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arXiv:quant-ph/0301100

Superluminality in Quantum Theory

Giovanni Andrea Fantasia

Published Jan 20, 2003• 0 citations
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Abstract

In the present work we investigate the possibility of superluminal information transmission in quantum theory. We give simple and general arguments to prove that the general structure (Hilbert's space plus instantaneous state reduction) of the theory allows the existence of superluminal communication. We discuss how this relates with existing no-signalling theorems.

DOI
10.48550/arxiv.quant-ph/0301100

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In the present work we investigate the possibility of superluminal information transmission in quantum theory. We give simple and general arguments to prove that the general structure (Hilbert's space plus instantaneous state reduction) of the theory allows the existence of superluminal communication. We discuss how this relates with existing no-signalling theorems.
It is a frequent assumption that—via superluminal information transfers—superluminal signals capable of enabling communication are necessarily exchanged in any quantum theory that posits hidden superluminal influences. However, does the presence of hidden superluminal influences automatically imply superluminal signalling and communication? The non-signalling theorem mediates the apparent conflict between quantum mechanics and the theory of special relativity. However, as a ‘no-go’ theorem there exist two opposing interpretations of the non-signalling constraint: foundational and operational. Concerning Bell’s theorem, we argue that Bell employed both interpretations, and that he finally adopted the operational position which is associated often with ontological quantum theory, e.g., de Broglie–Bohm theory. This position we refer to as “effective non-signalling”. By contrast, associated with orthodox quantum mechanics is the foundational position referred to here as “axiomatic non-signalling”. In search of a decisive communication-theoretic criterion for differentiating between “axiomatic” and “effective” non-signalling, we employ the operational framework offered by Shannon’s mathematical theory of communication, whereby we distinguish between Shannon signals and non-Shannon signals. We find that an effective non-signalling theorem represents two sub-theorems: (1) Non-transfer-control (NTC) theorem, and (2) Non-signification-control (NSC) theorem. Employing NTC and NSC theorems, we report that effective, instead of axiomatic, non-signalling is entirely sufficient for prohibiting nonlocal communication. Effective non-signalling prevents the instantaneous, i.e., superluminal, transfer of message-encoded information through the controlled use—by a sender-receiver pair —of informationally-correlated detection events, e.g., in EPR-type experiments. An effective non-signalling theorem allows for nonlocal quantum information transfer yet—at the same time—effectively denies superluminal signalling and communication.
Since Bell's theorem, it is known that quantum correlations cannot be described by local variables (LV) alone: if one does not want to abandon classical mechanisms for correlations, a superluminal form of communication among the particles must be postulated. A natural question is whether such a postulate would imply the possibility of superluminal signaling. Here we show that the assumption of finite-speed superluminal communication indeed leads to signaling when no LV are present, and more generally when only LV derivable from quantum statistics are allowed. When the most general LV are allowed, we prove in a specific case that the model can be made again consistent with relativity, but the question remains open in general.
Based on quantum entanglement and corresponding quantum communication, first we research a simple superluminal entangled communication scheme, whose key is to establish two mutually entangled particles or devices A and B. We observe and control the information of A position, then can know the corresponding results of the other B. This is not to send directly information each other. It may be superluminal. Next, in special relativity we provided that there are necessarily two symmetrical topological structures separated by the light-cone, which includes the generalized Lorentz transformation (GLT) for the spacelike interval, in which phase velocity is superluminal. This complete special relativity is base of this scheme, and should agree and test GLT. Further, it may be developed to the extensive special relativity, in which only
In a compound quantum system with EPR–like correlations a measurement of one subsystem induces instantaneously changes of the other subsystem, irrespective of the relative distance of the two subsystems. We consider several arguments which were put forward in recent years in order to show that these nonlocal effects cannot be used for superluminal communication. It turns out that the arguments mentioned above are merely plausible but not really stringent and convincing. This means that the question in the title of this paper is still open.