View Full Version : what exactly is the solution for principle of locality and speed of light?
meni ohana
Sep2-09, 05:45 AM
how do physicists solve this contradiction (when information moves faster then the speed of light)?
thanks
There is no contradiction because information never travels faster than the speed of light.
Although I am not sure what you are refering to by "principle of locality"?
Note that entaglement etc can NEVER be used to transfer information FTL, no one has ever identified a situation where QM contradicts SR.
how do physicists solve this contradiction (when information moves faster then the speed of light)?
I would say that at the present state of things there are several alternative solutions for this contradiction but none of them says that information moves faster then the speed of light.
Good thing is that all the alternatives relay on the same mathematical formalism. So we can expect that there will be some job for Occam's razor in the future.
meni ohana
Sep2-09, 06:49 AM
so how one particle affect other at the time? (if it does)
so how one particle affect other at the time? (if it does)
Obviously they don't as that would involve FTL interaction.
But we can speak how measurements affect each other as they are communicated no faster than light speed.
no one has ever identified a situation where QM contradicts SR.
A controversial exception has already been identified, Günter Nimtz, a German physicist has already demonstrated that photon particles carrying information can travel at superluminal velocities while quantum tunneling via virtual photons.
1994 Nimtz and Horst Aichmann shown an experiment at the laboratories of Hewlett-Packard using microwaves through a straitened passage of a waveguide. Nimtz says that the Frequency modulated (FM) signals transports the 40th symphony of Wolfgang Amadeus Mozart 4.7 times faster than light due to the effect of quantum tunneling.
This experiment is video demonstrated in reference 2, the differential signals arrive on an oscilloscope detector that demonstrates the tunneling photon signals arrive faster than vacuum photon signals, also while carrying information, however the received information is attenuated.
I have also corresponded with a professor at the University of Cologne that has studied Nimtz scientific papers and concluded that the superluminal quantum tunneling effect is also possible with particles with mass.
Although theoretical, I have never seen an experiment that demonstrated a superluminal quantum tunneling virtual mass particle.
Reference:
Günter Nimtz - superluminal velocities - Wikipedia (http://en.wikipedia.org/wiki/G%C3%BCnter_Nimtz)
Günter Nimtz - waveguide experiment video (http://www.youtube.com/watch?v=UI7nPmlgBEk)
Quantum tunnelling - Wikipedia (http://en.wikipedia.org/wiki/Quantum_tunnelling)
Dmitry67
Sep2-09, 07:35 AM
The understanding of Nimtz and Stahlhoven is that tunneling is the one and only observed violation of special relativity[5] but according to them, that is not a violation of causality: due to the temporal extent of every signal it is impossible to transport information into the past. They claim that tunneling can be explained with virtual photons like Richard Feynman predicted.[6]
Criticism sound not very convincing at wavelength was 33mm and gap was 1 meter wide, while GPS in my smartphone have a precision of 5 meters measuring the ‘arrival times’ of the satellite signals. I believe such intervals can be measured very accurately.
A controversial exception has already been identified, Günter Nimtz, a German physicist has already demonstrated that photon particles carrying information can travel at superluminal velocities while quantum tunneling via virtual photons.
[...]
This experiment is video demonstrated in reference 2, the differential signals arrive on an oscilloscope detector that demonstrates the tunneling photon signals arrive faster than vacuum photon signals, also while carrying information.
Not that crap again. This has been discussed in these forums several dozen times and it is pretty clear that the tunneling photon do NOT travel faster than c. Nimtz uses the speed of the pulse peak for measuring signal propagation, which is nonsense, especially if the shape of the pulse changes like in Nimtz' experiments. The speed of the peak is not the speed at which information is transmitted and it is also not the speed of particles.
This is like trying to measure the speed of a moving train and taking the position of the passengers as the measure of the speed of the train. If all of the passengers move from the back to the front of the train you will measure a faster train according to your definition although the speed of the train is constant all the time.
Dmitry67
Sep2-09, 07:46 AM
What if there is only one peak (delta function)? Only one very short pulse?
Nimtz' experiments rely on the fact that his tunnel barriers cause nonlinear pulse damping. The "front part" of the wave is less damped and the "back part" gets damped heavily. If you just have a delta peak, you will only see a damped peak coming out without any shift in time. He uses just a clever version of pulse shaping using anomalous dispersion.
A photon tunneling through the barrier is therefore most likely to arrive before a photon traveling unimpeded at the speed of light. Our experiment confirmed this prediction. But we do not believe that any individual part of the wave packet moves faster than light. Rather the wave packet gets "reshaped" as it travels, until the peak that emerges consists primarily of what was originally in front. At no point does the tunneling-photon wave packet travel faster than the free-travelling photon.
In 1982 Steven Chu of Stanford University and Stephen Wong, then at AT&T Bell Laboratories, observed a similar reshaping effect. They experimented with laser pulses consisting of many photons and found that the few photons that made it through an obstacle arrived sooner than those that could move freely. One might suppose that only the first few photons of each pulse were 'allowed' through and thus dismiss the reshaping effect. But this interpretation is not possible in our case, because we study one photon at a time. At the moment of detection, the entire photon 'jumps" instantly into the transmitted portion of the wave packet, beating its twin to the finish more than half the time. Although reshaping seems to account for our observations, the question still lingers as to why reshaping should occur in the first place. No one yet has any physical explanation for the rapid tunneling.
Although reshaping does occur especially for quantum tunneling multi-photons, it does not account for superluminal quantum tunneling single-photons.
I also refuse to accept the argument that Stanford University and AT&T Bell Laboratories professors that are aware of the reshaping effect are incapable of measuring the velocity of quantum tunneling photons.
Reference:
Faster than Light - Raymond Chiao, Paul Kwait, Aephraim Steinberg Scientific American Aug 93 (http://www.dhushara.com/book/quantcos/qnonloc/qnonloc.htm)
Although reshaping does occur especially for quantum tunneling multi-photons, it does not account for superluminal quantum tunneling single-photons.
I also refuse to accept the argument that Stanford University and AT&T Bell Laboratories professors that are aware of the reshaping effect are incapable of measuring the velocity of quantum tunneling photons.
Reference:
Faster than Light - Raymond Chiao, Paul Kwait, Aephraim Steinberg Scientific American Aug 93 (http://www.dhushara.com/book/quantcos/qnonloc/qnonloc.htm)
A reference constantly misspelling Paul Kwiat as Paul Kwait is pretty suspect. Fortunately there are the original publications of the authors to check, what they really intended to say. Check for example:
A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao
Measurement of the single-photon tunneling time
Phys. Rev. Lett. 71, 708 - 711 (1993)
Where they conclude:
"Our measurements indicate that the peak of the undistorted (but attenuated) single-photon wave packet appears on the far side of a tunnel barrier earlier than it would were it to propagate at c. There is, however, no genuine violation of Einstein causality, as explained above."
As explained in the paper this is a result of postselection combined with low probabilities. You only select the transmitted photons and the transmission probability is indeed low. See references 22 and 23 in the paper I quoted for further discussion on that topic.
So in conclusion: The authors do not draw the conclusion you would like them to draw. There is no information transfer at superluminal velocities according to the authors you mentioned.
Although the apparent tunneling velocity (1.7c) is superluminal, this is not a genuine signal velocity.
If the tunneling photon (virtual photon) is not a genuine signal then virtual photons could not relay quantum information and also frequency modulated photons could not traverse the barrier, that is the photons that leave the barrier would still be attenuated but not frequency modulated.
If the tunneling photon (virtual photon) is not a genuine signal, then polarized photons (quantum information) that enters the barrier would leave the barrier as non-polarized photons.
The tunneling velocity is too high for 'pulse reshaping' because the wave packet distribution for photons are extremely small and this would violate the Heisenberg Uncertainty Principle.
The paper claims that the tunneling time differential is due to 'pulse reshaping', however it does not state a theorem that proves it.
Reference:
Measurement of the single photon tunneling time - A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao (www.ino.it/~azavatta/References/PRL71p708.pdf)
Heisenberg_Uncertainty_Principle - Wikipedia (http://en.wikipedia.org/wiki/Uncertainty_principle)
Pulse shaping - Wikipedia (http://en.wikipedia.org/wiki/Pulse_shaping)
You are completely misinterpreting the paper.
If the tunneling photon is not a genuine signal then virtual photons could not relay quantum information and also frequency modulated photons could not traverse the barrier, that is the photons that leave the barrier would still be attenuated but not frequency modulated.
If the tunneling photon (virtual photon) is not a genuine signal, then polarized photons (quantum information) that enters the barrier would leave the barrier as non-polarized photons.
The paper does not say that the tunneling photons are not genuine signals. It says that the tunneling times are not the times, which it takes to transmit information.
The tunneling velocity is too high for 'pulse reshaping' because the wave packet distribution for photons are extremely small and this would violate the Heisenberg Uncertainty Principle.
As you can see in the HOM-dip in figure 3 of the quoted paper the wave packets are indeed pretty broad and long compared to the time difference of 1.47 fs between free space propagation and barrier propagation. Pulse reshaping does not violate the HUP in this case.
The paper claims that the tunneling time differential is due to 'pulse reshaping', however it does not state a theorem that proves it.
The paper does not even claim that directly. It claims that pulse reshaping is the cause of the tunneling time differential in classical optics and says that the mechanism is a bit different for single photons. However, the mechanism in this case is in fact pretty similar. As you see in figure 3 there is still significant destructive interference for time delays as large as +/- 40 fs showing the underlying detection probability density is of the same width as well. It does really not surprise me that the time dependence of the photon detection probability density is "shaped" in the same way a classical pulse will be shaped. If the peak shift was larger than the HOM-dip this would be a good indication for FTL-information transfer. In this case, it is not.
meni ohana
Sep2-09, 02:52 PM
people, concentrate, i was talking about EPR paradox, is there a solution?
Dmitry67
Sep2-09, 02:59 PM
Is there a problem? :)
As Dmitry67 has already: Is thera a problem?
It is important to remember that what Einstein and co ASSUMED was a paradox in QM is actually not.
The starting point of their argument is basically that a certain type of experiments will "obviously" yield a result X (because information can not travel FTL); i.e. they ASSUMED a certain outcome.
However, when people actually started doing these experiments many years alter this was NOT what was seen meaning the whole line of reasoning leading up to the paradox is actually incorrect.
And yes; I am simplifying this quite a bit here (both the physics and the history) but the main point is that there IS no paradox; QM is consistent (at least mathematically; that many people enjoy spending ages discussing various intepretations related to the EPR is another story.
Also, I would like to stress that I am in no way trying to say that the EPR paper was not important because it was -it stimulated an enourmous amount of important work- but that does not change the fact that what they were trying to show in the paper (that QM was inconsistent) turned out to be incorrect.
DrChinese
Sep2-09, 04:04 PM
As Dmitry67 has already: Is thera a problem?
It is important to remember that what Einstein and co ASSUMED was a paradox in QM is actually not.
The starting point of their argument is basically that a certain type of experiments will "obviously" yield a result X (because information can not travel FTL); i.e. they ASSUMED a certain outcome.
However, when people actually started doing these experiments many years alter this was NOT what was seen meaning the whole line of reasoning leading up to the paradox is actually incorrect.
And yes; I am simplifying this quite a bit here (both the physics and the history) but the main point is that there IS no paradox; QM is consistent (at least mathematically; that many people enjoy spending ages discussing various intepretations related to the EPR is another story.
Also, I would like to stress that I am in no way trying to say that the EPR paper was not important because it was -it stimulated an enourmous amount of important work- but that does not change the fact that what they were trying to show in the paper (that QM was inconsistent) turned out to be incorrect.
To add to the above, with which I agree entirely:
The QM answer is: "This makes the reality of P[position] and Q[momentum] depend upon the process of measurement carried out on the first system..." These words are from the EPR paper itself, although they rejected this idea because they thought it was not a "reasonable definition of reality".
how do physicists solve this contradiction (when information moves faster then the speed of light)?
Somehow solve, one way or another ;)
... without any information moving faster then the speed of light.
people, concentrate, i was talking about EPR paradox, is there a solution?
If you want solution for you I can recommend deterministic viewpoint involving hidden variables. You can imagine that hidden variables does not hold (yet) any known physical meaning - it is just sophisticated way of numbering particles :)
With that view in mind you should draw some analogy between wave function collapse and discarding of some particles (subsampling). That way you pick the part of sample that show required correlations in postselection process that does not require any faster than light information transfer.
There might arise small problem if you afterwards will consider Malus' law. That's because implied explanation for Malus' law is that photons have hidden variable of polarization.
So it turns out that this way EPR experiments conflict with intuitive understanding of Malus' law.
However this can be solved if you assume that polarization is not hidden variable of single photon but rather property of sample of photons e.g. their configuration relative to one another plus certain strange arrangement between polarizers that might not seem so strange if you like Bomian interpretation of QM or even have heard about The Invariant Set Postulate hypothesis.
Thought that I might add this link as it seems relevant to what I said about Malus' law (not completely sure however)
http://www.springerlink.com/content/0136072643546224/
It's Hnilo et al "Low Dimension Dynamics in the EPRB Experiment with Random Variable Analyzers"
haushofer
Sep3-09, 06:42 AM
Ok, it has been a long time since I've thought about this EPR-stuff, but basically I always thought the problem was the following:
Both particles are in a superposition. If I measure one particle's spin, it's wavefunction will collapse to a spin eigenfunction. But the other particle's wavefunction will also collapse to the other spin eigenfunction. I always considered this to be some sort of "information exchange", because the wavefunction is collapsed by the measurement.
In the classical case, I let a red and a white ball travel in opposite directions, without knowing which one goes where. If I measure one ball's colour, I also know the other colour. But in this case, I don't have any "information exchange", because classically there isn't a superposition and the ball was already in the "colour eigenfunction" before I measured.
I didn't read all the posts here, so maybe I'm repeating things, but this point of view on "information exchange" is wrong? Apparently I never really understood the meaning of "information exchange" and the EPR-situation.
I didn't read all the posts here, so maybe I'm repeating things, but this point of view on "information exchange" is wrong? Apparently I never really understood the meaning of "information exchange" and the EPR-situation.
Actually you are quite right. What the EPR experiments show is that there is a superluminal causal connection and superluminal information transmission in a single measurement. What is not seen is superluminal matter or energy transport, or any possibility of superluminal controllable signalling.
The latter signalling thing is what people confuse with 'information transmission' - signalling refers to what happens when you repeat the experiment many times. It would be something like transmitting a message in Morse code by going 'up-up-up down-down-down up-down-up' - there is no possibility of this because the quantum randomness washes out the controllability.
I haven't read the previous posts either, so I apologize if someone has already made this point.
Both particles are in a superposition. If I measure one particle's spin, it's wavefunction will collapse to a spin eigenfunction. But the other particle's wavefunction will also collapse to the other spin eigenfunction. I always considered this to be some sort of "information exchange", because the wavefunction is collapsed by the measurement.
Well but entanglement measurement happens when you correlate measurements from both sites. So if you say that measurement collapses wavefunction then correlation of spin measurements from both sites collapses wavefunction to "entanglement eigenfunction" if this can be said this way.
That's without sarcasm of the other answer :smile:
That's without sarcasm of the other answer :smile:
Sorry, why is my answer (which I presume is what you're referring to) sarcastic?
Sorry, why is my answer (which I presume is what you're referring to) sarcastic?
transmitting a message in Morse code by going 'up-up-up down-down-down up-down-up'
I found this funny
Do you say that I missed your point?
I found this funny
Do you say that I missed your point?
Given that you can apparently instantly transmit information to the other side of the universe (something like 'since here is up, over there it must be down') then - if only you could control what happens at your end - you could transmit a message in Morse code instantaneously to Alpha Centauri (a controllable signal) with ups and downs replacing dots and dashes. With the universe as it apparently is, then all you would actually get is random noise.
It's a bit silly certainly, but it isn't sarcastic.
Given that you can apparently instantly transmit information to the other side of the universe (something like 'since here is up, over there it must be down') then - if only you could control what happens at your end - you could transmit a message in Morse code instantaneously to Alpha Centauri (a controllable signal) with ups and downs replacing dots and dashes. With the universe as it apparently is, then all you would actually get is random noise.
It's a bit silly certainly, but it isn't sarcastic.
Ups, I didn't realized :redface:
Then maybe consider other a bit more scientific option that each separate spin measurement actually IS wavefunction of entanglement? And it collapses when by perfectly classical information transfer it is transferred to coincidence counter and is correlated with other side?
Actually you are quite right. What the EPR experiments show is that there is a superluminal causal connection and superluminal information transmission in a single measurement. What is not seen is superluminal matter or energy transport, or any possibility of superluminal controllable signalling.
There is another possibility -- nonseparability. The EPR-Bell experiments imply nonlocality and/or nonseparability.
There is another possibility -- nonseparability. The EPR-Bell experiments imply nonlocality and/or nonseparability.
Indeed it is a possibility. But sadly one that doesn't appear to make any sense - I have never seen this explained in words that a bear of little brain like myself can actually understand. Go on, try me. And remember, I really am very stupid.
Indeed it is a possibility. But sadly one that doesn't appear to make any sense - I have never seen this explained in words that a bear of little brain like myself can actually understand. Go on, try me. And remember, I really am very stupid.
Ok :smile: We have an explanation of our particular method using the famous "face-vase" illusion. It's a paragraph in the Conclusion (section 6) of arXiv 0908.4348, the paragraph begins with "We have already presented a mathematically detailed account of our approach so here we supply a caricature ... ." That paragraph should provide a picture of a nonseparable ontology.
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,
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
Sep4-09, 11:00 AM
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.
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.
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.
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?
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
Sep7-09, 10:54 PM
Thanks for the suggestion, I wish it had worked.
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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.
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.
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)
Thanks for the suggestion, I wish it had worked.
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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??).
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
Sep9-09, 08:05 AM
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.
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.
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.
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 any one 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).
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 any one 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.
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.
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.
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.
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.
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.
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
Sep10-09, 10:35 PM
what are other thing that more faster than the speed of light
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?
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.
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
Sep13-09, 04:33 AM
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
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 text book 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.
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
Sep13-09, 11:28 AM
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 blackhole, points also heavily in the direction of background independent theory of QG(emergent spacetime).
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
Sep13-09, 12:11 PM
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 scince, i see no reason to abandon it(though background-independent QG is probably the hardest approach).
"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 scince, 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 :wink:
WaveJumper
Sep13-09, 04:52 PM
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 :wink:
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).
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 text book 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 :bugeye:.
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 :bugeye:.
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.
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.
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.
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.
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