Does Schrodinger's Cat Paradox Suck?

[Ken G]

I should point out that, classically, this is ontological point of view is merely a simplification, rather than something demanded by the mathematics of classical statistical mechanics.

Yes, it is not a definition of a mixed state, it is a way to help recognize them.

Classically, mixtures remains stable; they can be neither created not destroyed. Furthermore, the components do not influence each other in any way.

They can certainly be destroyed, by looking (which reduces them, even all the way to a pure state for particularly simple systems). But yes, they don't influence each other, that's one key difference with superpositions.

In other words, you cannot design an experiment that can distinguish between "nature does know which" and "nature doesn't know which".

Preferring to imagine that nature itself knows is just a philosophical stance, called realism. But it's quite a common view, along the lines of Einstein's decree that the Moon is still there when we are not looking at it. I don't argue for realism, I find it as limited as any other philosophical specialization.

This doesn't really make sense, unless by "quantum mechanical state" you really mean to restrict your attention solely to the states that are pure.

Yes, that is what I mean by a "quantum mechanical state"-- I was just drawing the distinction with a classical state. It all comes back to the Copenhagen notion that states are however we treat a system, versus the fairly common approach that a state is "what nature knows about itself". The latter is a pure state, it involves complete information of the system. Personally, I don't think there's any such thing as "the wavefunction of the universe", I'm in the Copenhagen camp.

 

[Ken G]

If you place left and right circular polarisers in front of the left and right slits respectively, you will NOT get a two slit diffraction pattern.

You're right, that's not really the experiment I intended, my bad. I meant to add a linearly polarized screen after the slits, so all photons hit the wall linearly polarized in the same way they started out. Please add that to what I said above, and thanks for the correction! With that modification, you will get a two-slit pattern, but not if you first completely entangle the particle polarizations with a paired photon that can be used to obtain independent which-way information (even if you don't ever use or extract that information). That entanglement has a vastly subtle influence on the outcome of the experiment, but the upshot is that the experimental outcome can be better predicted by treating the single particles coming through the slits as being in a mixed state rather than a superposition state, even though the combined wavefunctions are pure states. I suspect that is very analogous to the cat-in-the-box, with a much simplified apparatus, and note it resolves the usual way the paradox is expressed-- but not the real dispute between Copenhagen and Many Worlds, which is whether or not there is really in some sense an alive and dead cat "somewhere in the greater reality," i.e., whether or not the closed system (not the cat by itself, that's just wrong quantum mechanics) can be in a pure state.

 

[Rap]

With that modification, you will get a two-slit pattern, but not if you first completely entangle the particle polarizations with a paired photon that can be used to obtain independent which-way information (even if you don't ever use or extract that information).

I don't believe that down-converting the photon and sending one thru the two-slit/circular polarizer/linear polarizer device will remove the diffraction pattern. If you use the other photon to select a subset of the photons going thru the device, then that subset will not form a diffraction pattern.

 

[Ken G]

I don't believe that down-converting the photon and sending one thru the two-slit/circular polarizer/linear polarizer device will remove the diffraction pattern. If you use the other photon to select a subset of the photons going thru the device, then that subset will not form a diffraction pattern.

I think it's the other way around. The only way to get a pattern is to correlate with results of the other photons, while erasing which-way information on both sets. If any which-way information survives, even if it is never used, you can't get a pattern.

 

[Ken G]

I think your question comes down to, do physicists make physics, or does physics make physicists? If you take the latter approach, the the "true state" of a system can be distinguished from whether or not we know something about that system. If you take the former approach, there is no true state, there's just all the different things that the different physicists know about a system, and the ways they use that knowledge to make a prediction about it. And even though I've heard many people claim to be of the "shut up and calculate" school, I've found very few of them actually willing to embrace that latter stance.

 

[Rap]

I think it's the other way around. The only way to get a pattern is to correlate with results of the other photons, while erasing which-way information on both sets. If any which-way information survives, even if it is never used, you can't get a pattern.

Hmm - I am still thinking about this. But I think I agree with that, I just don't see it as that much different from what I said. A photon going thru a 2-slit/circular polarizer/linear polarizer device has which-way information erased. Looking at the other photon of the pair will not give you which-way information, thus you get a diffraction pattern. Removing the linear polarizer from the device yields which-way information, and removes the diffraction pattern.

"shut up and calculate" sounds like the "calculate" part is cut and dried, and as our discussion on SC shows, and some of the Bell-related experiments are concerned, its not, at least not in my mind. As long as the "calculate" part is not cut and dried, nobody should shut up about that. As you say, "there's just all the different things that the different physicists know about a system, and the ways they use that knowledge to make a prediction about it." Our brains are designed by evolution to intuitively understand classical physics, but not relativity or quantum physics, and in classical physics its easy to postulate an objective un-measured reality. We have not needed to intuitively understand relativity or QM in order to survive, so expecting to shoe-horn some classical intuition into them is a tall order. Maybe we can train ourselves to intuitively understand post-classical physics, but clinging blindly to classical concepts is not the most productive way to get there. Drop the classical intuition, start out with a clean slate, and start building from there, that's my program. The only thing I won't drop is logical consistency, and that seems to be maximized in Copenhagen QM. I won't reject the idea that it is a stepping stone to some deeper theory.

 

[Ken G]

Hmm - I am still thinking about this. But I think I agree with that, I just don't see it as that much different from what I said. A photon going thru a 2-slit/circular polarizer/linear polarizer device has which-way information erased. Looking at the other photon of the pair will not give you which-way information, thus you get a diffraction pattern. Removing the linear polarizer from the device yields which-way information, and removes the diffraction pattern.

Let's make sure we have the same apparatus in mind. We have a laser with a linear polarizer, creating a superposition of left and right circular polarization in each photon. We have two slits, one with a left circular polarizer in it, the other right. Then after the slits, we have a linear polarizing plane, for simplicity aligned the same way as the original linear polarizer. I think we agree this will give a two-slit diffraction pattern on the wall.

Now we insert down-converters, and say that each photon splits into two with the same superposition of left and right circular polarization as their parent. One of those photons is passed through the two slits, the other is put in a box somewhere. Now we will not get a two-slit pattern, because that apparatus does not erase which-way information-- the photon in the box could be used to determine which path the other followed (if it makes it to the screen at all). There is no way to get a diffraction pattern, because no photon making it to the wall could receive contribution from amplitudes of both slits, and still be consistent with the information in the box.

So to recover a two-slit pattern, we need to open the box and pass each photon in there through an erasing apparatus such that the information of its polarization is lost. Then if we sort the original wall pattern (which is not a two-slit pattern) into two batches, based on different outcomes of the erased pair result, we can find that there were two two-slit patterns, slightly offset (that's the huge subtlety here), that made up the original non-pattern, but we could not extract it until correlating with the outcomes of the erased pair experiment.

I'm saying that the cat paradox could be viewed as analogous to the alive/dead cat is like the mixed state of the photons hitting the wall, which is not a superposition pattern. The only way to find a superposition in there is to be able to erase the information in the rest of the box and then correlate the outcomes, but since the rest of the box is also classical (or it can't kill a cat), that's no easier than getting a cat in a superposition state.

As long as the "calculate" part is not cut and dried, nobody should shut up about that.

I agree-- often a good pedagogy is quite helpful in getting the answers right.

 

[yuiop]

Let's make sure we have the same apparatus in mind. We have a laser with a linear polarizer, creating a superposition of left and right circular polarization in each photon.

Hi Ken, I consider it my job to nit-pick the details .. hope you don't mind

Here are some details I think worth considering.

1)Yes, a linearly polarised photon can be considered a superposition of left and right handed polarization.

2)The use of the word superposition here is in the strictly Newtonian sense and I am not sure if this differs from the way superposition is normally used in quantum theory.

3)Can we consider each photon as splitting into a left handed circular polarised (LHCP) and a right handed circular polarised (RHCP) version of itself with one version passing through one slit and the other version passing through the other? I think not.

We have two slits, one with a left circular polarizer in it, the other right.

4)You need to make clear the orientation of the "circular polarisers". In the quantum erasure experiments linked to earlier by DrC, the "circular polariser" on the left slit has its fast axis at -45 degrees and the other has its fast axis at + 45 degrees (looking from the source). I think it would be good to stay with that arrangement so that we can stay with linked papers for reference and avoid confusion.

5)I have put "circular polariser" is scare quotes because I think you are using "circular polariser" to mean "quarter wave plate". To convert light from a source that produces linearly polarised light with random orientations into circular polarisation of a given handedness, you need a combination of a linear polariser followed by a quarter wave plate (QWP). I guess you might consider the combination of an initial (shared) linear polariser followed by a QWP at each slit as a "circular polariser" at each slit.

6)You need to be clear that light passing through a linear polariser followed by a QWP does not always result in circularly polarised photons coming out the other end. If the linear polariser is aligned with the fast axis or the slow axis of the quarter wave plate, then linearly polarised light entering the QWP, will exit as linearly polarised light with its orientation unchanged. In other words a "circular polariser" does not always result in circular polarised light coming out. For this reason, I think the term "circular polariser" can be confusing.

7)If the two quarter wave plates are orientated as in (4) then linearly polarised light with a vertical orientation will be converted to LHCP light at the left QWP and RHCP light at the QWP of the right slit. Linearly polarised light with a horizontal orientation will be converted to RHCP light at the left QWP and LHCP light at the right QWP. Therefore whether the light exits a given QWP with left handed or right handed circular polarisation depends on whther the initial linear polariser was vertical or horizontal, so calling one QWP the left circular polariser and the other the right circular polariser is ambiguous if the initial linear polariser does not have a fixed orientation.

8)A "circular polariser" in photography is a linear polariser glued to a QWP. Is that what you intended? A linear polariser and a QWP at each slit as well as the initial and final shared linear polarisers?

Then after the slits, we have a linear polarizing plane, for simplicity aligned the same way as the original linear polarizer. I think we agree this will give a two-slit diffraction pattern on the wall.

9)An initial shared linear polariser (aligned vertically or horizontally) followed by a QWP at each slit (at 90 degrees to each other) will produce a double slit fringe (or anti-fringe) pattern at the screen. The second linear polariser after the QWPs is not required in this case to produce an interference pattern.

10)An initial shared linear polariser (aligned at + or - 45 degrees) followed by a QWP at each slit (at 90 degrees to each other) will produce a single slit fringe (or anti-fringe) pattern at the screen. A second linear polariser after the QWPs, with the same orientation as the first, will make no difference.

11)Taking (9) and (10) into account, it is probably reasonable to conclude that a second linear polariser after the QWPs has no effect on the results if it has the same orientation as the initial linear polariser.

Now we insert down-converters, and say that each photon splits into two with the same superposition of left and right circular polarization as their parent. One of those photons is passed through the two slits, the other is put in a box somewhere. Now we will not get a two-slit pattern, because that apparatus does not erase which-way information-- the photon in the box could be used to determine which path the other followed (if it makes it to the screen at all). There is no way to get a diffraction pattern, because no photon making it to the wall could receive contribution from amplitudes of both slits, and still be consistent with the information in the box.

12)I am not clear here whether you still have linear polarisers before and after the QWPs or just a single initial polariser before the the QWPs or no linear polarisers at this stage. Whichever it is, I can guarantee that what you see at the interference screen is completely unaffected by the presence of the entangled partner until you carry out coincidence checks at later stage.

So to recover a two-slit pattern, we need to open the box and pass each photon in there through an erasing apparatus such that the information of its polarization is lost. Then if we sort the original wall pattern (which is not a two-slit pattern) into two batches, based on different outcomes of the erased pair result, we can find that there were two two-slit patterns, slightly offset (that's the huge subtlety here), that made up the original non-pattern, but we could not extract it until correlating with the outcomes of the erased pair experiment.

I think what you are getting at in this last statement is basically correct (assuming no linear polarisers in the double slit path with the QWPs). This is consistent with the experiment described here http://grad.physics.sunysb.edu/~amarch/Walborn.pdf here http://grad.physics.sunysb.edu/~amarch/ and here http://www.mat.ufmg.br/~tcunha/2003-07WalbornF.pdf

I think the best way to give a consistent description of the experiment you intend to use is to use the experiments in those links as the basis of your experiment and clearly state how your experiment differs (if it does).

Although I can not be absolutely sure all my "points" are 100 percent correct, the main point is that there is a lot to consider in clearly defining and analysing this experiment.

P.S. I agree with your hint that there is a "huge subtlety" involved in the slight offset in the diffraction patterns. Does that provide which way information in itself? Maybe that is a subject for a thread of its own.

 

[Ken G]

2)The use of the word superposition here is in the strictly Newtonian sense and I am not sure if this differs from the way superposition is normally used in quantum theory.

It's the same in QM, that's a good superposition state.

3)Can we consider each photon as splitting into a left handed circular polarised (LHCP) and a right handed circular polarised (RHCP) version of itself with one version passing through one slit and the other version passing through the other? I think not.

There's no need to make any claims about what the photon is doing, it suffices that the prediction receives contribution from amplitudes going through both slits, which interfere. It's the same with classical fields, the only wrinkle QM adds is that it's a quantum doing it.

4)You need to make clear the orientation of the "circular polarisers". In the quantum erasure experiments linked to earlier by DrC, the "circular polariser" on the left slit has its fast axis at -45 degrees and the other has its fast axis at + 45 degrees (looking from the source). I think it would be good to stay with that arrangement so that we can stay with linked papers for reference and avoid confusion.

We don't need a quarter wave plate, that's if you want to convert the polarization. I just want something that let's a given linear polarization through half the time, and circularly polarizes it, by excluding the opposite circular polarization. We could do something as simple as introduce a birefringent material with different refraction angles for the two circular polarizations, and just let one of the angles through each slit, such that left-circular gets through one of the slits, and right the other.

8)A "circular polariser" in photography is a linear polariser glued to a QWP. Is that what you intended?

No, I intended a "circular polarizer" in the same way we would speak of a "linear polarizer"-- not a conversion, but a gate that allows only one polarization through while blocking the other. Interesting that the two types of polarizer are referred to so differently in photography! I'm glad you clarified.

9)An initial shared linear polariser (aligned vertically or horizontally) followed by a QWP at each slit (at 90 degrees to each other) will produce a double slit fringe (or anti-fringe) pattern at the screen. The second linear polariser after the QWPs is not required in this case to produce an interference pattern.

That's true, but that's not the setup I have in mind. Your setup would allow half of all the photons to hit the screen if there were a second linear polarizer, or all of them if there wasn't. My setup already excludes half the photons at the slits, and another half of what's left at the second polarizer, so only 1/4 make the diffraction pattern, the other 3/4 never make it to the screen. The second linear polarizer is needed because the two opposite circular polarizations coming from the slits won't interfere otherwise, the key correction you made above.

10)An initial shared linear polariser (aligned at + or - 45 degrees) followed by a QWP at each slit (at 90 degrees to each other) will produce a single slit fringe (or anti-fringe) pattern at the screen. A second linear polariser after the QWPs, with the same orientation as the first, will make no difference.

Right, because the opposite polarizations won't interfere. But that's not the setup here.

12)I am not clear here whether you still have linear polarisers before and after the QWPs or just a single initial polariser before the the QWPs or no linear polarisers at this stage. Whichever it is, I can guarantee that what you see at the interference screen is completely unaffected by the presence of the entangled partner until you carry out coincidence checks at later stage.

That's not true, the mere presence of entanglement destroys the interference pattern in the experiment I'm describing. The kinds of coincidence sorting you are referring to is what you need to recover the interference pattern via additional sorting of the outcomes.

P.S. I agree with your hint that there is a "huge subtlety" involved in the slight offset in the diffraction patterns. Does that provide which way information in itself? Maybe that is a subject for a thread of its own.

I agree that the source of that offset is definitely worth a thread of its own-- there is something very subtle in that kind of entangled state that is capable of destroying an interference pattern by dividing and offsetting it.

 

[Rap]

I just want something that let's a given linear polarization through half the time, and circularly polarizes it, by excluding the opposite circular polarization.

Lets call CP=circular polarizer of Ken G., let's call Yuiop's a QP, a quarter wave plate, and VP=Vertical polarizer. Are you saying that the presence of a diffraction pattern on the 2-slit/CP/VP device will depend upon whether the photons entering the device are downshifted or not? I strongly doubt that this is so.

 

[yuiop]

Lets call CP=circular polarizer of Ken G., let's call Yuiop's a QP, a quarter wave plate, and VP=Vertical polarizer. Are you saying that the presence of a diffraction pattern on the 2-slit/CP/VP device will depend upon whether the photons entering the device are downshifted or not? I strongly doubt that this is so.

I tend to agree. If the diffraction pattern was at all influenced by the presence of an entangled partner, then it would be easy to construct a signalling device that could transmit meaningful information FTL.

 

[Ken G]

I tend to agree. If the diffraction pattern was at all influenced by the presence of an entangled partner, then it would be easy to construct a signalling device that could transmit meaningful information FTL.

No, that would not be possible. Try it.

 

[Ken G]

Lets call CP=circular polarizer of Ken G., let's call Yuiop's a QP, a quarter wave plate, and VP=Vertical polarizer. Are you saying that the presence of a diffraction pattern on the 2-slit/CP/VP device will depend upon whether the photons entering the device are downshifted or not? I strongly doubt that this is so.

Yes, it will depend on that. But this should be clear-- if we don't downconvert, we all agree we'll get a two-slit pattern, but if we do downconvert, we can know which slit each photon went through just by testing its pair photon. So if we could get a two-slit pattern in the raw data with the 2-slit/CP/VP set of photons, and pair that with the polarization info from the paired set, we can know both which-way info on every photon, and also have those photons participate in a two-slit pattern. That's just what we can not do.

It's surprising, yes, but it has to work out this way-- an entangled system is just a very different system, we can't pretend its parts are unaffected. That's basically my whole point here-- projecting entangled systems tends to give you mixed states. That's why the cat paradox is normally told wrong, about the cat itself, but there is an interesting paradox there when addressed to the entire system.

 

[yuiop]

No, that would not be possible. Try it.

I agree that it is not possible, but it is not possible precisely because the interference pattern is not affected by whether there are entangled partners or not.

Maybe I am misunderstanding your set up. Let us say we have your 2-slit/CP/VP set up with an non-entangled source of 702nm wavelength and an interference pattern is observed at screen (s) after the slits. Now we replace the source with a 351nm wavelength laser and pass it through a down converter so that entangled photons with 702nm wavelength are produced and these are directed to path s with the screen and path p for the entangled partners. Now Rap and myself are saying that what is seen at the screen with the entangled source is exactly the same as with the non-entangled source (as long as the wavelength arriving at the slits is the same in both cases). Now if we place a polariser in path p and manipulate it various positions it will make no difference at all to what is seen at screen s and and removing the polariser from path p will also make no difference. In fact there is nothing at all you can do to the entangled photons in path p that make any difference at all to what is observed in path s (unless you do coincidence counting at a later time) and if you could do anything to path p that instantly affects what is observed at path s, then you would have an FTL communication device.

 

[Ken G]

I agree that it is not possible, but it is not possible precisely because the interference pattern is not affected by whether there are entangled partners or not.

I'm saying, use the apparatus I describe, with the outcome I describe, and try to get FTL information out of it. You claimed that's possible, but didn't say how.

Maybe I am misunderstanding your set up. Let us say we have your 2-slit/CP/VP set up with an non-entangled source of 702nm wavelength and an interference pattern is observed at screen (s) after the slits. Now we replace the source with a 351nm wavelength laser and pass it through a down converter so that entangled photons with 702nm wavelength are produced and these are directed to path s with the screen and path p for the entangled partners. Now Rap and myself are saying that what is seen at the screen with the entangled source is exactly the same as with the non-entangled source (as long as the wavelength arriving at the slits is the same in both cases).

And that's what is not true. That is a different system there, it is a subspace of a larger entangled system, and you have to account for that. The key is that we entangled the state after we set up its pure wavefunction (the original linear polarization). Had we entangled first, then done the linear polarization, that's the usual way we set up experiments-- ignoring their history because we already have a pure state.

In fact there is nothing at all you can do to the entangled photons in path p that make any difference at all to what is observed in path s (unless you do coincidence counting at a later time) and if you could do anything to path p that instantly affects what is observed at path s, then you would have an FTL communication device.

I know, that's why you will not get a two-slit pattern on path p, no matter what you do with the entangled pair on path s-- unless you erase and correlate with that pair.

 

[Rap]

I should not say that I disagree totally with Ken G. - he is correct when he says that if you use down converted photons, you will be able to determine which slit every photon that strikes the screen in the 2-slit/CP/VP device went through. A diffraction pattern is evidence that you do not know it. Its the EPR paradox, that I guess I still don't have an intuitive handle on, because now this implies that if you send a vertically polarized plane wave from the Andromeda galaxy thru a 2-slit/CP/VP device, you cannot predict whether a diffraction pattern will be observed (i.e. whether Maxwell's equations will give the right answer) until you can determine whether the beam was downconverted in the Andromeda galaxy or not.

 

[Ken G]

Perhaps we are getting hung up on particular details of the apparatus. All I am attempting to show is that a state like |R>|R>+|L>|L> is a pure state for two particles (they could be bosons or distinguishable particles, it doesn't seem to matter), but it does not mean that either of those particles are in a pure state like |R>+|L>. I am trying to get the |R>|R>+|L>|L> state with down-conversion, but if you don't think that works (I think it does, but I'm not married to it), then get it any other way you like.

What this all gets back to is if we describe the complete state of the cat-and-box like |A>|a>+|D>|d>, where A is an alive cat and a is the apparatus than can kill it in a non-kill configuration, and so forth, then this does not mean the cat is in the state |A>+|D>. An entangled state, projected onto a subspace, is not a superposition state, and that is why it is just wrong quantum mechanics to assert that a cat can be in a superposition of dead and alive.

However, this does not mean the cat paradox sucks, because one can still ask what the heck is going on with a state like |D>|d>+|A>|a>, when all we ever see are alive or dead cats.

 

[yuiop]

I'm saying, use the apparatus I describe, with the outcome I describe, and try to get FTL information out of it. You claimed that's possible, but didn't say how.
And that's what is not true. That is a different system there, it is a subspace of a larger entangled system, and you have to account for that. The key is that we entangled the state after we set up its pure wavefunction (the original linear polarization). Had we entangled first, then done the linear polarization, that's the usual way we set up experiments--

Yes, that is the normal way we set up experiments and I seem to have missed the part where you mention that your set up is unusual. In fact I invited you to use one of the experiments in the links which are described in detail and say how your set up differs and you declined to do that.

Anyway, if we (vertically) polarize the photons before down converting them what do you think will happen? Do you think the entangled photons will all have a consistent orientation when they are emitted from the BBO crystal? I think it almost certain that is not the case. I can show if the entangled photons coming from the BBO crystal do not have random orientations, then you will have a means to communicate FTL. I work by the unwritten "law" that "If your thought experiment predicts FTL communication, then you have made a mistake in your assumptions".

Let's say you have a source that sends entangled beams in opposite directions to observers A and B (using whatever set up you like). Ask A to make whatever tests he likes on his beam and he will not be able to determine if his photons are entangled or not, without reference to the photons or tests in beam B. It is only when coincidence counting and correlations between beams A and B are made that it can be determined that the two beams are entangled.

I still strongly maintain that whether the source is entangled or not makes NO difference to what is seen or measured on a given beam if no comparison is made with the other beam.

 

[Ken G]

Yes, that is the normal way we set up experiments and I seem to have missed the part where you mention that your set up is unusual. In fact I invited you to use one of the experiments in the links which are described in detail and say how your set up differs and you declined to do that.

I was just too lazy to go back and read them, because all I want is a state like |R>|R>+|L>|L>, so if those papers get that, use them instead, and if they don't, they're not relevant to what I'm saying.

Anyway, if we (vertically) polarize the photons before down converting them what do you think will happen? Do you think the entangled photons will all have a consistent orientation when they are emitted from the BBO crystal? I think it almost certain that is not the case. I can show if the entangled photons coming from the BBO crystal do not have random orientations, then you will have a means to communicate FTL.

You can't get FTL from a state like |R>|R>+|L>|L>, and that's what I think you'll get when you down-convert. If I'm wrong, let's just get it another way, any way will do.

I work by the unwritten "law" that "If your thought experiment predicts FTL communication, then you have made a mistake in your assumptions".

I am fine with that law-- of course, winning the Nobel prize by finding a case where it is not true would sure be nice, but since we're dealing in gedankenexperiments, we'll have to stick to that principle.

Let's say you have a source that sends entangled beams in opposite directions to observers A and B (using whatever set up you like). Ask A to make whatever tests he likes on his beam and he will not be able to determine if his photons are entangled or not, without reference to the photons or tests in beam B. It is only when coincidence counting and correlations between beams A and B are made that it can be determined that the two beams are entangled.

There is no problem with FTL involved with knowing if a beam is entangled or not, since the entanglement is in the past light cone. We deal with entangled systems all the time, if I do an experiment on a beam of photons, and find they are all polarized the same way, I can pretty well conclude those photons have been entangled with something that says "polarization up" in their recent history, and I'm not violating FTL to know that.

I still strongly maintain that whether the source is entangled or not makes NO difference to what is seen or measured on a given beam if no comparison is made with the other beam.

Look at quantum erasure experiments-- the "signal" photons behave in ways where it is easy to tell that they have been entangled with the "idler" photons. For example, see http://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser , and consider this quote: "Note that the total pattern of all signal photons at D0, whose entangled idlers went to multiple different detectors, will never show interference regardless of what happens to the idler photons."

 

[Ken G]

I should not say that I disagree totally with Ken G. - he is correct when he says that if you use down converted photons, you will be able to determine which slit every photon that strikes the screen in the 2-slit/CP/VP device went through. A diffraction pattern is evidence that you do not know it.

Then I don't see how you are disagreeing with me at all, because that's pretty much the crux of what I'm saying. The state |R>|R>+|L>|L> causes its individual particles to behave differently from how |R>+|L> behaves, and that is trying to tell us something about the cat paradox.

 

[Rap]

Then I don't see how you are disagreeing with me at all, because that's pretty much the crux of what I'm saying. The state |R>|R>+|L>|L> causes its individual particles to behave differently from how |R>+|L> behaves, and that is trying to tell us something about the cat paradox.

I am having trouble believing that down-converted electromagnetic radiation disobeys Maxwell's equations.

If you analyse a vertically polarized plane wave impinging on the 2-slit/CP/VP setup using Maxwell's equations, you will get a diffraction pattern. To say that you will not get a diffraction pattern is to violate Maxwell's equations.

 

[Ken G]

I am having trouble believing that down-converted electromagnetic radiation disobeys Maxwell's equations.

Maxwell's equations aren't quantum mechanics. Didn't the Wiki I just cited make it perfeclty clear that entangled particles don't make double-slit patterns if the entanglement allows which-way information?

 

[Ken G]

Let's dispense with the polarization, since we just want a state like |R>|R>+|L>|L>, we may as well use the setup in the Wiki article at http://en.wikipedia.org/wiki/Delayed...quantum_eraser . Then we don't have to worry what down-conversion does to polarization, we can use "R" and "L" to mean down-conversion at the "right" and "left" slits instead. Since the Wiki article asserts that we do not get a two-slit pattern in that case, it suffices to hold the point I'm making-- |R>|R>+|L>|L> does not yield the two-slit pattern that |R>+|L> doea, so by analogy to the cat in the box, the cat is not in a superpositon state like |Alive>+|Dead>. That's all I'm saying, it's wrong quantum mechanics to claim that the cat continues to stay in a pure state even if we could imagine that it was in a pure state when put in the box. If we take that full system and start asking about the state of the cat within that system, then we have a complicated entity that is a subspace of an entangled system, and it will behave much more like a mixed state than a superposition state.

So even though the official meaning of a mixed state is a situation where we have incomplete information, there is another situation where we can have complete information about the whole system, yet the cat subspace acts like a mixed state. We can get an effective mixed state even in a situation where we have complete information of the box before we open it, and this sets aside the usual way the cat paradox is expressed. What remains, and what distinguishes CI from MWI, is whether we believe that we really do possesses complete information about that system (MWI), or if the structure of quantum mechanics actually does not access all the information there. If we take the latter stance, and say that our approach to physics (determinism) is what makes it impossible to address the full information there, and the part that doesn't fit has to be treated statistically, we are using CI. If we think the full information there follows the basic prescriptions of how we do physics (i.e., is deterministic) but is not accessible to us by some pernicious limitation (akin to a kind of blindness), we are using a Bohm model. I think these distinctions make it clear why until there is some way to either access the information that is kept from us, or demonstrate that it does not exist, we will not be able to distinguish these interpretatons.

 

[Rap]

Let's dispense with the polarization, since we just want a state like |R>|R>+|L>|L>, we may as well use the setup in the Wiki article at http://en.wikipedia.org/wiki/Delayed...quantum_eraser . Then we don't have to worry what down-conversion does to polarization, we can use "R" and "L" to mean down-conversion at the "right" and "left" slits instead. Since the Wiki article asserts that we do not get a two-slit pattern in that case, it suffices to hold the point I'm making-- |R>|R>+|L>|L> does not yield the two-slit pattern that |R>+|L> does.

Just to be clear, is it true that you are saying that in the original case of a 2-slit/CP/VP device, Maxwell's equations will not hold for down-converted radiation - i.e. an interference pattern will not be observed for a vertically polarized plane wave?

Regarding the wiki article, the introduction section, which I read, is not at all clear to me. I am not sure where the two slit device is located, I am not sure what "target" and "target phase" mean. Is the target the two slits or the detector? This section continually talks about which path the photon takes, or maybe both at once, and with my Copenhagen mentality, I have to continually interpret these classical-mentality statements in terms of measured results and the interpretation is difficult if not impossible at various points in the introduction.

This means I have to study the actual experimental setup and results, looking at the article itself and the various links. This will take me a while. Can we concentrate on one particular problem to its conclusion rather that bouncing from SC, to 2-slit/CP/VP, to quantum erasure, to your next gedanken experiment, etc. every time I have a question? Does this particular experiment illustrate your point? If so, let's stick with it to the conclusion.

 

[Tyrannical]

If it was possible that opening the box (looking) could resurrect a dead cat (change the result) than it would have been a better example. No less bizarre, but a better example.

 

[Ken G]

Just to be clear, is it true that you are saying that in the original case of a 2-slit/CP/VP device, Maxwell's equations will not hold for down-converted radiation - i.e. an interference pattern will not be observed for a vertically polarized plane wave?

The question is whether or not entangled polarizations can be said to be vertically polarized, or if one must say they are entangled-polarized. This is such a subtle point that I really don't even know the answer-- we know that lasers don't do this, they can prepare many photons in the same single-photon state without entangling their polarizations, so I don't know of BBO crystals work in effect just like lasers. or if there is additional entanglement there which insures that both members of the pair must show with the same circular polarization on the grounds that they are in some sense constrained to act the same, or if they should give opposite polarization to conserve angular momentum, or if they should give statistically uncorrelated angular momenta like a laser does. So I'm realizing this is a technical detail that is probably worth its own thread, but is not really the thrust of what I'm saying about the cat paradox.

Regarding the wiki article, the introduction section, which I read, is not at all clear to me. I am not sure where the two slit device is located, I am not sure what "target" and "target phase" mean. Is the target the two slits or the detector? This section continually talks about which path the photon takes, or maybe both at once, and with my Copenhagen mentality, I have to continually interpret these classical-mentality statements in terms of measured results and the interpretation is difficult if not impossible at various points in the introduction.

That is probably not the best Wiki article I ever read, but the important point is that it has down-converters in front of each slit, which splits into "signal" and "idler" photons, and which-way information of the signal photon can be extracted by looking at the trajectory of the idler photon. As a result, if you don't do anything with the idler photons, the signal photons do not yield a two-slit pattern. Hence, if there was a black box where the BBO crystals are, you could tell that entanglement is occurring in that black box because of the absence of the two-slit pattern in the signal data, and the ability to recover the two-slit pattern by erasing and correlating with idler photons. There's nothing FTL there, you can get information about a black box by looking at what comes out of it. But if it's a cat and a kill-mechanism, you could never erase-and-correlate with anything going on in the kill mechanism, such that you could end up with superposition behavior in the cat-- even if the cat started out in a pure state.

Can we concentrate on one particular problem to its conclusion rather that bouncing from SC, to 2-slit/CP/VP, to quantum erasure, to your next gedanken experiment, etc. every time I have a question? Does this particular experiment illustrate your point? If so, let's stick with it to the conclusion.

As I've said, the only thing that matters about any of these gedankenexperiments is the basic quantum mechanical truth that |R>|R>+|L>|L> is not going to behave the same way as |R>+|L>, as the former will act like a mixed state and the latter a superposition state in regard to experiments on the single-particle component of the system. I should have just said that from the outset, and not brought in any gedankens-- the point was simply to boil down the cat-and-box as much as possible.

 

[Dadface]

The discussions are still continuing.Great stuff.I wonder if anyone here can answer these questions:
1.Does Schroedingers experiment demand that all of the contents of the box be isolated from the surroundings when the box is closed?
2.If the answer to question 1. is yes then does the isolation need to be total,in other words is it necessary that the contents of the closed box have no interactions at all,not even gravitational interactions,with the surroundings?
3.If the answer to question 1. is yes and the answer to question 2. is no then can the needed level of isolation be defined and if so what is the needed level?
Thanks if anyone can answer these questions.I made some reference to these issues earlier on in this thread but did not pursue the matter to get exact answers.

 

[Ken G]

1.Does Schroedingers experiment demand that all of the contents of the box be isolated from the surroundings when the box is closed?

It demands that they be isolated in the sense that any outside influences are of no significance to the experimental outcomes, the usual meaning of "isolated" in physics.

2.If the answer to question 1. is yes then does the isolation need to be total,in other words is it necessary that the contents of the closed box have no interactions at all,not even gravitational interactions,with the surroundings?

Since it is a gedankenexperiment, we are free to either assert no gravity, or that gravity will not have a significant influence. Since gravity is not included fully self-consistently in quantum mechanics, it is never clear what gravity might do to the situation.

3.If the answer to question 1. is yes and the answer to question 2. is no then can the needed level of isolation be defined and if so what is the needed level?

That's exactly what is not clear. But the same is true even for a truly isolated system of a cat in a box-- the only way physics can answer if a system is truly isolated is if the outcomes of the experiment don't change as we further reduce the level of interaction with the environment. But the outcomes of the experiment are already the same, whether we have a pure or a mixed-state treatment of the entire system, so we could never tell how possible interactions with the environment adjudicate between a pure and a mixed state. What I've pointed to above is that it doesn't matter if the system as a whole is in a pure or a mixed state, because all results when we open the box and look at the cat are the same either way. That means we can always treat the cat as if it were alive or dead and we just don't know which, so if we can always treat the cat that way, how does it benefit us to imagine that something else might actually be true? What is "truth" outside of a consistent way for us to interact with and understand our environmental condition?

Thanks if anyone can answer these questions.I made some reference to these issues earlier on in this thread but did not pursue the matter to get exact answers.

I think that's because we already find a resolution to the situation even if we imagine that a truly isolated cat-and-box is possible, and introducing the impossibility of complete isolation does not appear to alter that resolution. If we want to know if one resolution works in every situation, we must confront that resolution with its most difficult challenge, which in this case is an idealized perfectly isolated system.

If you don't like that way of thinking about it, then recognize the cat-and-box is just an allegory for the entire universe. If the entire universe is like a cat in a box, then we can say we do have a truly isolated system, because what is outside the universe that could interact with it? (Barring some ambiguous meaning of what a "universe" is, like a multiverse "landscape".)

However, maybe your comments could be summarized as pointing out that the next theory of gravity might have something to say about the cat paradox, and I think that is probably true.

 

[Rap]

The question is whether or not entangled polarizations can be said to be vertically polarized, or if one must say they are entangled-polarized.

I read the wiki article ( http://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser ) you provided. It does not appear to me that Maxwell's equations are violated in the wiki article. To someone analyzing it from an electromagnetic wave viewpoint (i.e. without detecting individual photons) there are no surprising results. One-slit patterns show no interference, two-slit patterns do - no problem. The only surprising results are when you analyze it photon-by-photon.

Three points:

1. In the wiki article, there were many noise photons, so that only a simultaneous hit on D0 and D1-4 could be counted as two entangled photons. In the 2-slit/CP/VP device, I assumed no stray photons. The way I analyzed the 2-slit/CP/VP device was : I assumed that both signal and idler downshifted photons were circularly polarized in the same direction - possibly left, possibly right. The signal photon went thru a left-CP filter to a detector. The idler photon went thru a double slit, with a right-CP filter after the right slit, a left-CP filter after the left slit, then everything thru a VP filter just before the screen, then the screen. You can have four cases:

signal idler conclusion
------------------------------
no hit no hit downshifted photons were right polarized, idler photon slit inconclusive
no hit hit downshifted photons were right polarized, idler photon went thru right slit
hit no hit downshifted photons were left polarized, idler photon slit inconclusive
hit hit downshifted photons were left polarized, idler went thru left slit

In other words, for every idler photon hit on the 2-slit/CP/VP device, it could be decided which slit it came through, depending on whether or not there was a hit on the signal detector. This is in contrast to the wiki article which only counts simultaneous signal hits due to photon noise.

2. I am appealing to the correspondence principle here - QM must give the same results as classical physics when dealing with a classical problem. Dealing with the above setup classically, i.e. Maxwell's equations, you must observe an interference pattern on the 2 slit/CP/VP device, that is the idler beam must form an interference pattern.

3. Using the complementarity principle, you cannot have an interference pattern while knowing which slit the photon came through.

Points 1, 2, and 3 are incompatible, one must be wrong or incorrectly applied, I cannot figure out which at this point. My intuition is that 1 is the problem. Note that this problem is not encountered in the wiki article - only simultaneous hits are considered. If you consider only simultaneous hits in our second device, then you must extract from the set of idler photon hits the subset of idler photons which were simultaneous with signal hits, and this subset of photons will not display an interference pattern on the idler device.

 

[Ken G]

I read the wiki article ( http://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser ) you provided. It does not appear to me that Maxwell's equations are violated in the wiki article.

The point is that putting down-converters in front of the slits destroys the two-slit pattern. You can see that, it jumps right out. Now does that violate Maxwell's equations? It certainly does if you think Maxwell's equations are describing a superposition of classical in-phase wave amplitudes emanating from the two down-converters. This does not mean Maxwell's equations are actually violated, it means they are being applied incorrectly if one imagines that the down-converters are acting classically.

That is the prevailing point here-- although I'm not sure how down-converters will act in every situation (particularly in regard to polarization), in that uncontroversial Wiki setup we have an example where down-converters are simply not behaving as if they were operating on classical wave amplitudes and doing nothing more than reducing the field strength by 1/root(2) as the waves come through. If one imagines that is what Maxwell's equations tell us is happening there, then we can say that Maxwell's equations are wrong, expressly because Maxwell's equations have no clue what entanglement is. If, however, we incorporate the effects of entanglement manually, we can get Maxwell's equations to work on the modified outputs (which basically amounts to getting them to incorporate those subtle shifts that divide the entangled populations).

To someone analyzing it from an electromagnetic wave viewpoint (i.e. without detecting individual photons) there are no surprising results. One-slit patterns show no interference, two-slit patterns do - no problem.

That depends entirely on how they are analyzing it. Let's say they treat each down-converter as if it simply multiplied the wave amplitude by 1/root(2), sent it along, and shunted a second wave of that amplitude off somewhere else. How could you tell them that they were applying Maxwell's equations incorrectly to the down-conversion process? It would seem like a perfectly natural way to apply Maxwell's equations there, the problem is that Maxwell's equations are not quantum mechanics.

1. In the wiki article, there were many noise photons, so that only a simultaneous hit on D0 and D1-4 could be counted as two entangled photons.

I don't see any fundamental issue here, no doubt things would work fine if photons were sent through one at a time and all possibilities tracked.

You can have four cases:

signal idler conclusion
------------------------------
no hit no hit downshifted photons were right polarized, idler photon slit inconclusive
no hit hit downshifted photons were right polarized, idler photon went thru right slit
hit no hit downshifted photons were left polarized, idler photon slit inconclusive
hit hit downshifted photons were left polarized, idler went thru left slit

In other words, for every idler photon hit on the 2-slit/CP/VP device, it could be decided which slit it came through, depending on whether or not there was a hit on the signal detector. This is in contrast to the wiki article which only counts simultaneous signal hits due to photon noise.

I'm not sure what you mean here, a straightforward change in the apparatus in the Wiki article could easily obtain which-way information from every idler photon, in analogy to the polarization version.

2. I am appealing to the correspondence principle here - QM must give the same results as classical physics when dealing with a classical problem.

But one has to know how to do the classical problem. If you tell me how you would treat the Wiki apparatus entirely in the language of Maxwell's equations applied to fields, I could understand.

3. Using the complementarity principle, you cannot have an interference pattern while knowing which slit the photon came through.

We definitely agree there.

Points 1, 2, and 3 are incompatible, one must be wrong or incorrectly applied, I cannot figure out which at this point. My intuition is that 1 is the problem.

I don't know that the polarization apparatus achieves the desired |R>|R>+|L>|L> state, but I do know that the Wiki setup does, so I think we should just use the Wiki setup. Everything I'm saying applies just as well there.