Abstract
Bell’s theorem implies that any completion of quantum mechanics which uses hidden variables (that is, preexisting values of all observables) must be nonlocal in the Einstein sense. This customarily indicates that knowledge of the hidden variables would permit superluminal communication. Such superluminal signaling, akin to the existence of a preferred reference frame, is to be expected. However, here we provide a protocol that allows an observer with knowledge of the hidden variables to communicate with her own causal past, without superluminal signaling. That is, such knowledge would contradict causality, irrespectively of the validity of relativity theory. Among the ways we propose for bypassing the paradox there is the possibility of hidden variables that change their values even when the state does not, and that means that signaling backwards in time is prohibited in Bohmian mechanics.
Highlights
In this paper, we provide a protocol that allows any party with knowledge of quantum hidden variables [1,2,3] to communicate to her own past, leading to a breakdown of causality in the strong sense
All interpretations of quantum mechanics that rely on hidden variables, such as the de Broglie–Bohm theory [28], have some kind of censorship mechanism which prevents the revelation of the values of the hidden variables in practice, e.g., see [34]
Previous investigations on whether Bohmian mechanics implies change of the past hidden variables in the context of quantum erasure concluded that “there is no change of the past whatsoever” [35]
Summary
We provide a protocol that allows any party with knowledge of quantum hidden variables [1,2,3] to communicate to her own past, leading to a breakdown of causality in the strong sense. The three hypotheses (i) “special relativity”, (ii) “weak causality” (a cause temporally precedes an effect) and (iii) “superluminal signaling” lead to a contradiction: either one has to drop causality (namely, Alice walks free), or one has to drop superluminal signaling (these projectiles do not exist), or one has to drop special relativity. We show that knowledge of contextual hidden variables enables Backwards-In-Time Signaling (BITS) This is a stronger statement as is evident from the observation that Newtonian mechanics is a theory that does allow superluminal communication but does not allow any communication with one’s own past. In Bohmian Mechanics spin hidden variables do not exist, and the only hidden variables are the positions of particles [23], we show below in which sense our argument applies to this case
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