Register to reply

Cat in a box paradox

by ArielGenesis
Tags: paradox
Share this thread:
cesiumfrog
#37
Sep14-07, 05:37 AM
P: 2,050
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
#38
Sep14-07, 06:14 AM
Sci Advisor
Demystifier's Avatar
P: 4,569
Quote Quote by ZapperZ View Post
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 [itex]\psi = a_1|x> + a_2|y>[/itex] 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
#39
Sep14-07, 06:19 AM
Sci Advisor
Demystifier's Avatar
P: 4,569
Quote Quote by ZapperZ View Post
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
#40
Sep14-07, 10:40 AM
P: 1,520
Quote Quote by Demystifier View Post
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
#41
Sep14-07, 11:59 AM
Sci Advisor
P: 1,082
StatusX
Quote Quote by StatusX View Post
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 eachother, 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
#42
Sep14-07, 01:41 PM
Sci Advisor
PF Gold
f95toli's Avatar
P: 2,241
Quote Quote by reilly View Post
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
#43
Sep14-07, 01:47 PM
HW Helper
P: 2,566
Quote Quote by reilly View Post
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
#44
Sep14-07, 05:56 PM
Sci Advisor
PF Gold
f95toli's Avatar
P: 2,241
Quote Quote by StatusX View Post

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
#45
Sep14-07, 08:01 PM
HW Helper
P: 2,566
Quote Quote by f95toli View Post
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
#46
Sep14-07, 08:22 PM
Sci Advisor
PF Gold
f95toli's Avatar
P: 2,241
Quote Quote by StatusX View Post
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 apparantly 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
#47
Sep14-07, 11:23 PM
P: 2,050
Quote Quote by f95toli View Post
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
#48
Sep15-07, 02:01 AM
P: 451
Quote Quote by ZapperZ View Post
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
#49
Sep15-07, 02:05 AM
P: 451
Quote Quote by reilly View Post
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
#50
Sep15-07, 02:15 AM
P: 451
Quote Quote by StatusX View Post
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.

Quote Quote by StatusX View Post
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.

Quote Quote by StatusX View Post
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.
Anonym
#51
Sep15-07, 02:24 AM
P: 451
Quote Quote by f95toli View Post
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.
I am sure the opposite. E. Schrödinger would have pleasure.

Quote Quote by f95toli View Post
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 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'.
For your information, the Theoretical Physics is the theory of closed systems since Copernicus/Galileo Postulate of Relativity is the Principal Physical Postulate.

You completely correct in all your statements, but “unfortunately” the results of your measurements will be useless since you can’t convince anybody that they are correct. You need another lab to confirm your results. But if you claim that that lab has the same environment, nobody will believe you (it is simply wrong).

For information of all respectable contributors in the discussion, I reproduce A.Einstein notion and definition of the objective reality. I guess that A.Einstein even had no chance to read EPR paper before publication. If some stupid idiot taught and convinced you something different when you were students, you were bad students.

f95toli don’t worry, the job done. We did it (I am a math-ph, in case you haven't guessed that already)

Regards, Dany.

P.S.
Quote Quote by f95toli View Post
in order to stop the "collapse" (i.e. increase the coherence time)…
What is the value of the experimentally measured time of the wave packet collapse? I hope you are not talking about gedanken measurements.
f95toli
#52
Sep15-07, 06:20 AM
Sci Advisor
PF Gold
f95toli's Avatar
P: 2,241
Quote Quote by cesiumfrog View Post
Quite a few still do. Do you have any evidence that they are incorrect?
Well, if you use the same type of calculations you would use to estimate the coherence times of a qubit on a real cat (or rather an object the size of a cat) you will find that the time is extremely short; it is just too big to be insulated from the enviroment. Hence, you can't use cats to e.g. implement quantum gates. The fact that we can't KNOW if the cat is dead or alive until we open the box is to me (and I think most physicists) irrelevant from the QM point of view.
One can of course just add the condition that the cat IS insulated (using some mysterious technique) from the enviroment to the gedanken experiment, and then the cat would actually be in a "real" superposition. However, this could never be observed in a real experiment. Hence, the "cat paradox" is only a paradox if you add conditions that are unphysical. It is still an interesting philosophical problem, but I can't see it being very relevant to physics anymore.

As I pointed out above wa CAN observe superpositions in macroscopic objects in the lab, but only in systems that can be reasonably well decoupled from the environment; this means that we are now sure that there is no strange "transition" from QM on the microscopic level (atoms) to classical physics on at the macrosopic level (cats).
Anonym
#53
Sep15-07, 07:58 AM
P: 451
Quote Quote by f95toli View Post
it is just too big to be insulated from the enviroment...One can of course just add the condition that the cat IS insulated (using some mysterious technique) from the enviroment to the gedanken experiment.
It is quite new for me that the M.Faraday cage and A.Einstein free falling lift are mysterious experimental apparatus. And it is not clear what else your environments are.

Regards, Dany.
StatusX
#54
Sep15-07, 01:36 PM
HW Helper
P: 2,566
f95toli,

You seem to be using decoherence as a mechanism to remove any superposiiton, and thus collapse the cat's wavefunction. My understanding is that decoherence simply renders the alive and dead states in the superposition incoherenet, so that they no longer interact. When we observe the cat, we become entangled with its state in the following way:

|scientist before>(|alive cat> + |dead cat>)

evolves unitarily into:

|happy scientist>|alive cat>+|sad scientist>|dead cat>

Since these two wavefunctions are incoherent, they evolve independently, as if the other didn't exist. In other words, we get a many worlds interpretation, simply by denying that collapse ever occurs and acknowledging the effect of decoherence. Decoherence by itself does not cause real collapse, only an observed collapse in each world. What are you suggesting really happens, or are you not worried about this?


Register to reply

Related Discussions
1-D Box. Paradox? Quantum Physics 6
The Twin Paradox Paradox. Special & General Relativity 3
Resolving the Barber Paradox and the Russell's Paradox General Discussion 18
What is the resolution of the The Bug-Rivet Paradox paradox in special relativity? Special & General Relativity 4