Editing Time travel (section)

==== No-communication theorem ====
When a signal is sent from one location and received at another location, then as long as the signal is moving at the speed of light or slower, the mathematics of [[Relativity of simultaneity|simultaneity]] in the theory of relativity show that all reference frames agree that the transmission-event happened before the reception-event. When the signal travels faster than light, it is received ''before'' it is sent, in all reference frames.<ref name="Jarrell">{{cite web|url=http://www.physics.uc.edu/~jarrell/COURSES/ELECTRODYNAMICS/Chap11/chap11.pdf|title=The Special Theory of Relativity|access-date=October 27, 2006|last1=Jarrell|first1=Mark|pages=7–11|archive-url=https://web.archive.org/web/20060913173236/http://www.physics.uc.edu/~jarrell/COURSES/ELECTRODYNAMICS/Chap11/chap11.pdf <!-- Bot retrieved archive -->|archive-date=September 13, 2006}}</ref> The signal could be said to have moved backward in time. This hypothetical scenario is sometimes referred to as a [[tachyonic antitelephone]].<ref>{{cite journal|last=Kowalczyński|first=Jerzy|date=January 1984|title=Critical comments on the discussion about tachyonic causal paradoxes and on the concept of superluminal reference frame|journal=[[International Journal of Theoretical Physics]]|publisher=[[Springer Science+Business Media]]|volume=23|issue=1|pages=27–60|doi=10.1007/BF02080670|bibcode=1984IJTP...23...27K|s2cid=121316135}}</ref>

Quantum-mechanical phenomena such as [[quantum teleportation]], the [[EPR paradox]], or [[quantum entanglement]] might appear to create a mechanism that allows for faster-than-light (FTL) communication or time travel, and in fact some interpretations of quantum mechanics such as the [[Bohm interpretation]] presume that some information is being exchanged between particles instantaneously in order to maintain correlations between particles.<ref name="Bohm">{{cite web|url=http://plato.stanford.edu/entries/qm-bohm/|title=Bohmian Mechanics|date=March 27, 2017|access-date=April 26, 2017|last1=Goldstein|first1=Sheldon|archive-date=January 12, 2012|archive-url=https://web.archive.org/web/20120112030926/http://plato.stanford.edu/entries/qm-bohm/|url-status=live}}</ref> This effect was referred to as "[[action at a distance (physics)#spooky action at a distance|spooky action at a distance]]" by Einstein.

Nevertheless, the fact that causality is preserved in quantum mechanics is a rigorous result in modern [[Quantum field theory|quantum field theories]], and therefore modern theories do not allow for time travel or [[Superluminal communication|FTL communication]]. In any specific instance where FTL has been claimed, more detailed analysis has proven that to get a signal, some form of classical communication must also be used.<ref name="Nielsen and Chuang">{{cite book|last1=Nielsen|last2=Chuang|first1=Michael|first2=Isaac|title=Quantum Computation and Quantum Information|url=https://archive.org/details/quantumcomputati00niel_056|url-access=limited|publisher=Cambridge|year=2000|page=[https://archive.org/details/quantumcomputati00niel_056/page/n55 28]|isbn=978-0-521-63235-5}}</ref> The [[no-communication theorem]] also gives a general proof that quantum entanglement cannot be used to transmit information faster than classical signals.