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MZapperZ said:I don't think this is correct. For some reason, you had to invoke an "excited state" transition, which isn't necessary. You are describing a system in which the final outcome is not known. This is no different than throwing a dice and not knowing which number will turn up.
ZapperZ said:The Schrodinger cat state illustrates the principle of superposition, and in fact, such superposition CAN be detected if you measure the non-commuting observable. This is what is done in the Delft/Stony Brook SQUID experiment. The coherent energy gap is a direct outcome of such superposition.
Zz.
Martin Brock said:Explain more specfically what is incorrect. I don't call the state "unknowable". I say, "we can't easily know" it. I'm not suggesting that the device is fundamentally non-deterministic. I say the system is "described" in terms of probabilities. It is like throwing a dice or spinning a roulette wheel. If we don't precisely control and cannot precisely measure the rate of spin during an "excited state", we can't predict the final state.
ZapperZ said:These are the papers that clearly show the Schrodinger Cat-type states (alive+dead, and not alive or dead). All the relevant details are there and anyone interested should read them. Also included is the reference to a couple of review articles which are easier to read, and the reference to two Leggett's papers, who was responsible in suggesting this type of experiments using SQUIDs in the first place. Again, the papers have a wealth of citations and references.
The two experiments from Delft and Stony Brook using SQUIDs are:
C.H. van der Wal et al., Science v.290, p.773 (2000).
J.R. Friedman et al., Nature v.406, p.43 (2000).
Don't miss out the two review articles on these:
G. Blatter, Nature v.406, p.25 (2000).
J. Clarke, Science v.299, p.1850 (2003).
However, what I think is more relevant is the paper by Leggett (who, by the way, started it all by proposing the SQUIDs experiment in the first place):
A.J. Leggett "Testing the limits of quantum mechanics: motivation, state of play, prospects", J. Phys. Condens. Matt., v.14, p.415 (2002).
A.J. Leggett "The Quantum Measurement Problem", Science v.307, p.871 (2005).
This paper clearly outlines the so-called "measurement problem" with regards to the Schrodinger Cat-type measurements.
"Superposition" describes the wave function. The wave function is theoretical. The wave function is a description, not the reality described. I'm not suggesting that superposition and entanglement have no measurable effects in Quantum Mechanics. A coupling of states does involve energy. The states of the left and right rods above are coupled. We could complicate the system by making the long rod less rigid, allowing oscillation of the short rods about the axis of the long rod. The "entanglement" of the two short rods then changes and the coupling between them can store energy.
I am claiming that observation does not cause the wave function to collapse. This point motivates the example. I don't claim to explain the Quantum Mechanical description of a hydrogen atom.
ZapperZ said:But that is precisely what is not correct. This has nothing to do with a quantum system.
ZapperZ said:Before I flup a coin, I know that the outcome of the situation is either heads, OR tail. That is crucial. There was never at any stage where the "reality" of a mixture of heads and tail enters into my physical understanding of the system.
ZapperZ said:In fact, there's nothing that I can measure to indicate that there is a superposition of these two orthorgonal outcome. Even after I flip the coin but don't look at it, the system is in one particular state OR the other, not a superposition of both.
ZapperZ said:If this is all there is about a QM system, then it wouldn't have been so weird. I am certain that even before QM, people were already gambling and flipping coins. So why would QM be so strange?
ZapperZ said:This is becuase the superposition of those states (the linear combination of "heads" and "tails") CAN and DO cause a physical property of a QM system.
ZapperZ said:While the act of measurement of an observable causes the system to only reveal ONE possible outcome of that observable, the measurement of an observable that DO NOT COMMUTE with the first observable will produce an outcome that can only be explained if the first observable is in a superposition of states. In other words, before one "collapses" that observable, there ARE detectable measurement that indicates the presence of such superposition where ALL of the possible outcomes are "intermingling" with each other.
ZapperZ said:I have written and made citations to relevant papers on this many times (one can do a search on here). I will simply quote what I've written elsewhere if you wish to check on this yourself:
ZapperZ said:You have attempted to highlight a lot of issues that aren't related to the original Schrodinger Cat experiment, including "entanglement", which isn't part of the SC-type scenario.
ZapperZ said:The main principle that is relevant here is the principle of superposition. Considering that you did verify my description of your system as identical to flipping a dice or a coin, this then confirms to me that it is not an illustration of superposition. Schrodinger could have easily illustrated this thought experiment by flipping a coin if this were the case. Yet, he chose something else to illustrates the "weirdness" of QM.
Zz.
Martin Brock said:As I said, I describe a classical system. The system is "quantum mechanical" in the sense I describe above, i.e. it can absorb and release a quantum, and it has discrete states described in terms of probabilities. I nowhere claim to describe a Quantum Mechanical system in terms of modern physics.
There is no literal "mixture" of dead and living cats either. That's my point. We can call the spinning system a "mixture" of "left up-right down" and "left down-right up" states if we want, but we mustn't take this description too literally, and the description has nothing to do with any cause of a transition to a stable state.
I believe the measurable effect in SQUID is entanglement, not superposition.
Martin Brock said:The Schrodinger's Cat thought experiment does involve release of a quantum. Radioactive decay releases a photon triggering a geiger counter to release a poison killing the cat.
I'm off to work and can't play further now, but I'll return later. If I'm wrong about entanglement in the SQUID experiment, thanks for the correction. I can't agree with your limitation of the topic, but you may discuss your grievance with the moderator.
Tomsk said:Can we take the view that Schrodinger's Cat is an observer too, and could break out of his box to find a 28 Days Later/Day of the Triffids type situation (which would have to be in a superposition with a bunch of scientists sitting around waiting for the results, as well as any other possible scenario, before he broke out)? If not why not?
eehiram said:...since I started the thread originally and I can explain what I was looking for:
First, Martin Brock, thank you for your attempt to assist me with, as you said, a classical physics example. Let us say that it is worth what all classical physics examples are worth in trying to explain QM, and now proceed to return to QM, as I have about a high school level understanding of it.
And ZapperZ, thanks for your attempts to elucidate me, although some of your technical terms are a bit unclear to me. I will hopefully try to learn about the SQUID experiment, but I have not done so yet.
Having addressed both of you, let me get to my original point:
What I meant by asking about the superposition of a half-living and half-dead cat is simply that, unlike the living and dead states, the half-and-half state can not be observed once the box is opened. Only "sensible" states can be observed. How then is the half-and-half state verified? Is there some experiment by which it can be detected, and thus it's equation is therefore validated? Perhaps the SQUID experiment is that experiment. But without mincing words ("detected" vs. "observed"), as I already recognized the half-and-half is not "sensible" and can not be observed -- not directly -- in any experiment that involved anything like observation. It always collapses to either a living or a dead state upon observation.
ZapperZ said:But the Schrodinger cat-state involves NO "transition" between energy levels, nor "absorbe and release" of a "quantum" of anything. That is what I've been trying to get across. Your example have nothing to do with the topic of this thread, which is the superposition of orthorgonal states as illustrated in the Schrodinger Cat scenario.
Again, there is no transition of any kind, or of a 'stable' state. ALL the states in the superposition ARE "stable".
ZapperZ said:You are wrong. I suggest you read those papers, especially Tony Leggett's extensive paper on the measurement problem and the conclusion of both experiments.
ZapperZ said:Please note that this thread is a discussion of a specific issue regarding superposition. If your system, by your admission, doesn't illustrate a quantum superposition, then you have brought up an example that is not relevant to the thread, and in fact, may add confusion to it. You have already stated that your example is identical to the classical probability. It makes no sense to equate this to a quantum system, and it shouldn't. Thus, it has no relevance to this topic.
Zz.
ZapperZ said:You are confusing the source with the principle of the scenario. This is where if you ONLY understand the description without understanding the mathematics (which is what Schrodinger was trying to illustrate in the first place), then you only saw the shadow of the animal without fully seeing the animal itself.
ZapperZ said:The emission of the "radioactive particle" is actually incidental to the scenario. All that was supposed to do is add the quantum probability into the system. That's it. If flipping a coin is a quantum process, then schrodinger would have used it to trigger the poison. He didn't because it isn't a quantum process that's governed by quantum probability as interpreted by the Copenhagen school.
ZapperZ said:Note that when a photon passes through a 2-slit experiment, that IS also an example of superposition. In fact, there are MANY processes that are clear illustration of superpostion (bonding-antibonding bands in H2 molecule). None of these produces an "energy release". You are stuck with an example while ignoring the principle that is being illustrated. By doing that, you have somehow illustrated exactly what I described in one of my essays on why QM is so difficult to understand when people do not have a solid grasp of its mathematical formalism.
ZapperZ said:I AM one of the moderator!
Zz.
eehiram said:...since I started the thread originally and I can explain what I was looking for:
First, Martin Brock, thank you for your attempt to assist me with, as you said, a classical physics example. Let us say that it is worth what all classical physics examples are worth in trying to explain QM, and now proceed to return to QM, as I have about a high school level understanding of it.
eehiram said:What I meant by asking about the superposition of a half-living and half-dead cat is simply that, unlike the living and dead states, the half-and-half state can not be observed once the box is opened. Only "sensible" states can be observed.
In my humble opinion, as someone who has studied QM in high school physics, chemistry, and biology classes, I think classical systems are useful to introduce a classically educated science student to the quantum level. High school students fit that bill, as they have been taught almost nothing but the classical science up until about 9th or 10th grade.Macroscopic, classical systems with properties we observe in Quantum Mechanical systems aid understanding in my opinion. ZapperZ apparently disagrees.
In regards to the cat and the quantum release that triggers poison gas, it was my understanding that the cat, being in the box, goes into an entanglement with the quantum release and this entanglement decoheres when the box is opened and the cat, living or dead, is observed. However, this is the Copenhagen interpretation again, the one taught first and foremost in my introductory books.As Schrodinger himself suggests, the half-and-half or indeterminate state does not apply to the cat. It applies to a quantum mechanical system. The system enters a discrete, lower energy state, which is not an indeterminate or mixed state, and this transition is associated with emission of a quantum of energy (a photon), and this photon kills the cat.
Martin Brock said:The release of a quantum of energy involves a state transition, and Schrodinger's Cat dies when a quantum is released. I linked an article with Schrodinger's description of the thought experiment. Here it is.
"One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.
"It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a "blurred model" for representing reality."
If the experiments don't involve entanglement, so be it. You're the physicist here.
The thread announces itself as a discussion of Schrodinger's Cat, and Schrodinger himself devised the thought experiment to ridicule the idea of a cat in mixture of states in which it is either living or dead.
The cat dies when a quantum is emitted. I don't doubt your expertise, but I suppose Schrodinger had some point he wanted to make, and his point seems to be that observation of the cat does not replace a half-emitted quantum and a half-dead cat with a fully emitted quantum and a fully dead cat.
My point remains that observation does not cause a quantum mechanical state transition, like the transition associated with emission of a photon. Observation reveals a state. A system can exist in an intermediate or indeterminate state or a superposition of states.
I'm not denying superposition of states. I'm denying that observation causes a quantum mechanical system to enter a discrete state associated with the release of a quantum, which seems to be Schrodinger's point. I constructed an example with an energy release, because Schrodinger constructed an example with an energy release. I constructed a macroscopic, classical example, because people more easily comprehend this example.
ZapperZ said:There are so many misinterpretation on so many levels here, I do not know where to begin.
...
You got this all wrong. Schrodinger never intended to ridicule the situation. I have said this before, but you obviously missed it. If he illustrates the weird quantum properties with H2 molecule, no one other than physicists would pay attention. He used something that other people would understand (and maybe emphathized). This has nothing to do with ridiculing superposition. It is to illustrate that if you carry over what we know to occur at the quantum scale, the result looks very strange.
ZapperZ said:This is very difficult to understand. The observation "collapses" the wavefunction, putting it into one of the EIGENSTATE of the wavefunction.
ZapperZ said:You are clear on this, no?
Martin Brock said:"One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, ... It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a "blurred model" for representing reality."
I'm quoting Schrodinger himself here. These words are Schrodinger's description of the thought experiment. He isn't ridiculing the idea of an indeterminate state in a quantum mechanical system. He is ridiculing the idea that of a half-emitted photon and a half-dead cat. No indeterminate state implies a half-emitted photon or a half-dead cat, and observation of a system does not cause the system to leave an indeterminate state and enter a definite state. Observation reveals a definite state. "Undetermined until observed" does not mean that observation itself causes the end of an indeterminate state. It means that we can't know a specific, determinate state until we've observed it.
The eigenstates of the system are time-invariant, steady states with a discrete energy. It's not so difficult to understand if we don't take the half-dead cat literally, and Schrodinger doesn't want us to take the half-dead cat literally. Schrodinger specifically denies that an indeterminate or mixed state, in which the photon might or might not have been emitted and killed the cat, exists. This denial is the whole point of his thought experiment. Again, I've quoted Schrodinger himself directly in this regard. He isn't denying superposition. He's denying that a half-dead cat is what "superposition" means in this scenario.
I do not think that knowledge has anything to do with it. Finding something weird is an attitude not knowledge.ZapperZ said:We ALL know (don't we?) that quantum behavior IS "weird".
MeJennifer said:I do not think that knowledge has anything to do with it. Finding something weird is an attitude not knowledge.
I do not find it weird at all. Clearly we are not smart enough to understand it. So I find it incomprehencible but not weird.
To call something weird because we do not understand it is a cop out IMHO.
Authors: Hiroaki Terashima, Masahito Ueda
Comments: 20 pages, 2 figures
It is shown that a large class of weak disturbances on the Schrodinger cat state can be canceled by a reversing operation on the system. We illustrate this for spin systems undergoing an Ising-type interaction with the environment and demonstrate that both the fidelity to the original cat state and the purity of the amended state can simultaneously be increased by the reversing operation. A possible experimental scheme to implement our scheme is discussed.
ZapperZ said:But it is RIDICULOUS if you try to apply it IN THE CONTEXT of our classical world, where two properties that are different are now intermixing simultaneously! He wasn't ridiculing QM, nor superposition! Talk about taking things out of context! And since when did Schrodinger wrote in English?!
ZapperZ said:But really, this is besides the point. We ALL know (don't we?) that quantum behavior IS "weird". That's the whole point of all of these demonstrations and thought experiments. Einstein tried to do that with EPR, and Schrodinger tried to show how weird it is using his Cat experiment. I will against tell you right away that if he had used H2 molecule as an example, you won't be so captivated by it and we won't be having this conversation. It is AS "ridiculous" when applied to the H2 molecule where an electron occupies two different locations simultaneously.
ZapperZ said:All of this is what is meant by the wavefunction having a linear superposition of ORTHORGONAL basis states! This is what is "ridiculous" as far as classical mechanics is concerned.
ZapperZ said:First of all, what is a "half-dead cat"? If you LOOK at the cat, the cat will either be DEAD, or ALIVE. The "observable" for "deadness" and "aliveness" is NEVER "half-dead". The same thing with the 2-slit. The position observable if you measure it, will detect only a photon passing through the left slit, or the right slit, never "half-right" or "half-left".
ZapperZ said:So already you are either consciously, or unconsciously causing an immediate confusion. So if you care so much about the exact "words" that Schrodinger used (assuming you TRUST the translation and that you put more emphasis on the "words" rather than the mathematics), then you have already used phrases that have vague meanings.
ZapperZ said:Let's settle this once and for all.
1. Would you say that this is an example of a quantum wavefunction that one would get by solving a schrodinger equation, where the u's are orthornormal basis functions?
|\Psi> = a_1|u_1> + a_2|u_2> + a_3|u_3> + ... a_N|u_N>
ZapperZ said:2. If you do, then do you accept one of the postulates of quantum mechanics that states that such wavefunction, in principle, describes ALL the properties of that system upon a measurement of an observable?
ZapperZ said:3. If you accept #1 and #2, tell me what happened if you make a single measurement of an observable that is an eigen-operator of the basis function represented by the u's.
ZapperZ said:4. Assuming you have completed #3, compare what you got with the ORIGINAL description of the system, which is |\Psi>. Now tell me, in your own words, not Schrodinger's, the difference between the two.
MeJennifer said:I do not think that knowledge has anything to do with it. Finding something weird is an attitude not knowledge.
I do not find it weird at all. Clearly we are not smart enough to understand it. So I find it incomprehencible but not weird.
To call something weird because we do not understand it is a cop out IMHO.
Martin Brock said:It's a translation into English. Here's the whole paper. See section 5 titled "Are the variables really blurred?"
http://www.tu-harburg.de/rzt/rzt/it/QM/cat.html
He not only calls the half-dead cat ridiculous. He calls acceptance of a "'blurred model' for representing reality" naive. If you want, you can explain what he means here. "It's weird" is not an explanation. He doesn't seem to be saying "it's weird".
I don't know what "weird" means in this context. Schrodinger was not trying to show "weirdness" with his thought experiment. He was ridiculing a "weird" interpretation. The quantized energy levels of hydrogen don't seem weird to me. The shape of the electron "clouds" (\Psi*\Psi) don't seem weird to me. That each cloud does not radiate does not seem weird to me. That a transition from one of these states to another radiates a quantum doesn't seem weird to me. I simply take this description for granted.
There is nothing weird about decomposing a function into components along orthogonal basis functions. Any piecewise continuous function whatsoever can be expressed as a superposition of sines and cosines of discrete frequences, precisely because these functions form an orthonormal basis. This superposition is the Fourier series expansion of the function. Many other sets of functions also form an orthogonal basis for various function spaces. The eigenstates of a quantum mechanical system seem to have some physical significance as well. I'd like to understand this physical significance better.
A "half-dead cat" is what Schrodinger ridicules in the thought experiment. He says, "The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts." If you don't like "living and dead cat ... smeared out in equal parts", you agree with Schrodinger as I do.
I'm trying to clarify rather than confuse. If you have some reason to distrust the translation, explain the reason. The translator is John Trimmer. It appeared Quantum Theory and Measurement edited by John Wheeler and published by Princeton University Press. Wheeler was a professor of physics at Princeton and UT Austin. His grad students include Feynman and Kip Thorne.
I recognize the notation, but it's less common in mathematics than in physics. You don't specify the functions { u_i }, so I don't know whether they form an orthogonal basis. I can tell you how to know that a set of vectors is an orthogonal basis. I know that <f,g> typically denotes an inner product of vectors, and I understand vector spaces, inner products and orthogonal bases. I understand that we can view certain functions as vectors in an infinite dimensional vector space, and I understand the inner product in this sense.
The wave function describes the state of the system. It tells you what the theory says you can know about the system after an observation. The same function can be decomposed along many different sets of orthogonal basis functions. I understand that eigenstates have a particular physical significance in Quantum Mechanics, but I'm not a great authority on the physics, as I acknowledged eariler.
I'm not sure what you're asking me here. The outcome of a measurement is physical information regardless of the mathematical formalism. You're the physicist. I'm curious to know how the operator associated with an observable is determined.
If you want to explain this notation to me, that's fine. I've already acknowledged that my background is more mathematical than physical, and I've already acknowledged your greater expertise in physics, so I'm not sure what your test is supposed to settle once and for all. I would be happy for you to share some of your expertise with me.
It means counter intuitive.Martin Brock said:I don't know what "weird" means in this context.
Schrodinger was not trying to show "weirdness" with his thought experiment. He was ridiculing a "weird" interpretation.
But it is exactly the "physical significance " that is "weird". This is exactly what you want to understand and that is very normal. If it were so intuitive, you would not have asked this question.There is nothing weird about decomposing a function into components along orthogonal basis functions. Any piecewise continuous function whatsoever can be expressed as a superposition of sines and cosines of discrete frequences, precisely because these functions form an orthonormal basis. This superposition is the Fourier series expansion of the function. Many other sets of functions also form an orthogonal basis for various function spaces. The eigenstates of a quantum mechanical system seem to have some physical significance as well. I'd like to understand this physical significance better.
Did Schrödinger actually talked about a half dead cat ? What is that ? How did he define that ? I have never met this terminology, though i use QM every day for my work. What have i missed ?A "half-dead cat" is what Schrodinger ridicules in the thought experiment. He says, "The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts." If you don't like "living and dead cat ... smeared out in equal parts", you agree with Schrodinger as I do.
this is untrue. Besides, the actual formula is mathematics, nothing more.I recognize the notation, but it's less common in mathematics than in physics.
But Zz wrote they are orthogonal by definition. This is very correct. You don't need to know the actual function or what it represents (they can represent ANYTHING) because Zz wanted to outline the formalism.You don't specify the functions { u_i }, so I don't know whether they form an orthogonal basis.
I can tell you how to know that a set of vectors is an orthogonal basis. I know that <f,g> typically denotes an inner product of vectors, and I understand vector spaces, inner products and orthogonal bases.
What is that supposed to mean ?It tells you what the theory says you can know about the system after an observation.
Well, the eigenstates correspond exactly to the orthogonal functions that Zz was talking about. Actually this is what he eventually wanted to say to you.The same function can be decomposed along many different sets of orthogonal basis functions. I understand that eigenstates have a particular physical significance in Quantum Mechanics, but I'm not a great authority on the physics, as I acknowledged eariler.
I'm not sure what you're asking me here. The outcome of a measurement is physical information regardless of the mathematical formalism.
This is basic QM stuff. You really should know that before engaging into this kind of discussions. A lot of your misconceptions would have already been cleared out. Don't take this the wrong way, please, BUT IT IS TRUE !You're the physicist. I'm curious to know how the operator associated with an observable is determined.
Martin Brock said:I agree. I don't find it entirely incomprehensible, but it can be counter-intuitive until one develops an intuition for it.
Classical physics can be too for that matter.
ZapperZ said:It appears that from the way you responded to my series of questions, I would have to TEACH you quantum mechanics, something which I have no patience to do on here since students spend a year in school to grasp such a thing.
If you truly believe that your classical model is analogous to the Schrodinger-Cat type experiment, then as I've said before, submit it to AJP and prove me wrong.
I'm leaving this thread because I notice no progress that any of my explanation has gotten through.
Zz.
marlon said:Are you saying that classical physics is counter intuitive in the same way as QM ? If so, you really must have missed out on some basic points of the QM's formalism.
marlon
Martin Brock said:No, I didn't say it.
marlon said:It means counter intuitive.
marlon said:What do you mean by "weird" in this context ?
marlon said:But it is exactly the "physical significance " that is "weird". This is exactly what you want to understand and that is very normal. If it were so intuitive, you would not have asked this question.
marlon said:Did Schrödinger actually talked about a half dead cat ? What is that ? How did he define that ? I have never met this terminology, though i use QM every day for my work. What have i missed ?
marlon said:this is untrue. Besides, the actual formula is mathematics, nothing more.
marlon said:But Zz wrote they are orthogonal by definition. This is very correct. You don't need to know the actual function or what it represents (they can represent ANYTHING) because Zz wanted to outline the formalism.
marlon said:But this is irrelevant. All mathematical requirements for orthogonality are respected by definition. Just accept that these functions are orthogonal.
marlon said:What is that supposed to mean ?
marlon said:Well, the eigenstates correspond exactly to the orthogonal functions that Zz was talking about. Actually this is what he eventually wanted to say to you.
marlon said:There is only ONE formalism : QM
marlon said:This is basic QM stuff. You really should know that before engaging into this kind of discussions. A lot of your misconceptions would have already been cleared out. Don't take this the wrong way, please, BUT IT IS TRUE !
I would say that QM is more fundamentally weird, than, say, curved spacetime in general relativity (which is certainly not very intuitive or easy to picture), because unless you add some additional assumptions as in the various "interpretations" of QM, it does not give you any objective description of the universe as a self-contained system; this is a problem in formulating quantum cosmology, for example. You can only get the probabilities for how a given system behaves by plugging in the choice of variables to measure, and when the measurement is made, by hand--if you try to describe the measuring-system itself using the rules of QM in order to predict when and what it measures, then to get any definite probabilities you need some second measuring system whose measurements must be put in by hand, and so on. You can't describe the dynamics of the entire universe, measuring systems and all, using some fundamental mathematical rules and initial boundary conditions, as you can in other theories of physics.ZapperZ said:I'm using it in the sense of describing the "pedestrian" view of it. I personally do not find it weird, because as I've said many times, one is trying to force a square peg into a round hole. There's nothing here that says that the "weirdness" isn't due to our insistance that our classical idea of physical quantities such as position and momentum and energy should have the same well-defined concepts at the quantum scale.
Besides, even if it IS weird, it doesn't necessarily be a bad thing. As scientists, we LOOK for weird stuff, because it means that there's new physics in it that we don't understand yet. That is the whole reason why we are employed.
Zz.
marlon said:Then what did you mean by saying "Classical physics can be too for that matter" ?
marlon
eehiram said:Perhaps this is what Martin Brock meant. His example of the rotating bar was a little hard to follow, and I had to read it carefully several times. It's not a perfect classical analogy to the quantum phenomenon of Schroedinger's cat, as has been noted, but I would prefer not to take sides in the debate going on here. I just try to read all the posts with much interest and eagerness.
o| Hiram
But what if you consider the cat and photon as a single entangled system, isolated from the outside world? (You can imagine a simulation of a 'cat' on a quantum computer to make this slightly more realistic.) In the case of the double-slit experiment, one way of looking at the idea that you can't assume the particle definitely went through one slit or another is that if you calculate the probability of the particle hitting the detector at a particular location by doing a path integral where you integrate over paths that go through both slits, you'll get a different answer than if you calculated (probability particle hits detector when you integrate over only paths going through first slit) + (probability particle hits detector when you integrate over only paths going through the second slit). This is different from a classical situation like a ball going through one of two slits and hitting a wall, where you could indeed assume the probability the ball hits the wall at a particular spot is given by (probability ball hits that spot if it goes through first slit) + (probability ball hits that spot if it goes through second slit).Martin Brock said:Schrodinger's cat dies when a Quantum Mechanical system changes state thus emitting a quantum of energy (a photon). This photon kills the cat by triggering the release of poison. No one needs to observe the Quantum Mechanical system for this state change and photon release to occur. I don't believe the Copenhagen Interpretation implies that anyone must observe the system for the state change to occur.
eehiram said:I wrote something that was ignored by the debaters: isn't the cat's state entangled with the radiating atom that triggers the capsule? One of you said entanglement was irrelevant to Schroedinger's cat, and the other one said it was relevant.
eehiram said:Without entanglement, the radiation of the atom would not have anything to do with the life or death of the cat (as it would have to not trigger the poison), and the cat would remain a classical system, right? Or, no?
eehiram said:The cat is a macroscopic object and it's own Heisenberg Uncertainty value would be low according to it's large mass (which would confer to momentum, although I'm not sure about the velocity...)
JesseM said:But what if you consider the cat and photon as a single entangled system, isolated from the outside world? (You can imagine a simulation of a 'cat' on a quantum computer to make this slightly more realistic.) In the case of the double-slit experiment, one way of looking at the idea that you can't assume the particle definitely went through one slit or another is that if you calculate the probability of the particle hitting the detector at a particular location by doing a path integral where you integrate over paths that go through both slits, you'll get a different answer than if you calculated (probability particle hits detector when you integrate over only paths going through first slit) + (probability particle hits detector when you integrate over only paths going through the second slit).
JesseM said:This is different from a classical situation like a ball going through one of two slits and hitting a wall, where you could indeed assume the probability the ball hits the wall at a particular spot is given by (probability ball hits that spot if it goes through first slit) + (probability ball hits that spot if it goes through second slit).
JesseM said:So the question is, suppose you open the box containing Schroedinger's cat after some time, and you want to know the probability you'll find it in some exact quantum state A: can you assume the probability of finding it in this state is given by (probability system is in state A when you sum over paths where photon was emitted and cat died) + (probability system is in state A when you sum over paths where photon was not emitted and cat lived)? It may be that if you open it shortly after the photon was or wasn't emitted, then no matter what happened you'll be able to tell unambiguously whether it was or wasn't in retrospect (because the cat clearly was or wasn't poisoned), so you can indeed sum the probabilities that way just like you could in the double-slit experiment if you had a detector which made an unambiguous measurement of which slit the particle went through. But suppose you waited a billion years to open the box, and that by the time you opened it the matter making up the cat and poison had gone to a state of maximum entropy, so there was no record of whether the cat had or hadn't been poisoned? In this case I think you really would need to sum over all possible paths to get the probability that you'd find it in some particular quantum state A, so you couldn't say that the cat had definitely either been poisoned or not poisoned all those years ago, just like you couldn't say which slit the particle went through in the double-slit experiment when you had no measuring-device at the slits (at least, not in the Copenhagen interpretation; as I said in a previous post, I think Bohm's interpretation would say there was a definite answer to these questions, even though you couldn't determine it).
But the Schroedinger's cat experiment is only a thought-experiment in the first place--if you're concerned about realism, then you should just point out that decoherence makes it impossible in practice to isolate the cat from the outside environment even briefly. But this is a bit like saying that since we can't do experiments at the Planck scale, we should just ignore the whole issue of quantum gravity. Theorists are interested in how nature works in the most fundamental way, so the question of whether the cat would be alive or dead if it were possible to fully isolate it from the outside world (a practical impossibility at present, but not a theoretical impossibility) is of interest to them. And if you conclude the cat wasn't alive or dead in the scenario where you wait a billion years, then unless you believe the cat's state can somehow "anticipate" how soon you'll open the box, you should be forced to conclude it wasn't alive or dead in the scenario where you opened the box more quickly.Martin Brock said:Particles are theoretical fictions. Even classical particles are theoretical fictions. Matter does not exist at a point and isn't realistically described with only six degrees of freedom in three dimensions. An electron is not a particle, and it is not a classical wave either. It is neither of these and something else. When a cathode ray passes through double slits, we get an interference pattern we expect from a wave, but the same ray behaves like a stream of charged particles in an electric field.
A cat is not like this.
JesseM said:But the Schroedinger's cat experiment is only a thought-experiment in the first place--if you're concerned about realism, then you should just point out that decoherence makes it impossible in practice to isolate the cat from the outside environment even briefly.
JesseM said:But this is a bit like saying that since we can't do experiments at the Planck scale, we should just ignore the whole issue of quantum gravity. Theorists are interested in how nature works in the most fundamental way, so the question of whether the cat would be alive or dead if it were possible to fully isolate it from the outside world (a practical impossibility at present, but not a theoretical impossibility) is of interest to them.
JesseM said:And if you conclude the cat wasn't alive or dead in the scenario where you wait a billion years, then unless you believe the cat's state can somehow "anticipate" how soon you'll open the box, you should be forced to conclude it wasn't alive or dead in the scenario where you opened the box more quickly.
JesseM said:Anyway, as I suggested above, if large quantum computers ever become possible, one could probably design an experiment analogous to the "waiting for the cat to go to maximum entropy" experiment--an experiment where the outcome of a single event such as the photon emission has a large-scale effect on some other complex entangled system simulated by the computer, but where if you wait a certain time before measuring the system then it will no longer contain a "record" of the event.
If one is a reductionist, then the behavior of macroscopic systems should just be the product of all the interactions between its component particles. Most physicists are reductionists in this sense. Would you propose new fundamental laws to describe the behavior of large systems? Where would the cutoff be? Would there be a maximum number of particles that can be in a system and have it still obey the laws of quantum mechanics, and adding a single extra particle would cause it to stop obeying these laws?Martin Brock said:Realism is not the issue. Schrodinger developed his theory to describe quantum mechanical systems like the hydrogen atom, not cats. A cat is not a system confined to discrete energy states. A cat does not absorb or emit quanta. It's not a quantum mechanical system at all. The whole idea of applying Schrodinger's theory to this scenario is ridiculous, according to Schrodinger.
Are you really arguing that experiments which are not practical to perform today cannot be the subject of science? Is the the question of what happens to an observer falling into a black hole "not a scientific question", for example? I don't think you would find many theorists who'd agree with this philosophy.Martin Brock said:It's not a scientific question. No one can perform your billion year experiment
JesseM said:And if you conclude the cat wasn't alive or dead in the scenario where you wait a billion years, then unless you believe the cat's state can somehow "anticipate" how soon you'll open the box, you should be forced to conclude it wasn't alive or dead in the scenario where you opened the box more quickly.
You misunderstood, when I said "if you conclude the cat wasn't alive or dead in the scenario where you wait a billion years", I wasn't talking about whether you know if the cat was alive or dead, I was talking about the question of whether the cat was ever in a single definite state at all, analogous to the question of whether the particle in the double-slit experiment ever went through one of the slits (which is a separate question from whether, even if it did, you know which one it went through). Again, the conclusion of the billion-year thought-experiment was that you couldn't assume it had been definitely alive or definitely dead in the past, because when you open the box and measure the system inside, the probability it is in a given quantum state A would not be equal to the sum (probability system is in state A when you sum over paths where photon was emitted and cat died) + (probability system is in state A when you sum over paths where photon was not emitted and cat lived). As always, in the thought-experiment the inside of the box is perfectly insulated from the outside world so there is no environmental decoherence, the system inside would be described by a single complicated entangled pure state. Few physicists would say the laws of physics fundamentally forbid such an experiment, even if it's far beyond our practical abilities.Martin Brock said:I conclude that I don't know whether the cat is alive or dead before opening the box in the scenario where I open the box more quickly. I can reach the same conclusion without waiting a billion years.
JesseM said:If one is a reductionist, then the behavior of macroscopic systems should just be the product of all the interactions between its component particles. Most physicists are reductionists in this sense. Would you propose new fundamental laws to describe the behavior of large systems? Where would the cutoff be? Would there be a maximum number of particles that can be in a system and have it still obey the laws of quantum mechanics, and adding a single extra particle would cause it to stop obeying these laws?
JesseM said:Are you really arguing that experiments which are not practical to perform today cannot be the subject of science?
JesseM said:Is the the question of what happens to an observer falling into a black hole "not a scientific question", for example?
JesseM said:I don't think you would find many theorists who'd agree with this philosophy. You misunderstood, when I said "if you conclude the cat wasn't alive or dead in the scenario where you wait a billion years", I wasn't talking about whether you know if the cat was alive or dead, I was talking about the question of whether the cat was ever in a single definite state at all, analogous to the question of whether the particle in the double-slit experiment ever went through one of the slits (which is a separate question from whether, even if it did, you know which one it went through).
JesseM said:Again, the conclusion of the billion-year thought-experiment was that you couldn't assume it had been definitely alive or definitely dead in the past, because when you open the box and measure the system inside, the probability it is in a given quantum state A would not be equal to the sum (probability system is in state A when you sum over paths where photon was emitted and cat died) + (probability system is in state A when you sum over paths where photon was not emitted and cat lived).
JesseM said:As always, in the thought-experiment the inside of the box is perfectly insulated from the outside world so there is no environmental decoherence, the system inside would be described by a single complicated entangled pure state. Few physicists would say the laws of physics fundamentally forbid such an experiment, even if it's far beyond our practical abilities.
Martin Brock said:I declare categorically that my classical system is far more illustrative of the essential elements of Schrodinger's thought experiment than anything we're discussing now. I wish Schrodinger himself could comment, but unfortuately, his fate is also the same as the cat's.
