Chapter 16: Faster-than-Light Implications of Quantum Entanglement and Nonlocality

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                                Notes by David A Roffman on Chapter 16 of

                                FRONTIERS IN PROPULSION SCIENCE

    Chapter by John G. Cramer, University of Washington, Seattle, Washington State


   Two particles are typically thought to be independent of one another, even if they emerged from the same event.  However, this is wrong, as the two particles still interact through quantum entanglement.  This at a distance connection is a principle known as nonlocality.  Einstein, Podolsky, and Rosen argued that nonlocal connections require faster than light travel (which is odd, since Einstein invented special relativity-this appears to be in direct conflict).  Their work was known as the EPR experiment/paper.  What must be unraveled is whether this concept is in nature only or can it be extended to manipulation?   

    Whatever happens to one photon must happen to the other.  Entanglement is typically the result of a conservation law within a system.  The Bell inequalities deal with topics in this area, when polarization is considered.  These demonstrate that semi classical, local, and hidden-variable theories are in conflict with standard quantum mechanics.  The EPR experiments have validated quantum mechanics, and have helped to refute the other theories.  When the inequalities were violated, this indicates that either parameter independence or outcome independence is broken.

    While outcome independence is evident in quantum formalism, parameter independence is not necessarily evident.  These will become important in “no-signal” theorems.  Results such as those in the EPR experiments lead to the conclusion (for some) that faster than light effects cannot be used for communication.  This is due to the claim that one change in a subsystem will not be apparent in another.  These are “proofs,” but they are not necessarily solid.  Nonlocal signaling will only be allowed if parameter independence is allowed.

     Nonlocal communication is not against special relativity.  Faster than light travel in special relativity is banned due to its intrinsic property of un-leveling the playing field for reference frames.  There can be no fixed simultaneous action (even for time traveling signals) as signals have no fixed set of timing or order.  Transmission and arrival cannot be synchronized, as both paths are delay-dependent variables.  Special relativity is maintained due to the light-like lines falling into place under than Lorentz invariance.

    If nonlocal signaling is possible, then causality is violated. There might be a universal reference frame, but nonlocal signaling cannot verify this. Einstein made an objection about quantum mechanics due to a gedanken (thought) experiment (which pertained to momentum domain). Nonlocal signaling (if possible) would most likely occur in Einstein’s original domain. A way of producing entangled photon pairs employs the optical process of spontaneous parametric down-conversion. This uses a laser to pump, and a nonlinear crystal to transform a photon into two photons, with components that add up to the original photon.

    A famous experiment in this area is the Shih group’s “ghost interference” experiment.  Vertically polarized photons that pass through a single or double slit produce interference.  There are some nonlocal signals, but this is not communication, because a classical communication link is used to impose coincidence upon the photons.  Coincidences are needed to preserve interference. It is still not known with certainty whether the coincidence requirement can be removed. Coherence and entanglement are important for nonlocal communication. However, an increase in one cuts down the other. A trade off point is being searched for to optimize the situation.

    To send a meaningful signal, binary code could be used.  Multiple photons would have to be sent in order to have progress in communication.  At least 10-100 photons would have to be sent.  This is very difficult, so maybe people could transmit signals in bursts. Signals could be received before they are sent if nonlocal communication is possible.

    If the previous situation occurs, a time loop could be created by resending the message back after it is received. If one sends a book script back in time years and the receiver publishes it, then the book was never written.  Information was sent, but in the new reality (the receiving end), the book wasn’t written, only received. This is a paradox. 

    Weinberg and Polchinski have published ideas that may allow the previous situation to work. Their work is detrimental for Copenhagen representation of a wave function as “observer knowledge.” Polchinski has shown that a small change (nonlinear) turns a hidden nonlocality of regular quantum mechanics into one that can be used for nonlocal communication.  Due to weak gravity and relatively flat space, quantum mechanics may be nonlinear. This effect may be very small.  More experiments are needed in this area. There is one experiment in progress that might produce a coincidence-free version of the ghost interference experiment. An important note is that quantum mechanics ignores gravity's curvature of space. That doesn't mean that one can't plug in gravitational potential. One can insert it into the Schrodinger equation, but the results are only an approximation.