What exactly is the solution for principle of locality and speed of light?

[zonde]

Ruta,
If I understand correctly this nonseparability relays on blockworld that in everyday language we would call destiny. Is it right?
What would you say about such mind experiment:
Three entangled photons with the same polarizations are sent to three sites where one photon stream is analyzed with polarization beam splitter (PBS) at angle 0° relative to common reference other with PBS at angle 45° and third with PBS at angle 22.5°.
What we would see if we correlate results each with each?

 

[RUTA]

Ruta,
If I understand correctly this nonseparability relays on blockworld that in everyday language we would call destiny. Is it right?

In a blockworld, the future, past and present are equally "real." So, yes, your future is "determined" in a blockworld.

What would you say about such mind experiment:
Three entangled photons with the same polarizations are sent to three sites where one photon stream is analyzed with polarization beam splitter (PBS) at angle 0° relative to common reference other with PBS at angle 45° and third with PBS at angle 22.5°.
What we would see if we correlate results each with each?

Photon 1 (and 2 and 3) is in the |1> eigenstate of operator 1 (representing the polarizer set at 0 deg), so it will always pass (call that eigenvalue 1, not pass eignevalue is 0) and correlated results will require outcomes at polarizers 2 & 3 are also 1. The initial state is |1,1,1> where each |1> is in the eigenbasis of operator 1. To find the probability of correlated results (1,1,1 outcomes), you just find the projection of the |1> state in eigenbasis of operator 1 on the |1> state of each of the other operators' eigenbases. Multiply and square for the probability of a 1,1,1 outcome. The angle of the polarizer is the angle of the eigenbasis for photons, (whereas it's cut in half for spin) so that when your polarizer is at 90 deg relative to the polarization state you get 0 (not pass), which means the |1> eigenstate of the 90 deg operator is |0> in the eigenbasis of the 0 deg operator. Experimentally you don't measure 0, so if you wanted info on outcomes for the |0> state you have to measure 1 at 90 deg from the angle in question and infer 0 for the angle in question.

There is a good paper showing all the theory for an entangled pair plus experimental data and equipment, “Entangled photons, nonlocality, and Bell inequalities in the undergraduate laboratory,” D. Dehlinger and M.W. Mitchell, Am. J. Phys. 70, Sep 2002, 903-910. I have the following typos: RHS of Eq (15) should be inverted (and I get theta = 44 deg instead of 46 deg); either a = 45 deg or b' = -22.5 deg for polarizer angles in deriving Eq (23). They don't provide the individual values of E for computing S immediately after Eq (25). I obtain E(a,b) = .49661, E(a, b') = -.58742, E(a', b) = .68861, and E(a', b') = .52468 so that S = 2.297 (they obtain 2.307, less than 1% difference fm rounding).

If you have questions about this, you should probably contact me directly. I think we're getting a bit off topic for this thread.

 

[WaveJumper]

There is another possibility -- nonseparability. The EPR-Bell experiments imply nonlocality and/or nonseparability.

There is one more - realism. Though one could argue that locality contains an implicit form of realism.

There is also the 'option' of giving up the arrow of time. Either way, it apears impossible to maintain the classical notion of realism without sacrificing one or more of the intuitive notions.

 

[zonde]

If you have questions about this, you should probably contact me directly. I think we're getting a bit off topic for this thread.

I will slowly read trough what you wrote but a quick question. If I understood you correctly you considered only cases where all three photons are detected. But my question was more about cases where there are two photons detected at two locations. So we have 3 interdependent entanglement measurements.

 

[RUTA]

I will slowly read trough what you wrote but a quick question. If I understood you correctly you considered only cases where all three photons are detected. But my question was more about cases where there are two photons detected at two locations. So we have 3 interdependent entanglement measurements.

I thought you were talking about coincidence counts at three detectors, so of course you'd need three photons. In any event, if you read that AJP paper, you'll see how to do the math for two photons easy enough. And, you'll see how the experiments are actually carried out, e.g., how coincidence counts involving the |0> state are obtained when |0> means the photon didn't get through the polarizer.

 

[zonde]

I thought you were talking about coincidence counts at three detectors, so of course you'd need three photons. In any event, if you read that AJP paper, you'll see how to do the math for two photons easy enough. And, you'll see how the experiments are actually carried out, e.g., how coincidence counts involving the |0> state are obtained when |0> means the photon didn't get through the polarizer.

I was implying that I doubt whether or not your proposed alternative e.g. nonseparability provide any useful insights into the discussed question.
Therefore I proposed to look how you would analyze from your perspective particular experiment.
I would try to explain this experiment another way.

We have three entangle photons with the same polarization that are directed at three different sites (A, B and C).
Lets consider it in two steps. First step:
We make measurements only at two sites (A and B). Relative angle between their PBSes is 45°. So assuming ideal conditions (zero photon count at 90°) measurements from two outputs of their PBSes (say outputs #1) will show correlation 0 or 50% from supposed maximum at 0°.
Second step:
We make measurements at site C too. PBS in site C is rotated so that it makes 22.5° with A and 22.5° with B (right in the middle between A and B). And now we find out two additional correlations - A output#1 vs C output#1 and B output#1 vs C output#1
And these correlations are:
A#1,C#1 - 0.7 or 85% from supposed maximum at 0°
B#1,C#1 - 0.7 or 85% from supposed maximum at 0°
If you like to express it using three photon correlations then it would be like this:
For |A,B,C>:
A#1,C#1 - |1,1,1> + |1,0,1> =probability 0.425 (considering all possible combinations)
B#1,C#1 - |1,1,1> + |0,1,1> =probability 0.425
And correlation from first step is:
B#1,C#1 - |1,1,1> + |1,1,0> =probability 0.25

Is it right from your perspective so far?

Next step
because |1,1,1> + |1,1,0> has probability 0.25 maximum probability for |1,1,1> is 0.25 (|1,1,1> <= 0.25)
because |1,1,1> + |1,0,1> has probability 0.425 minimum probability for |1,0,1> is 0.175
(|1,1,1> + |1,0,1> - |1,1,1> = |1,0,1> >= 0.425 - 0.25 = 0.175)
so we can write inequality |1,1,1> + |0,1,1> + |1,0,1> (+ |0,0,1>) >= 0.425 + 0.175 = 0.6

So we must conclude that there are more photons arriving at output#1 at site C than at output#2. But if we do symmetric calculation for all outputs#2 then we should arrive at exactly opposite conclusion and that is contradiction.

Do you agree with derivation of this inequality and if you agree then where is the problem of this contradiction from your perspective?

 

[RUTA]

I was implying that I doubt whether or not your proposed alternative e.g. nonseparability provide any useful insights into the discussed question.
Therefore I proposed to look how you would analyze from your perspective particular experiment.

Do you agree with derivation of this inequality and if you agree then where is the problem of this contradiction from your perspective?

I would not use lattice gauge theory (which is the kind of formalism we propose in arXiv 0908.4348) to solve this problem, which is easy to solve with the Hilbert space formalism as I explained before. There are no contradictions in the formalism of QM. If you believe you've found one, you've made a mistake. Are you asking me to find your mistake?

 

[bluestarlee]

Thanks for the suggestion, I wish it had worked.

calcul financement courtier | simulation pret immobilier | taux credit de france [/color]simulation crédit immobilier sera le total du prêt[/color] calcul financement courtier | simulation pret immobilier | taux credit de france [/color]

 

[zonde]

I would not use lattice gauge theory (which is the kind of formalism we propose in arXiv 0908.4348) to solve this problem, which is easy to solve with the Hilbert space formalism as I explained before. There are no contradictions in the formalism of QM. If you believe you've found one, you've made a mistake. Are you asking me to find your mistake?

Yes, please do find my mistake.

 

[RUTA]

We have three entangle photons with the same polarization that are directed at three different sites (A, B and C).
Lets consider it in two steps. First step:
We make measurements only at two sites (A and B). Relative angle between their PBSes is 45°. So assuming ideal conditions (zero photon count at 90°) measurements from two outputs of their PBSes (say outputs #1) will show correlation 0 or 50% from supposed maximum at 0°.
Second step:
We make measurements at site C too. PBS in site C is rotated so that it makes 22.5° with A and 22.5° with B (right in the middle between A and B). And now we find out two additional correlations - A output#1 vs C output#1 and B output#1 vs C output#1
And these correlations are:
A#1,C#1 - 0.7 or 85% from supposed maximum at 0°
B#1,C#1 - 0.7 or 85% from supposed maximum at 0°
If you like to express it using three photon correlations then it would be like this:
For |A,B,C>:
A#1,C#1 - |1,1,1> + |1,0,1> =probability 0.425 (considering all possible combinations)
B#1,C#1 - |1,1,1> + |0,1,1> =probability 0.425
And correlation from first step is:
B#1,C#1 - |1,1,1> + |1,1,0> =probability 0.25

Is it right from your perspective so far?

Next step
because |1,1,1> + |1,1,0> has probability 0.25 maximum probability for |1,1,1> is 0.25 (|1,1,1> <= 0.25)
because |1,1,1> + |1,0,1> has probability 0.425 minimum probability for |1,0,1> is 0.175
(|1,1,1> + |1,0,1> - |1,1,1> = |1,0,1> >= 0.425 - 0.25 = 0.175)
so we can write inequality |1,1,1> + |0,1,1> + |1,0,1> (+ |0,0,1>) >= 0.425 + 0.175 = 0.6

So we must conclude that there are more photons arriving at output#1 at site C than at output#2. But if we do symmetric calculation for all outputs#2 then we should arrive at exactly opposite conclusion and that is contradiction.

Do you agree with derivation of this inequality and if you agree then where is the problem of this contradiction from your perspective?

Assuming the photons are polarized along A, there are only four states with non-zero amplitudes:

|1,0,0> probability is (.5)(.15) = .075
|1,1,0> probability is (.5)(.15) = .075
|1,0,1> probability is (.5)(.85) = .425
|1,1,1> probability is (.5)(.85) = .425

The probability of a click at B is 50% while that at C is 85%, so the probability that neither B nor C click is (.5)(.15), etc.

 

[zonde]

Assuming the photons are polarized along A, there are only four states with non-zero amplitudes:

|1,0,0> probability is (.5)(.15) = .075
|1,1,0> probability is (.5)(.15) = .075
|1,0,1> probability is (.5)(.85) = .425
|1,1,1> probability is (.5)(.85) = .425

The probability of a click at B is 50% while that at C is 85%, so the probability that neither B nor C click is (.5)(.15), etc.

So you decided against looking for error in my derivation but instead tried to provide counter example. Well this should be ok if example is consistent with expected results.

About example:
I somewhat do not understand why you modified my proposed setup with preliminary polarization of all photon streams but it seems that your example fails anyways.
Probabilities between A and B and probabilities between A and C are consistent with prediction. However probabilities between B and C are incorrect. After taking into account imbalance in intensities due to initial polarization they show no correlation at all (complete statistical independence).

Probabilities for photon detection in B and C should be like this:
|1,0,0> probability 0.85*I(=0.15) = 0.1275
|1,1,0> probability 0.15*I(=0.15) = 0.0225
|1,0,1> probability 0.15*I(=0.85) = 0.1275
|1,1,1> probability 0.85*I(=0.85) = 0.7225
And this of course creates contradiction with your example. (Now A-C probabilities are correct but A-B probabilities are 0.25 for |1,0> and 0.75 for |1,1> namely incorrect)

 

[zonde]

Thanks for the suggestion, I wish it had worked.

calcul financement courtier | simulation pret immobilier | taux credit de france simulation crédit immobilier sera le total du prêt calcul financement courtier | simulation pret immobilier | taux credit de france

What is the reason for your hidden link? Is it some kind of rising google's rating for some site?

P.S. It's ok to delete this post as it is irrelevant to discussion (along with this quoted post??).

 

[RUTA]

So you decided against looking for error in my derivation but instead tried to provide counter example. Well this should be ok if example is consistent with expected results.

About example:
I somewhat do not understand why you modified my proposed setup with preliminary polarization of all photon streams but it seems that your example fails anyways.
Probabilities between A and B and probabilities between A and C are consistent with prediction. However probabilities between B and C are incorrect. After taking into account imbalance in intensities due to initial polarization they show no correlation at all (complete statistical independence).

Probabilities for photon detection in B and C should be like this:
|1,0,0> probability 0.85*I(=0.15) = 0.1275
|1,1,0> probability 0.15*I(=0.15) = 0.0225
|1,0,1> probability 0.15*I(=0.85) = 0.1275
|1,1,1> probability 0.85*I(=0.85) = 0.7225
And this of course creates contradiction with your example. (Now A-C probabilities are correct but A-B probabilities are 0.25 for |1,0> and 0.75 for |1,1> namely incorrect)

Where are you getting your probabilities? The polarizer at B (45 deg) clicks in 50% of the trials. The polarizer at C clicks in 85% of the trials. The polarizer at A always clicks and establishes that in fact there was a trial to consider. Therefore, the probability that all three click on any given trial is (1)(.5)(.85) = .425. Think about your number (.7225) -- it says the probability of all three clicking in a given trial exceeds the probability that B will click on any given trial. Clearly that's wrong.

 

[Demystifier]

people, concentrate, i was talking about EPR paradox, is there a solution?

There is a solution, but the problem is that there are actually many solutions and nobody knows which solution is the correct one.

My preferred solution is that nature is nonlocal and allows information to travel faster than light. This is not necessarily in conflict with the principle of relativity saying that the laws of physics do not depend on the choice of spacetime coordinates.

 

[RUTA]

There is a solution, but the problem is that there are actually many solutions and nobody knows which solution is the correct one.

My preferred solution is that nature is nonlocal and allows information to travel faster than light. This is not necessarily in conflict with the principle of relativity saying that the laws of physics do not depend on the choice of spacetime coordinates.

Correct, in general there are two ways to explain EPR-Bell phenomena (nonlocality and nonseparability), but there exist many different instantiations of these two themes.

 

[zonde]

Where are you getting your probabilities? The polarizer at B (45 deg) clicks in 50% of the trials. The polarizer at C clicks in 85% of the trials. The polarizer at A always clicks and establishes that in fact there was a trial to consider. Therefore, the probability that all three click on any given trial is (1)(.5)(.85) = .425. Think about your number (.7225) -- it says the probability of all three clicking in a given trial exceeds the probability that B will click on any given trial. Clearly that's wrong.

You are analyzing this situation from perspective of A. And you can't get the probabilities between B and C right that's the point.

 

[RUTA]

You are analyzing this situation from perspective of A. And you can't get the probabilities between B and C right that's the point.

Are you saying the probability for |1,1,1> is .7225? As I stated before, the probability for all three clicking in any given trial can't exceed the probability for anyone to click. So, I don't know where you're getting your numbers, but I know they're not obtained from quantum mechanics.

If you want to know the overall coincidence rate for A and B, it's just |1,1,1> + |1,1,0> = .425 + .075 = .5 (must be, since polarization is along A and B is at 45 deg). If you want to know the coicidence rate for A and C it's |1,1,1> + |1,0,1> = .425 + .425 = .85 (must be, since C is at 22.5 deg). Finally, the coincidence rate for B and C is |1,1,1> + |1,0,0> = .425 + .075 = .5 (which is not equal to A and C because the situation is not symmetrical about C).

 

[zonde]

Are you saying the probability for |1,1,1> is .7225? As I stated before, the probability for all three clicking in any given trial can't exceed the probability for anyone to click. So, I don't know where you're getting your numbers, but I know they're not obtained from quantum mechanics.

I am saying that probability for click in B and click in C without initial polarization is 0.85/2.
And probability for no click in B and click in C without initial polarization is 0.15/2.
You have numbers like:
|1,0,1> probability is (.5)(.85) = .425
|1,1,1> probability is (.5)(.85) = .425
And I do not see how your introduced initial polarization can change 0.85/2 and 0.15/2 into 0.425 and 0.425.

 

[zonde]

There is a solution, but the problem is that there are actually many solutions and nobody knows which solution is the correct one.

My preferred solution is that nature is nonlocal and allows information to travel faster than light. This is not necessarily in conflict with the principle of relativity saying that the laws of physics do not depend on the choice of spacetime coordinates.

Actually nonlocal would mean instantaneous travel of information. Another thing is that nonlocality undermines concept of space.

So I say that much more delicate solution is to assume that polarization measurement represents wave function that collapses after measurement process where role of measurement equipment is played by other polarization measurement. So that measurement actually is interference of two wavefunctions but part of information is of course dumped.

 

[RUTA]

I am saying that probability for click in B and click in C without initial polarization is 0.85/2.
And probability for no click in B and click in C without initial polarization is 0.15/2.
You have numbers like:
|1,0,1> probability is (.5)(.85) = .425
|1,1,1> probability is (.5)(.85) = .425
And I do not see how your introduced initial polarization can change 0.85/2 and 0.15/2 into 0.425 and 0.425.

You said the initial state had the photons polarized in the same direction. Since you said the angle of A was 0 deg, I assumed that was the initial polarization. If you're not in the eigenbasis for A, simply specifiy the state and repeat the simple calculations.

Now you write, "without initial polarization." You have to specify the initial state, probabilities are computed for THAT state with respect to the eigenbases of the various polarizers. My probabilities were for the initial state |1,1,1> in the eigenbasis of A. Do you see where my numbers come from, given that initial state? If so, simply repeat the calculations for your initial state. If not, let me know and I'll explain it so you can repeat the calcs for some other initial state. Again, QM will not give contradictory answers.

 

[zonde]

You said the initial state had the photons polarized in the same direction. Since you said the angle of A was 0 deg, I assumed that was the initial polarization. If you're not in the eigenbasis for A, simply specifiy the state and repeat the simple calculations.

Now you write, "without initial polarization." You have to specify the initial state, probabilities are computed for THAT state with respect to the eigenbases of the various polarizers. My probabilities were for the initial state |1,1,1> in the eigenbasis of A. Do you see where my numbers come from, given that initial state? If so, simply repeat the calculations for your initial state. If not, let me know and I'll explain it so you can repeat the calcs for some other initial state. Again, QM will not give contradictory answers.

Photons are entangled with the same polarization state. That does not mean that there are additional polarizers after entangled photon source.

And it seems that you reject to answer my question: "And I do not see how your introduced initial polarization can change 0.85/2 and 0.15/2 into 0.425 and 0.425."
Instead you are saying that I should try myself to get the "right" answer. And if I can't get the "right" answer I can repeat my calculations as long as I wish.

Well, thanks for nothing as it seems.

Btw QM can not restore the same wavefunction in it's initial state as it is done in this experiment. So it would be small wonder if some contradictions arise.

 

[RUTA]

Photons are entangled with the same polarization state. That does not mean that there are additional polarizers after entangled photon source.

And it seems that you reject to answer my question: "And I do not see how your introduced initial polarization can change 0.85/2 and 0.15/2 into 0.425 and 0.425."
Instead you are saying that I should try myself to get the "right" answer. And if I can't get the "right" answer I can repeat my calculations as long as I wish.

Well, thanks for nothing as it seems.

Btw QM can not restore the same wavefunction in it's initial state as it is done in this experiment. So it would be small wonder if some contradictions arise.

How did you compute .85/2 without an initial state? Show me the initial state in the eigenbasis of one of the polarizers so I can verify your claim.

 

[zonde]

How did you compute .85/2 without an initial state? Show me the initial state in the eigenbasis of one of the polarizers so I can verify your claim.

That's simple. Probability 0.85 I took from experimental results of photon entanglement (relative angle between polarizations 22.5 deg probability of coincidence =cos^2(22.5 deg)) and /2 is because 0.85 result you have for two combinations from four (other two combinations have probability 0.15 accordingly). So not really calculation.

 

[RUTA]

That's simple. Probability 0.85 I took from experimental results of photon entanglement (relative angle between polarizations 22.5 deg probability of coincidence =cos^2(22.5 deg)) and /2 is because 0.85 result you have for two combinations from four (other two combinations have probability 0.15 accordingly). So not really calculation.

cos^2(theta) where theta is the angle between polarizers doesn't necessarily give you the coincidence rate. Let's look at an example.

Let one polarizer be set at 0 deg (A) and the other at 22.5 deg (B). The probability that both detectors will click on a given trial is P = <psi|1,1*>^2, where |1> is a click at A and |1*> is a click at B. There are four possible outcomes, |1,0*>, |1,1*>, |0,0*>, |0,1*>. The coincidence rate (probability of like outcomes) is then given by the probability of both A and B clicking plus the probability of neither A nor B clicking, i.e., <psi|1,1*>^2 + <psi|0,0*>^2 = (<Apsi|1><Bpsi|1*>)^2 + (<Apsi|0><Bpsi|0*>)^2. Clearly this outcome depends on |psi>.

Suppose the initial polarization of both photons is 45 deg so |psi> is |A of 1 = 45 deg>|B of 1 = 22.5 deg>. The coincidence rate for clicks at both locations is (<Apsi|1><Bpsi|1*>)^2 = cos^2(45)cos^2(22.5) = (.5)(.85) = .425. The coincidence rate for no clicks at both locations is (<Apsi|0><Bpsi|0*>)^2 = cos^2(45)cos^2(67.5) = (.5)(.15) = .075. The total coincidence rate is therefore .425 + .075 = .5. This is not in accord with your equation, i.e., cos^2(theta).

Now suppose the initial polarization of both photons is 0 deg so |psi> is |A of 1 = 0 deg>|B of 1 = 22.5 deg>. The coincidence rate for clicks at both locations is (<Apsi|1><Bpsi|1*>)^2 = cos^2(0)cos^2(22.5) = (1)(.85) = .85. The coincidence rate for no clicks at both locations is (<Apsi|0><Bpsi|0*>)^2 = cos^2(90)cos^2(112.5) = (0)(.15) = 0. The total coincidence rate is therefore .85 + 0 = .85. Notice this is the equation you gave for the coincidence rate, i.e., cos^2(22.5).

Of course, there is a simple way to see that the initial state is relevant to the coincidence rate. Suppose the initial state is |1,1*>, then both detectors always click, so P = 1. Likewise, P = 1 if |psi> = |0,0*> because both detectors never click. If |psi> = |1,0*> , A always clicks and B never clicks so P = 0. Likewise, P = 0 if |psi> = |0,1*> since A never clicks and B always clicks.

This is the way I see it. Do you disagree?

 

[leehom04]

Speed of Light.

what are other thing that more faster than the speed of light

 

[zonde]

This is the way I see it. Do you disagree?

Ok, before I blurt out something like yes or no I would like to understand more about this psi.
You have shown how coincidence depend from psi. So this psi is variable, right?
The question is when you want to make theoretical prediction for actual experiment what you do with this psi? Do you choose it at some fixed value say the same as angle of one of the polarizers or do you integrate over all possible values of psi?

 

[RUTA]

Ok, before I blurt out something like yes or no I would like to understand more about this psi.
You have shown how coincidence depend from psi. So this psi is variable, right?
The question is when you want to make theoretical prediction for actual experiment what you do with this psi? Do you choose it at some fixed value say the same as angle of one of the polarizers or do you integrate over all possible values of psi?

psi is what the source produces. The Hilbert space H is a characterization of the measurements done on psi, H contains the eigenbases of the operators representing measurements and the eigenvalues represent the outcomes of those measurements. What you have to do is figure out where the eigenbasis is in H for the measurements you want to make and provide a characterization of what is subject to these measurements, i.e., psi. So, one desires psi in terms of the measurements that will be conducted on it. psi can change as a function of time, that time evolution is given by the propagator as constructed from the Hamiltonian. The problem you described had a time-independent psi (as in most experiments of this type since coincidence rates for various polarizer settings are done consecutively not concurrently). Again, I suggest you read and work through all the equations given in “Entangled photons, nonlocality, and Bell inequalities in the undergraduate laboratory,” D. Dehlinger and M.W. Mitchell, Am. J. Phys. 70, Sep 2002, 903-910.

 

[zonde]

psi is what the source produces. The Hilbert space H is a characterization of the measurements done on psi, H contains the eigenbases of the operators representing measurements and the eigenvalues represent the outcomes of those measurements. What you have to do is figure out where the eigenbasis is in H for the measurements you want to make and provide a characterization of what is subject to these measurements, i.e., psi. So, one desires psi in terms of the measurements that will be conducted on it. psi can change as a function of time, that time evolution is given by the propagator as constructed from the Hamiltonian. The problem you described had a time-independent psi (as in most experiments of this type since coincidence rates for various polarizer settings are done consecutively not concurrently).

Thanks for your explanation. But your physical interpretation of math does not seem very consistent.
In one place psi is something existing objectively like "initial polarization of both photons".
In other psi depends from context like one psi is subject to measurement another psi is not.

One way how to make consistent picture is to view psi as certain position in phase space that characterizes photon source. That way phase space is property of photon source but psi is relation between measurement device and photon source.
But if psi has to be extended to individual photons then there are additional aspects to consider.
So does it conflict with your viewpoint if I see psi as position in phase space of photon sample.

Again, I suggest you read and work through all the equations given in “Entangled photons, nonlocality, and Bell inequalities in the undergraduate laboratory,” D. Dehlinger and M.W. Mitchell, Am. J. Phys. 70, Sep 2002, 903-910.

Thanks, but I read through part of the paper and went over the rest and I didn't found much that can help in current discussion. There are a lot of fine details about optical part of entanglement experiment that could be very helpful should I ever decide to try myself at experimenting.

 

[WaveJumper]

how do physicists solve this contradiction (when information moves faster then the speed of light)?
thanks

Most string theorists consider spacetime to be an emergent phenomenon, i.e. there is a scale below which it's meaningless to talk about time or space and hence why the two realms(described by QM and GR) are so different. It appears to be another case of - 'the whole is greater than the sum of its parts'(see superconductivity, ferromagnetism, life, consciousness, surface tension of liquids, boiling and freezing point of liquids, etc., etc.), i.e. a partcilular configuration of strings causes the 'emergence' of spacetime. See:

http://arxiv.org/abs/hep-th/0601234

 

[RUTA]

Thanks for your explanation. But your physical interpretation of math does not seem very consistent. In one place psi is something existing objectively like "initial polarization of both photons". In other psi depends from context like one psi is subject to measurement another psi is not.

It's not an "interpretation," it's how you use the formalism.

One way how to make consistent picture is to view psi as certain position in phase space that characterizes photon source. That way phase space is property of photon source but psi is relation between measurement device and photon source. But if psi has to be extended to individual photons then there are additional aspects to consider. So does it conflict with your viewpoint if I see psi as position in phase space of photon sample.

You specify psi in the eigenbases of the operators representing the measurements you intend to carry out. Have you taken a course in QM? If not, you better start with an introductory QM text before engaging in discourse of this type.

Thanks, but I read through part of the paper and went over the rest and I didn't found much that can help in current discussion. There are a lot of fine details about optical part of entanglement experiment that could be very helpful should I ever decide to try myself at experimenting.

The entire paper is relevant to this discussion. Read it in its entirety, noting the section detailing the construction of psi. Also, verify ALL the equations therein, i.e., YOU do the calculations and obtain those results. I use this paper when I teach QM, making the students do exactly what I'm telling you to do. It's how a person learns physics. But, don't bother with this unless you've already taken a QM course. Again, if you haven't actually studied QM, get an intro textbook and work through the problems and examples. You can't simply READ it, you must actually DO the calculations. There's nothing else I can do to teach you QM over the internet.