Understanding the Cat in a Box Paradox

[cesiumfrog]

Are you saying that QM can't describe irreversible processes?

I'd like to see you give an example of an irreversible process.

 

[cesiumfrog]

I'm afraid cesiumfrog is wrong. [..]

Perhaps you could specify where, since for this interpretation you seem both to have agreed with my representation of one "view" (your term; I used "take") and also agreed about the presence of a contradictory view?

 

[Demystifier]

I'd like to see you give an example of an irreversible process.

Environment induced decoherence.
Of course, not true irreversible, but effectively (FAPP) irreversible. Just like "irreversible" processes in classical mechanics.

 

[lightarrow]

I'd like to see you give an example of an irreversible process.

When I asked "Are you saying that QM can't describe irreversible processes?" I intended that as a question and nothing else, because I still don't know much about it; I'm aware that you know QM physics much better than me.
Or you intended to ask me a practical physical example?

 

[shaun_o_kane]

The Copenhagen Interpretation does not say that "collapse" occur when a quantum system interacts with a macroscopic system (how big does it have to be to be macroscopic?). Instead Bohr talked about a quantum-classic boundary - which can be chosen to be anywhere. Hence the Schrodinger's Cat Paradox.

One of goals of the Copenhagen school was to destroy the idea that somehow QM are described by a "real" waveform that evolves according to Schrodinger's equation. It seems in recent years that "real" waveforms have made a comeback (decoherence etc). There is no "paradox" if the waveform is not real. Each observer has different information, and therefore describes the situation using a different waveform.

 

[Rade]

If I place a coin in a box, and shake, is the coin: (1) alive (heads) or dead (tails) or (2) alive (heads) and dead (tails) ? imo, the correct answer is both (1) and (2) at the same moment of time and space. When you open the box you observe either heads or tails facing you, thus # 1 answer is correct. But at all times, whether observed or not, the coin has both head and tail aspects, thus # 2 answer is also equally correct at any time, including the time you observe when you open the box. I view this what Schrödinger was trying to say with the cat problem--that is, at the very same moment of time and space, the cat is a dialectic superposition of two opposite states (1) it is alive or dead and (2) it is alive and dead, thus [or state + and state ] = quantum reality.

 

[lightarrow]

[...]
quantum reality.

Isnt'it a contradiction? It's real what you measure, not what you write down in a notebook.

 

[mn4j]

1. Your claim that "neither x nor y" is identical to "both x and y".

In Logic 101
by definition:
dead = not(alive)
alive = not(dead)

not(not(alive)) = alive

neither alive = dead
nor dead = alive
therefore the following statements are identically nonsensical:
- The cat is both alive and dead . ( The cat is not(dead) and dead )
- The can is neither alive nor dead. (The cat is dead and not(dead)It follows therefore that the two statements have exactly identical meaning. They are not even false, they are illogical or nonsensical.

 

[mn4j]

If I place a coin in a box, and shake, is the coin: (1) alive (heads) or dead (tails) or (2) alive (heads) and dead (tails) ? imo, the correct answer is both (1) and (2) at the same moment of time and space. When you open the box you observe either heads or tails facing you, thus # 1 answer is correct. But at all times, whether observed or not, the coin has both head and tail aspects, thus # 2 answer is also equally correct at any time, including the time you observe when you open the box. I view this what Schrödinger was trying to say with the cat problem--that is, at the very same moment of time and space, the cat is a dialectic superposition of two opposite states (1) it is alive or dead and (2) it is alive and dead, thus [or state + and state ] = quantum reality.

The problem with a lot of these discussions is a confusion between epistemological issues and physical issues. Bohr's approach is epistemic rather than physical. And that's why Einstein had problems following it. To illustrate using your example

First, by definition if the coin is showing heads, it MUST not be showing tails.
ie. heads = not(tails) and not(heads) = tails. heads and tails are mutually exclusive PHYSICAL STATES. However, heads and tails are not mutually exclusive EPISTEMIC states.

Within the box, only one state can exist. Within the mind however, without adequate information (the box has not been opened), both states can have a certain probability adding up to 1. With absolutely no extra information, each physical state, will have an epistemic probability within the mind of 0.5 (heads=0.5, tails=0.5). Thus the "wavefunction" has two superposed states. The moment you open the box, you now have complete information "heads" for example, and the wave function collapses to a single point (heads=1, tails=0). Nothing is happening in the system, but a lot is happening in your mind.

The moment you start confusing epistemic states with physical states, you start contradicting yourself. Fortunately, or rather unfortunately, if you had a million coins in the box, you will notice that the physical state matches very closely the epistemic state of and opening the box does not give you any significant extra information.

This is fortunate in the sense that most quantum phenomena to date have been studied using ensembles of large numbers of individual entities. And this is the only reason the faulty copenhagen interpretation has appeared to work to date.

It is unfortunate because to date, QM continues to be paradoxical and unclear when explaining phenomena involving individual particles.

 

[ZapperZ]

In Logic 101
by definition:
dead = not(alive)
alive = not(dead)

not(not(alive)) = alive

neither alive = dead
nor dead = alive
therefore the following statements are identically nonsensical:
- The cat is both alive and dead . ( The cat is not(dead) and dead )
- The can is neither alive nor dead. (The cat is dead and not(dead)


It follows therefore that the two statements have exactly identical meaning. They are not even false, they are illogical or nonsensical.

If you are looking for someone and asked me where this person is, and I answered "he is neither in that room, nor in the other room", do you still go looking for this person in those 2 rooms?

The response given clearly stated that this person is not in that room, and this person is also not in the other room. Try it. Ask someone and see what it means.

This is still besides the point since I had clearly cited a reputable article by a respectable physicist who unambiguously used the same identical phrase that I had used in saying in English the Schrodinger Cat-state wavefunction. We could continue with this on and on without own preferences, but I have seen no one else providing me with exact references where these other forms of describing this situation has been used.

Zz.

 

[mn4j]

If you are looking for someone and asked me where this person is, and I answered "he is neither in that room, nor in the other room", do you still go looking for this person in those 2 rooms?

This is a straw man. The question has to do with DEAD and ALIVE. There is a relationship between those two states, which your 2 rooms do not have. If by definition, not being in one room meant the person was in the other, the same as the relationship between dead and alive , then I would think you were smoking something by asserting the person was in neither room. And in that case, it would mean exactly the same thing as saying the person is in both rooms.

Read my logic again. The relationship between "dead" and "alive" can not be ignored in your analysis. If the OP had been about two rooms, the issue will be different. But so long as "not dead" IS "alive" and "not alive" is "dead", the phrases "neither dead nor alive" and "both dead and alive" mean exactly the same thing. This is logic 101, no need for a reference.

 

[f95toli]

This is fortunate in the sense that most quantum phenomena to date have been studied using ensembles of large numbers of individual entities. And this is the only reason the faulty copenhagen interpretation has appeared to work to date.

It is unfortunate because to date, QM continues to be paradoxical and unclear when explaining phenomena involving individual particles.

But there has also been a LOT of work done on systems consisting of single objects that STILL can be put in a superposition; solid state qubits are a good example (single ions in ion traps is another). Superpositions are as " real" as any other state; if they were just due to "classical probability" quantum computers would not work (not to mention the fact that much of atomic and molecular physics would also not work).

 

[ZapperZ]

This is a straw man. The question has to do with DEAD and ALIVE. There is a relationship between those two states, which your 2 rooms do not have. If by definition, not being in one room meant the person was in the other, the same as the relationship between dead and alive , then I would think you were smoking something by asserting the person was in neither room. And in that case, it would mean exactly the same thing as saying the person is in both rooms.

Read my logic again. The relationship between "dead" and "alive" can not be ignored in your analysis. If the OP had been about two rooms, the issue will be different. But so long as "not dead" IS "alive" and "not alive" is "dead", the phrases "neither dead nor alive" and "both dead and alive" mean exactly the same thing. This is logic 101, no need for a reference.

It isn't a straw man. The ONLY time we need to actually talk about something like this is when we communicate to the general public who has no clue on the mathematical description! We seldom have to use such words when we communicate among physicists, and certainly this issue is completely irrelevant when we make use of it.

Thus, it is with that audience in mind that such phrases are used. You are saying that the cat is "not dead" and also "not alive". It means that there are no alive property and there are no dead properties associated with that system. You can no longer force this into a binary system where by if it is not 1, it MUST be zero, because now, not 1 no longer means it is 0. That's the whole point of having a QUBIT where the states in between these two binaries are allowed before a measurement!

In the Stony Brook/Delft experiment, in fact, these two orthorgonal states oscillate between these two states! So now if you think things don't make sense, try figuring out that a cat can in fact oscillate not only from dead to alive and back to dead, but also transition in between those two states! These are not "strawman", they are experimental observations!

Zz.

 

[f95toli]

This is a nice paper for people who still think that superpositions in QM are only due to probabilistic effects.

http://www.arxiv.org/abs/0709.2135

Note that this system is EXACTLY analogous to a cavity-QED (QED=Quantum electrodynamics) experiment in the dispersive regime (this field is called circuit-QED). The difference is that in cavity-QED experiments microscopic systems like atoms and ions are used; here the two-state systems are superconducting qubits that are so large that you can easily see them an optical microscope. Despite this you still can see all the "usual" QM effects.

 

[OOO]

Let me ask several interconnected questions. Maybe they have already been answered and I haven't noticed. Maybe this is at the heart of my misunderstanding of the cat in a box paradox.

If we have a quantum system that is in a superposition of two states that decide between dead or alive:

1) Isn't the mechanism (the gun) that reads out this quantum system in order to make its decision a measuring device ?
2) Doesn't this measurement put the two-state system into one of the eigenstates such that the system isn't in a superposition anymore after the measurement ?
3) Aren't we obliged to press a red button in order to decide when the measurement ought to take place ?
4) Doesn't our pressing the red button decide about dead or alive unequivocally ?

So where is the paradox ?

 

[f95toli]

In my view the main problem with this paradox (or at least with the way it is often interpreted) is that there is a mysterios "observer" involved which performs the measurement. This observer is usually assumed to be a human (e.g. Schrödinger himself), meaning there is an implied assumption that the "collapse" must happen because a human is looking at the cat.

Now, obviously this is unphysical (unless one belives that humans are for some reason "special" in QM).
One could e.g. imagine replacing the cat with a Ph.D student; with the exception for the fact that the student is somewhat bigger than the cat (but not by orders magnitude) we have NOT changed the experimental conditions in any way. Hence, we must draw the conclusion that a Ph.D student can also be put in a superpostion of dead and alive.
In my view this shows quite clearly that there is something wrong with this gedanken experiment, and presumably the error comes from the fact that it is also implied that the cat is is not subject do decoherence due to interaction with the environment which ultmately will put it in a pointer state whether or not someone is looking or not.

 

[Rade]

...Within the box, only one state can exist. Within the mind however, without adequate information (the box has not been opened), both states can have a certain probability adding up to 1...

Thank you for your comments, but I do not agree with your first sentence above. Within the box, two coin states exist at any time, they are only separated by space. Within the box the coin has both head state and tail state by definition of being a coin (ontology), and it has either head state or tail state as relates to human knowledge of it after observation (epistemology). Now, a cat is not a coin, I think we all agree. As relates to the ontology, a cat in a closed box has both alive and dead states by definition of being a cat, and it has either alive state or dead state as relates to human knowledge after observation. As I see it, the key is to grasp the dialectic of the [and + or] as the basis of reality, quantum or classical. There are not two different realities, one classical and one quantum, they are a dialectic of a more basic synthesis of the [and + or] states of existence. This is how I see it, perhaps I error.

 

[ZapperZ]

In my view the main problem with this paradox (or at least with the way it is often interpreted) is that there is a mysterios "observer" involved which performs the measurement. This observer is usually assumed to be a human (e.g. Schrödinger himself), meaning there is an implied assumption that the "collapse" must happen because a human is looking at the cat.

Now, obviously this is unphysical (unless one belives that humans are for some reason "special" in QM).
One could e.g. imagine replacing the cat with a Ph.D student; with the exception for the fact that the student is somewhat bigger than the cat (but not by orders magnitude) we have NOT changed the experimental conditions in any way. Hence, we must draw the conclusion that a Ph.D student can also be put in a superpostion of dead and alive.
In my view this shows quite clearly that there is something wrong with this gedanken experiment, and presumably the error comes from the fact that it is also implied that the cat is is not subject do decoherence due to interaction with the environment which ultmately will put it in a pointer state whether or not someone is looking or not.

I quite agree with this line. I've always said that, unlike the Delft/Stony Brook experiments, we can't construct a similar measurement that will allow us to measure a non-commuting or non-contextual observable to "dead" and "alive" operator. The cat is definitely in contact with its environment. The fact that we started with a "cat" already implies a classical object that isn't subject to such quantum rules. So the thought experiment itself isn't correct in the first place.

However, if we consider this as nothing more than an illustration of the superposition concept, it certainly has done its job in highlighting the issue. It is unfortunate that for most people, their first encounter of QM is via this thought experiment rather than something more fundamental.

Zz.

 

[OOO]

Hence, we must draw the conclusion that a Ph.D student can also be put in a superpostion of dead and alive.

Why superposition ? When I press the red button the student is either dead or alive, tertium no datur. If the mechanism threw a coin instead, the student was either dead or alive after the red button had been pressed. If I pull the trigger myself having drunk too much coffee, trembling heavily, the Ph.D. student would either be dead or alive, regardless whether I closed my eyes and put something into my ears to not hear him moan.

Am I just too stupid to get this damn paradox ?

Edit: I did notice that you have emphasized on the "mysterious observer" but that seems to contradict what you say thereafter. If the observer is irrelevant then there is no superposition after pushing the button, in my opinion.

 

[cesiumfrog]

Hence, we must draw the conclusion that a Ph.D student can also be put in a superpostion of dead and alive.
In my view this shows quite clearly that there is something wrong with this gedanken experiment, and presumably the error comes from the fact that it is also implied that the cat is is not subject do decoherence due to interaction with the environment which ultmately will put it in a pointer state whether or not someone is looking or not.

Why do you treat decoherence as a separate process? Isn't the proper conclusion that "the cat and its local environment" will be in a superposition? And then, that "the cat, the PhD student, the scientific literature, and the world, including all of its environment" will be in a superposition of individually consistent (classical seeming) states? Otherwise you're still implying a mysterious irreversible collapse-like process at some point.

 

[cesiumfrog]

Does everyone remember learning Maxwell's equations in classical electrodynamics? Remember the textbook justifying his fix to Ampere's law, with an example such as: taking an Amperian loop around some part of a capacitor-containing circuit? "The current enclosed by the loop" is ill defined because you are free to arbitrarily choose the shape of the enclosing surface (so as to either slip between the capacitor plates OR cut a conducting wire)?

Griffiths said "in Maxwell's time there was no experimental [..inconsistency.] The flaw was a purely theoretical one, and Maxwell fixed it by purely theoretical arguments." To me, Schroedinger's cat seems like a highly analogous example: sure there are no experimental problems, but states are ill defined due to the arbitrary freedom to choose where collapse occurs, and so it is still desirable to find an interpretation free of these theoretical flaws.

 

[mn4j]

Thank you for your comments, but I do not agree with your first sentence above. Within the box, two coin states exist at any time, they are only separated by space. Within the box the coin has both head state and tail state by definition of being a coin (ontology)

This is a fallacy. In coin tossing, an outcome of "head" means one thing. You need to distinguish the fact that the coin has both a "head" and a "tail" from the outcome of tossing, which can only be one and not the other.

By definition, the states being discussed have to do with which face of the coin is up, not which whether the coin has two faces. It is a given. So the real issue is, can both faces of the coin be up at the same time?

By definition of what a coin is, if "heads" is up, "tail" is down. Therefore to say both "heads" and "tails" are up is a logical contradiction even before we have started discussing any physics. The same applies to any talk of "probability wavefunctions" being real entities. It doesn't even survive the language and logic test so there is no point trying to discuss the physics.

Lets look at it another way. To say that the cat is neither dead or alive until we look is the same as saying we create the reality by observing it. It then begs the question what reality you are trying to observe? To say the cat is neither dead or alive and then trying to determine whether it is dead or alive is utter stupidity in the first place. There are tons of reasons why this interpretation of QM does not make sense and I've only hinted at a few.

As relates to the ontology, a cat in a closed box has both alive and dead states by definition of being a cat, and it has either alive state or dead state as relates to human knowledge after observation. As I see it, the key is to grasp the dialectic of the [and + or] as the basis of reality, quantum or classical. There are not two different realities, one classical and one quantum, they are a dialectic of a more basic synthesis of the [and + or] states of existence. This is how I see it, perhaps I error.

This is a fallacy. It is true that ontologically, cats CAN be either dead or alive. This is probability. Both states are possible for cats. But no single cat can physically be in both states at the same time. It is clearer in macroscopic examples like the cat in the box situation because the states are clearly determined with enough experimental evidence for any reasonable human being to know that cats can not both be dead and alive at the same time.

What is astonishing is that many people skip the logical contradictions and jump right into fantastic metaphysical theories that have nothing to do with science.

 

[mn4j]

But there has also been a LOT of work done on systems consisting of single objects that STILL can be put in a superposition; solid state qubits are a good example (single ions in ion traps is another). Superpositions are as " real" as any other state; if they were just due to "classical probability" quantum computers would not work (not to mention the fact that much of atomic and molecular physics would also not work).

Can you cite some examples?

 

[OOO]

sure there are no experimental problems, but states are ill defined due to the arbitrary freedom to choose where collapse occurs, and so it is still desirable to find an interpretation free of these theoretical flaws.

I think I know now what my comprehension problem is. I have always thought implicitely that the collapse of the wave function could one day be explained by some more fundamental process (similar for example to critical points in classical mechanics). But of course my view is not congruent with standard interpretations of quantum mechanics.

So the problem with the cat in the box paradox is that the collapse of the wave function is not described by the Schrödinger equation, although it apparently happens all the time, right ? So there's only two alternatives: either reality independent of the observer does not exist or the wave function collapse can be explained by something outside the framework of quantum mechanics.

But what is so far-fetched with the proposition that the collapse can be explained by some physical law one day ?

Yes I know there's some restrictions like Bell's theorem (which I haven't ever tried to understand), but isn't there an enormous multitude of possible future theories left ?

(Sorry for being so noisy.)

 

[OOO]

Couldn't the cat in the box paradox probably be boiled down to the following question:

Is there any specific property of a quantum mechanical process that indicates whether or not it triggers the collapse of the wave function ?

 

[ZapperZ]

I don't think I quite follow the issue we seem to be having here, especially when I think I see at least a couple of different tracks of discussion this thread to be on.

Are we talking about a generic Schrodinger Cat-type state, or are we discussing specifically the problems with an actual Cat-in-a-box-with-radioactive-material thought experiment?

The generic Schrodinger Cat-type state and the related measurement problem have been extensively presented in that Leggett paper that I've mentioned. This also includes the clearest evidence for quantum superposition of LARGE conglomerate of particle on the order of 10^11 particles (macroscopic when compared to other situations). Why do we want to go to bigger sizes? To see if at some scale if QM transitions into classical even if we can still maintain coherence, and the possibility of observing the dynamics of a measurement, which one expects a priori to be easier to do with a larger object.

If this is an issue about the cat itself, we can always get someone to actually perform the experiment! (don't tell PETA though). However, unlike the Delft/Stony Brook experiments, as I've said before, how are we going to detect the presence of such superposition? What observable do we measure that is either non-commuting or non-contextual to the "alive-dead" observable to detect the presence of such superposition? So to me, the actual cat experiment itself is ill-defined to an actual test. This is before we even consider if the cat is in coherence with the radioactive source or if it is interacting with its environment that induce decoherence, etc.. etc... so the problem here is in trying to actually test what we want to show. As an experimentalist, and as any other experimentalist can tell you, if you don't know what to actually measure, there's no experiment to construct.

Zz.

 

[OOO]

So to me, the actual cat experiment itself is ill-defined to an actual test. This is before we even consider if the cat is in coherence with the radioactive source or if it is interacting with its environment that induce decoherence, etc.. etc... so the problem here is in trying to actually test what we want to show. As an experimentalist, and as any other experimentalist can tell you, if you don't know what to actually measure, there's no experiment to construct.

I'm not sure if I have understood what you say. A superposition of states cannot be measured as the wave function cannot be measured without destroying it. But doesn't the cat in the box experiment rather indicate that we don't understand the measurement process since we cannot tell when the cat actually died or not as we finally open the box ?

 

[ZapperZ]

I'm not sure if I have understood what you say. A superposition of states cannot be measured as the wave function cannot be measured without destroying it. But doesn't the cat in the box experiment rather indicate that we don't understand the measurement process since we cannot tell when the cat actually died or not as we finally open the box ?

That is why I mentioned about non-commuting and non-contextual observables.

Remember, if an operator A operates on a wavefunction, only those observables that commute with A will also have the wavefunction "collapsing" for them (assuming non-degenerate states). Those that do not commute with A still have undetermined values.

In the SQUID experiments, they measure the coherence energy gap due to the superposition of the supercurrent. This is the non-contextual observable with respect to the actual measurement of the direction of the supercurrent. Such coherence gap would not occur if there are no superposition. So indirectly, you have measured the superposition of the current direction without having to actually make a measurement of the current. This is why we know such superposition is real.

Zz.

 

[OOO]

That is why I mentioned about non-commuting and non-contextual observables.

Remember, if an operator A operates on an observable, only those observables that commute with A will also have the wavefunction "collapsing" for them (assuming non-degenerate states). Those that do not commute with A still have undetermined values.

In the SQUID experiments, they measure the coherence energy gap due to the superposition of the supercurrent. This is the non-contextual observable with respect to the actual measurement of the direction of the supercurrent. Such coherence gap would not occur if there are no superposition. So indirectly, you have measured the superposition of the current direction without having to actually make a measurement of the current. This is why we know such superposition is real.

Zz.

I interpret your statement as: for working out the paradox it would be better not to use a cat but a SQUID since the superpositition in the latter can be detected without destroying it. Is that right ?

 

[ZapperZ]

I interpret your statement as: for working out the paradox it would be better not to use a cat but a SQUID since the superpositition in the latter can be detected without destroying it. Is that right ?

Kinda.. the problem with the cat is that we haven't defined the observables involved in the system. We certainly can't tell what would be commuting and non-commuting.

Note that the effects of superposition is extremely common in chemistry. The existence of bonding and antibonding states are clear evidence of such a thing. So it isn't just restricted to SQUIDs. The reason that Leggett suggested the SQUID experiment in the first place is that it would involve the superposition of not just one or two or three particles, but a gazillion particles, thus testing the the "size" effect for detecting quantum behavior. Superconductors are idea for that because the supercurrent behaves as a single, coherent "entity", causing Carver Mead to proclaim that nowhere in nature is there a better demonstration of quantum mechanics[1].

Zz.

[1] C. Mead, PNAS v.94, p.6013 (1997).