Editing Faster-than-light (section)

==Superluminal communication==
{{Main|Superluminal communication}}
Faster-than-light communication is, according to relativity, equivalent to [[time travel]]. What we measure as the [[speed of light]] in vacuum (or near vacuum) is actually the fundamental physical constant ''c''. This means that all [[inertial]] and, for the coordinate speed of light, non-inertial observers, regardless of their relative [[velocity]], will always measure zero-mass particles such as [[photon]]s traveling at ''c'' in vacuum. This result means that measurements of time and velocity in different frames are no longer related simply by constant shifts, but are instead related by [[Poincaré transformation]]s. These transformations have important implications:
*The relativistic momentum of a [[mass]]ive particle would increase with speed in such a way that at the speed of light an object would have infinite momentum.
*To accelerate an object of non-zero [[mass in special relativity|rest mass]] to ''c'' would require infinite time with any finite acceleration, or infinite acceleration for a finite amount of time.
*Either way, such acceleration requires infinite energy.
*Some observers with sub-light relative motion will disagree about which occurs first of any two events that are separated by a [[spacetime interval|space-like interval]].<ref>
{{cite book
|last=Einstein |first=A.
|year=1927
|title=Relativity:the special and the general theory
|publisher=Methuen & Co
|pages=25–27
}}</ref> In other words, any travel that is faster-than-light will be seen as traveling backwards in time in some other, equally valid, frames of reference,<ref>
{{cite web
|last=Odenwald |first=S.
|title=If we could travel faster than light, could we go back in time?
|url=http://einstein.stanford.edu/content/relativity/q295.html
|work=NASA Astronomy Café
|access-date=7 April 2014
}}</ref> or need to assume the speculative hypothesis of possible Lorentz violations at a presently unobserved scale (for instance the Planck scale).{{Citation needed|date=March 2013}} Therefore, any theory which permits "true" FTL also has to cope with [[time travel]] and all its associated paradoxes,<ref>
{{cite book
|last=Gott |first=J. R.
|year=2002
|title=Time Travel in Einstein's Universe
|pages=82–83
|publisher=[[Mariner Books]]
|isbn=978-0618257355
}}</ref> or else to assume the [[Lorentz invariance]] to be a symmetry of thermodynamical statistical nature (hence a symmetry broken at some presently unobserved scale).
*In special relativity the coordinate speed of light is only guaranteed to be ''c'' in an [[inertial frame of reference|inertial frame]]; in a non-inertial frame the coordinate speed may be different from ''c''.<ref>
{{cite book
|last=Petkov |first=V.
|year=2009
|title=Relativity and the Nature of Spacetime
|url=https://books.google.com/books?id=AzfFo6A94WEC&pg=PA219
|page=219
|publisher=[[Springer Science & Business Media]]
|isbn=978-3642019623
}}</ref> In general relativity no coordinate system on a large region of curved spacetime is "inertial", so it is permissible to use a global coordinate system where objects travel faster than ''c'', but in the local neighborhood of any point in curved spacetime we can define a "local inertial frame" and the local speed of light will be ''c'' in this frame,<ref>
{{cite book
|last1=Raine |first1=D. J.
|last2=Thomas |first2=E. G.
|year=2001
|title=An Introduction to the Science of Cosmology
|url=https://books.google.com/books?id=RK8qDGKSTPwC&pg=PA94
|page=94
|publisher=[[CRC Press]]
|isbn=978-0750304054
}}</ref> with massive objects moving through this local neighborhood always having a speed less than ''c'' in the local inertial frame.