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Anamitra
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We consider a typical version of the EPR paradox where an electron and a positron are produced collinearly in the +y and -y with the spins polarized in the positive and negative z directions. The pair is emitted with zero linear and zero spin-angular momentum.
If the positron is detected in the spin state -1/2 the electron has to be in the state +1/2 no matter what be the distance between them.
Now let the spin of the positron change to +1/2. This change is some sort of a random change. But what is a random change? Is it something that occurs without a stimulus or is it something in response to some SIGNAL.One may consider signals responsible for such changes.These signals may be of "internal" or "external" origin. In our case we have an isolated two-particle system. Of course we have our interacting detector[we assume a pair of detectors for the two particles]
I am assuming that the change in spin of the first particle is due to some signal from the second one coupled with the interaction from the detector which may be represented by a separate signal. So the second particle while releasing the signal had an estimate of the type of change it might induce on the first one[and the expected time for that change] even if it is a large distance from it! With such considerations we can always devise signal models of the EPR paradox consistent with Special Relativity .
An example:
We have two particles A and B and a pair of detectors to measure their spin values.
There is a change in the spin value of A,as observed by the detector.
Reason: Signal from B+Internal Signal of A+Detector Interaction[which may be represented by another signal]
As the particles separate after their creation, each is assumed to be continuously influenced by signals emitted by the other. So the presence of the signal from B[and acting on A] is mandatory for all instants.
Particle B: can emit external signals B1 and B2[but not simultaneously]
Particle A can emit internal signals of the type A1 and A2[But not simultaneously]
Detector Interaction [on A] may be represented by DS [detector signal]
The model assumes:
(B1+Ds-A1) acting on existing plus half spin of A changes it minus half spin.This signal combination leaves the minus half spin state of A unchanged
(B1+Ds-A2) acting on existing plus half spin of A changes it minus half spin.This signal combination leaves the minus half spin state of A unchanged
In so far as spin is concerned B1+Ds-A1 and B1+ds-A2 produce the same effect on A. They may produce different effects in other areas [ex: they may induce changes in the position and the momentum of A in a manner consistent with the uncertainty principle] (B2+Ds-A2) acting on existing minus half spin of A converts it to the plus half spin state.It leaves the plus half spin state unaffected.
(B2+Ds-A1) acting on existing minus half spin of A converts it to the plus half spin state.It leaves the plus half spin state unaffected.
(B2+Ds-A2) and (B2+Ds-A1) produce the same effect on the spin state of A. They may produce different effects in other areas.
B knows that:
B1 always changes the spin of A from +1/2 to minus ½. It leaves the +1/2 state unaffected.
B2 always changes the spin of the spin of A from -1/2 to +1/2. It leaves the -1/2 state unaffected.
Therefore B is aware of the spin state of A[and the time of expected change]
[Important point to note : As the particles separate after their creation, each is continuously under the influence of signals emitted by the other. We don’t have signals like Ds-A1 or Ds-A2.Either B1 or B2 have to be present[Assumption]. Consideration of Ds-A1 or Ds-A2 may be important for a single particle system]]
One may formulate much better models to make the EPR paradox consistent with Special Relativity[in relation to the finite speed of signal transmission]. One may formulate interesting models to contradict Special Relativity. We simply exclude them as inadmissible options .Of course there may be a large number of successful options.
If the positron is detected in the spin state -1/2 the electron has to be in the state +1/2 no matter what be the distance between them.
Now let the spin of the positron change to +1/2. This change is some sort of a random change. But what is a random change? Is it something that occurs without a stimulus or is it something in response to some SIGNAL.One may consider signals responsible for such changes.These signals may be of "internal" or "external" origin. In our case we have an isolated two-particle system. Of course we have our interacting detector[we assume a pair of detectors for the two particles]
I am assuming that the change in spin of the first particle is due to some signal from the second one coupled with the interaction from the detector which may be represented by a separate signal. So the second particle while releasing the signal had an estimate of the type of change it might induce on the first one[and the expected time for that change] even if it is a large distance from it! With such considerations we can always devise signal models of the EPR paradox consistent with Special Relativity .
An example:
We have two particles A and B and a pair of detectors to measure their spin values.
There is a change in the spin value of A,as observed by the detector.
Reason: Signal from B+Internal Signal of A+Detector Interaction[which may be represented by another signal]
As the particles separate after their creation, each is assumed to be continuously influenced by signals emitted by the other. So the presence of the signal from B[and acting on A] is mandatory for all instants.
Particle B: can emit external signals B1 and B2[but not simultaneously]
Particle A can emit internal signals of the type A1 and A2[But not simultaneously]
Detector Interaction [on A] may be represented by DS [detector signal]
The model assumes:
(B1+Ds-A1) acting on existing plus half spin of A changes it minus half spin.This signal combination leaves the minus half spin state of A unchanged
(B1+Ds-A2) acting on existing plus half spin of A changes it minus half spin.This signal combination leaves the minus half spin state of A unchanged
In so far as spin is concerned B1+Ds-A1 and B1+ds-A2 produce the same effect on A. They may produce different effects in other areas [ex: they may induce changes in the position and the momentum of A in a manner consistent with the uncertainty principle] (B2+Ds-A2) acting on existing minus half spin of A converts it to the plus half spin state.It leaves the plus half spin state unaffected.
(B2+Ds-A1) acting on existing minus half spin of A converts it to the plus half spin state.It leaves the plus half spin state unaffected.
(B2+Ds-A2) and (B2+Ds-A1) produce the same effect on the spin state of A. They may produce different effects in other areas.
B knows that:
B1 always changes the spin of A from +1/2 to minus ½. It leaves the +1/2 state unaffected.
B2 always changes the spin of the spin of A from -1/2 to +1/2. It leaves the -1/2 state unaffected.
Therefore B is aware of the spin state of A[and the time of expected change]
[Important point to note : As the particles separate after their creation, each is continuously under the influence of signals emitted by the other. We don’t have signals like Ds-A1 or Ds-A2.Either B1 or B2 have to be present[Assumption]. Consideration of Ds-A1 or Ds-A2 may be important for a single particle system]]
One may formulate much better models to make the EPR paradox consistent with Special Relativity[in relation to the finite speed of signal transmission]. One may formulate interesting models to contradict Special Relativity. We simply exclude them as inadmissible options .Of course there may be a large number of successful options.
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