Does Schrodinger's Cat Paradox Suck?

[Rap]

Having read the last few posts in this thread, there is still some confusion about whether the cat is (1) in superposition of dead AND alive or (2) is definitely either alive or dead but not both, while the box is closed and the observer can make no observations of the state of the cat. Now persons taking either position (1) or (2) are making claims about the state of the cat with absolutely no evidence to support their position because by the definition of the thought experiment no observations can be made, only suppositions.

Now let us say you have introduced a student to quantum physics by way of Schroedinger's cat example and then go on to state that a quantum particle is also in a state of superposition before measurement. A student can then reasonably conclude that "superposition" is just physicists' "mumbo jumbo" for "we do not know what the state of the particle is, simply because we have not yet measured it". If there is a deeper meaning to superposition, then Schroedinger's cat is doing a very poor job of demonstrating what it is.

The short answer is yes, "superposition" is just physicists' "mumbo jumbo" for "we do not know what the state of the particle is, simply because we have not yet measured it" and there is no deeper meaning to superposition.

The problem is again, the use of the word "state". Let's define "state" as the wave function or, equivalently, the quantum state of the particle. I think you are using the word "state" at a particular time to mean the quantum state of a particle if it were measured at that time. Let's call that the "measure-state". (Note that a particle is not in a well defined measure-state unless you specify what measurement you would make - If you measure position, then you get a different measure-state than if you measure momentum. For the cat, this is not something to worry about.)

So I think your statement is: "superposition" is just physicists' "mumbo jumbo" for "we do not know what the measure-state of the particle is, simply because we have not yet measured it"

So yes, I agree completely, its obviously true. A superposition consists of a bunch of possible measure-states, each with their own amplitude. It is an indication of the fact that the scientist does not know which measure-state the particle is in. When you make a measurement, the state collapses to one of those measure-states, and then you know.

If you have a measure state, Schroedingers equation tells you how it changes as time goes on. As time goes on, it becomes a superposition. The measure state evolves into a superposition state, which is a bunch of possible measure states, which is physicist's "mumbo jumbo" for "we do not know which measure state it has evolved into".

To Copenhagen people, there is no deeper meaning to superposition.

NOTE - this only applies to quantum wave functions, in a very isolated system. If you flip a coin and cover it with your hand without looking at it, it is not in a superposed state because you cannot describe it with a wave function. A wave function analysis only works for an isolated system, and your hand, the coin, everything else is open to the universe so you can't do QM. Thats why the cat is inside a box. Its the same with classical mechanics - if you take 12 toothpicks and create a little box, and stand outside, you cannot calculate the thermodynamics or velocities or anything inside that box for the next day or two just knowing what goes on inside the box at time zero. You have to know what the rest of the universe is doing, what the weather will be in an hour or a day or two. Quantum mechanics is much more restrictive. You cannot even have a stray photon wander into your box without upsetting the QM calculations.

 

[Ken G]

So you are saying that even in priciple, we cannot assign a wave function to a macroscopic object because "too much of the data (all the phase coherences) that would need to be tracked is going to be entangled with the instruments doing the measuring". I do not understand this "too much data being entangled with the instrument" effect. I assume this effect is continuous, gets continually worse as the size of the system being investigated contains more and more particles. Can you describe this effect a bit more fully, perhaps with just a few particles which demonstrates the effect, even if the effect is miniscule?

What I'm saying is that you don't get pure states naturally, they happen only in very controlled environments, and even then only in the mind of the physicist. The classic way to get a pure state is to pass a single particle through a Stern-Gerlach arrangement so that it has spin up or spin down, but of course that is not actually the state of the particle-- the particle has a zillion indistinguishable partners all over the universe and there's no such thing as a single particle wave function for real. However, we can isolate the particle to the point where the "true" wavefunction isn't needed, and we get instead the concept of a "single particle wavefunction." It's a good concept because it gives us correct predictions, so we get away with it even though it is not the quantum mechanically correct state of the particle in the universe. Or put differently, it is only the correct wavefunction if we allow that quantum mechanics is a tool used by physicists, not a true description of nature. So let's adopt that stance for now-- quantum mechanics is a set of rules that a neural processor uses to make correct predictions of macroscopic measurements.

So in this way of thinking, we do get pure states of single particles, but only just after we do a measurement. As you say, this then evolves into a superposition if all that happens is the particle is acted on by potentials-- but that does not include doing measurements on the particle. So the pure state only exists as a kind of interloper between two measurements, and neither measurement is itself describable as a pure state of anything. Now we can ask the question of whether a cat could ever be in a pure state, even in principle (it obviously could't ever be in practice). Could we imagine measuring every particle in a cat, and piecing together all those individual particle wave functions? No, because a cat is comprised of lots of identical particles with exchange energies and so on, so we need to measure multiple-particle wave functions to get the right coherences. How do we do that? Worse, we have to find ways to measure each part of the cat in such a way that it does not mess up other measurements. To avoid completely obliterating the cat with devastating energies, the measurements have to take a finite time, so there will be uncertainty as to exactly what time the measurements applied to. So if we get electron A had spin up and electron B had spin down at some time t, it could really have been spin up at time t+dt. and the other spin down at time t-dt, so how do we know that the measurement on the one electron didn't mess up the other one during that intervening time? I would say it is not even possible in principle to put a cat into a pure state.

Now, this is not just an issue of the number of particles in a cat-- we could imagine sending a beam of particles through a Stern-Gerlach and separating any number of them into pure-state "spin up" and "spin down", and if they were identical particles we could imagine the appropriate Slater determinent to get the full wavefunction. But that's just a beam of particles that are basically independent entities, it's not doing anything, it's not being a cat. And it can't be alive or dead. So the whole crux of the paradox is that we don't think cats can be alive and dead at the same time, but that's expressly because they are complex systems of interacting particles, not a beam of sterile interactions. So the fact that cats are complex enough to be alive or dead is exactly why they cannot be in pure states, and that's just what our intuition says about them.

The situation is even worse for the concept of a superposition state of alive/dead cat. To the universe, a cat is just a collection of particles and fields, there is no need for the universe to decide if a cat is alive or dead or even a cat. That's all going on in the mind of the physicist, it's a result of a certain type of information processing, and to judge if a cat is alive or dead requires coupling to that information processor. So now we are not only trying to specify the state of every particle in a cat, we are trying to also decide if it is a cat, and if it is alive or dead, so we also have to specify the state of every particle in the brain that is making that determination-- or at least include how the brain makes that decision. So now we have couplings to noise modes we are not including in our description of the pure state of the alive/dead cat, just to say that it is indeed a cat in the first place, and if the state we are treating it as will really test out correctly. So we have yet another reason why a cat cannot be in a pure state-- the meaning of "a cat" necessitates that it be in a mixed state, as a substate of the cat+brain that allows us to say that it is a cat. If we try to say the brain is also in a pure state, we need another brain to give that meaning, so we have the Wigner's friend problem. For these reasons, I conclude it is impossible even in principle for a cat to be in a pure state, it would just be wrong quantum mechanics.

As for how that state of affairs gets built up in a sequence of ever more complex systems, I would say the key is when the entanglements between the system and the brain doing the quantum mechanics on that system become important. For a single spin up particle, the way the brain gets entangled with that spin up state doesn't matter, because when you project onto the outcome of experiments on that particle, the brain entanglements project out-- everything going on in the brain that associates with "spin up" is separate from everything going on that would have been associated with "spin down" had that been the outcome. But that's not true when you entangle a brain with a cat-- there could be a lot going on in the brain that connects to either a dead cat or an alive cat, because the entanglements are to the individual particles in the cat, not the whole cat as if it was a single particle. So aliveness is not like spin-- it is not an attribute of a particle, it is an outcome of mental processing that mixes all kinds of different behaviors of the individual particles in the cat. So when you couple the brain to the cat, then project onto just the cat, you always end up with a mixed state, never a pure one-- even in principle.

I would say there is no paradox even if you did have a pure wave function. What is the paradox that occurs in assuming a pure state is known when the box is closed? Is it just the effect you mentioned above - i.e. it cannot be done?

The paradox is that if a cat can be in a pure state, we get a disconnect with our intuition that says the pure state could never involve both an alive and dead cat. But the unitary evolution of a pure state could easily lead to a superposition state in regard to aliveness, and that's what seems impossible to our intuition. We know it is always sufficient to treat a cat as being in a mixed state of alive or dead, so if quantum mechanics says it can be a superposition, we wonder why we never needed to think of it that way. I think the resolution of that paradox, which is the usual way the cat paradox is expressed but I don't see as the real paradox here, is that a cat is never in any kind of pure state, let alone a superposition of dead and alive. But that still leaves the real paradox here-- even if the substate that is the cat is in a mixed state, how do we actualize one or the other if the pure state of the larger closed system that includes us is in a pure state that has both alive and dead cats embedded into it as projections? In other words, the core paradox of quantum mechanics is not how you get mixed states, that's easy, you get mixed states when you couple to macro systems and then project onto substates that yield particular outcomes. The core paradox is how do you collapse the mixed state into a single outcome, not how you collapse the superposition into a mixed state.

There IS quantum mechanics at the mixed state level - Upon closing the box, having measured a mixed state, each pure state of the mixture is propagated forward by e.g. the Schroedinger equation. Each pure state propagates to a another pure state, yielding a fully defined propagated mixed state at a time just before the box is opened, which is then used to calculate the probability of finding the cat dead or alive when the box is opened.

That is all true, but you have to ask, when is the propagation of the pure states the key physics there, and when is the statistical behavior of the mixture what matters. When we derive ideal gas laws, we don't need to propagate all the individual particle wavefunctions-- we know the mixture allows us to average over the detailed behavior, and the relevant physics comes after the averaging, not before it. We can essentially replace all the detailed quantum mechanics with a simple assumption of ergodicity, and pow, we get statistical mechanics and the behaviors of gases. Same for cats, I would say, although Penrose thinks the extent to which they are conscious requires some survival of the quantum realm. I'm not convinced that is true.

Note - when I say "having measured a mixed state", it may be as little as saying "I see a live cat, geiger counter not clicked", and then assigning equal probability to every pure state of the mixture which conforms to this observation, zero to the rest, which is, of course, more than just a measurement.

A lot more, yes. And that's just the problem-- when you say you see those things, all kinds of information processing is going on that says as much about your mind as it says about cat electron wavefunctions. So an "alive cat" is not a set of equally probable cat-electron wavefunctions consistent with aliveness, it is a much richer system that includes your brain, and projections onto the cat are not mixtures of pure-state cats, because there is no such thing as a pure-state cat. A cat is a fundamentally different construct than a wavefunction.

 

[Rap]

Now we can ask the question of whether a cat could ever be in a pure state, even in principle (it obviously could't ever be in practice). Could we imagine measuring every particle in a cat, and piecing together all those individual particle wave functions? No, because a cat is comprised of lots of identical particles with exchange energies and so on, so we need to measure multiple-particle wave functions to get the right coherences. How do we do that? Worse, we have to find ways to measure each part of the cat in such a way that it does not mess up other measurements. To avoid completely obliterating the cat with devastating energies, the measurements have to take a finite time, so there will be uncertainty as to exactly what time the measurements applied to. So if we get electron A had spin up and electron B had spin down at some time t, it could really have been spin up at time t+dt. and the other spin down at time t-dt, so how do we know that the measurement on the one electron didn't mess up the other one during that intervening time? I would say it is not even possible in principle to put a cat into a pure state.

I agree that you could not measure the pure wave function of a cat without destroying the cat, but this would also be the case if the contents of the box were classical particles. We could not measure the position and momentum of every classical particle in a cat without destroying the cat, so I don't see this as a particularly quantum problem. In the classical case, we could say that IF we knew the position and momentum of every particle in the box just after we closed it, and we had a large enough computer, we could calculate with practical certainty the position and momentum of every particle at some time later, just before we open the box, and, with a large enough computer, we could also calculate with practical certainty whether that arrangement corresponded to a live cat or a dead cat, which is what we would observe when we opened the box. Similarly, in the quantum case, we could say that IF we knew the pure wave function of the contents of the box just after we closed it, and we had a large enough computer, we could calculate with practical certainty the wave function at some time later, just before we open the box, and we could also calculate from that wave function the probability that the cat would be seen as alive or dead when we open the box. Of course, in the quantum case, we would have a choice of initial wave functions, but I think we could choose one in which, say, the uncertainties in position and momentum of the center of mass of the box and contents were "microscopic in magnitude". We would also face a similar choice of how to interpret the final wave function, but again, we could choose a set of "eigencats" whose uncertainties were microscopic, i.e. corresponding to the fact that upon opening the box, the "measurement" that occurs is not a destructive collapse of the wave function to a particular eigencat, but rather to a mixture.

So the fact that cats are complex enough to be alive or dead is exactly why they cannot be in pure states, and that's just what our intuition says about them.

This is again the difference between "we cannot measure the microstate of a cat without destroying it" which does not imply "we cannot assume a pure wave function for a cat".

The situation is even worse for the concept of a superposition state of alive/dead cat. To the universe, a cat is just a collection of particles and fields, there is no need for the universe to decide if a cat is alive or dead or even a cat. That's all going on in the mind of the physicist, it's a result of a certain type of information processing, and to judge if a cat is alive or dead requires coupling to that information processor. So now we are not only trying to specify the state of every particle in a cat, we are trying to also decide if it is a cat, and if it is alive or dead, so we also have to specify the state of every particle in the brain that is making that determination-- or at least include how the brain makes that decision. So now we have couplings to noise modes we are not including in our description of the pure state of the alive/dead cat, just to say that it is indeed a cat in the first place, and if the state we are treating it as will really test out correctly. So we have yet another reason why a cat cannot be in a pure state-- the meaning of "a cat" necessitates that it be in a mixed state, as a substate of the cat+brain that allows us to say that it is a cat. If we try to say the brain is also in a pure state, we need another brain to give that meaning, so we have the Wigner's friend problem. For these reasons, I conclude it is impossible even in principle for a cat to be in a pure state, it would just be wrong quantum mechanics.
...
As for how that state of affairs gets built up in a sequence of ever more complex systems, I would say the key is when the entanglements between the system and the brain doing the quantum mechanics on that system become important.

I don't see how the brain of the physicist interacts with the process. The question of whether the arrangement of particles in the classical case or the eigencats in the quantum case correspond to dead or alive cats is a computational problem. The brain of the physicist does not interact before the box is opened, and by that time the calculation is finished. Ok, the step from the final wave function to the prediction of what the scientist will observe upon opening the box is fuzzy in my mind, maybe this is where the crux of the problem is. But my point is that it is not in the steps leading up to that point.

The paradox is that if a cat can be in a pure state, we get a disconnect with our intuition that says the pure state could never involve both an alive and dead cat. But the unitary evolution of a pure state could easily lead to a superposition state in regard to aliveness, and that's what seems impossible to our intuition.

It is not unintuitive if you accept the wave function as an encoding of our (quantum) uncertainties about the situation. In the pure wave function scenario, I see the uncertainty in alive/dead as essentially stemming from the Heisenberg uncertainty. If we measure the position of a particle to a high degree of accuracy, then that wave function will be a superposition of precise momentum states. This does not mean that the particle possesses all these momenta at once (not very intuitive), it simply means we are uncertain about the momentum we would measure if we made a momentum measurement just after the position measurement (quite intuitive).

 

[yoda jedi]

Having read the last few posts in this thread, there is still some confusion about whether the cat is (1) in superposition of dead AND alive or (2) is definitely either alive or dead but not both, while the box is closed and the observer can make no observations of the state of the cat. Now persons taking either position (1) or (2) are making claims about the state of the cat with absolutely no evidence to support their position because by the definition of the thought experiment no observations can be made, only suppositions.

not with nonlinear quantum mechanics, there is a self induced collapse.

 

[Ken G]

Similarly, in the quantum case, we could say that IF we knew the pure wave function of the contents of the box just after we closed it, and we had a large enough computer, we could calculate with practical certainty the wave function at some time later, just before we open the box, and we could also calculate from that wave function the probability that the cat would be seen as alive or dead when we open the box.

We can all agree any real physicist will be forced to treat that cat as a mixed state, but the issue of the paradox is whether or not that is also the reality of the situation, or if there is some deeper pure state there that the physicist is involved in but cannot make use of. I think we both agree that in any correct application of quantum mechanics, the cat by itself is going to have to be treated as a mixed state, as it will always be a substate of a larger system based on the history of how it got there and the impossibility of separating it from that history without destroying it. I agree the same thing would be true of a purely classical cat for different reasons-- owing to the butterfly effect, a deterministic treatment of a classical cat would also have to destroy the cat to achieve the impossibly precise initial conditions needed to predict the future evolution as anything but a (classical) mixed state.

The bottom line is inescapable: a cat is a mixed state, quantum mechanically or classically. What survives of the quantum mechanical cat paradox, though, is if we expand the system to include everything that could possibly influence that (even its whole past light cone if necessary), and treat that as a pure state, where in that pure state is there a dead cat and an alive cat? In other words, the "right" paradox there was never how does a pure state become a mixed state, because the cat is always a mixed state, there's no "becoming" involved. The right paradox is, how does a mixed state get actualized as a single experimental outcome? Classically, we have no issue with that, we just say that the mixed state was a kind of mistake, the reality itself was always one or the other. Such a cavalier interpretation of what reality is does not conform to the postulates of quantum mechanics, unless one takes the Copenhagen approach of treating those postulates as tools rather than as an actual description of reality.

This is again the difference between "we cannot measure the microstate of a cat without destroying it" which does not imply "we cannot assume a pure wave function for a cat".

The reason we cannot assume a pure wavefunction for a cat is that we have no way to establish such a thing. Reality by itself is never going to do it-- quite the opposite, reality is going to couple and entangle that cat all over the show, forcing the cat to live in a subspace of whatever might possibly be construed as a pure wavefunction there. In my view, pure states just don't work that way, we must look to smaller and smaller systems, and closely observed ones, to find the meaning of a pure state-- not look to larger and larger ones, taking us ever farther from the actual demonstrated usefulness of the concept in some vain hope that it is easier to herd a trillion cats than ten of them (and what I'm counting here is modes, not particles-- a huge number of particles all in the same state is just one mode, like a Bose-Einstein condensate).

I don't see how the brain of the physicist interacts with the process. The question of whether the arrangement of particles in the classical case or the eigencats in the quantum case correspond to dead or alive cats is a computational problem.

Not so-- saying that a cat is alive or dead is not something that can be determined from what the electrons are doing, the electrons are just obeying the laws of physics if they are in a cat or in a rock. There has to be a brain somewhere to process that information and make the judgement that the cat is alive or dead. We might use the cat's own brain for that, and "ask the cat" if you will, but you certainly will never get a superposition that way-- if you ask the cat, you'll only get the answer of one cat.

The brain of the physicist does not interact before the box is opened, and by that time the calculation is finished. Ok, the step from the final wave function to the prediction of what the scientist will observe upon opening the box is fuzzy in my mind, maybe this is where the crux of the problem is. But my point is that it is not in the steps leading up to that point.

You're saying there's a concept of a wave function as a function of time, which is later used by the physicist to make a prediction or understand an outcome. I'm saying that wave function has no independent meaning, its whole purpose is to be used by the physicist to make a prediction or understand something. And I'm disputing that there ever was a pure state wavefunction there in the first place, there never was anything there to evolve in the way you describe. Instead, there as a vast mixture of wavefunctions, whose ultimate behavior is both statistical and classical. The classical part appears when we are forced to take a statistical average over the quantum mechanical elements, destroying all the phase coherences that were the hallmark of quantum mechanics in the first place. This does not mean that a quantum mechanical process can't happen in a cat, it just means that a cat cannot be a quantum mechanical pure state.

It is not unintuitive if you accept the wave function as an encoding of our (quantum) uncertainties about the situation. In the pure wave function scenario, I see the uncertainty in alive/dead as essentially stemming from the Heisenberg uncertainty. If we measure the position of a particle to a high degree of accuracy, then that wave function will be a superposition of precise momentum states. This does not mean that the particle possesses all these momenta at once (not very intuitive), it simply means we are uncertain about the momentum we would measure if we made a momentum measurement just after the position measurement (quite intuitive).

I agree with that description of a single particle, I'm saying that it doesn't apply to a cat. It applies to the parts of a cat, but those parts come together in a way that we will always have to statistically average with random phases, because we can never connect them to some "mother" pure state.

 

[Rap]

We can all agree any real physicist will be forced to treat that cat as a mixed state, but the issue of the paradox is whether or not that is also the reality of the situation, or if there is some deeper pure state there that the physicist is involved in but cannot make use of. I think we both agree that in any correct application of quantum mechanics, the cat by itself is going to have to be treated as a mixed state, as it will always be a substate of a larger system based on the history of how it got there and the impossibility of separating it from that history without destroying it. I agree the same thing would be true of a purely classical cat for different reasons-- owing to the butterfly effect, a deterministic treatment of a classical cat would also have to destroy the cat to achieve the impossibly precise initial conditions needed to predict the future evolution as anything but a (classical) mixed state.

This is a point that has to be resolved first, because the rest of your argument, if I understand correctly, is based on the idea that we cannot consider a cat in a pure state when the box is closed. I agree that a wave function cannot be assigned to a given box and contents without destroying it, just as in the classical case you cannot measure the momentum and position of every particle in it without destroying it.

Just to be clear, do you agree that we could postulate a pure wave function representing a hypothetical cat etc., just as we can postulate a set of classical particles with specific position and momenta corresponding to a hypothetical cat, etc.? I understand that this will not apply to a real situation. Also that, given this situation, we could propagate forward with practical certainty, given a large enough computer. Also that, given sufficient knowledge of what microstates constitute a cat, dead or alive, a calculation could be made as to what the final state, classical or quantum, represents, classical being a certainty as to what the physicist observes when opening the box, quantum being not so much.

Note that the butterfly effect says that your errors will increase exponentially as you propagate, not that they will become infinite, so this is not a valid objection to either case. The number of significant digits you must carry in your computer will increase exponentially as the time interval you consider increases linearly. A finite time interval will yield a finite number of significant digits needed, thus a finite computer. Sure it might be 10^10000 times the size of the universe, but this is a practical limitation, not a limitation in principle.

 

[Ken G]

Just to be clear, do you agree that we could postulate a pure wave function representing a hypothetical cat etc., just as we can postulate a set of classical particles with specific position and momenta corresponding to a hypothetical cat, etc.?

It's not clear that is possible, but it doesn't seem to matter terribly, so I'll work with the assumption that in principle there is such a thing as a "pure state cat wavefunction", it just never appears in nature. The reason I am skeptical there is any such thing is that the process of making a cat is so fundamentally connected with classical phenomena, I'm not sure it would even be possible to identify a theoretical pure-state cat wavefunction. But I don't think it will matter if this is possible or not, what will matter is that it never happens in nature. Note also that we must include in the pure state enough surrounding air to keep the cat alive as long as needed.

Also that, given this situation, we could propagate forward with practical certainty, given a large enough computer. Also that, given sufficient knowledge of what microstates constitute a cat, dead or alive, a calculation could be made as to what the final state, classical or quantum, represents, classical being a certainty as to what the physicist observes when opening the box, quantum being not so much.

Yes, if a pure state is possible, we can imagine isolating it, and it will evolve deterministically into a new pure state, according to the correspondence principle.

Note that the butterfly effect says that your errors will increase exponentially as you propagate, not that they will become infinite, so this is not a valid objection to either case.

It just means that in the classical case, you'd again have to disintegrate the cat to measure its parts closely enough to predict its future for any significant amount of time, just as you would in the quantum case. The limitation is again that it takes energy to make precise measurements, as per entropic requirements even in classical physics.

 

[Rap]

It's not clear that is possible, but it doesn't seem to matter terribly, so I'll work with the assumption that in principle there is such a thing as a "pure state cat wavefunction", it just never appears in nature.

Ok, I just wanted to make sure I wasn't missing some point you were making. Next, can we describe a real cat in a real box as a mixture of a set of these hypothetical wave functions, each hypothetical wave function being consistent with whatever rather non-destructive measurements we make when we close the box, each hypothetical wave function being assigned equal weight in the mixture? Would that be an acceptable way of characterizing the situation when the box was closed (again, in principle only)?

 

[Ken G]

Ok, I just wanted to make sure I wasn't missing some point you were making. Next, can we describe a real cat in a real box as a mixture of a set of these hypothetical wave functions, each hypothetical wave function being consistent with whatever rather non-destructive measurements we make when we close the box, each hypothetical wave function being assigned equal weight in the mixture? Would that be an acceptable way of characterizing the situation when the box was closed (again, in principle only)?

If such a pure-state cat is possible, there's no need for us to even mix them together in the original state, we may as well just take the pure cat. No real cat can be described as a mixture of pure-state cats, the mixing happens throughout the cat, based on the history of all the cat subsystems, it's not just a global mixture of whole cats. But if it is possible in principle to have a pure state cat, then we may as well do the gedanken with a pure state alive cat in the box with a pure state undecayed nucleus and a pure state hypodermic needle attached to the undecayed nucleus, and go from there.

 

[Rap]

If such a pure-state cat is possible, there's no need for us to even mix them together in the original state, we may as well just take the pure cat. No real cat can be described as a mixture of pure-state cats, the mixing happens throughout the cat, based on the history of all the cat subsystems, it's not just a global mixture of whole cats.

It is possible in principle to postulate a pure state cat, but it is not possible to measure the pure state of a cat without destroying it. This is analogous to classical mechanics where it is possible to postulate the microstate of a gas in an isolated container at equilibrium, giving all the positions and momenta of the particles in the isolated container, but it is not possible to measure the actual microstate without destroying it. Nevertheless, we can assign equal probabilities to every microstate which yields the same temperature and pressure that we measure before isolating the container (i.e. closing the box). We can then propagate forward and prove that the temperature and pressure will very likely be practically the same when we check it at some time later. Statistical mechanics is just a way of carrying out that propagation approximately without having to track 10^23 particle positions and momenta of an enormous number of possible microstates.

But if it is possible in principle to have a pure state cat, then we may as well do the gedanken with a pure state alive cat in the box with a pure state undecayed nucleus and a pure state hypodermic needle attached to the undecayed nucleus, and go from there.

I am fine with such a gedanken experiment, the pure state at some time later consists of a superposition of live and dead cat wave functions, and these simply allow me to calculate the probability of finding a live or dead cat when the box is opened. To inquire into what is "really" going on inside the box before it is opened is not something that can be measured, therefore it is not a proper scientific question.

But then there is always the nagging problem that you pointed out, that it cannot be used in a real situation. When someone says it can never happen in practice, and if I'm such a Copenhagen sympathizer, how do I respond?

Its possible to have a hypothetical pure state cat, but one cannot take a real situation and assign a pure state to it, because, as you say, it will be destroyed by the measurement. I'm just trying to use these hypothetical pure states to analyze a real situation, analogous to the way hypothetical microstates could be used in classical mechanics and are used in statistical mechanics to analyse macroscopic (i.e. thermodynamic, measurable) states.

 

[Ken G]

I am fine with such a gedanken experiment, the pure state at some time later consists of a superposition of live and dead cat wave functions, and these simply allow me to calculate the probability of finding a live or dead cat when the box is opened.

But that's what I'm saying isn't true-- even if we start with pure states for each component of the system, when we couple them, the only pure state is now a combined system. The cat is now a substate of that system, and substates don't evolve according to the Shroedinger equation, so they don't evolve unitarily and they don't become superposition states. There is really no such thing as the state of a part of a system, but we as physicists can make correct predictions by using the concept of a mixed state to treat such substates, or in some special circumstances, we have enough information to treat a substate as a pure or superposition state. That ability is quickly lost for the cat in the box, even if it starts out in an impossible-to-know pure state.

In classical language, a mixed state is "one or the other we just don't know which, but nature does", but in quantum mechanical language, that is not actually the state of the cat, it is only the state we are choosing to use to treat the cat because it is going to make correct predictions. If one sympathizes with Bohr (as I do), one says that there is no such thing as "the real state" of anything in physics, there is only how we the physicist are choosing to treat the situation, so for me a mixed state is a fine treatment of that cat-- the cat is either alive or dead we just don't know which. If one takes a literal belief in quantum mechanical wavefunctions, then the cat simply has no real state at all, it is part of a larger system, period.

So my point is, whether we start with a putative (but impossible) pure-state cat, or if we adopt a mixture of pure states with some statistical distribution, doesn't matter for the cat paradox-- because correct quantum mechanics says that once we couple that cat to the mechanism that can kill it, there is no longer any such thing as the state of the cat in quantum mechanics. There is only a projection of the full state onto the cat degree of freedom, but that isn't a quantum mechanical state, it is a classical treatment of a quantum mechanical state. It makes no difference to the quantum mechanics if we now assert that the cat "really is" alive or dead and we have no way of knowing which, or if we assert that we have chosen to treat it that way in our mathematics-- the correct quantum mechanics is completely moot on the point, there is no cat-state wavefunction so there is no superposition of alive or dead.

So that would seem like the end of the cat paradox, but I'm saying that's just the end of the wrong cat paradox, the one that uses wrong quantum mechanics. The right cat paradox survives-- it is the one that says whether we treat the cat as already alive or dead and we just don't know which, or if we say that is simply how we are conceptualizing the cat, there should be a pure-state wavefunction for the whole system. Where in that pure state is there information about what we will observe when we open the box? It is nothing but statistical information-- that's what Einstein objected to, god is rolling dice, but there's no dice anywhere in the physical setup.

That is what I think forces us to the Copenhagen interpretation: our approach to doing physics is necessarily limited, we cannot recover what reality is actually doing there, it simply doesn't make sense. We don't have a fundamental theory, we have an effective theory, because we do physics by coupling quantum mechanical systems to classical processors, and something is lost in translation. And I would further add that we should have always expected that-- there is almost no more purely mystical idea than the idea that we create fundamental theories rather than effective ones.

 

[Rap]

But that's what I'm saying isn't true-- even if we start with pure states for each component of the system, when we couple them, the only pure state is now a combined system. The cat is now a substate of that system, and substates don't evolve according to the Shroedinger equation, so they don't evolve unitarily and they don't become superposition states. There is really no such thing as the state of a part of a system, but we as physicists can make correct predictions by using the concept of a mixed state to treat such substates, or in some special circumstances, we have enough information to treat a substate as a pure or superposition state. That ability is quickly lost for the cat in the box, even if it starts out in an impossible-to-know pure state.

Hmm - well I have been sloppy about the distinction between the cat alone and the cat plus the box plus all the other stuff. I never meant to imply that we were dealing with anything but the pure wave function of the box and all its contents (i.e, the "system"). But I don't understand why propagating the system wave function forward results in a wave function in which the cat is ill-defined. I agree, it won't be perfectly defined, there are miniscule probabilities that the cat will evaporate, or something, but the overwhelming probability is that there will be a cat in there somewhere.

I wonder if you would be willing to consider a simpler system which may help me to more fully understand what you are saying. Consider a box with constant volume containing a stoichiometric mixture of hydrogen and oxygen at a particular temperature and pressure, and a tiny piece of radioactive material which emits, I don't know, an alpha particle every hour on average. Suppose this alpha particle greatly increases the probability that the mixture will explode and produce water vapor (maybe not true, but that's not the point). The gas is like the cat, alive when you have the stoichiometric mixture, dead when you have water vapor. The only other parts of the system are the box and the bit of radioactive material. We could come up with any number of impossible-to-know pure states that describe the system. I will modify your quote to read:

"There is really no such thing as the state of a part of a system, but we as physicists can make correct predictions by using the concept of a mixed state to treat such substates, or in some special circumstances, we have enough information to treat a substate as a pure or superposition state. That ability is quickly lost for the gas in the box, even if it starts out in an impossible-to-know pure state."

Is this still a valid statement?

The next question is - how would you treat this simple system quantum mechanically? Can we speak of a superposition of exploded/unexploded after a certain time?

I would say that when we close the box we would describe the system as a mixed state consisting of every pure wave function corresponding to a microstate of the unexploded gas at that particular pressure and temperature along with the box and the un-emitted radioactive material, multiplied by a probability that is equal for each pure wave function. (Unlike the classical case we have a choice of wave functions corresponding to the momentum/position tradeoff for a single particle). This mixed state can be propagated forward. I understand that treating the gas alone as a separate entity which evolves unitarily is not correct, but I am having trouble imagining the implications of this. It seems to me that practically every interpretation of the evolved wave function will involve exploded or unexploded gas and a tiny piece of radioactive material.

That is what I think forces us to the Copenhagen interpretation: our approach to doing physics is necessarily limited, we cannot recover what reality is actually doing there, it simply doesn't make sense. We don't have a fundamental theory, we have an effective theory, because we do physics by coupling quantum mechanical systems to classical processors, and something is lost in translation. And I would further add that we should have always expected that-- there is almost no more purely mystical idea than the idea that we create fundamental theories rather than effective ones.

On this, I totally agree.

 

[Ken G]

"There is really no such thing as the state of a part of a system, but we as physicists can make correct predictions by using the concept of a mixed state to treat such substates, or in some special circumstances, we have enough information to treat a substate as a pure or superposition state. That ability is quickly lost for the gas in the box, even if it starts out in an impossible-to-know pure state."

Is this still a valid statement?

Yes, and although I like your simplification, I would say let's go whole hog and simplify it even more. Let's take a two-slit experiment, where we put a left circular polarizer in one slit, and a right circular polarizer in the other. Then let's send photons that are linearly polarized (so in a superposition of left and right circular polarization) through the slits, and get a two-slit diffraction pattern. Now let's do it again, but first down-convert the photons into a photon pair, both linearly polarized like the original (I think that's what down conversion would do, but if not we entangle them in some other way). So all we did is take a single-particle superposition state (like our imagined pure state cat) and convert it to a two-particle superposition state (with highly entangled correlations embedded in it, like the cat plus the device that can kill it). Will the individual particle substates of that entangled pair act like a superposition state? In other words, if we send one of the photons in each pair through the slits, will it make a two-slit diffraction pattern?

As I understand these things, the answer is no-- we will no longer get a two-slit pattern after down-converting those photons, because now it is the whole two-photon system that is in a superposition, but the substate projections of such a tightly entangled pair encodes "which way" information, so will not yield a two-slit pattern any more-- instead, the single-piarticle treatment will need to be that of a mixed state of the two polarizations, to make the correct predictions. In the analogy, the same holds for the cat.

Now, you are probably thinking about quantum erasure, so you know that we can get a two-slit pattern in a particularly ingenious way out of my apparatus, but it requires that we do two more things than what I said so far-- we have to sort the pattern into two batches, correlated with two possible outcomes on the other members of the pairs, and we have to use outcomes on the other members that "erases" which-way information. But we still don't get a two-slit pattern for the whole set of original photons, only the two sorted batches, so we cannot say the first photons were in a superposition state. However, they weren't strictly in a mixed state either-- there is additional information there we could imagine accessing such that the mixed state isn't officially correct either, it's just the treatment we choose when we pretend we have a one-particle state rather than a whole system.

And above all, there's no way to correlate cat outcomes with apparatus outcomes, such that we could sort the cat outcomes into two sets that behaved like superpositions of alive and dead cats in each set, because we can't do anything clever with the apparatus to erase "alive/dead" information, since the apparatus is classical too. There would need to be a way to kill a cat with a pure-state wavefunction, rather than a classical system, and I don't think that would ever be possible-- that's one manifestation of the "Heisenberg gap" right there.

On this, I totally agree.

Then we are fellow Copenhagen sympathizers, there seem to be fewer of us all the time!

 

[Hurkyl]

In classical language, a mixed state is "one or the other we just don't know which, but nature does"

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.

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

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

Occam's razor applies, then, for the theory and philosophy of classical mechanics. However, Einstein's razor applies in the quantum case: "Make things as simple as possible, but not simpler."

There is only a projection of the full state onto the cat degree of freedom, but that isn't a quantum mechanical state, it is a classical treatment of a quantum mechanical state.

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.

 

[yuiop]

Yes, and although I like your simplification, I would say let's go whole hog and simplify it even more. Let's take a two-slit experiment, where we put a left circular polarizer in one slit, and a right circular polarizer in the other. Then let's send photons that are linearly polarized (so in a superposition of left and right circular polarization) through the slits, and get a two-slit diffraction pattern. Now let's do it again, but first down-convert the photons into a photon pair,...

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. See this counterexample https://www.physicsforums.com/showpost.php?p=3118570&postcount=63 to a comment by DrC. The two polarisers give potential "which way" information which destroys the interference pattern.

You only recover an interference pattern in the case of entangled photons after you carry out coincidence counting or in the case of "un-entangled" photons by placing a linear polariser in the path before or after the two circular polarisers.

P.S. Dr.C has not yet responded to the counterexample in that post.

 

[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.