Understanding the Cat in a Box Paradox

[ArielGenesis]

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?

 

[Demystifier]

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.

 

[genneth]

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.

 

[ZapperZ]

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.

 

[f95toli]

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.

 

[Demystifier]

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.

 

[Demystifier]

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.

 

[ZapperZ]

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.

 

[Demystifier]

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.

 

[ZapperZ]

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.

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.

 

[mattex]

Man, you guys are crazy.

 

[genneth]

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?

 

[Demystifier]

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.

 

[ZapperZ]

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...

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.

 

[Demystifier]

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.

 

[genneth]

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.

 

[Demystifier]

Genneth, I think you are right!

 

[nrqed]

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?

 

[ZapperZ]

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

\psi = a_1|u_1> + a_2|u_2>

implies that the system has neither basis state |u_1> nor basis state |u_2>, 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.

 

[genneth]

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:

 

[ZapperZ]

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:

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.

 

[Demystifier]

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.

 

[reilly]

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

 

[ZapperZ]

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.

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.

 

[ZapperZ]

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.

 

[setAI]

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-

 

[f95toli]

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.

 

[Anonym]

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.

 

[lightarrow]

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.

 

[ZapperZ]

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.

 

[lightarrow]

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.

 

[ArielGenesis]

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.

 

[StatusX]

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.

 

[Demystifier]

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?

 

[Demystifier]

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).

 

[ZapperZ]

What does it mean? Are 8 and -1 also both there in 7? Is any number there in any other number?

Then you are missing the entire point of my original question to you if something as direct as this is "mystifying" you.

There are two separate points here that needed to be repeated:

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

2. That the mathematical equation representing the superposition of state such as \psi = a_1|x&gt; + a_2|y&gt; can accurately be described as "neither x nor y".

What you have been trying to argue so far with these number games is #1. This is a logical fallacy. Those 2 statements are not identical, no matter what kind of "interpretation" you wish to use. Try telling someone that A is neither in that room, nor in this room. Do you think that is the same as saying A is both in this room and in that room? It is not!

As for #2, I have already pointed out the weirdness by bringing out examples using the H2 molecule and the double slit. If that equation implies "neither x nor y", then the system does NOT have the property of x and y. When we apply that to the double slit, we are then saying the particle did not pass through the left slit nor the right slit. Yet, we detect a particle on the other side of the slit. How did that happen? By magic? This scenario creates MORE problems than saying the particle passed through BOTH slits. At least there' now no question on why we would detect the particle on the other side.

Again, I asked you for sources that actually adopts your wording and interpretation. I had presented to you my sources out of respect for your knowledge in such matters, rather than just claim something without justification. I would hope that you'd reciprocate in similar manner.

Zz.

 

[cesiumfrog]

Sheesh, get a room.

It's a purely grammatical debate: Zz is saying it's in a superposition. Demy is agreeing it's state is not equal to the first eigenstate, and neither is it's state the second eigenstate. I don't think anyone needs to cite a source for that.

 

[Demystifier]

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

2. That the mathematical equation representing the superposition of state such as \psi = a_1|x&gt; + a_2|y&gt; can accurately be described as "neither x nor y".

No, I do not claim that. In particular, I do not use words "identical" and "accurately". I agree with cesiumfrog that this discussion becomes pointless.

 

[Demystifier]

When we apply that to the double slit, we are then saying the particle did not pass through the left slit nor the right slit. Yet, we detect a particle on the other side of the slit. How did that happen? By magic?

Well, if you do not accept the existence of hidden variables, then "magic" is the best explanation that remains.

 

[lightarrow]

Well, if you do not accept the existence of hidden variables, then "magic" is the best explanation that remains.

Or that the particle doesn't exist from source to detector.

 

[reilly]

StatusX

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.

Let's take a careful view of probability. First, it is part of the language of physics. Why? It's a very useful tool in many branches of physics and engineering, and has been so for at least a few hundred years. In contrast, until modern QM arrived, Hilbert Space methods were considered to be of little use, and so few people put Hilbert into their bag of tricks. My how things have changed.

Mathematicians develop probability as a branch of measure theory for a space of so-called events -- a win, drawing a certain hand in poker, measuring an electron arriving at some point in a double-slit experiment, will there be a recession in three months, and so on. Nowhere in the theory is there any restriction of application. If the shoe fits, ...

This abstract approach tells us that classical and quantum probabilities are generically the same -- they both can be described by dynamical equations for the probablity distribution-- the differences between the details, like interference phenomena, are due to the different dynamics, and to generally different initial conditions.

In fact, in at least one case the quantum and classical probability distributions are identical -- the Rutherford cross section for an electron scattering from a positive point charge at low energies(target at rest)can be derived, as Rutherford did, strictly from classical electrodynamics and mechanics. And the exact same cross section can be derived from non-rel QM. Note that scattering is defined experimentally, as events: a counter indicates yes or no, yes, an electron hit the target. The resulting set of events defines a distribution, which when properly normalized, is a probability distribution in an abstract space of scattering events. That space could care less whether the events are described by QM or classical theory. It makes no difference whether the need for a probability description is due to a lack of knowledge, or is required to make sense of a theory, or involves a highly complex system -- perhaps many components,a gas for example, or the non-linear dynamics that might describe economic phenomena

There are plenty of opportunities for interference phenomena outside of quantum physics. When I play the piano and I play middle C, I create a superposition of piano states, basically the overtone series. Changing the overtone structure, changes the sound of the note. In extreme cases, beats are produced, generally caused by two interfering vibrations. Young's experiment is nicely explained classically. Most communication transmitted by electromagnetic means involves superposition of various frequencies, like sidebands "carried" by a carrier wave. The polarization of light, a rowboat crossing a river with a downward current involve superposition The description of anything by a vector space or vector field involves superposition. We use a lot of vector concepts in physics to explain a huge range of phenomena.

Finally, don't forget that QM is weird because it was developed to describe, if not explain some very strange phenomena -- atomic spectra, electron diffraction, the Stern-Gehrlich experiment, and so on. Indeed, QM is the child of experiments.

Regards,
Reilly Atkinson







'

 

[f95toli]

StatusX


This abstract approach tells us that classical and quantum probabilities are generically the same -- they both can be described by dynamical equations for the probablity distribution-- the differences between the details, like interference phenomena, are due to the different dynamics, and to generally different initial conditions.

'

But there are some major differences. First of all the "probabilistic" nature of quantum mechanics only comes into play when we want to MEASURE something (neglecting the effect of dissipation for the moment), as long as a system is left to evolve on its own it is complettely deterministic; this is why we can use superposition to build quantum computers and in other QIP applications.
Real systems are of course always open meaning we still usually need to use statistical quantum mechanics to predict the outcome of experiments, but that is a "technical" detail which rarely changes any qualitative properties of a system; the only difference between Rabi oscillations in a closed and an open system is that they are attenuated in the latter, but there are still oscillations and the basic physics is the same.

 

[StatusX]

This abstract approach tells us that classical and quantum probabilities are generically the same -- they both can be described by dynamical equations for the probablity distribution-- the differences between the details, like interference phenomena, are due to the different dynamics, and to generally different initial conditions.

It's true that the dynamical equations could both be written in matrix form, but for a classical system the relevant matrices would all be diagonal, showing that the matrix approach is not really necessary, just a means to organize information. In a quantum system, the non-zero off-diagonal terms are completely unexpected from a classical point of view, and show that the superpositions are not merely formal devices but real physical features.

There are plenty of opportunities for interference phenomena outside of quantum physics...

This is true, and the strange thing about quantum mechanics is not really the vector space structure, but the accompanying wavefunction collapse (and more generally, with reconciling the quantum and classical descriptions of the world). Without this, quantum mechanics would just be another classical field theory, the fields being the probability distributions. But in observing, say, the position of a particle, the wavefunction collapses to a delta function, giving the appearance of a particle underlying the field. For example, in the double slit experiment, the interference fringes are not strange in themselves, what's weird is that they appear as a cummulative affect after many single particles strike specific places on the screen.

The reason I addressed your post was because it seemed you were suggesting the schrodinger cat paradox had nothing to do with quantum mechanics. It's true that before quantum mechanics, people could have imagined a similar experiment with, say, a coin flip rather than radioactive decay, and ask what the state of the cat is before we observe it. But this would just be idle philosophizing - there's no practical problem here.

The difference in the case where we have a quantum superposition is that the dynamical equations imply that a microscopic superposition, which isn't really much stranger than, say, a superposition of overtones on a piano note, should evolve into a superposition of macroscopic objects, which is something very strange, and not something we seem to observe. The cat paradox is designed to expose this problem.

 

[f95toli]

The difference in the case where we have a quantum superposition is that the dynamical equations imply that a microscopic superposition, which isn't really much stranger than, say, a superposition of overtones on a piano note, should evolve into a superposition of macroscopic objects, which is something very strange, and not something we seem to observe. The cat paradox is designed to expose this problem.

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.
Now, first of all, as I have already pointed out we now DO understand why this never happens to real cats; the theory of open quantum systems as well as measurement theory is now so well developed that there is no real mystery anymore. Hence, there is no 'paradox'.

Secondly, we DO observe superposition in macroscopic objects. E.g. superconducting qubits might not be very large but they are certainly macroscopic (a few square microns, you can easily see a flux qubit in an ordinary optical microscope). The interesting thing with modern QIP (=quantum information processing) is that it has taken many problems from the realm of philosophy to what is basically engineering: in order to observe superpositions in a real experiments on superconducting qubits we use good magnetic shields, low noise amplifiers and a lot of filtering; in order to stop the "collapse" (i.e. increase the coherence time) we design the environment of the qubit in such a way as to maximize the impedance it sees (basically microwave engineering) etc. Hence, there is nothing particulary 'esoteric' about QIP anymore. I suspect many of the things we do in the lab nowadays would have shocked Schrödinger.

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.
It is worth remembering that thermodynamics and Newtonian mechanics also got their fair share of issues but these are rarely talked about nowadays, simply because we take those theories for granted.

 

[StatusX]

Now, first of all, as I have already pointed out we now DO understand why this never happens to real cats; the theory of open quantum systems as well as measurement theory is now so well developed that there is no real mystery anymore. Hence, there is no 'paradox'.

In what sense has it been resolved? There's no dispute about the predicted observations in the Schrodinger's cat experiment: there is a certain chance we'll observe the cat to be alive and a certain chance its dead. The thought experiment is meant to address issues of interpretation, and I'm pretty sure there's nothing approaching a consensus on the correct interpretation of quantum mechanics. As I said above, I take the thought experiment to most naturally lead to a many worlds interpretation, but not everyone would agree with me (and not everyone wouldn't). And this is probably not just philosophy, as its likely we'll need to have a firm grasp of what quantum mechanics really means (not just predicts) before we can move beyond it to a unified theory.

 

[f95toli]

The thought experiment is meant to address issues of interpretation, and I'm pretty sure there's nothing approaching a consensus on the correct interpretation of quantum mechanics.

I agree. But the point I was trying to make was that originally quite a few people actually DID think that a real cat would be in a superposition of states, it wasn't merely a gedanken experiment. You can find quite a lot of older (and some newer) texts that go on about the role of a rather mysterious "observer" that apparently caused the wavefunction to collapse etc.
Dissipation, measurement theory etc are relatively new topics in QM so the concept of decoherence was rather mysterious for a long time (and is still not fully understood).

Hence, while it is true that there is no consensus about the interpretation of QM I think it is fair to say that quite a few PRACTICAL issues relating to what you can actually observe in an experiment have been sorted out during the past 20 years or so.

Moreover, I am not quite sure I agree that I believe it is all that important to understand what QM really "means", at least not from a scientific point of view. To me physics is all about predicting what I can measure in the lab (I am an experimentalist, in case you haven't guessed that already), the rest is philosophy which means that there is little hope of ever reaching a "correct" answer (but it can still be interesting).

 

[cesiumfrog]

the point I was trying to make was that originally quite a few people actually DID think that a real cat would be in a superposition of states

Quite a few still do. Do you have any evidence that they are incorrect?

 

[Anonym]

Can you cite for me any papers that actually adopted your interpretation of this scenario?

E. Schrödinger, Ann. Physik, 79, 361,(1926); 79, 489,(1926); 79, 734,(1926);80, 437, (1926); 81, 109,(1926).

Regards, Dany.

 

[Anonym]

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.

Please, provide the reference. It would be highly appreciated if you will give M&W or somebody rank 1 or 2 in Landau classification.

Regards, Dany.

 

[Anonym]

It's true that the dynamical equations could both be written in matrix form, but for a classical system the relevant matrices would all be diagonal, showing that the matrix approach is not really necessary, just a means to organize information. In a quantum system, the non-zero off-diagonal terms are completely unexpected from a classical point of view, and show that the superpositions are not merely formal devices but real physical features.
This is true, and the strange thing about quantum mechanics is not really the vector space structure, but the accompanying wavefunction collapse (and more generally, with reconciling the quantum and classical descriptions of the world). Without this, quantum mechanics would just be another classical field theory.

And without the collapse the classical field theory would just be another quantum field theory.

what's weird is that they appear as a cummulative affect after many single particles strike specific places on the screen.

Wrong. Read P.A.M.Dirac and A.Tonomura.

The reason I addressed your post was because it seemed you were suggesting the schrodinger cat paradox had nothing to do with quantum mechanics. It's true that before quantum mechanics, people could have imagined a similar experiment with, say, a coin flip rather than radioactive decay, and ask what the state of the cat is before we observe it. But this would just be idle philosophizing - there's no practical problem here.

The difference in the case where we have a quantum superposition is that the dynamical equations imply that a microscopic superposition, which isn't really much stranger than, say, a superposition of overtones on a piano note, should evolve into a superposition of macroscopic objects, which is something very strange, and not something we seem to observe. The cat paradox is designed to expose this problem.

Precisely. But then you contradict yourself. Then you will observe Rabi oscillations in the single particle macroscopic system.

Regards, Dany.