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I have read this question:

Does photon interference violate causality?

where S.Mcgrew says:

Edit 8/10/18 Bottom line: you're right that wave function collapse violates the principle of causality. The term "measurement problem" encompasses that issue. This article discusses the measurement problem, but does not provide clear explanations. This paper: dives into the philosophical aspects of various approaches to resolving the measurement problem, but is a difficult read. The frustration of trying to come up with an intuitively satisfying interpretation has led to the "stop worrying about it and just do the math" approach to quantum mechanics -- which works, but doesn't fulfill our desire to understand what the math means. End edit

How does electron spin change instantaneously without violating inertia principle?

where Jasper says:

Most importantly, it is important to realize that instantaneous is meaningless in QM, since this can never be accurately determined. To determine a change in a system requires two measurements, which themselves take time to complete. In this way it is impossible to say when things "exactly" occurred. That being said, in QM you can determine the time-scale over which the dynamics occurs.

Now causality is where a process (cause) that contributes to another process, an effect. Causes all lie in the past, and effects in the future.

https://en.wikipedia.org/wiki/Causality

Now I suppose that wavefunction collapse is when a wave function (in a superposition), appears to reduce to a single eigenstate, due to interaction with the external world (observation).

https://en.wikipedia.org/wiki/Wave_function_collapse

Now I have not found why wave function collapse (that is, apparent reduction to a single eigenstate) would violate causality.

Question:

  1. Why does wave function collapse violate causality?
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  • $\begingroup$ Causality prohibits you from interacting with Nature faster than light, but Nature may interact with itself at any speed. Even if a wavefunction collapses everywhere at once, you still could not use this to send signals faster than light. So the causality is preserved. $\endgroup$ – safesphere Jun 27 at 21:39
  • $\begingroup$ "Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true." - Bertrand Russell $\endgroup$ – Michael Walsby Jun 27 at 21:55
  • $\begingroup$ @MichaelWalsby This is very true and there are many cases in physics where math is taken beyond the physical reality (e.g. wormholes). However, specifically in QM, as related to this question, the math actually works fine predicting valid results. The problem is with understanding them. There are 20 some different interpretations of QM, but all of them refer to exactly the same math. $\endgroup$ – safesphere Jun 27 at 23:27
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Collapse of wave function (if real) does not violate causality (cause and effect relationship) in its most basic form. But it does violate the speed limit of transmission of the effect of the cause. This speed limit is c and is set in theory of relativity.

If causality in its basic form is violated, that will be end of experimental science. Because, then we can not rely on any scientific experiment. All scientific experiments are - if you do this, then that will happen. Meaning all experimental science is based upon causality.

Collapse of wave function puts speed of causality into question, not causality itself.

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    $\begingroup$ Faster-than-light transfers of information and violations of causality are synonymous in special relativity. By claiming that one holds but not the other, you're essentially claiming that special relativity does not hold for this process. Care to comment on the specifics of your claim? $\endgroup$ – Emilio Pisanty Jun 28 at 10:10
  • $\begingroup$ @EmilioPisanty: I did not say FTL transmission of info, I said FTL transmission of effect. You are considering only SR definition of causality when you say the two are synonymous. Classical definition does not consider speed. Yes, FTL transmission of info violates SR, and that is why all this discussion and historical mystery around entanglement. But in this case we have settled to not call it FTL transmission of info. But considering collapse as real, we can not deny FTL transmission of effect of the cause. We can not use it as information, but nature has to. $\endgroup$ – kpv Jun 28 at 16:01

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