Understanding the Cat in a Box Paradox

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In summary: I also said that it is different from being dead or alive.Yes, I think we're on the same page now. The point that I've been trying to make is that the common interpretation of the Schroedinger's Cat paradox is that it is in a superposition of states. That means that ALL of those states exist simultaneously. What seems to be often missed in this is the word "superposition". Many people would say that the cat is either dead OR alive, and we just don't know which one. But that's not what a superposition means.Zz.In summary, the conversation discusses the cat in a box paradox as an analogy for particles in quantum
  • #1
ArielGenesis
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I just learn the cat in a box paradox, where we cannot know whether the cat is dead or alive until we open the box, so the cat is in a superposition between life and death. yup, got it!

I am about to learn quantum physics. And I think it would be really good if I got a grasp of it first. So this cat thing, is analogy for particle, and its life, is for particle's properties. So far so good.

What I don't understand is that if we don't know the particle state, then I would assume that the particle state is irrelevant as it won't affect anything, because when it affect something, we know its state, in other words, the box had been opened. Thus would it really matter what the particle state is before the box is opened?
 
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  • #2
Basically, there are two schools of thoughts.

1. Until you look, the cat is neither dead nor alive.

2. It is allways either dead or alive even if you do not look. But in this case, a sort of nonlocal communication between physical objects is possible.

At the moment, nobody knows with certainty which view is the correct one.
 
  • #3
Or:

3. When you look, the world splits in 2, one for the possibility that it's alive, and one for it's dead.
4. Whether it's dead or alive only exists in your head, and so it's a trivial truism that it's neither dead or alive until you look. Any interaction where you learn more about the cat is going to have an effect on the cat, because you're a clumsy physicist and all you can do is a deliver a well-aimed poke.
5. ...

There's probably countless others. In practise, it doesn't matter: you model the problem in the language of quantum mechanics, follow the procedure, and you will be able to calculate the probability that the cat is alive or dead, without ever wondering about what exactly happened in between. It says a lot that experimentalists never worry about the measurement problem but the theorists do all the time.
 
  • #4
Demystifier said:
Basically, there are two schools of thoughts.

1. Until you look, the cat is neither dead nor alive.

2. It is allways either dead or alive even if you do not look. But in this case, a sort of nonlocal communication between physical objects is possible.

At the moment, nobody knows with certainty which view is the correct one.

You are missing a #3: The cat is BOTH dead and alive. That is what a superposition implies, the existence of BOTH orthogonal states at the same time.

If it is #1 or #2, then you would never have bonding-antibonding in chemistry, and no coherence energy gap in the Delft/Stony Brook experiments. I certainly haven't seen anyone formulating any physics using #1 and #2 to derive what have been observed.

Zz.
 
  • #5
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).

This is the reason why it is so difficult to e.g. build good quantum bits out of macroscopic objects; they interact with the environment (or, more specifically, enviromental degrees of freedom) and decay very quickly leading to short coherence times.
 
  • #6
genneth said:
Or:

3. When you look, the world splits in 2, one for the possibility that it's alive, and one for it's dead.
4. Whether it's dead or alive only exists in your head, and so it's a trivial truism that it's neither dead or alive until you look. Any interaction where you learn more about the cat is going to have an effect on the cat, because you're a clumsy physicist and all you can do is a deliver a well-aimed poke.
3. is a variant of my 1.
4. is a variant of my 2.
 
  • #7
ZapperZ said:
You are missing a #3: The cat is BOTH dead and alive. That is what a superposition implies, the existence of BOTH orthogonal states at the same time.
The cat cannot be both dead and alive. It can be in a superposition of dead and alive, but this is neither dead nor alive, but something else - the superposition. But this is just a matter of language. In fact, your #3 is actually rephrased 1.
 
  • #8
Demystifier said:
The cat cannot be both dead and alive. It can be in a superposition of dead and alive, but this is neither dead nor alive, but something else - the superposition. But this is just a matter of language. In fact, your #3 is actually rephrased 1.

No, it isn't. Being dead AND alive is different than being dead OR alive. The latter means that the cat has a DEFINITE state. We just don't know what it is. This is classical statistics where you've tossed a coin, but you haven't seen it yet whether it is head OR tail. This is not a superpostion.

My interpretation isn't something I invented. The Leggett paper that I've highlighted before many times on here regarding the measurement problem clearly stated this position. When you have a state being described as a linear sum of orthogonal states, then the obvious interpretation here is that ALL of those states exists at the same time. If not, then the Schrodinger Cat paradox isn't anything unusual. The cat is either dead or alive, which isn't new nor strange. Why would Schrodinger go to all that trouble illustrating something that is not unusual?

Zz.
 
  • #9
ZapperZ said:
No, it isn't. Being dead AND alive is different than being dead OR alive.
But we agree on that. I said that being dead and alive is actually a clumsy way of saying that the cat is in a superposition. I also said that it is different from being dead or alive.
 
  • #10
Demystifier said:
But we agree on that. I said that being dead and alive is actually a clumsy way of saying that the cat is in a superposition. I also said that it is different from being dead or alive.

Demystifier said:
1. Until you look, the cat is neither dead nor alive.

2. It is allways either dead or alive even if you do not look. But in this case, a sort of nonlocal communication between physical objects is possible.

You have a funny way of saying that then.

Zz.
 
  • #11
Man, you guys are crazy.
 
  • #12
mattex said:
Man, you guys are crazy.

It really is a lot of arguing over something which doesn't actually affect any experiment that we can currently do. Moreover, each possibility has a different flaw/distaste to it, so it's pretty much subjective. Obviously Dany is in favour of Bohmian mechanics (does anyone here *not* already know that?), but that is, again, a matter of taste. If we all just sat down and did some calculations of well-posed problems, we'd all agree on the outcomes. How much Platonic reality can we really ask for from mathematical models?
 
  • #13
ZapperZ said:
You have a funny way of saying that then.
You completely misunderstood me. My 1. and 2. refer to two mutually exclusive schools of thoughts. My later responses to you refer only to the 1. school of thought. My whole point is that there are essentially only TWO different schools of thought, while all others (3., 4., #3, ...) are nothing but variants of these two.

Of course, as a Bohmian, I prefer 2. Still, I believe that I am able to speak consistently about 1. as well.
 
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  • #14
Demystifier said:
You completely misunderstood me. My 1. and 2. refer to two mutually exclusive schools of thoughts. My later responses to you refer only to the 1. school of thought. My whole point is that there are essentially only TWO different schools of thought, while all others (3., 4., #3, ...) are nothing but variants of these two.

Of course, as a Bohmian, I prefer 2. Still, I believe that I am able to speak consistently about 1. as well.

OK, let's see...

Demystifier said:
The cat cannot be both dead and alive. It can be in a superposition of dead and alive, but this is neither dead nor alive, but something else - the superposition. But this is just a matter of language. In fact, your #3 is actually rephrased 1.

1. So you are claiming that

#3 The cat is BOTH dead AND alive

is identical to

#1 The cat is neither dead nor alive?

2. When you toss a coin but don't look at the outcome, do you say that it is (i) either head OR tail, or (ii) head AND tail?Zz.
 
  • #15
ZapperZ said:
a) So you are claiming that

#3 The cat is BOTH dead AND alive

is identical to

#1 The cat is neither dead nor alive?

b) When you toss a coin but don't look at the outcome, do you say that it is (i) either head OR tail, or (ii) head AND tail?
a) You don't read what I say. So, let me repeat. The cat cannot be both dead and alive, it is a logical contradiction. Still, it can be in a superposition of dead and alive. In this case, it is neither dead nor alive. Sometimes we say for such a state that the cat is "both dead and alive", but it is simply an incorrect (or imprecise) language.

b) I say it is in the superposition of head and tail (recall that I am still talking within the 1. paradigm, despite the fact that I actually prefer 2.)

By the way, this is my 666th post.
 
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  • #16
Guys ... come on! We're arguing over words, not meaning! We invented mathematics to make words less slippery! Dany and ZapperZ: I think you already understand each other, and agree that you use the same words in different meanings; as far as who's "correct", I say it doesn't matter.
 
  • #18
genneth said:
It really is a lot of arguing over something which doesn't actually affect any experiment that we can currently do.

I disagree. That's the whole point of Bell's theorem. The only way to interpret EPR type experiments (liek the ones done by Alain Aspect) which violate Bell's inequality is to conclude that the photons are in linear superposition of two spin states before being observe (unless one introduces nonlocality). That's the wonderful thing about Bell's inequality: it permitted to teexperimentally something that seemed to be a purely philosophical issue!

Moreover, each possibility has a different flaw/distaste to it, so it's pretty much subjective. Obviously Dany is in favour of Bohmian mechanics (does anyone here *not* already know that?), but that is, again, a matter of taste. If we all just sat down and did some calculations of well-posed problems, we'd all agree on the outcomes. How much Platonic reality can we really ask for from mathematical models?
 
  • #19
Demystifier said:
a) You don't read what I say. So, let me repeat. The cat cannot be both dead and alive, it is a logical contradiction. Still, it can be in a superposition of dead and alive. In this case, it is neither dead nor alive. Sometimes we say for such a state that the cat is "both dead and alive", but it is simply an incorrect (or imprecise) language.

OK, let's go back one more step.

You are saying that this equation

[tex]\psi = a_1|u_1> + a_2|u_2>[/tex]

implies that the system has neither basis state [itex]|u_1>[/itex] nor basis state [itex]|u_2>[/itex], instead of saying it contains BOTH basis states in superposition?

Simply by using the term "superposition", it automatically implies that you have two different "things" that are being added. In fact, if you look at the original thought experiment, that is what is being said, that they both exist. That is what made it so strange in the first place.

Secondly, if an electron in an H2 molecule is located at neither near one of the H atom or the other, then it would not create any kind of bonding state because it isn't there, so what is there to "interfere" with? One can say the same thing about the superposition of paths in a double slit experiment. Using your argument, one would say the particle pass through neither one slit nor the other. Then what went through that we detected? If you care about "logical inconsistency", I would say the way you describe it creates one as well.

I am not saying that describing such position by saying "The cat is both dead and alive" is the de facto description of this QM scenario. There is always a major shortcoming when we try use ordinary words and language to describe QM's mathematical formulation, and I've always said that all along. However, I truly believe based on what I've read and seen, that saying that the cat is "neither dead nor alive" is even more inaccurate than saying that it is "both dead and alive". When I do "A = B + C", then A contains BOTH B and C. I never say that A has neither B nor C.

If we're dealing with just physics papers and issues, I wouldn't have cared since we would be dealing with the mathematics. But with a forum like this, and especially when many do not understand the underlying mathematics that we're trying to put words into, this difference DOES matter in trying to accurately convey (to the extent that it is possible), what the formalism is trying to indicate. I would rely on the standard interpretation of what has been said already, and you're welcome to check the Leggett paper on the exact wording that has been used there.

Zz.
 
  • #20
nrqed said:
I disagree. That's the whole point of Bell's theorem. The only way to interpret EPR type experiments (liek the ones done by Alain Aspect) which violate Bell's inequality is to conclude that the photons are in linear superposition of two spin states before being observe (unless one introduces nonlocality). That's the wonderful thing about Bell's inequality: it permitted to teexperimentally something that seemed to be a purely philosophical issue!

Indeed, but I doubt that either Dany or Zz was ignorant of this fact. Searching for the correct interpretation of the EPR-esque experiments often leads to this sort of misunderstandings of language, as people rarely define in completely rigorous ways their vocabulary in the middle of a posting to PF. However, everyone is in complete agreement over the results of such an experiment, no matter how they justify the events which occur. Thus, we were arguing over trifles.

P.S. Hmm... trifles... I wonder if I've got one in my fridge... :greedy:
 
  • #21
Addendum

In Leggett's paper (J. Phys: cond. matt,v.14, p.415 (2002)), on page 417, Sec. 2, in describing the Schrodinger Cat experiment, he explicitly stated this:

Leggett said:
In Schrodinger's original 'quite absurd' thought-experiment, a superposition of microscopically distinct states (the decay and undecay of states of a radioactive nucleus) leads inexorably to a superposition of macroscopically distinct states (states in which a cat in a closed box is respectively dead AND alive (my caps).

He continues with the rest of the paper with that kind of argument, and followed through with that view in interpreting the Delft/Stony Brook experiments.

So this is not something that *I* invented, or something that I have a choice in interpreting.

Zz.
 
  • #22
ZapperZ,
7=4+3
Nevertheless, 7 is not both 4 and 3. Moreover, 7 is neither 4 nor 3. 7 is a superposition of 4 and 3, but it is also a superposition of 5 and 2. I think the analogy with quantum mechanics is obvious.
 
  • #23
How do we know that an electron measured now, was an electron before? Seems to me, taken to a silly extreme, that some might say that the measurement created the electron.

I recently went to the U. of Washington -- Boise State football game, which the U of W won. Prior to the end of the game, each team has a chance to win; and, of course, a chance to lose. Let's suppose that we know the driver of the probability system that describes the football game. In fact, the dynamics of the probability system is described by a dynamical equation based on a transition matrix, so that

dP/dt = T*P

with P the probability vector -- if there are N outcomes, then P is an N dimensional vector, and T is an NxN matrix. Sorta like the Schrodinger Eq. So, we can say that each team can win or lose; is in a superposition of win and lose according to the probability description. And, of course, the teams are entangled -- think overtime until a score.

It's no big deal to describe the Cat problem in the terms of classical probability theory, which is why I've written numerous time that the Cat problem has precious little to do with QM.

Thus, to me, it seems that all the superposition stuff is in our minds, and is simply a powerful concept we use as part of the language of physics. If we suffer from cognitive dissonance, we are clearly dealing with contradictions messing up our thought processes. In fact, the human mind can easily imagine any number of outcomes for virtually any process. And, surely we can imagine, for example, that the U of W wins and, simultaneously, that the U of W loses. Thus, with the stochastic equation above, we can say that our mind supports the idea of superposition for football teams, and, hence, for virtually anything.

Collapse? No problem. Once the outcome is known, the probability of the alternatives is zero, and the probability of the outcome is 1. Our knowledge changes = collapse. (Sir Rudolph Peierls was the major big-timer to support QM as describing our knowledge rather than the "reality" of the system. )
Regards,
Reilly Atkinson
 
  • #24
Demystifier said:
ZapperZ,
7=4+3
Nevertheless, 7 is not both 4 and 3. Moreover, 7 is neither 4 nor 3. 7 is a superposition of 4 and 3, but it is also a superposition of 5 and 2. I think the analogy with quantum mechanics is obvious.

I think it is you now who are not reading what I wrote. I didn't say 7=3 or 7=4. I said 4 and 3 are both there in 7.

ZapperZ said:
When I do "A = B + C", then A contains BOTH B and C. I never say that A has neither B nor C.

Furthermore, the 5 and 2 sum is irrelevant here, because if we consider the analogy with QM, it is the "4 and 3" that are in "superposition" to describe the COMPLETE state of 7.

Can you cite for me any papers that actually adopted your interpretation of this scenario? I think I've gone to great extent in producing references that used what I wrote word-for-word.

Zz.
 
  • #25
reilly said:
It's no big deal to describe the Cat problem in the terms of classical probability theory, which is why I've written numerous time that the Cat problem has precious little to do with QM.

And I agree. However, I am dealing with the Schrodinger Cat states that we deal with in QM. The cat is only being used here as an illustration of such states. I myself do not buy into the actual macroscopic situation of the cat being both dead and alive (or any other combination of interpretation of the superposition of such states). At the QM level, superposition is as real as anything with measurable consequences.

Zz.
 
  • #26
Unitary QM is very clear- there are parallel universes in which the cat is alive and dead and the observers in these different worlds are equally real- the Copenhagen and the various hidden variable interpretations don't necessarily argue with this- they merely ignore the other outcomes and deal with the case that is observed-

there would also be more than just 2 parallel worlds- the superposition contains every possible state of the matter- including all the states where the cat survived and died in different ways- as well as every possible kind of extremely rare outcome- such as when something random occurs and the cat's atoms tunnel elsewhere or a random quantum fluctuation forces them into different states- so there are always also parallel worlds where the cat turned into a bowl of petunias or a sperm whale-
 
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  • #27
reilly said:
Thus, to me, it seems that all the superposition stuff is in our minds, and is simply a powerful concept we use as part of the language of physics. If we suffer from cognitive dissonance, we are clearly dealing with contradictions messing up our thought processes. In fact, the human mind can easily imagine any number of outcomes for virtually any process. And, surely we can imagine, for example, that the U of W wins and, simultaneously, that the U of W loses. Thus, with the stochastic equation above, we can say that our mind supports the idea of superposition for football teams, and, hence, for virtually anything.


The problem with your example is that you are trying to apply the concept of superposition to a situation where it has no significance(I am not familiar with the players in the teams in your example, but I assume they are macroscopic). Gedankenexperiments are useful but one has to be very careful not to draw the conclusion that something is wrong just because it appears "silly" as in your example.

As I pointed out above: in a real experiment with a real cat it will always be dead OR alive, the cat is an open quantum system (it is interacting strongly with enviromental degrees of freedom) which means that 'simple' QM simply doesn't work (it is a bit similar to thermodynamics in that respect: there is a very significant difference between open and closed systems). The theory of open quantum systems is quite well developed (the most famous example being the Caldeira-Legget model, but there are more sophisticated model) and is closely connected to quantum measurement theory.
Most of the "philosophical" problems one encounters in QM (like what an "observer" really is etc) tend to disappear once a real experiment is analyzed.
 
  • #28
genneth said:
Obviously Dany is in favour of Bohmian mechanics…
Dany and ZapperZ: I think you already understand each other.

Sorry, but I am completely confused. Which Dany you have in mind? To avoid any misidentification, I didn’t participate in that session and I expressed my POV on Bohmian mechanics clearly here in PF: “Not even wrong”.

Regards, Dany.

P.S. Perhaps you mean Demystifier? His private name is Hrvoje.
 
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  • #29
genneth said:
It says a lot that experimentalists never worry about the measurement problem but the theorists do all the time.
As it says a lot that theorists like Einstein changed the Physics, while experimentalists not.
 
  • #30
lightarrow said:
As it says a lot that theorists like Einstein changed the Physics, while experimentalists not.

You may want to double check that with Harry Lipkin (who happens to be a theorist himself) and his article "Who Ordered Theorists?" According to him (and he gave numerous examples), it was experimentalists who made discoveries that were never even hinted in any existing theories at that time. And he even left out superconductivity and fractional quantum hall effect in that article.

I strongly suggest we do not go down this path, especially in this thread.

Zz.
 
  • #31
ZapperZ said:
You may want to double check that with Harry Lipkin (who happens to be a theorist himself) and his article "Who Ordered Theorists?" According to him (and he gave numerous examples), it was experimentalists who made discoveries that were never even hinted in any existing theories at that time. And he even left out superconductivity and fractional quantum hall effect in that article.
Zz.
I'm well conscious of this. But theorists are the ones which create or modify physics, or establish that a certain experimental discover can or cannot be placed inside the current understanding of physics; with this I absolutely don't mean to negate importance to experimental physics.
 
  • #32
Wait, I don't understand anything...
the cat in the box is under superposition, okay.
So in QM, what is the significant, and if you want to say something very technical like, the bell, phenomena, or whatever it is, can you please give more explanation, I am not really into these sort of things yet.
 
  • #33
reilly said:
It's no big deal to describe the Cat problem in the terms of classical probability theory, which is why I've written numerous time that the Cat problem has precious little to do with QM.

There's a difference between classical probability "superpositions", in which we quantify our lack of complete knowledge of the system by expressing the system as being in a sort of probability weighted average of different states, and a quantum superposition. For one thing, the quantum superposition is assumed to not be due to a lack of knowledge, but is an intrinsic feature of the world. And more importantly, it is only in quantum mechanics that the different constituent states can "interfere" with each other, and affect the outcome of measurements.

For example, say we want to determine the expectation value of an observable O for a system in a superposition (A+B)/2 of two states A and B. Classically, if the values for each state are O(A) and O(B), then the expectation value for the superposition is just (O(A)+O(B))/2. However, for quantum mechanical superpositions, there is also a term of the form <A|O|B>, and this will affect the probabilities in a non-trivial way (in fact, this is essentially where the strangeness of quantum mechanics comes from).

The degree of this interference is determined roughly by the overlap (scalar product) of the different states, and in the limit of a macroscopic system, there are so many degrees of freedom that different states that are likely to come up in a superposition are almost certainly nearly orthogonal, and the expectation values computed quantum mechanically reduce to their classical values (ie, with no cross terms).

Personally, I think the only way to avoid an arbitrary distinction between big and small is to assume that macroscopic systems can be in superpositions, just ones whose consituent states don't interact (because of negligible overlap) but evolve independently, ie, a many worlds view.
 
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  • #34
ZapperZ said:
I said 4 and 3 are both there in 7.
What does it mean? Are 8 and -1 also both there in 7? Is any number there in any other number?
 
  • #35
Anonym said:
Sorry, but I am completely confused. Which Dany you have in mind? To avoid any misidentification, I didn’t participate in that session and I expressed my POV on Bohmian mechanics clearly here in PF: “Not even wrong”.

Regards, Dany.

P.S. Perhaps you mean Demystifier? His private name is Hrvoje.
Some people here call me Demy, which can easily be confused with Dany.
By the way, I also expressed my opinion that RELATIVISTIC Bohmian mechanics may be even wrong (but also even right).
 

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