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StevieTNZ
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Anyone who follows some of my posts knows I've fallen in love with GianCarlo Ghirardi's thought experiment.
(apologises for the equations - I don't know how to work LaTeX).
The experimental set-up is a 45 degree polarised photon goes through a birefringent crystal. On the other side of the crystal is an apparatus which detects whether a photon comes from the ordinary ray (vertical polarisation – apparatus shows A+1) or extraordinary ray (horizontal polarisation – apparatus shows A-1). This apparatus does not absorb the photon, so allows us to perform a further test on the photon.
The whole situation is now described by the following equation:
=1/2 |45>(1/2 |A+1>+|A-1>) + |135> (1/2 |A+1>-|A-1>)
The photon is in a superposition of V and H polarisations, and when going through a subsequent polariser, orientated at 45 degrees, has 1/2 probability of passing or failing.
On the apparatus that measures which way the photon exits the crystal, is another observable called Z, which takes on the value X if the apparatus is in the state |A+1>+|A-1> or Y if in the state |A+1>-|A-1>. Observable Z takes on X if the photon passes the 45 degree test, and Y if not.
All of this seems to be in accord with QM. As no collapse is meant to occur after the crystal, we should describe the photon as being in a superposition of V and H, as well as 45 and 135.
The issues I'm going to raise:
If we observe the apparatus in either A+1 or A-1, then the photon is in V or H polarisation. Observable Z takes on X or Y (A+1: 1/2 X, Y; A-1: 1/2 X, Y [as a consequence of the inverse above]). So, if observable Z is showing X, the photon can fail the test.
What I'm wondering is if we've set up the experiment and prior to sending the photon through the subsequent polariser see a definite pointer, how does QM take that into account when its saying it shouldn't occur (and obviously affects subsequent results)?
In Bohm Mechanics, after the photon exists the crystal and is detected by the apparatus, is it in a definite polarisation? Then if we look at the apparatus, we'll see A+1 or A-1, and subsequently send the photon through the polariser, we would still see quantum mechanical results (X correlated to passing, etc.) If Bohm Mechanics is correct, and QM is describing the situation, looking at the apparatus shouldn't make a difference because even not looking at it doesn't change the fact that it is in a definite A+1 or A-1. But if we do see it, and if we do see X being correlated to passing (due to hidden variables), then we might need to conclude Bohm Mechanics is correct.
But I'm seeing an issue as because we CAN look at the apparatus, and because it SHOULD be in a superposition before the photon reaches the polariser, how to account this if QM is correct (obviously we should be saying the apparatus is in a superposition, even though we're seeing otherwise)?
Whether we update the wave function after we look, I'm not sure. Because Brian Cox seems to make it clear that if we want to compute the probability of future events, we need to take into account everyway those future states can arise from. From what I gather, he is saying everytime we see a definite state, we can't strictly say coherence is lost.
I'm not too sure, though. Hoping to get some views on this.
(apologises for the equations - I don't know how to work LaTeX).
The experimental set-up is a 45 degree polarised photon goes through a birefringent crystal. On the other side of the crystal is an apparatus which detects whether a photon comes from the ordinary ray (vertical polarisation – apparatus shows A+1) or extraordinary ray (horizontal polarisation – apparatus shows A-1). This apparatus does not absorb the photon, so allows us to perform a further test on the photon.
The whole situation is now described by the following equation:
=1/2 |45>(1/2 |A+1>+|A-1>) + |135> (1/2 |A+1>-|A-1>)
The photon is in a superposition of V and H polarisations, and when going through a subsequent polariser, orientated at 45 degrees, has 1/2 probability of passing or failing.
On the apparatus that measures which way the photon exits the crystal, is another observable called Z, which takes on the value X if the apparatus is in the state |A+1>+|A-1> or Y if in the state |A+1>-|A-1>. Observable Z takes on X if the photon passes the 45 degree test, and Y if not.
All of this seems to be in accord with QM. As no collapse is meant to occur after the crystal, we should describe the photon as being in a superposition of V and H, as well as 45 and 135.
The issues I'm going to raise:
If we observe the apparatus in either A+1 or A-1, then the photon is in V or H polarisation. Observable Z takes on X or Y (A+1: 1/2 X, Y; A-1: 1/2 X, Y [as a consequence of the inverse above]). So, if observable Z is showing X, the photon can fail the test.
What I'm wondering is if we've set up the experiment and prior to sending the photon through the subsequent polariser see a definite pointer, how does QM take that into account when its saying it shouldn't occur (and obviously affects subsequent results)?
In Bohm Mechanics, after the photon exists the crystal and is detected by the apparatus, is it in a definite polarisation? Then if we look at the apparatus, we'll see A+1 or A-1, and subsequently send the photon through the polariser, we would still see quantum mechanical results (X correlated to passing, etc.) If Bohm Mechanics is correct, and QM is describing the situation, looking at the apparatus shouldn't make a difference because even not looking at it doesn't change the fact that it is in a definite A+1 or A-1. But if we do see it, and if we do see X being correlated to passing (due to hidden variables), then we might need to conclude Bohm Mechanics is correct.
But I'm seeing an issue as because we CAN look at the apparatus, and because it SHOULD be in a superposition before the photon reaches the polariser, how to account this if QM is correct (obviously we should be saying the apparatus is in a superposition, even though we're seeing otherwise)?
Whether we update the wave function after we look, I'm not sure. Because Brian Cox seems to make it clear that if we want to compute the probability of future events, we need to take into account everyway those future states can arise from. From what I gather, he is saying everytime we see a definite state, we can't strictly say coherence is lost.
I'm not too sure, though. Hoping to get some views on this.