Date: Fall 2013
(While this references a previous question [see "Quantum Entanglement at Point of Creation," submitted by Eric in Spring 2013], I have an important new, but related, question. My question, in brief: Why is it never said that even instantaneous transmission of information cannot explain the EPR paradox, due to the relativity of simultaneity? This is _not_ addressed in the quoted submission.)
In discussions of the EPR paradox, it is often said the measurement of one particle "affects" the outcome of a later measurement of the other, even when the measurements are space-like, thereby appearing to violate special relativity. But how can one say that the measurement of particle A affects the outcome of the later measurement of particle B when there exists at least one reference frame in which the measurement of particle B actually _precedes_ the measurement of particle A! Thus there can be no cause and effect -- only the initial superposition of eigenstates and the final experimental outcome. (Yes, I know that relativity is not violated, as one cannot use the EPR experimental setup to transmit information faster than light between the experimenters.)
Why, then, do scientists bother to measure the speed at which the "information" travels? (See http://en.wikipedia.org/wiki/Quantum_entanglement, e.g.) The relativity of simultaneity of space-like events shows that there can be no cause and effect, _even if it is instantaneous_. (Well, I suppose you could say that there is "relative" cause and effect!)
Consequently, this is even "worse" than instantaneous cause and effect! Why have I never read anything about this aspect of the EPR paradox? Has this not yet been recognized by EPR scientists? This aspect makes the whole thing even more fascinating! (One might even say that it brings the spookiness to a whole new level.)
You can look for a limiting speed, but if one is found, how can you square that with special relativity? This would make this basically a test of special relativity itself.
I actually thought of this myself many years ago (and I have emails to prove it) and am finally bringing this up here. I did know that there is no initial state that can be the precursor of all possible outcomes of all possible combinations of measurements. The GHZ paradox makes this even more clear and fascinating!
Please let me take this in steps via analogies. There probably is a universal speed limit. We do not know what it is, it is not c, but it is most likely asymptotic.
For the time being, given the fact we are so much slower, c is pretty close. Instantaneous transfer is a whole different world from c!
Transfer approximately follows: Lim(t->infin) [ F(space-time relation@speed(t))/G(space-time relation@speed limit(t)) ~ 1. For space-time relationships the reciprocal is also true. These are profoundly oversimplified, they are more individualized through eigenstates expressed as energetic quanta.
Simplistically, a hand must shake another, instantaneously. Please consider a typical redox reaction in basic chemistry: one chemical is reduced as another is oxidized. There is no such thing as a chemical being oxidized: something must be reduced at the same time. Consider a ball rolling: the ball rolls East, but in terms of information, the felt of the billiard table must move West.
The eigenstates of matter and energy must move simultaneously and at a relative time frame. That is the key, a relative time frame. An approximation of the time constant for such instantaneous activity will give valuable clues to the universal speed limit and the rate(s) of change for eigenstates. Knowing that something took so long to get there may well lead to insight as to its original position.
Issac Newton predicted simultaneous geometric information transfer long before the EPR paradox was considered. Please refer: Newton, I. ; 1704; Tractatus de Quadratura Curvarum,. Here he discusses the use of the term "limits".
Hoping this helps; Peter E. Hughes, Ph.D. Milford, NH
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