Superluminal communication is a hypothetical process in which information is sent at faster-than-light (FTL) speeds. The current scientific consensus is that faster-than-light communication is not possible, and to date it has not been achieved in any experiment.
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Superluminal communication is believed to be impossible because, in a Lorentz-invariant theory, it could be used to transmit information into the past. This contradicts causality and leads to logical paradoxes.
A number of theories and phenomena related to superluminal communication have been proposed or studied, including tachyons, quantum nonlocality, and wormholes.
Tachyons
Tachyonic particles are hypothetical particles that travel faster than light. These would allow superluminal communication, and for this reason are widely believed not to exist. By contrast, tachyonic fields - quantum fields with imaginary mass - certainly do exist, and exhibit superluminal group velocity under some circumstances. However, such fields have luminal signal velocity and do not allow superluminal communication.
Quantum nonlocality
Quantum mechanics is non-local in the sense that distant systems can be entangled. Entangled states lead to correlations in the results of otherwise random measurements, even when the measurements are made nearly simultaneously and at far distant points. The impossibility of superluminal communication lead Einstein, Podolsky, and Rosen to propose that quantum mechanics must be incomplete (see EPR paradox).
However, it is now well-understood that quantum entanglement does not allow any influence or information to propagate superluminally. Technically, the microscopic causality postulate of axiomatic quantum field theory implies the impossibility of superluminal communication using any phenomena whose behavior can be described by orthodox quantum field theory. A special case of this is the no-communication theorem, which prevents communication using the quantum entanglement of a composite system shared between two spacelike-separated observers. Some authors have argued that using the no-communication theorem to deduce the impossibility of superluminal communication is circular, since the no-communication theorem assumes that the system is composite.
Wormholes
If wormholes are possible, then ordinary subluminal methods of communication could be sent through them to achieve superluminal transmission speeds. Considering the immense energy that current theories suggest would be required to open a wormhole large enough to pass spacecraft through, it may be that only atomic-scale wormholes would be practical to build, limiting their use solely to information transmission. Some hypotheses of wormhole formation would prevent them from ever becoming "timeholes", allowing superluminal communication without the additional complication of allowing communication with the past.