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Thank you all for your comments and questions! I will try to do justice to them.
1. Dear Miroljub, the only variables I considered were those taking values ±1 and averages of many such variables. The goal was to investigate simple correlations subject to the Bell-CHSH inequality. I did not attempt to investigate anything beyond such correlations, such as the center of mass of an ensemble of “the world’s smallest soccer balls” [p. 336 of M. Arndt, O. Nairz, A. Zeilinger, “Interferometry with macromolecules: quantum paradigms tested in the mesoscopic world” in Quantum (Un)speakables: From Bell to Quantum Information, eds. R. A. Bertlmann and A. Zeilinger (Berlin: Springer), 2002, pp. 333-550]. At least at this stage, where I consider only post-quantum correlations, I don’t need to derive the classical limit of macromolecules: quantum mechanics dictates their classical limit, and it is doubtless consistent with relativistic causality, because quantum mechanics is.
2. Dear Travis Norsen, I thank you for your critique of my claim via Bohmian mechanics. Let me try to summarize your argument in terms of quantum mechanics with nonlocal hidden variables. We assume that each particle in each shared triplet comes with hidden instructions how to respond to possible measurements on the part of Alice, Bob and Jim. In the scenario of interest, Jim measures last. At an intermediate moment – after Alice and Bob have made their measurements – what is left of the nonlocal hidden variables are instructions to Jim’s particles regarding the result (±1) of each of his two possible measurements. Then when he measures what he measures, all he does is create facts in his own laboratory. Nothing retrocausal here, right?
I claim that this analysis is valid but not exhaustive. Here is a different analysis: Alice and Bob announce that they are about to perform the first absolutely loophole-free test of Bell’s inequality. To their laboratories flock physicists and journalists, who are given complete access to every last detail of the measurements and results. The same goes for Jim’s measurements, the results of which are available in real time. His only decision concerns what to measure on all his particles, i.e. whether Alice and Bob will succeed or fail. Of course, the success or failure of our efforts is often unpredictable. But if Alice and Bob succeed, they succeed, by all accounts, because they made their measurements on a mixture of entangled states, which they could later bin appropriately. And if they fail, they fail, by all accounts, because it is pointless to try to test Bell’s inequality on product states. The accounts in this case differ fundamentally from seemingly similar accounts in which we say, “In retrospect, if we had only known…” or “What made me believe that…”). Here it is not just new information or a new perspective that affects our account of the past, but incompatible facts (entangled states or product states) that depend on Jim’s later decision.
But – thanks to your analysis – I am considering whether my claim assumes a particular interpretation of quantum mechanics. See also my reply to Ken (next).
3. Dear Ken, I agree that Asher Peres had a different aim, but his thought-experiment suits me fine (as does the fact that it went from thought to laboratory).
You write that the apparent retrocausation disappears if we don’t think of “entanglement” as a state of reality. I prefer the safer terminology of preparation of a state and measurement of a state – what defines the state is its preparation. Then, regardless of interpretation, we can account for different results, confirming quantum predictions, obtained from measurements on one state or another. And then you write as follows: “I understand that you’re looking at Alice and Bob’s measurement outcomes, not the wavefunction, but in standard QM those outcomes result from the wavefunction, which is in turn unchanged by anything a future Jim might do.” It is precisely here that I disagree with you: Jim’s decision of what to measure is part of the preparation of the state that Alice and Bob measure!
I can already hear your objection: “No, it is Alice and Bob who prepare Jim’s state!” But that is a circumlocution when my way of putting it is apt. It will catch on. I am reminded of a beautiful NYT article about an evangelical Christian college that had constrained the teaching of evolutionary theory on its campus. The article ends with an interview with the president of the college, who is quoted as saying, “But this is Bryan College, and this is something that’s important to us. It’s in our DNA. It’s who we are.”
4. Dear Michael B. Heaney, I’m sorry that you didn’t spell out your comment at length. I understand that path integrals offer the possibility of imposing arbitrary initial and final boundary conditions, i.e. pre- and post-selection, which, in the approach of Yakir Aharonov et al., allows “weak” measurements to yield “weak” values. Backward (in addition to forward) causation emerges very naturally in this approach.
5. Dear David Miller, first, I thank you for your comment about physicists’ “grip on reality”!
In response to your questions: First, what my GHZ example has to add to EPRB steering is nonlocality, i.e. the possibility of testing Bell’s inequality. If all we have is EPRB steering, in which Jim measures in the future light cone of measurements already made on the systems paired with his, what is the case for retrocausality? I could only make what Travis rightly calls a “silly” claim. Second, DCES is…is…aha! Delayed Choice Entanglement Swapping! I suppose that Jim’s additional options in the DCES case would allow variations on my argument but would not add to nor detract from its essence. Third, my reply to Travis explains that the retrocausality I have in mind is not retrocorrelation (a good idea and a good word) – if it boils down to correlations, we are back to nonlocal hidden variables.
6. Dear Nathan, thank you (again) for your comments in the past and in the present. You wrote a sentence that needs lots of elaboration: “I do find it surprising that the exponential complexity issue is hardly ever brought up as another indication in this direction.” Who should elaborate it, if not you, and if not now, when?
With best wishes,