Thanks for answering. Is your answer the same? – BCLC Aug 26 '20 at 11:39
  • anyhoo i'll just upvote your answer for effort since it was my fault for being unclear – BCLC Aug 26 '20 at 11:57
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    Thanks. That's a simpler question. Will update my answer. – Eric David Kramer Aug 26 '20 at 13:14
  • Oh wow good answer. I'll just give you bounty instead of accepting your answer. This way it's like I accept 2 answers. – BCLC Aug 31 '20 at 23:33
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    Glad you liked it. Thanks! – Eric David Kramer Sep 01 '20 at 10:18
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Interpretation in quantum mechanics is explaining how seemingly counter-intuitive quantum mechanical behavior comes about. There exist many interpretations.

Interpretations of probability are explaining what probability is (i.e., how it is correctly defined). There are exactly two of them: frequentist and Bayesian interpretations - I do not discuss them here, since I have done it just yesterday in an answer to a different question.

In other words, these are two different disciplines that require explaining/interpreting rather different things. (Moreover, QM is a physical discipline, whereas probability theory is more a mathematical one, although the need for interpretation comes from applying it to real data - not necessarily physics data.)

In terms of philosophical standpoints there is some overlap between the interpretations of QM and those of probability, as pointed out in the answer by @EricDavidKramer.

Roger V.
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  • Part 1. Right so your last paragraph I think is not really relevant to what my question - which i recently edited to hopefully be clearer - was meant to be. Similarly, some of the other answers I think are not really relevant or maybe I don't really understand those other answers. – BCLC Aug 26 '20 at 11:43
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    Part 2. Anyway, thanks for answering. so you're saying that interpretations of quantum mechanics are explanations of physical (or mechanical or whatever) phenomena but while interpretations of probability are more philosophical (or even ontological or whatever) into the nature of what probability is? – BCLC Aug 26 '20 at 11:43
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    @BCLC Precisely! QM and probability are really two different animals, even though probability is essential for QM. – Roger V. Aug 26 '20 at 11:45
  • Part 3. is your answer similar to Guy Inchbald's? – BCLC Aug 26 '20 at 11:46
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  • My answer is similar to the second part of that by Guy Inchbald's. I don't quite agree with his view of Bayesian/frequentist interpretation and the following suggestions about the time reversal symmetry
    • – Roger V. Aug 26 '20 at 11:52
  • Part 4. to be clear, is it CORRECT to say that interpretations of quantum mechanics are NOT philosophical/ontological statements or whatever as to the nature of quantum mechanics itself? – BCLC Aug 26 '20 at 11:53
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  • It is disputable. There is "shut up and calculate school", usually associated with Feynmann or Landau, which takes condescending view of interpreting QM as philosophical and irrelevant to practice. Others however believe that we may eventually come up with the experiments to test different QM interpretations, and then it is more than mere philosophy.
    • – Roger V. Aug 26 '20 at 11:55