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

[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.

 

[RUTA]

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

It's an interesting idea. If they TRULY subscribe to it, why is their formalism not background independent?

 

[WaveJumper]

It's an interesting idea. If they TRULY subscribe to it, why is their formalism not background independent?

It's a work in progress, and most theorists(both in ST and in LQG), i believe, are now working on background independent models of QG.
Certain approaches to string theory dispense with the notion of space-time completely. Yet, they seem to produce the same set of results as string theories with normal space and time.
To some theorists, this strongly suggests that space and time are superfluous.

My personal opinion is that a dynamical spacetime geometry is the least appropriate basis for a final formulation of a TOE(be that ST, LQG or another approach). A background dependant theory is not the answer, as Einstein's background is not fixed - gravitational waves not only travel through this background, they change it in the process. Another unresolved issue - what happens to spacetime at the centre of a black hole, points also heavily in the direction of background independent theory of QG(emergent spacetime).

 

[RUTA]

It's a work in progress, and most theorists(both in ST and in LQG), i believe, are now working on background independent models of QG.
Certain approaches to string theory dispense with the notion of space-time completely. Yet, they seem to produce the same set of results as string theories with normal space and time.
To some theorists, this strongly suggests that space and time are superfluous.

LQG, yes, but I have not heard of any backgnd-ind ST. Can you give me a reference to one?

 

[WaveJumper]

LQG, yes, but I have not heard of any backgnd-ind ST. Can you give me a reference to one?

http://arxiv.org/abs/hep-th/9305026



"Indeed the string field action has background dependence; it uses,
for example, the BRST operator of the conformal field theory. This necessity to fix a conformal
field theory to get started writing a string field action is usually referred to as the issue
of background independence of string field theory. It is certainly the central question facing
string field theory. A background independent string field theory would most likely be the
formulation of string theory we are looking for.
The problem of setting up a background independent string field theory is exactly analogous
as that of reconstructing Einstein’s theory if we only knew the expansion of the Einstein
lagrangian around flat space."

http://arxiv.org/abs/hep-th/9311009

http://arxiv.org/abs/hep-th/9208027

Some random quotes from leading ST'ists:

"Very likely space and even perhaps time have constituent parts. Space and time could turn out to be emergent properties of a very different looking theory". David Gross

"Space and time may be doomed". Ed Witten


If good old reductionsim can't find the constituents of spacetime, then likely spacetime must be an emergent phenomenon. This principle has worked so far with great success in all fileds f science, i see no reason to abandon it(though background-independent QG is probably the hardest approach).

 

[RUTA]

"Indeed the string field action has background dependence; it uses, for example, the BRST operator of the conformal field theory. This necessity to fix a conformal field theory to get started writing a string field action is usually referred to as the issue of background independence of string field theory. It is certainly the central question facing string field theory. A background independent string field theory would most likely be the formulation of string theory we are looking for."

If good old reductionsim can't find the constituents of spacetime, then likely spacetime must be an emergent phenomenon. This principle has worked so far with great success in all fileds f science, i see no reason to abandon it(though background-independent QG is probably the hardest approach).

So, as I thought, there are no bkgnd-ind versions of ST.

I agree with you, QG must be BI. Thus, ST is BS

 

[WaveJumper]

So, as I thought, there are no bkgnd-ind versions of ST.

Those were papers from 1993, it appears the focus has shifted since the introduction of M-theory in 1995 by Witten. The unifying M-version is supposed to be background-independent(though it's still being worked out):

Lee Smolin in 'The Trouble with Physics'(p.126):

"Recall that each of the many string theories is a background-dependent theory that describes strings moving in a particular background spacetime. Since the various approximate string theories live on different spacetime backgrounds, the theory that unifies them must not live on any spacetime background. What is needed to unify them is a single, background-independent theory. The way to do this was thus clear: Invent a Meta-theory that would itself be background-independent, then derive all the background-dependent string theories from this single meta-theory."

Also:
http://arxiv.org/abs/hep-th/9903166

I agree with you, QG must be BI. Thus, ST is BS

Haha, BS sounds scientific next to QG, ST and BI. No, seriously, both approaches to QG may compliment each other in the end and produce a single theory, as Smolin suggests in '3 roads to QG'(maybe god didn't have a choice, as Einstein wondered - provided such a theory exists).

 

[zonde]

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

Things like "initial polarization of both photons" ARE interpretation.
I found a sentence in wikipedia under article "Interpretation of quantum mechanics": "Physicists usually consider an interpretation of quantum mechanics as an interpretation of the mathematical formalism of quantum mechanics, specifying the physical meaning of the mathematical entities of the theory."
This reflects what I was meaning with interpretation when I commented about inconsistency of your interpretation.
If you do not agree with that than clearly you have very specific own definition what an interpretation is.

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.

Actually I do not asked to teach me QM. Original topic I proposed was results of mind experiment involving three entangled photon streams drawing analogy with results of real experiments involving two entangled photon streams.
You just kept asking meaningless questions until we went away from subject. Like that:

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).

This is complete nonsense but you used it to demonstration that - cos^2(theta) where theta is the angle between polarizers doesn't necessarily give the coincidence rate .

 

[RUTA]

Things like "initial polarization of both photons" ARE interpretation.
I found a sentence in wikipedia under article "Interpretation of quantum mechanics": "Physicists usually consider an interpretation of quantum mechanics as an interpretation of the mathematical formalism of quantum mechanics, specifying the physical meaning of the mathematical entities of the theory."
This reflects what I was meaning with interpretation when I commented about inconsistency of your interpretation.
If you do not agree with that than clearly you have very specific own definition what an interpretation is.

You stated a problem and asked for an analysis. I showed you the calculation using detailed formalism. What else can I do?

Actually I do not asked to teach me QM. Original topic I proposed was results of mind experiment involving three entangled photon streams drawing analogy with results of real experiments involving two entangled photon streams.
You just kept asking meaningless questions until we went away from subject. Like that:

This is complete nonsense but you used it to demonstration that - cos^2(theta) where theta is the angle between polarizers doesn't necessarily give the coincidence rate .

This calculation and those that accompanied it show the correlation rate does not necessarily go as cos^2(theta). If this is "complete nonsense," then simply point out the error(s) and make the correction(s). You have yet to supply a single calculation in support of your assertion. Time to put up or shut up. Show me the physics.

 

[zonde]

You stated a problem and asked for an analysis. I showed you the calculation using detailed formalism. What else can I do?

Your calculation does not agree with supposed experimental results. I do not know what else you can do.

This calculation and those that accompanied it show the correlation rate does not necessarily go as cos^2(theta). If this is "complete nonsense," then simply point out the error(s) and make the correction(s). You have yet to supply a single calculation in support of your assertion. Time to put up or shut up. Show me the physics.

If your calculation does not agree with cos^2(theta) then it contradicts experimental results and therefore is not applicable.
Calculations do agree with experimental results of two photon entanglement if you use state vectors that are eigenvectors of operators. For arbitrary chosen state vector you have no application in this context (I have no idea about other possible contexts).
You said yourself: "You specify psi in the eigenbases of the operators representing the measurements you intend to carry out."
In particular example I quoted psi is not in the eigenbases of the operators.

If we look where this all started you proposed calculation where two out of three measurements are correctly calculated because they can use the same eigenbase but for third measurement you have to take different eigenbase and perform separate calculation in order to come to correct result that is one part of the problem.

 

[RUTA]

If your calculation does not agree with cos^2(theta) then it contradicts experimental results and therefore is not applicable.

That's ridiculous, your claim amounts to saying the correlation rate is only a function of the angle between polarizer measurements and is independent of the polarizations of the photons themselves. Suppose the measurements are both at 0 deg and the photons are polarized at 0 deg and 90 deg. According to your claim, the correlation rate is cos^2(0) = 1, but we KNOW the correlation rate is zero -- one detector will always click and the other will never click.

Calculations do agree with experimental results of two photon entanglement if you use state vectors that are eigenvectors of operators. For arbitrary chosen state vector you have no application in this context (I have no idea about other possible contexts).
You said yourself: "You specify psi in the eigenbases of the operators representing the measurements you intend to carry out."
In particular example I quoted psi is not in the eigenbases of the operators.

Psi is in the eigenbasis of SOME operator because that's how you construct the Hilbert space.

But, if you disagree, just show me the "correct" calculations. You're not showing me any physics, zonde.

 

[zonde]

That's ridiculous, your claim amounts to saying the correlation rate is only a function of the angle between polarizer measurements and is independent of the polarizations of the photons themselves. Suppose the measurements are both at 0 deg and the photons are polarized at 0 deg and 90 deg. According to your claim, the correlation rate is cos^2(0) = 1, but we KNOW the correlation rate is zero -- one detector will always click and the other will never click.

If light is not polarized then why should it depend from some arbitrary angle?
But I am not speaking about single photons and as far as I understand you too are not including in your calculations anything related to single photon (if you do not use integration over all possible values then it's the whole sample you describe with vector).

Psi is in the eigenbasis of SOME operator because that's how you construct the Hilbert space.

But, if you disagree, just show me the "correct" calculations. You're not showing me any physics, zonde.

But just SOME operator will give you SOME eigenvalue but we are interested what a masurement will be in particular setup.

If all the physics for you stops at Hilbert space then we have a problem. Maybe then it's not worth to continue this discussion? Not to mention the you have sent me already couple of times to study some intro QM.