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I have a simple question regarding the law of causality. Is there any phenomenon or process in physics that does not obey the principle of causality? Such a phenomenon doesn't have to be deterministic.

Amit
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Luxdragon
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    No, it would violate the principle of relativity and that would be huge. The closest you get is with virtual processes in quantum mechanics: these can be thought to be particles out of shell but they still cant communicate any information. – FriendlyLagrangian Jun 12 '23 at 08:53
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    Some would argue that the "delayed-choice quantum eraser" experiment violates causality in the sense that causation appears to work backward in time. For a basic description, see https://en.wikipedia.org/wiki/Delayed-choice_quantum_eraser – Andrew Jun 12 '23 at 11:06
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    @Andrew ""some would argue" incorrectly" would be a better description, as is explained clearly in the wiki article you quote. – Oбжорoв Jun 12 '23 at 12:07
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    Really, how would we know? I suppose at one time, something like radioactive decay seemed to violate causality, when the cause was not understood... – Amit Jun 12 '23 at 13:49

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As far as we know, up to now, there is no evidence of violation of causality in physics. I.e., there is no way to transmit physical information between regions of the spacetime which cannot be connected by causal curves: causally separated aka spatially separated regions.

QM seems to imply some causality violation in view of the collapse postulate of the state during measurements, when one assumes the standard Copenhagen (in Bohr's view) intepretation of the formalism.

However, it is disputable if the collapse really instantaneously takes place and, in general, if it is a completely physical phenomenon. See in particular the well known analysis by Hellwig and Kraus.

What it is nowaday not disputable is the existence of correlations between the outcomes of the measurements produced at causally separated regions of the spacetime in Bell-like experiments. It is not possible to explain these correlations in terms of a common cause if assuming a realism hypothesis (the outcomes already exist before the measurement). Local Realism (in Legget's view) is nowadays untenable as a consequence of that empirical evidence.

However, due to the intrinsic randomness of QT, one cannot exploit these non-local correlations to transmit information in order to violate causality. So the issue is quite subtle.

Valter Moretti
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  • So quantum mechanics is causal but not deterministic? – Luxdragon Jun 12 '23 at 12:12
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    It is just matter of jargon. The substance is the one illustrated above: there are non-local correlations of outcomes of measurments between causally separated regions, this is an observed fact, predicted by QT. There is no way to transmit information between two causally separated regions of the spacetime: this is a theoretical result of QT. There is no evidence in experiments of the failure of this last theoretical result. – Valter Moretti Jun 12 '23 at 12:17
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    @Luxdragon Quantum mechanics is a theory of ensembles. The state changes of the ensemble states are fully causal. The individual measurement on a single system is uncertain. I would be careful with the word "non-deterministic" because it implies "random", at least to the casual listener. If you want to measure a quantum with a certain angular momentum "here" that automatically implies that there has to be a quantum with an opposite angular momentum somewhere else. It was like that already in classical mechanics, we could simply ignore the consequences in the classical case. – FlatterMann Jun 12 '23 at 16:38
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Orthodox quantum mechanics appears to have events that are uncaused in a fairly strong sense. When a measurement is done of a quantum state in a superposition there are theorems showing that the result is logically independent of the other information in the state (Paterek et al. 2010). That is, the information needed to predict the outcome is not in the state (and people generally disfavour hidden variable theories needed to fake this, due to Bell's theorem and its experimental tests).

Anders Sandberg
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Wavefunction collapse in a pair of entangled particles which are separated at a distance $\ell$, in case one of the particles state is measured,- happens instantly in the other particle as well, and not after time $t=\ell/c$. This is not a full breakdown of causality, because the effect of the measurement does not happen before the measurement itself. But if both wavefunction collapse events in entangled particles $A$ and $B$ happens at the same "now" and not in the future light cone of one of particles, then certainly we can call this weak "breakdown" of causality principle, because it violates local realism. Einstein doesn't like it either, that's why he called it "spooky action at a distance". But... no matter we like how nature behaves or not,- it is as it is.

Agnius Vasiliauskas
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    It really doesn't break causality since the collapse do not transmit information. Causality regards information and entanglement does not propagate information faster than light. It's a "spread" state, or non local state, but it certainly does not break causality, as proven by experiments of this year nobel prizes. – LolloBoldo Jun 12 '23 at 10:02
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    It is disputable if the collapse really istantaneously takes place and, in general, if it is a physical phenomenon. What it is not disputable is the existence of correlations between the outcomes of the measurements produced at causally separated regions of the spacetime. However one cannot exploit these non-local correlations to transmit information in order to violate causality. So the issue is quite subtle. – Valter Moretti Jun 12 '23 at 10:02
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    @LolloBoldo Did you see my softening term "weak" before "causality break" ? Sure it does not break it, as it would require effect to happen first, before the cause. But it does break down local realism, because two events are not bound by distance. – Agnius Vasiliauskas Jun 12 '23 at 11:02
  • @ValterMoretti If some correlations exists between measurement outcomes at causally separated regions, then this means that local realism is violated. IMHO, this violation is just by "slight bit" further from a full-scale causality breakdown, because IF these correlations are instant, then neither event in $A,B$ particle can be identified as "cause" or "effect". But I agree that at first we need a firm proof that indeed this collapse IS instant. – Agnius Vasiliauskas Jun 12 '23 at 11:52
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    @Agnius Vasiliauskas Indeed we know that local realism is violated (failure of the CHSH-Bell inequalities). But it does not mean that causality is violated: We cannot transmit physical information outside the light cone through the known phenomenology up to now, including phenomena related to the failure of Bell's inequality. My (recent) opinion is that the collapse is subjective and it is not a physical process. This viewpoint is consistent when one assumes that QT's predictions are only about ensembles. However the situation is very intricate. – Valter Moretti Jun 12 '23 at 12:03
  • @AgniusVasiliauskas yes, local realism is violated, but it has nothing to do with causality. Locality is not causality – LolloBoldo Jun 12 '23 at 12:14
  • @ValterMoretti It depends what QM interpretation you prefer. Some QM interpretations allows wavefunction collapse, some - not. As far as I know all QM interpretations are equal,- i.e. there are no slightest proofs which interpretations are "more real" and why. So there are a lot of stuff in QM which must be clarified further. Not so simple. – Agnius Vasiliauskas Jun 12 '23 at 12:20
  • @ Agnius Vasiliauskas Yes I agree... – Valter Moretti Jun 12 '23 at 12:21
  • @LolloBoldo yes, local realism is violated, but it has nothing to do with causality I do not agree. "violation of local realism" is just another way to say that some events are not causally related, i,.e. they can't be each other's cause and effect. Hence, it is related to causality in one way or another. Otherwise, why do you think Einstein named it "spooky action at a distance" ? You can't have causality+non-locality, unless you re-define causality from a new, which QM probably tries to do, because it's more or less in conflict with relativity (see Quantum gravity, best proof of this). – Agnius Vasiliauskas Jun 12 '23 at 12:59
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    I depends on what you actually define causality to be i guess. I was thought that causality is the phenomen which dictates the direction in which information is transmitted. So, with the definition i qas thought, locality has nothing to do with information transmission from point to point – LolloBoldo Jun 12 '23 at 13:59
  • @AgniusVasiliauskas I don't see a conflict with relativity here. The usual implementation of quantum entanglement experiments uses angular momentum, which depends on the isotropy of spacetime, not on relativity. What is worse, whenever we actually want to measure something, we have to explicitly break relativity, isotropy and homogeneity. The loss of those symmetries is a necessary requirement to have a "detector". – FlatterMann Jun 12 '23 at 17:20