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Jon_Trevathan
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What would happen if adiabatic processes were applied in the context of a long-distance EPR Experiment? As background for my questions, see http://en.wikipedia.org/wiki/EPR_paradox" )
In the context of the foregoing, please visualize two particles that are http://en.wikipedia.org/wiki/Quantum_entanglement" ) At some distance from their common origin, Alice measures the spin of one of the particles and finds that the spin is in the up direction. If Bob were then to measure the spin of the second particle, he will find that its spin is in the down direction. As often as Alice and Bob wish to repeat this experiment, Bob will find that the spin of his particle is always opposite to that found by Alice.
Now, my specific question:
What would happen if Alice, instead of conducting an ideal measurement, adiabatically imposes a direction of spin on her particle?
Aharonov and Rohrlich in their book "Quantum Paradoxes: Quantum Theory for the Perplexed" provided the following introductory description to this concept:
"How do we eliminate quantum jumping? Consider a closed system in an eigenstate of Hf, a Hamiltonian with discrete, nondegenerate eigenvalues. If Hf does not depend on time, the system never jumps to another state. What if Hf does depend on time? It can depend on time. If we prepare the system in an eigenstate of Hf, and Hf changes quickly, the system may jump to another state. But let Hf change adiabatically (slowly); if Hf changes slowly enough, the system never jumps to another state. Instead of jumping, it adjusts itself to the changing Hamiltonian. The system behaves like a heavy weight hanging on a thin string. Pull the string quickly - it snaps and the weight falls. Pull the string slowly - the weight comes up with it." (See also the “http://en.wikipedia.org/wiki/Adiabatic_theorem" ”).
Based on the foregoing, what happens if Alice adiabatically imposes the up direction of spin on her particle? Is it permissible to assume that the spin of Alice's particle will, at the end of this adiabatic process, always be found to be in the up direction when her ideal measurement is eventually made? If so, what would happen if intermittent ideal measurements be conducted on Alice’s particle as the adiabatic processes are applied? Would also be permissible to assume that the probability of finding the spin of Alice’s particle to be in the up direction would gradually increase? If so, could we also assume that Alice’s findings would directly correlate with the duration of the adiabatic processes that Alice applies prior to each of her intermediate ideal measurements?
Are my assumptions reasonable to this point? If so, let’s now consider Bob’s particle. We know that Bob's particle was entangled with Alice's particle and, because of this entanglement; the spin of Bob's particle will (due to conservation of angular momentum) always be opposite to that found after Alice’s particle is measured. We also know that the purpose of an adiabatic process is to effect change without causing a state change. Accordingly, is it permissible to assume that at the end the adiabatic process that Alice uses to cause her particle to spin in the up direction, that Bob’s particle will still be entangled with Alice’s particle? If so, would it then be reasonable to assume that, for the same axes, the spin of Bob’s particle would always be in the down direction when Bob’s measurement is eventually made?
If so, we might then ask: what would happen if Alice never makes an ideal measurement? Must Alice conduct an ideal measurement on her particle in order to “cause” the spin of Bob’s particle to be in the down direction when his measurement is made? It is my conjecture that such an ideal measurement by Alice is not required. If there is any flaw in my logic or the applicable physics to this point, please help me identify it.
Previously, I speculated that the probability of finding the spin of Alice’s particle to be in the up direction would gradually increase as a function of the intensity and duration of the adiabatic processes that Alice applied prior to Alice making certain intermediate ideal measurements. In this context, we must again consider what happens to Bob’s particle. Here, as an extension of the foregoing, I would speculate, again assuming Bob’s particle has remained entangled with Alice’s particle, that any increase in the probability of finding the spin of Alice’s particle to be in the up direction would cause a corresponding increase in the probability of finding the spin of Bob's particle to be in the down direction; and that this finding would occur whether or not any ideal measurements were ever conducted by Alice on her particles. Your thoughts on this conjecture would be valued
I have not yet found any experiment that even touch on these conjectures. Is anyone aware of any studies that I may have missed? If relevant experiments have not occurred, is there some reason that such experiments could not be made? If such experiments are not otherwise precluded, could the 18km EPR experiment described below be adopted for this purpose?
In a paper titled “Space-like Separation in a Bell Test assuming Gravitationally Induced Collapses” (See: http://arxiv.org/PS_cache/arxiv/pdf/0803/0803.2425v1.pdf" ) D. Salart et. al describes a Franson-type test of the Bell inequalities is described where “pairs of entangled photons traveling through optical fibers are sent to two receiving stations physically separated by 18 km with the source at the center”. According to the paper’s authors, 18km established a new distance record for this type of experiment. The paper concludes that “under the assumption that a quantum measurement is finished only once a gravity-induced state reduction has occurred, none of the many former Bell experiments involve space-like separation, that is space-like separation from the time the particle (here photons) enter their measuring apparatuses (here interferometers) until the time the measurement is finished. In this sense, our experiment is the first one with true space-like separation. The results confirm the nonlocal nature of quantum correlations.” It is not my desire to contest or defend the conclusions of this paper.
However, I would very much like to know whether an experiment might be designed utilizing Salart’s 18km experimental setup wherein one of the photons would be adiabatically polarized. Can this be done?
https://www.physicsforums.com/member.php?u=23900"’s responding post seems to imply that, because the adiabatically manipulated photon would become increasingly entangled with the environmental means employed to alter its spin, the spin correlation between Alice’s and Bob’s photons, that in the EPE context has been found following Alice’s or Bob’s an ideal measurement, might be lost. I hope readers will comment on both Billy T’s and vanesch’s conjectures.
In any event, I hope there will be some agreement that some test involving adiabatic manipulations in an EPR experiment might generate some interesting science. If so, how might this adiabatic polarization process be performed? Should it or should it not be done in the context of the 18km experiment described above? Is any reader aware of experimenters with the requisite capacity and potential interest? Any speculations on any of the above that anyone might wish to share would be very much appreciated.
Thank you,
Jon Trevathan
In the context of the foregoing, please visualize two particles that are http://en.wikipedia.org/wiki/Quantum_entanglement" ) At some distance from their common origin, Alice measures the spin of one of the particles and finds that the spin is in the up direction. If Bob were then to measure the spin of the second particle, he will find that its spin is in the down direction. As often as Alice and Bob wish to repeat this experiment, Bob will find that the spin of his particle is always opposite to that found by Alice.
Now, my specific question:
What would happen if Alice, instead of conducting an ideal measurement, adiabatically imposes a direction of spin on her particle?
Aharonov and Rohrlich in their book "Quantum Paradoxes: Quantum Theory for the Perplexed" provided the following introductory description to this concept:
"How do we eliminate quantum jumping? Consider a closed system in an eigenstate of Hf, a Hamiltonian with discrete, nondegenerate eigenvalues. If Hf does not depend on time, the system never jumps to another state. What if Hf does depend on time? It can depend on time. If we prepare the system in an eigenstate of Hf, and Hf changes quickly, the system may jump to another state. But let Hf change adiabatically (slowly); if Hf changes slowly enough, the system never jumps to another state. Instead of jumping, it adjusts itself to the changing Hamiltonian. The system behaves like a heavy weight hanging on a thin string. Pull the string quickly - it snaps and the weight falls. Pull the string slowly - the weight comes up with it." (See also the “http://en.wikipedia.org/wiki/Adiabatic_theorem" ”).
Based on the foregoing, what happens if Alice adiabatically imposes the up direction of spin on her particle? Is it permissible to assume that the spin of Alice's particle will, at the end of this adiabatic process, always be found to be in the up direction when her ideal measurement is eventually made? If so, what would happen if intermittent ideal measurements be conducted on Alice’s particle as the adiabatic processes are applied? Would also be permissible to assume that the probability of finding the spin of Alice’s particle to be in the up direction would gradually increase? If so, could we also assume that Alice’s findings would directly correlate with the duration of the adiabatic processes that Alice applies prior to each of her intermediate ideal measurements?
Are my assumptions reasonable to this point? If so, let’s now consider Bob’s particle. We know that Bob's particle was entangled with Alice's particle and, because of this entanglement; the spin of Bob's particle will (due to conservation of angular momentum) always be opposite to that found after Alice’s particle is measured. We also know that the purpose of an adiabatic process is to effect change without causing a state change. Accordingly, is it permissible to assume that at the end the adiabatic process that Alice uses to cause her particle to spin in the up direction, that Bob’s particle will still be entangled with Alice’s particle? If so, would it then be reasonable to assume that, for the same axes, the spin of Bob’s particle would always be in the down direction when Bob’s measurement is eventually made?
If so, we might then ask: what would happen if Alice never makes an ideal measurement? Must Alice conduct an ideal measurement on her particle in order to “cause” the spin of Bob’s particle to be in the down direction when his measurement is made? It is my conjecture that such an ideal measurement by Alice is not required. If there is any flaw in my logic or the applicable physics to this point, please help me identify it.
Previously, I speculated that the probability of finding the spin of Alice’s particle to be in the up direction would gradually increase as a function of the intensity and duration of the adiabatic processes that Alice applied prior to Alice making certain intermediate ideal measurements. In this context, we must again consider what happens to Bob’s particle. Here, as an extension of the foregoing, I would speculate, again assuming Bob’s particle has remained entangled with Alice’s particle, that any increase in the probability of finding the spin of Alice’s particle to be in the up direction would cause a corresponding increase in the probability of finding the spin of Bob's particle to be in the down direction; and that this finding would occur whether or not any ideal measurements were ever conducted by Alice on her particles. Your thoughts on this conjecture would be valued
I have not yet found any experiment that even touch on these conjectures. Is anyone aware of any studies that I may have missed? If relevant experiments have not occurred, is there some reason that such experiments could not be made? If such experiments are not otherwise precluded, could the 18km EPR experiment described below be adopted for this purpose?
In a paper titled “Space-like Separation in a Bell Test assuming Gravitationally Induced Collapses” (See: http://arxiv.org/PS_cache/arxiv/pdf/0803/0803.2425v1.pdf" ) D. Salart et. al describes a Franson-type test of the Bell inequalities is described where “pairs of entangled photons traveling through optical fibers are sent to two receiving stations physically separated by 18 km with the source at the center”. According to the paper’s authors, 18km established a new distance record for this type of experiment. The paper concludes that “under the assumption that a quantum measurement is finished only once a gravity-induced state reduction has occurred, none of the many former Bell experiments involve space-like separation, that is space-like separation from the time the particle (here photons) enter their measuring apparatuses (here interferometers) until the time the measurement is finished. In this sense, our experiment is the first one with true space-like separation. The results confirm the nonlocal nature of quantum correlations.” It is not my desire to contest or defend the conclusions of this paper.
However, I would very much like to know whether an experiment might be designed utilizing Salart’s 18km experimental setup wherein one of the photons would be adiabatically polarized. Can this be done?
https://www.physicsforums.com/member.php?u=23900"’s responding post seems to imply that, because the adiabatically manipulated photon would become increasingly entangled with the environmental means employed to alter its spin, the spin correlation between Alice’s and Bob’s photons, that in the EPE context has been found following Alice’s or Bob’s an ideal measurement, might be lost. I hope readers will comment on both Billy T’s and vanesch’s conjectures.
In any event, I hope there will be some agreement that some test involving adiabatic manipulations in an EPR experiment might generate some interesting science. If so, how might this adiabatic polarization process be performed? Should it or should it not be done in the context of the 18km experiment described above? Is any reader aware of experimenters with the requisite capacity and potential interest? Any speculations on any of the above that anyone might wish to share would be very much appreciated.
Thank you,
Jon Trevathan
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