Schrodinger's Cat

Discussion in 'Physics & Math' started by chuk15, Jan 2, 2010.

1. chuk15Registered Senior Member

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For those of you who don't know about the experiment, it goes like this:

There is a cat in a sealed box with a flask of poison taped to its head. The flask of poison is attached to a Geiger counter. It measures an atom that has a 50% chance of decaying in one hour. If it decays the cat will die. If it doesn't decay the cat will live. We put the cat in the box and wait one hour, since radioactive decay is completely random, is the cat dead or alive? We wont know until we open the box.

Using the Copenhagen interpretation of quantum physics, the cat is a wave function and therefore is in superposition (both death AND alive) until we collapse the wave function by opening the box. The cat is 50% alive and 50% dead until it is observed.

I think that Copenhagen interpretation is insane. Why can't we say that we just don't know if the cat is dead or alive? The cat is either dead or it is alive; it can't be both at the same time. We just don't know the state it is in. Therefore we should withhold our final judgement until we can observe if the cat is dead or alive. The cat is not in superposition, it is just that we are ignorant of its state. We just don't know and therefore we shouldn't make a judgement one way or the other (such as the the Copenhagen interpretation saying it is both 50% dead AND 50% alive without information.)

3. CptBorkValued Senior Member

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If the cat existed as a superposition of states, it would theoretically be possible for those states to interfere so that when the box is opened, you don't get the same result that the cat is either shot or unscathed, but possibly something inbetween (i.e. half a bullet lodged inside). But of course that presumes the contents of the box are 100% isolated from anything in the outside universe, including the total elimination of gravity, and that the atoms inside aren't collapsing each others' wave functions when they interact.

I'm pretty sure I've read that Schrodinger used the cat example just to show how attempts to explain the underlying mechanisms of quantum mechanics are futile and arbitrary, and can get as strange and kooky as you like. As far as I understand, no one has yet thoroughly explained where and when measurements and wave collapses supposedly take place, just that there are certain physical situations where it happens extremely quickly, like when a particle detector attempts to spot a particle.

5. DinosaurRational SkepticValued Senior Member

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Few (if any) serious physicists believe that any object as large as a cat can be in a superposition state.

7. BenTheManDr. of Physics, Prof. of LoveValued Senior Member

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Let me point out that

Is actually the whole point of the thought experiment

Well, it depends on what you mean.

This is actually what the many worlds'' interpretation would have to say about the experiment. Most physicists I have talked to think that this is the only way to think about quantum mechanics. Granted, most people I have talked to about this are theoretical physicists, and not experimentalists

8. kurrosRegistered Senior Member

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Yeah the cat is just a flashy example of the superposition principle, for it to really work you'd need to totally isolate it from everything, including things like electromagnetic fields and gravitational waves, not to mention neutrinos and other weakly interacting junk, because the superposition would be so fragile that even the tiniest perturbation would destroy it. Also thermal fluctuations of course, so the cat couldn't survive such an isolation procedure.

"Why can't we say that we just don't know if the cat is dead or alive? The cat is either dead or it is alive; it can't be both at the same time. We just don't know the state it is in. Therefore we should withhold our final judgement until we can observe if the cat is dead or alive."

you need only remember the Bell inequalities. What you are describing is know as a local hidden variable theory, in other words there are some "hidden" degrees of freedom in the system which record which state the cat is "actually" in, and we just can't access them without making a measurement which screws up that state. Experiments have shown that no such theory can explain the observed quantum behaviour, particularly quantum entanglement experiments. If the degrees of freedom are NON-local, then such a theory is possible, but generally people hate this idea more than the copenhagen interpretation. You can evade Bells theorem in other ways, but they are all pretty drastic, for instance in the Many-Worlds interpretation you don't need non-local degrees of freedom, but instead the superposition never collapses, with each outcome of an experiment realised in it's own sector of the theory, or it's own "world". The flashy term is that you throw away contra-factual definiteness, which is just the assumption that experiments can only yield ONE result from the various possible outcomes.

9. DinosaurRational SkepticValued Senior Member

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To the best of my knowledge, there is no evidence of superposition or other quantum weirdness for objects as big as a cat. I doubt that there is such evidence for objects as large as a grain of sand.

Schrodinger proposed the thought experiment as a reductio-ad-absurdum disproof of either the Copenhagen interpretation or some other aspect of Quantum Theory. It only emphasizes the split between reality at the quantum level & reality at the classical level.

Schrodinger developed his wave function as an attempt to provide a classical explanation for Quantum phenomena. He once said that if he had known how it would work out, he would have become a chemist or a mathematician instead of a physicist. Like Einstein, he was emotionally a believer in classical physics. Had either man lived to the end of the last century, he would have accepted the concept that the Quantum World does not obey classicl laws.

In spite of the opinions of some people with serious credentials, I consider the Many Worlds interpretation to be silly. It is a refuge for those who prefer a silly interpretation which is understandable to a more cogent interpretation which is highly counterintuitive and perhaps impossible to fully understand.

An entire universe for every possible outcome of some quantum phenomenon? Each new universe spawning more universes? At least billion or so universes springing into existence every second for every 100 kilograms of matter? The same number springing into existence for every 100kg of matter in each new universe? I have yet to see a believer discuss the implications of the number of spawned universes. Why do they not interact? Where do you put all of them to keep them from interactiing. Assuming higher dimensional spaces, how far apart are these universes? Not the implied distance between the far ends even if the some parts of two universes are near eachother.

The human brain is the result of more than 10 million years of evolution in a world which obeys classical laws. A brain capable of coping very well with that Classical World of our senses is not able to comprehend the Quantum World governed by probability, which allows for tunneling, discontinuous activity, & other Quantum capriciousness.

Interpretations invoking reverse causality are not as bad as Many Worlds, but are very implausible rather than out right silly. Folks who advocate such interpretations prefer reverse causality to lack of causality. I fail to understand how reverse causality does away with the probabilistic nature of the data related to quantum processes. Probabilistic data supports the notion of lack of causality.

If you think deeply about the Uncertainty Principle, you begin to realize that the Quantum World is counterintuitive. You realize that the mathematics tells the story, without providing an explanation understandable by a brain resulting from millions of years of evolution in a Classical World. Intuition tells us that the UC is due to limitations of measurement technology. The properties of a Bose-Einstein condensate (& other experiments) provide experimental support for the UC.

10. BenTheManDr. of Physics, Prof. of LoveValued Senior Member

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Ahhh you've succumbed to the name many worlds, instead of the actual interpretation! This is a mistake many make, based on bad pop-science explanations of Everett's original paper, which is called relative state formulation'', or something.

In his original paper, Everett asks---if we are willing to accept the superposition of states of an electron (for example), why don't we accept it for larger objects? A cat is made of atoms, and those atoms exist in a superposition. The collection of atoms has a well defined, if complicated, quantum description, including energy levels, and probabilities of existing in one place or another, and an uncertainty relation. Every state of the cat has a quantum description, and every quantum description is (in principle) realizable. This is where many worlds'' comes from---it is a way to cope with the fact that sometimes we find the cat dead, sometimes we find it alive. Whoever invented the name many worlds'' (his name escapes me, but he is famous) would say that the cat is alive in some universes, and dead in others. This is clearly just an exaggeration, though, and arguing about where the other universes exist, or how big they should be, or how far away they are is akin to discussing angels and pinheads

11. Physics MonkeySnow Monkey and PhysicistRegistered Senior Member

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I just want to comment that a great deal of wonderful experimental progress is being made on this front. For example, people have observed interference of Bose Einstein condenstates containing thousands (or more) of atoms. Of course, that's not a grain of sand, but it turns out we can do grains of sand too!

Especially in connection with LIGO, there has been much work on cooling gram scale objects to their quantum ground state! It's hard for me to even imagine that the center of mass degree of freedom of a gram sized mirror could be in its quantum ground state, but it's possible to achieve. I don't know what the current best official result is, I think somewhere in the neighborhood of five quanta, but my friend at MIT tells me that unofficially people can definitely reach much less than one quanta on average.

Given such amazing progress, should we really say that quantum interference of gram sized objects is outrageous or crazy? My personal opinion is that its not crazy anymore.

Technical note: what they have is really a coherent state, and I'm quoting the average number of quanta in the coherent state. A coherent state with much less than one quantum is effectively the ground state.

12. BenTheManDr. of Physics, Prof. of LoveValued Senior Member

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I just reread Everett's paper, and want to clarify my comments a bit.

If two electrons interact with each other, those electrons become entangled, and the set of states which describe the two electron system is now a linear superposition of two one electron systems.

Everett's question is, why should we separate this behavior from the process of observing''? The radioactive atom interacts with the cat in the same way that the two electrons interacted before---why, then, do we treat the cat/atom system differently than the electron/electron system? One is led to the conclusion that the cat/atom system exists in a linear superposition of states, which is exactly what Everett would say (I think).

This is what the many worlds'' interpretation is literally saying.

13. kurrosRegistered Senior Member

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I agree, however since after measurements are made on a system the wavefunction is no longer factorisable, and quantum mechanics is linear, then the seperate terms of the superposition can no longer have any influence on each other and so can fairly literally be thought of as seperate "worlds". I believe gravity is a wild card here though, since quantum gravity is presumed to be non-linear it would allow seperate worlds to interact, thus letting us detect them:

$O|\psi > = O|observer (hasn't looked)> ( |cat dead> + |cat alive> )$
$O|\psi> = |observer (saw dead cat)>|cat dead> + |observer (saw live cat)>|cat alive>$

where O is the linear operator describing the act of observing the cat.

14. Crunchy CatF-in' *meow* baby!!!Valued Senior Member

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The box, everything attached to the cat, the cat's fur, the cat's lungs, the cats bowels, etc. are all observers. Therefore the cat is definitively dead or alive but not both.

A persistent misinterpretation of the word "observer" is that it requires a conscious life form. An observer in physics is anything that can accept information. A block of cheese can be an observer for example. Somewhere amongst the eigenstates of any moment there may be a superposition of a cat being both dead and alive... but it collapses immediately into the most probable state (i.e. dead or alive).

15. kurrosRegistered Senior Member

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Well, no-one really knows what constitutes an observer anyway, since no-one really understands what "wave-function collapse" really is. And actually, the interesting thing if one likes the many worlds view (since we seem to be talking about it) is that even if a system (cat) is "observed" by some local observer A, observers far away who have not yet been in causal contact with this event can still consider the whole "cat + observer A" system to be in a perfectly good superposition, i.e. worlds "unzip" in a perfectly causal fashion, without need for any non-unitary semi-mysterious instantaneous wavefunction collapse. So the cat can be "definitely dead or alive" for one observer but in a superposition of the two for another.

Haha, perhaps I am giving the impression here that I believe in many worlds, which I assure you I don't (well, maybe a little), but I do quite like it's elegance. Maybe there is something right about it despite it's craziness.

16. BenTheManDr. of Physics, Prof. of LoveValued Senior Member

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What we DO know is that wave-function collapse'' is non-unitary, and quantum mechanics is manifestly unitary!

If you accept that the observer is a quantum mechanical system, I don't see how one can refute the many worlds interpretation. As kurros put it: worlds'' should just be read as possibilities''.

17. kurrosRegistered Senior Member

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Hmm I'm not sure I said that. I really can't see how you can look at many-worlds without admitting that it implies there are a whole mess of other universes (or rather a web of such all constantly "unzipping" from each other in a causal fashion) living superposed on top of us, yet disconnected from us by the linearity of quantum mechanics. If you can I would love to be enlightened

.

18. Crunchy CatF-in' *meow* baby!!!Valued Senior Member

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To an extent we do and there are limitations to our knowledge as well. We do know for sure that consciousness isn't a requirement to be an observer.

It depends on what level of granularity you're focusing on. We do know that a shrodinger wave is a real tangible entity of superposition that collapses into the most probable state once location info from it is required. n-slit experiments show this quite well. Of we go into deeper granularity then yep we don't know what the schrodinger wave is (to my knowledge).

I am not sure that's how it would work... I don't think there is a scenario where a system collapses to a local observer but remains in a superposition for a remote observer.

Hard to say... it is an interpretation of QM.

19. kurrosRegistered Senior Member

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Sure

Well we have no idea that it collapses, that's just what seems to happen and assuming such lets us calculate things. Maybe that's what you mean though. If we knew it collapsed for sure, at any level, then there'd be no point discussing things like many worlds where that doesn't happen.

That's what happens in Many-Worlds, which is all I was talking about. Nothing of the kind happens according to Copenhagen, the wave function collapse is instantaneous across the whole universe. It's not really a problem since it doesn't actually affect anything, though it makes entanglement correlations a lot more mysterious than they are in many-worlds. But also I don't think many people believe that's "really what happens".

20. funkstarratsknufValued Senior Member

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BenTheMan,

Isn't your view of the Many Worlds Interpretation missing an explanation of measurement? It seems like you're only focusing on the specific part of the MWI concerning the universal wave-function (including observers and observables), which would evolve deterministically. However, that doesn't seem to explain why the Born rule works...

21. DinosaurRational SkepticValued Senior Member

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Crunchy Cat had the right view when he said:
The requirement of a conscious observer was discarded long ago (assuming it was ever accepted as a valid view). It might have been the Cat controversy which killed the concept.

I do not remember reading anywhere that the Copenhagen view ever required a conscious observer to “collapse the wave function.”

The problem is probably moot because I think the mathematics indicates that an object as large as a cat would not exist in a superposition of states for a measurable amount of time.

It is an ill-defined concept, but I believe that most physicists (from the Bohr era to today) view the so-called collapse as occurring when a quantum level process has an effect on some classical level process. The boundary between the quantum & the classical level has moved quite a bit in the last half of the 20th century. At one time it was elementary particles on one side & larger entities on the other. Then various experiments indicated that atoms & groups of atoms must be viewed as being on the Quantum side under certain conditions. I think a Bose-Einstein condensate acts as a quantum object, even though it consists of hundreds of atoms.

A cat is definitely on the classical side of the boundary. Perhaps the boundary is ill-defined because it changes depending on circumstances.

Every description of the Many Worlds interpretation I have read seems to explicitly state that multiple universes come into existence whenever a quantum level process has more than one possible outcome. This might not have been explicitly stated in Everett’s original paper, which did not use the term “Many Worlds.” It seems to me that Wheeler (Everett’s academic mentor) made up the term. Many refer to the concept as Wheeler’s Many Worlds theory.

When reading various books on Quantum Theory, it seems to me that the experts use jargon as shorthand for more complex concepts. Observer seems to be Jargon shorthand. Collapse of the wave function seems to be jargon shorthand.

Note that the wave function provides probabilities for various results of quantum level processes. It is analogous to a table of probabilities relating to dice throws. One does not say that the probability table collapsed when a total of seven is rolled. “Wave function collapse” is merely shorthand for a more complex semantic description of quantum level activities. It might be more semantically correct to say: “Of all the possibilities described by the wave function, this particular one actually happened.” It is simpler to say “The wave function collapsed to this particular possibility.”

The Copenhagen view does not provide a pleasing explanation of quantum reality. It leaves much unexplained. It might be overturned in the future. It does not claim to provide a description of quantum reality in terms of our classical intuitive notions of reality. Many Worlds, Reverse causality, & other interpretations seem more pleasing because they seem to provide understandable explanations which seem to conform to classical intuition.

When analyzed those interpretations seem to be suspect at best & silly at worst. They attempt to deny the lack of causality implied by the Uncertainty Principle & the probabilistic data produced by quantum processes.

The UC & the probabilistic nature of quantum data imply that our notions of cause & effect are suspect. The advocates of non-Copenhagen interpretations seem unwilling to accept lack of causality & probabilistic views of the quantum worlds. When something better than Copenhagen-like views are discovered, I expect them to accept lack of causality & a probability view of the quantum world.

I like the comment by Bohr when asked what is really there at the quantum level: Particles or waves? He replied by referring to a common illusion (Following is a shortened paraphrase, not a verbatim quote)
While often seeming to be arrogant, Bohr was willing to admit to a lack of knowledge of what happens at the quantum level.

Note that Feynman once said: “Do not ask me what it really there. Nobody knows what is really there.”

22. kurrosRegistered Senior Member

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Yes this in essence is the whole problem with the Copenhagen view. The fact that there is a divide between the classical and quantum descriptions of the world is unsatisfying to begin with, and even worse is the fact that there is no reason one scale is any better than another to place the divide at. BEC's certainly act as quantum objects, and there seems no reason aside from technical challenges why we couldn't make BEC's out of billions of atoms, so it seems probable that there is no such divide, and it is just a useful device for doing calculations, which is all it was intended for anyway. The Copenhagen view is more of a practical tool than a philosophy about what "actually" is happening.
I like to think of it as a nice approximation, you know classical theory works in some domain and the quantum works in another, and the Copenhagen view just tells you how to get from one to the other. I am quite sure that there is a deeper picture to be understood here though, one that really explains how the classical emerges naturally from the quantum. Of course people are doing plenty of research on this question already, although not as many as one might think. I guess it is tricky to get funding for these kinds of esoteric questions