Understanding the Cat in a Box Paradox

[Anonym]

First of all, I want to be clear: I consider the experimental and theoretical investigations of the interconnection between the micro/meso/macrosystems most interesting development in QM today. However, your statements look to me as the decoherent mixture of facts and personal interpretations. For example:

Someone should perhaps point out that the "cat in a box" is a higly idealized gedanken experiment. A real cat would always be EITHER dead or alive inside the box, regardless if you open it or not.

The reason is that any object the size of a real cat is an open quantum system meaning it couples to the enviroment. Hence, it can never be in a superposition of dead/alive for very long (its "wavefunction" will decay extremely fast).

That “highly idealized gedanken experiment” was performed by famous American experimentalist at the beginning of 20 century in order to clean mass spectrometer. The second statement is correct. The third is obviously wrong. The fourth does not follow from the previous and is clearly the interpretation. And so on.

As far as I remember the cat "paradox" was orignally an attempt by Schrödinger to show how absurd QM was, i.e. he was implying that there must be something fundamentally wrong with the theory.

E. Schrödinger wrote:

” That prevents us from so naively accepting as valid a "blurred model" for representing reality. In itself it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.”

My point is that the cat "paradox" is not really a problem in physics anymore (and I don't think it ever was), in part simply because we got used to the idea; nowadays we instead use these effects to build useful devices. There are obviously quite a few philosophical issues, but these are largely irrelevant to the science…

I am not denying anything. The "collapse" is very real to me (although I don't really like this language) since the systems I work with are only useful BEFORE they collapse..

The purpose of my investigation is to make them useful after the collapse also. There is nothing in physics that interesting me more than what you are doing. I repeat: please, present clearly what you measure, how you measure and what are the obtained results. Please leave your explanations, philosophy and interpretations to others.

I guess you can say that I (like most experimentalist I know) use Poppers "definition" of a scientific theory, if can't be measured it ain't science.

I consider A.Einstein give a better advice for the physicist:

”Probably, I used the philosophy of that kind, but it nevertheless rubbish. Or, speaking more carefully, the remembering of what we are really observes and what we do not has probably some heuristic value. However, from the principal point of view, the attempt to formulate the theory based only on observable quantities is completely nonsense. Because in the reality everything that happens are just an opposite. Only the theory itself can decide what is and is not observable. You see, the observation, generally speaking, is very complicated notion…”

Regards, Dany.

 

[shaun_o_kane]

I think you guys miss the point of the "paradox". The equations of Quantum Mechanics say that the waveform describign the cat is in a state of half-alive and half dead. So the question is not what state the cat is in but what is the meaning of the waveform. Their is a problem only if you say that the half-dead / half-alive waveform => half alive / half dead cat.

 

[lightarrow]

Repeating the experiment many times, half of them we find a dead cat, half of them an alive cat. There's nothing more than this. The state of the cat is not changed by the experimenter opening the box, but by the interaction between the particle emitted from the radioactive substance and the detector. Before that event, the cat is alive; if that happens then the cat dies. No cat-superpositions.

 

[cesiumfrog]

No cat-superpositions.

On what basis do you make this claim?

 

[Fra]

Repeating the experiment many times, half of them we find a dead cat, half of them an alive cat. There's nothing more than this.

I personally don't find this definition sufficiently sophisticated.

This objections starts with the definition of probability itself in relation to reality. Repeating the experiment many times, raises at least three issues

1) To what degree of certainty can we guarantee that the experiment is indeed identical? Is the "certain enough" really satisfactory in the general case? I think not.

2) What about time? Repeating the experiment many times, gives us still an uncertainty in the measured true probability. And repeating the experiment infinitely many times is certainly impractical to the point of beeing ridicilous. This implies some kind of uncertainty relation at minimum.

3) What is the memory record utilized to store the potentially data infinite amount of data? Infinite storage capacity to store the correlations leads to the other absurdity. What happens to this description if we consider the memory records to have dynamical information capacities? Perhaps some observers can make observations at higher resolution due to higher complexity?

These issues does not have anything specifically to do with QM, but it relates more generally to probability theory coupled to reality, where we expect all notions to be induced from real interactions, and thus stored in real structures. Limited complexity can not possibly contain any infinite memory records, or infinitely resolved continuums? Or can it? If so, I would like to see a better argumentation.

This is one of the issues I see rooted in the QM interpretations.

/Fredrik

 

[Fra]

This was just my personal thinking and is in line with the reviews I'm personally doing, I'm sure many on here will strongly disagree.

These kind of questioning of QM foundations, interestingly also probably provides a fundamental connection to gravity. One unavoidably are lead to consider information capacities which gives a more or less intuitive connection to the generic concept of inertia which seems to give a first principle angle to the concepts of energy and mass. I think it has been a mistake to ignore the foundations for to long time. I don't see why a foundations historically seen to be reasonable satisfactory for major parts of particle physics (=special case), is necessarily solid enough for a unified theory for the general case, including not only gravity but also systems of arbitrary complexity.

/Fredrik

 

[Anonym]

On what basis do you make this claim?

Since the cat is the detector.

Repeating the experiment many times, raises at least three issues

1) To what degree of certainty can we guarantee that the experiment is indeed identical? Is the "certain enough" really satisfactory in the general case? I think not.

2) What about time? Repeating the experiment many times, gives us still an uncertainty in the measured true probability. And repeating the experiment infinitely many times is certainly impractical to the point of beeing ridicilous. This implies some kind of uncertainty relation at minimum.

3) What is the memory record utilized to store the potentially data infinite amount of data?

You will obtain the answers to your questions reading A. Tonomura et al, AJP, 57, 117 (1989). If you are curious enough.

Regards, Dany.

 

[Fra]

I will try to locate that article.

/Fredrik

 

[Fra]

I find nothing in arxiv, but it seems to be for sale at ajp website. Though seeing just the abstract it's not clear in what sense if might supply the answer to the above questions?

Of course there is sufficient memory in the environment to act as a record, but then the entire environment (ie the reminder of the universe) is the observer, which hardly makes sense either.

Does aynoone know if there's a preprint of this somewhere? It seems these older (pre-www) papers are usually hard to find in the free preprint archives.

/Fredrik

/Fredrik

 

[lightarrow]

On what basis do you make this claim?

According to one of the many possible interpretations, which I'm asserting now, the wavefunction collapse happens before the cat, between the radioactive substance and the detector (which then breaks the tube with poison). According to this interpretation, that interaction is the irreversible event, that is, the measure.
Of course it leave unanswered the question: what does "irreversible" mean and where this exactly happens? In my opinion irreversibility is the key point.

 

[shaun_o_kane]

Since the cat is the detector.

You will obtain the answers to your questions reading A. Tonomura et al, AJP, 57, 117 (1989). If you are curious enough.

The cat is a quantum system, not the detector. It should therefore be in a superimposition state according to QM. Is this supposed to be the paradox at the heart fo the measurement problem?

 

[cesiumfrog]

According to one of the many possible interpretations, which I'm asserting now, the wavefunction collapse happens before the cat, between the radioactive substance and the detector

Ah, yes. That was a popular take on the Copenhagen interpretation: that a collapse occurs when a microscopic quantum system interacts with a macroscopic classical system. Very pragmatic. Its main advantage seems to be that it says nothing new about the observer, but it also says very little about the collapse process it assumes.

It additionally has an obvious flaw, which is that in principle every (simple) macroscopic classical system can also be described as a (complicated) microscopic quantum system. If we were to write down a Hamiltonian for the (complicated) detector interacting with the atom, and numerically solve its Schroedinger equation, we would expect to always find the detector in a superposition state, in contradiction to your prior assertion. And indeed, experiments have demonstrated that large numbers of atoms can behave as a quantum-mechanical system. Do you reconcile this?

 

[Anonym]

Guys ... come on! We invented mathematics to make words less slippery!

Actually, I have nothing to add; perhaps, only to discuss the interconnection between the math and the physics.

The linear superposition of states is the mathematical property of the Schrödinger picture. It was not clear (1926-1935) what it means physically. However, E. Schrödinger demonstrated the mathematical equivalence of his and W. Heisenberg picture. In the Heisenberg picture it is translated into HUP and provide the clear definition what the QM system is: delta (A)*delta (B)>0. Also it provide the “clear” definition what the classical (macroscopic) system is: delta (A)*delta (B) = 0 (John von Neumann). And in CM every system is detector. Notice, however, that the notion of the dynamical variable as the self-adjoint operator is not defined in the Newtonian/Hamiltonian formulation of the classical physics.

Now, we know that the macroscopic system is the statistical ensemble of the microscopic subsystems. The transition from QM to CM (delta (A)*delta (B)>0 => delta (A)*delta (B) = 0) is called “the collapse of the wave packet”, that is, uses the Schrödinger picture. Physically it means that the system extended (“blurred”) in QM is imaged by the material points in CM (E. Schrödinger Cat).

Why the transition express itself as the collapse (A.Einstein, 5-th Solvay), whether the linear superposition property remains valid in CM and when and where it takes place (mesoscopic systems) – that is the Measurement Problem.

In my posts #51, #62 and #106 I referred to A.Einstein to demonstrate that he knew what going on precisely, he only didn’t know to say that mathematically.

Regards, Dany.

 

[lightarrow]

Ah, yes. That was a popular take on the Copenhagen interpretation: that a collapse occurs when a microscopic quantum system interacts with a macroscopic classical system. Very pragmatic. Its main advantage seems to be that it says nothing new about the observer, but it also says very little about the collapse process it assumes.

It additionally has an obvious flaw, which is that in principle every (simple) macroscopic classical system can also be described as a (complicated) microscopic quantum system. If we were to write down a Hamiltonian for the (complicated) detector interacting with the atom, and numerically solve its Schroedinger equation, we would expect to always find the detector in a superposition state, in contradiction to your prior assertion. And indeed, experiments have demonstrated that large numbers of atoms can behave as a quantum-mechanical system. Do you reconcile this?

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

 

[shaun_o_kane]

I'm afraid cesiumfrog is wrong. Copenhagen does not say QM waveform "collapses" as a result of the interaction with a macroscopic system. Copenhagen say that you can choose the quantum-classical boundary anyway you want, typically at the interaction with macroscopic measurement devices. Hence the paradox. Two views are possible: the cat is the measurement device (classical-quantum boundary) and the waveform "collapses" (not a Copenhagen term) at the cat, or the external observer is the measurement device (classical-quantum boundary).

Copenhagen is simply applying the equations differently but equally validly.

 

[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.