very new here - first question in fact.

So, don't be fooled by the title of my question. I understand that the Bell Paradox - and non-locality - prevents information being exchanged in a faster than light matter.

So, Spaceman A on Neptune, cannot send a morse-coded message to Earth using quantum entangled particles - the need to force a particle to choose a state releases the entangled particle at the other end from behaving (instantaneously) in a determined matter. Information from Spaceman A cannot be sent from Neptune to Earth at faster than light.

But - my question is - who cares about spaceman - or any conscious entity sending information - -the fact is the entangled particles themselves are affected at faster than light speed. Particle A observed on Neptune at midday will have the same state of spin as Particle B observed at an equal time on Earth. The observation and confirmation of the fact takes place retrospectively - but this doesn't detract from the fact that the wavefunction will be demonstrated to have collapsed simultaneously across a vast distance - something is acting on them at faster than light speed.

Any thoughts, or comments to explain why this is wrong, greatfully recieved !!

  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$ – ACuriousMind Dec 22 '17 at 23:36

You are attempting to compare the "velocity" of the wave function to the velocity of light, but these two velocities are not even measured in the same units, so it makes no sense to even ask which is greater.

More precisely: The wave function moves through some (projectivized) Hilbert space. A light beam moves through physical space (or more precisely, from some observer's point of view, through a particular spacelike submanifold of spacetime). You can measure the rate at which the light beam moves in meters per second. You can, if you want (though it's not clear why you'd want to) measure the rate at which the wave function moves as a distance in Hilbert space divided by a change in time. Distances in Hilbert space are not measured in meters.

  • $\begingroup$ If the wave function does not move through the real space, then what defines the probability of detecting a particle in a point of the real space? And what waves interfere in real space in a double slit experiment? $\endgroup$ – safesphere Dec 22 '17 at 4:10
  • $\begingroup$ @safesphere: At time $0$, the wave function is $U\otimes U+D\otimes D$. At time $1$, following an observation on the first particle, the wave function is at $U\otimes U$. How many meters did the wave function travel? $\endgroup$ – WillO Dec 22 '17 at 5:52
  • $\begingroup$ When a photon travels 1 meter from the slits to the screen, I believe its wave function travels approximately 1 meter with the speed of light as in meters per second. No? $\endgroup$ – safesphere Dec 22 '17 at 7:23
  • $\begingroup$ I think I may see what you mean. You seem to be saying that the wave function does not travel from one entangled particle to the other at the moment of observation. Of course it doesn't. The wave function travels with the particle (or rather vice versa), but not between two particles. In your example it simply changes in both places at the same time. $\endgroup$ – safesphere Dec 22 '17 at 7:28
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    $\begingroup$ @safesphere: No, actually I'm saying what I said, not what you said I seem to be saying. The wave function does not (and can not) "travel with the particle" because they travel in different spaces. By analogy: Can a particle's momentum change faster than the speed of light? Answer: The question makes no sense, because a change in momentum and a speed are measured in different units. A particle moves through a space $S$; its momentum moves through a different space $T_*S$. And its quantum state moves through yet another different space $H$. $\endgroup$ – WillO Dec 22 '17 at 13:45

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