Entangle 2 photons. 1 stays on earth, other to the moon. Measure: is the information simultaneously on the moon or does the theory of relativity apply here? What is the carrier of this information. Photons always move at the speed of light because they have no rest mass and mass can never go faster or equal to the speed of light.
Answer
According to all known theories, information never travels faster than light — although we don’t have a theory that puts everything together “nicely”, quantum theory and relativity theory are not contradictory. There are only cases where one does not know what to say, because things are not defined (eg in a black hole).
As for the entanglement:
Take entangled photons, in a state HH+VV (so either horizontal polarization on moon and Earth, or vertical on the two spots). When you measure on Earth, you get random H or V, and the same result on the Moon. However, the “sender of information” on Earth has no means of influencing whether he will get H or V by measuring, and thus no means of influencing what will be read by “the receiver” on the moon. Therefore, despite entanglement, he cannot send any information. This is just an example, but one can prove that it is generally impossible to send information purely through entanglement.
Answered by
prof.dr.ir. Alain Sarlette
control engineering, automation, robotics, dynamical systems, applied mathematics, quantum physics
http://www.ugent.be
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