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Benny
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various physics questions
« on: Jun 22nd, 2008, 3:36pm » |
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Schrodinger’s cat:
This is my understanding of this theoretical concept:
The quantum cat exists in two states at once: it is both alive and dead at the same time - a superposition of two states. Any kind of random disturbance or interaction will destroy the exquisitely delicate mix of coexisting quantum states, forcing a single classical state to emerge instead. Meaning, it will collapse to a simple classical one, that is either dead or alive.
Does this break the law of non-contradiction?
As Aristotle summed it up, “One cannot say of something that it is and that it is not in the same respect and at the same time.“
Could we say:
the states of Schrodinger’s cat before observation aren’t in a mutually exclusive state. In this case, the two states don’t actually contradict. Now if Schrodinger’s cat was in two states after someone looked in the box, then we’d have a problem.
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towr
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Re: various physics questions
« Reply #1 on: Jun 23rd, 2008, 12:47am » |
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Since Schrodinger's cat is an observer itself, the thought experiment fails.
That said, it is only an interpretation of a physical phenomenon. Reifying it would be a mistake, I think. Just as it would be a mistake to consider the many-world interpretation and pose that those many worlds actually exist, rather than conceptually.
And in any case, the cat wouldn't be both alive and dead; it would be alive with 50% probability and dead with 50% probability. Which of the two is determined at observation (by any interaction with the universe at large, not necessarily by a sentient). So there is no problem with contradiction.
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Benny
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Re: various physics questions
« Reply #2 on: Jun 23rd, 2008, 10:41am » |
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Take another example, a quantum coin.
Flip a coin in the quantum realm and the outcome won't be heads or tails. We will need new strategies to play traditional games in the quantum world. The quantum coin can also settle on heads and tails.
We expect that quantum computers will be able to use entirely new algorithms to solve a variety of problems more efficiently than conventional machines.
In quantum physics a state just gives the probabilities of finding the system in each of the possible outcomes of a measurement(well really it gives the square root of the possibility). So for example, considering the coin
1/Sqrt.{2} (Tails) + 1/Sqrt.{2} (Heads)
it doesnt necessarily have to be 50-50, you just change the coefficients of the possible outcome states. Also there doesnt have to be a finite number of possible outcome states, a system can have an infinite number of possible outcomes (1), (2), (3) ... and then the systems state is given by the sum of all these states each multiplied by a coefficient that gives their probability.
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Grimbal
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Re: various physics questions
« Reply #3 on: Jun 26th, 2008, 8:03am » |
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on Jun 22nd, 2008, 3:36pm, BenVitale wrote:| As Aristotle summed it up, “One cannot say of something that it is and that it is not in the same respect and at the same time.“ |
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But as F. Scott Fitzgerald said: "The test of a first-rate intelligence is the ability to hold two opposed ideas in the mind at the same time, and still retain the ability to function." 
on Jun 23rd, 2008, 12:47am, towr wrote:| Since Schrodinger's cat is an observer itself, the thought experiment fails. |
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I wonder. What is it that makes the cat an observer? What makes it different from a cloud of particles that might well live in a superposition of states? As I see it, the cat will experience a unique outcome and could believe (provided some training in physics) that the rest of the world collapsed to a single state. But another interpretation would be that the cat split in multiple versions, each of which experiences a single outcome.
I like the idea that if we do something to a particle when we observe it, then the particule does the same thing to us. It is true for gravity, why not for quantum pheonomena? If in our view the particle is in a superposition of quantum states and collapses to one when we observe it, in the view of the particle, WE are in a superposition of quantum states and OUR wave function collapse to a single state.
What I wonder about with Schrodinger's cat is that when a photon splits into 2 states, each going thru a different slit, they later interact into interference patterns. Shouldn't the superposition of cats interact in a similar way?
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| « Last Edit: Jun 26th, 2008, 8:06am by Grimbal » |
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towr
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Re: various physics questions
« Reply #4 on: Jun 26th, 2008, 8:40am » |
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on Jun 26th, 2008, 8:03am, Grimbal wrote:| I wonder. What is it that makes the cat an observer? |
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It's a macro system.
The way I tend to look at it is that with an increased number of particles, the probability gets skewed to one macro state. Whether that's a correct interpretation or not, the fact of the matter is that as long as there is any measurement, from man or machine, or animal, waveforms collapse.
Quote:| What makes it different from a cloud of particles that might well live in a superposition of states? As I see it, the cat will experience a unique outcome and could believe (provided some training in physics) that the rest of the world collapsed to a single state. But another interpretation would be that the cat split in multiple versions, each of which experiences a single outcome. |
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You can do the same with people; cats are not special in that sense. If Schrodinger is inside the room with the box, and I'm outside. Then the cases of Schrodinger having looked in the box to see what happened with the cat, and the case where Schrodinger hasn't looked at the cat, could be considered in superposition. (It's a matter of propagation of information from one part of the universe to the next; as long as the influence of one region hasn't been felt in the other, it can be considered unknown or in superposition).
But it is rather pointless, in my opinion. (Although it can be fun to consider the whole universe in one giant superposition; all the "many worlds" occupying the same space-time/whatever at the same time.)
Quote:| I like the idea that if we do something to a particle when we observe it, then the particule does the same thing to us. It is true for gravity, why not for quantum pheonomena? |
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It is. It is an interaction.
The term "observation" really muddles the issue, because it gives the suggestion that there is something magical entered into the equation by consciousness.
But if you do the two-split interference experiment, and set up a measurement device to check what slit the particle comes through, but you drop every measurement directly in the bin (such that no person will ever observe it), the waveform still collapse just the same, and there is no interference pattern.
Quote:| What I wonder about with Schrodinger's cat is that when a photon splits into 2 states, each going thru a different slit, they later interact into interference patterns. Shouldn't the superposition of cats interact in a similar way? |
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If it's going slow enough.
(Or rather, you wouldn't notice the interference pattern if it wasn't going slow enough. And you'd have trouble pushing the cat through the slit)
It'd be a very cool cat.
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| « Last Edit: Jun 26th, 2008, 8:49am by towr » |
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Re: various physics questions
« Reply #5 on: Jun 26th, 2008, 2:04pm » |
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on Jun 26th, 2008, 8:40am, towr wrote:
That could be a reason. I have read about the idea that it is a question of critical mass. There are experiments trying to create a superposition in larger and larger systems to see if it spontaneously collapses past some point.
If that's the case, an "observer" would just just be a system that tries to interact with the quantum state and is too heavy to do so in a quantum way.
Quote:| You can do the same with people; cats are not special in that sense. If Schrodinger is inside the room with the box, and I'm outside. Then the cases of Schrodinger having looked in the box to see what happened with the cat, and the case where Schrodinger hasn't looked at the cat, could be considered in superposition. (It's a matter of propagation of information from one part of the universe to the next; as long as the influence of one region hasn't been felt in the other, it can be considered unknown or in superposition). |
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I believe there is a fundamental difference between something being unknown and something being in quantum superposition. A superposition is not just a number of possible states with probabilities attached.
Quote:| But it is rather pointless, in my opinion. (Although it can be fun to consider the whole universe in one giant superposition; all the "many worlds" occupying the same space-time/whatever at the same time.) |
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It is more than just a philosophical way of seeing it. You can explain quantum physics in terms of multiple realities going on side by side (a particle following different paths or being in different states simultaneously). At some times some realities disappear. The idea that some part of reality just disappears is in my opinion less satisfying that the idea that we just loose the contact to that part of reality. And that second option naturally leads to the conclusion that many universes exist side by side.
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| « Last Edit: Jun 26th, 2008, 2:06pm by Grimbal » |
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towr
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Re: various physics questions
« Reply #6 on: Jun 26th, 2008, 2:32pm » |
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on Jun 26th, 2008, 2:04pm, Grimbal wrote:| I believe there is a fundamental difference between something being unknown and something being in quantum superposition. A superposition is not just a number of possible states with probabilities attached. |
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Well, regardless. If the cat can be in a superposition with an atom, then you can build as many layers of boxes around it on the same principle.
I do think it fundamentally comes down to information in a physical sense of the word though. (Which is related to a kind of knowing, but not so much in that some entity knows something).
As for the different between a superposition and a collection of states with probabilities. The only difference I can see is that in the latter case, you might have that only one state is real (and the probabilities are your best guesses); whereas for a superposition the probabilities are the chance a state will become real upon measuring it. (So probability there is more like casting a mathematical die, as opposed to uncertainty in knowledge of the true state of reality.)
Quote:| It is more than just a philosophical way of seeing it. You can explain quantum physics in terms of multiple realities going on side by side (a particle following different paths or being in different states simultaneously). At some times some realities disappear. The idea that some part of reality just disappears is in my opinion less satisfying that the idea that we just loose the contact to that part of reality. And that second option naturally leads to the conclusion that many universes exist side by side. |
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If I had to choose between the many worlds interpretation and the Copenhagen interpretation, I'd choose the latter; I don't feel like reifying an infinity of worlds for no good reason. One reality is plenty.
Also, we can keep conservation of mass, and energy etc if we stick to one universe. Not to mention problems with continuity, because the worlds don't split off neatly at decisions people make, the wave-functions are continuous; and each point along it would split off into each own universe; for every particle; at every time. It's a bit much. However, it's neatly resolved if we leave everything in superposition.
To come back to "The idea that some part of reality just disappears": they were never real in the first place. When a wavefunction collapses one of the states becomes real, the rest never were (and it wasn't real before it was observed either).
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Benny
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Re: various physics questions
« Reply #7 on: Jun 26th, 2008, 3:25pm » |
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Sorry to interrupt. I have a question :
What would make a wave function to collapse?
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Re: various physics questions
« Reply #8 on: Jun 26th, 2008, 11:54pm » |
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on Jun 26th, 2008, 3:25pm, BenVitale wrote:| What would make a wave function to collapse? |
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I could try to characterize the situation in which wave functions collapse (any interaction that makes a determined state of the quantum object necessary). But what exactly makes it happen in those cases, I can't say. And I don't know if there even is an answer.
Perhaps the wave function doesn't so much collapse, but just gets highly skewed towards one state.
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rmsgrey
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Re: various physics questions
« Reply #9 on: Jun 28th, 2008, 10:20am » |
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Roger Penrose speculated (possibly drawing ideas from others) in one of his books that, while small, light objects such as fundamental particles can exist simultaneously in superpositions of states, "sufficiently" different space-times can't superpose successfully - when the distribution of mass becomes sufficiently different between different states, a transition occurs, and the superposition collapses down to a single state (or single family of related states)
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Benny
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Re: various physics questions
« Reply #10 on: Jun 28th, 2008, 11:28am » |
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What about the standard Copenhagen interpretation?
Didn't the standard Copenhagen interpretation is that the cat is neither alive nor dead?
"Alive" or "dead" is what we observe when we open the box and collapse the wave function, and the probability of one observation or the other might be 50% (depending on the circumstances). But before we look, the cat exists in a nondeterministic state of superposition, that is, it is neither alive nor dead.
I understand that the standard Copenhagen interpretation came under severe criticisms recently.
Is it still valid or not?
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Grimbal
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Re: various physics questions
« Reply #11 on: Jun 28th, 2008, 3:14pm » |
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on Jun 26th, 2008, 2:32pm, towr wrote:| As for the different between a superposition and a collection of states with probabilities. The only difference I can see is that in the latter case, you might have that only one state is real (and the probabilities are your best guesses); whereas for a superposition the probabilities are the chance a state will become real upon measuring it. (So probability there is more like casting a mathematical die, as opposed to uncertainty in knowledge of the true state of reality.) |
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What I mean is that a superposition of a top spin and a bottom spin can have a definite spin oriented left or right depending on the phases. But a particle being top or bottom with 50% chance will always be measured left or right at 50%.
Also, a particle that goes through 2 slits interacts with its other self and produces inference patterns, while a particle that goes through one or the other slit doesn't.
Quote:| If I had to choose between the many worlds interpretation and the Copenhagen interpretation, I'd choose the latter; I don't feel like reifying an infinity of worlds for no good reason. One reality is plenty. |
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I feel it is like being in a corridor of a hotel with many doors, you can open only the one to your room, so you don't think there is anything behind the others.
Quote:| Also, we can keep conservation of mass, and energy etc if we stick to one universe. Not to mention problems with continuity, because the worlds don't split off neatly at decisions people make, the wave-functions are continuous; and each point along it would split off into each own universe; for every particle; at every time. It's a bit much. However, it's neatly resolved if we leave everything in superposition. |
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When a particle is in 2 positions simultaneously, isn't it already a multiple-world interpretation?
But I agree that I am not quite happy with the idea that something that is out of reach is considered to exist.
Quote:| To come back to "The idea that some part of reality just disappears": they were never real in the first place. When a wavefunction collapses one of the states becomes real, the rest never were (and it wasn't real before it was observed either). |
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You can not say for one state that it was never real and for the other that it becomes real. You must say it was always real. It just wasn't known. But quantum mechanics is incompatible with the idea that the state just wasn't known, as the EPR paradox demonstrates.
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| « Last Edit: Jun 28th, 2008, 3:18pm by Grimbal » |
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Re: various physics questions
« Reply #12 on: Jun 29th, 2008, 1:39am » |
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Is anybody familiar with the GRW theory (Ghirardi, Rimini and Weber)?
According to quantum theory, a particle does not sit in just one place, but occupies many places all at once. Its true position is defined by a fuzzy blob called a "wave function", which sets out the probability of finding the particle in various locations. With time, the wave function of any particle spreads out, bleeding into an expanding volume of space, as the particle's multiple existences proliferate.
Ghirardi, Rimini and Weber proposed a subtle change in the quantum rules that determine how wave functions evolve . Suppose, they said, wave functions usually spread out according to normal quantum rules, but very rarely-once every 100 million years or so -the wave- function of a single particle collapses and becomes localised to a tiny region. This change scarcely affects single particles, but has a huge effect on big things.
I don't really understand all of this.
They take an example, a cat or any other object of similar size contains some 1027 particles, and even though the wave function of any one is likely to take 100 million years to collapse, there are so many particles that it is overwhelmingly likely that the wave function of at least one particle will collapse within just 10-12 seconds.
The GRW theory doesn't really explain what would make a wave function collapse, nor why it should happen only every 100 million years.
I'm sure i'm missing something, even perhaps a lot of things. Could anyone clarify?
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towr
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Re: various physics questions
« Reply #13 on: Jun 29th, 2008, 7:30am » |
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on Jun 28th, 2008, 11:28am, BenVitale wrote:I understand that the standard Copenhagen interpretation came under severe criticisms recently.
Is it still valid or not? |
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It's an interpretation; it makes no difference for measurement, calculation, or prediction. Validity is irrelevant.
I can't say that I've heard anything about criticism of the Copenhagen interpretation though, but then I'm not really involved in the QM field, it might easily have slipped passed me.
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Re: various physics questions
« Reply #14 on: Jun 29th, 2008, 8:01am » |
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on Jun 28th, 2008, 3:14pm, Grimbal wrote:| When a particle is in 2 positions simultaneously, isn't it already a multiple-world interpretation? |
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I wouldn't see why (but then it's commonplace in science fiction with timetravel and all that.)
But when is a particle ever in two positions at once? If you try to measure it, it's always only in one, it's never seen in two.
Quote:| You can not say for one state that it was never real and for the other that it becomes real. You must say it was always real. |
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I don't see why. In one case you had a superposition, which isn't any of the 'superposed' states, but rather a state of its own. And when it 'collapses' you change from that state to another state (which is one of the states that only for narrative purposes was considered to 'make up' the superposition. It's like saying there's an oak in an acorn, it's not really in there, but potentially one can grow out of it.)
Just to make sure there's no confusion, my interpretation is that none of the superposed states are real before the wavefunction collapses. Not that "the real one" existed all along but was simply unknown.
Quote:| But quantum mechanics is incompatible with the idea that the state just wasn't known, as the EPR paradox demonstrates. |
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I thought EPR still left some room open for non-classical deterministic explanations. But I'm not very familiar with it beyond "spooky action at a distance".
Besides, any random universe can be sufficiently closely approximated in simulation by a large enough deterministic computer. 
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Re: various physics questions
« Reply #15 on: Jun 30th, 2008, 9:06am » |
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A timely link.
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Re: various physics questions
« Reply #16 on: Jun 30th, 2008, 2:23pm » |
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on Jun 29th, 2008, 8:01am, towr wrote:| But when is a particle ever in two positions at once? If you try to measure it, it's always only in one, it's never seen in two. |
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It can be in multiple positions as long as you don't measure it. You can hardly explain the interferences in the 2-slip experiment if the photons don't go through both slits.
Quote:| I don't see why. In one case you had a superposition, which isn't any of the 'superposed' states, but rather a state of its own. And when it 'collapses' you change from that state to another state (which is one of the states that only for narrative purposes was considered to 'make up' the superposition. It's like saying there's an oak in an acorn, it's not really in there, but potentially one can grow out of it.) |
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I see what you mean, but I don't feel comfortable with it. It is that "changing state" that bothers me. It breaks Schroedinger's equations. The other thing that bothers me is that instant action at a distance. If 2 entangled particles move away from each other, as long as you haven't measured one, the other can be in a number of quantum states. When you measure one, the wave function of the other one collapses to a definite state. It is like if your measurement forced the whole universe to align itself to it. I prefer to think that multiple universes exist, and that your measurement selects a path, affecting only yourself, not the whole universe. Since both outcomes existed before the measurement, then both exist after it. One of them is just out of reach.
This being said, what makes me think like that is intuition, and quantum mechanics is notorious for offending intuition badly.
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Re: various physics questions
« Reply #17 on: Jun 30th, 2008, 3:16pm » |
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on Jun 30th, 2008, 2:23pm, Grimbal wrote:| It can be in multiple positions as long as you don't measure it. |
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Well, if you don't measure it in two different position you can't really be sure it is.
Quote:| You can hardly explain the interferences in the 2-slip experiment if the photons don't go through both slits. |
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But if you measure what happens at both slits, it only goes through one. Something else must be happening there. It can't be modeled as the photon splitting in two and going through both slits.
Quote:| I see what you mean, but I don't feel comfortable with it. It is that "changing state" that bothers me. |
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States change all the time. But I suppose the apparent discontinuity of it is more what bothers you.
I'm not sure you can't just see it as an interaction between waveforms though, which 'simply' results in a more certain state for the measured particle. (Similar to how many uncertain measurements average to a more certain one; the interaction between particles could 'stabilize' them with respect to each other.)
Quote:| When you measure one, the wave function of the other one collapses to a definite state. It is like if your measurement forced the whole universe to align itself to it. I prefer to think that multiple universes exist, and that your measurement selects a path, affecting only yourself, not the whole universe. Since both outcomes existed before the measurement, then both exist after it. One of them is just out of reach. |
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So rather than realign a 'whole' universe (most of which isn't involved) you make a whole universe disappear instead 
Quote:| This being said, what makes me think like that is intuition, and quantum mechanics is notorious for offending intuition badly. |
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Then perhaps we should come up with whatever is most counter-intuitive. But then, anything we could come up with must necessarily be more intuitive that that which we can't come up with.
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| « Last Edit: Jun 30th, 2008, 3:19pm by towr » |
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Re: various physics questions
« Reply #18 on: Jun 30th, 2008, 10:32pm » |
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on Jun 30th, 2008, 3:16pm, towr wrote:But if you measure what happens at both slits, it only goes through one. Something else must be happening there. It can't be modeled as the photon splitting in two and going through both slits.
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Particles are like naughty children. As long as you watch them, they behave like angels. But as soon as you turn your back they do the craziest thing you didn't even think possible.
If the photon doesn't go through both slits in some way, then you don't have an interference.
Quote:| States change all the time. But I suppose the apparent discontinuity of it is more what bothers you. |
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Yes.
Quote:| I'm not sure you can't just see it as an interaction between waveforms though, which 'simply' results in a more certain state for the measured particle. (Similar to how many uncertain measurements average to a more certain one; the interaction between particles could 'stabilize' them with respect to each other.) |
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You seem to see the wave function as nothing more than some kind of probability distribution.
Quote:| So rather than realign a 'whole' universe (most of which isn't involved) you make a whole universe disappear instead |
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Of course not! I see it more like closing a door. And regarding how much can be involved, it would be interesting to see whether a whole cat can be involved.
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towr
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Re: various physics questions
« Reply #19 on: Jul 1st, 2008, 12:42am » |
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on Jun 30th, 2008, 10:32pm, Grimbal wrote:| If the photon doesn't go through both slits in some way, then you don't have an interference. |
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In some way, but not as a particle that goes through both. If you shoot two different photons through both slits, observing them as they do, do they interfere with eachother? I'm thinking they don't. So then you can't explain interference by a single photon splitting in two and interfering as if it went through both slits separately.
Quote:| You seem to see the wave function as nothing more than some kind of probability distribution. |
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Well, that's pretty much what it is mathematically speaking, isn't it? (I think you still need to square it to get a real probability.)
Quote:| Of course not! I see it more like closing a door. |
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? I don't quite get that, I'm afraid.
Quote:| And regarding how much can be involved, it would be interesting to see whether a whole cat can be involved. |
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Most quantum physicist say no. And if a cat could be involved there's no reason a human couldn't; and probably larger things. Why we see anything in the world as in a definite state becomes quite a mystery.
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| « Last Edit: Jul 1st, 2008, 12:58am by towr » |
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Benny
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Re: various physics questions
« Reply #20 on: Jul 1st, 2008, 8:40am » |
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I've asked an experimental physicist about this thought experiment, about the point of this experiment. He answered:
Schroedinger's cat's example is just a question of whether the atom decayed and set off a chain of events. If you get hung up on all the chain and not the atom, you've completely missed the point of the example.
A thought experiment is illustrative. It does not need to take into account every tiny effect. It needs to explore a big idea, with no effects included that are so big as to dominate the outcome.
The Copenhagen Interpretation of QM states that until a measurement is undertaken, that the atom simultaneously exists in two quantum states. Ignore the remainder of the window dressing. Both Schroedinger and Einstein did....
QM is a messy business. But it works extremely well.
What do you guys think?
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Grimbal
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Re: various physics questions
« Reply #22 on: Jul 1st, 2008, 3:06pm » |
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on Jul 1st, 2008, 12:42am, towr wrote:| In some way, but not as a particle that goes through both. If you shoot two different photons through both slits, observing them as they do, do they interfere with each other? I'm thinking they don't. So then you can't explain interference by a single photon splitting in two and interfering as if it went through both slits separately. |
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In fact, I believe photons do interact at the quantum level, or they wouldn't combine to create coherent light in lasers.
But it is not like the photon splits and becomes 2 particles. I don't know how to call what it does. But some of the "stuff" the wave function is made of spreads to multiple locations and follows both paths simultaneously. It is never completely in one position or the other. But it is different from a probability because with a probability you could consider the 2 cases of the particle going through each slit and sum the results. [/quote]
Quote:| Well, that's pretty much what it is mathematically speaking, isn't it? (I think you still need to square it to get a real probability.) |
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But by squaring and taking the norm, you loose the phases in the wave function. And the phase allows for much more complex behavior than you can explain with probabilities.
Quote:| ? I don't quite get that, I'm afraid. |
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You are in front of 2 doors, you chose one and enter the room. The door closes behind you, meaning the other room becomes inaccessible to you, but it still exists.
Quote:| Most quantum physicist say no. And if a cat could be involved there's no reason a human couldn't; and probably larger things. Why we see anything in the world as in a definite state becomes quite a mystery. |
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Frankly I don't know how many of them are on which side, but it seems to me the question is still debated.
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Benny
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Re: various physics questions
« Reply #23 on: Jul 1st, 2008, 6:51pm » |
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according to Quantum decoherence
http://en.wikipedia.org/wiki/Quantum_decoherence
we only have the appearance of wavefunction collapse.
According to decoherence theory, even a stray photon "counts" as an observer. Any particle interacting with an object in a mixed state will collapse the superposition and put the object into a pure state.
The idea is called "decoherence," and it is the reason we don't see quantum-mechanical effects [often] on the macroscopic level. All the billions of particles interacting with the system -- atoms of air, infrared photons, etc. -- all serve to keep macroscopic objects like cats out of quantum superpositions.
there are some ways to observe macroscopic quantum mechanical effects, but they don't involve
house pets, for example, superfluids.
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| « Last Edit: Jul 1st, 2008, 6:58pm by Benny » |
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towr
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Re: various physics questions
« Reply #24 on: Jul 2nd, 2008, 12:44am » |
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on Jul 1st, 2008, 3:06pm, Grimbal wrote:| You are in front of 2 doors, you chose one and enter the room. The door closes behind you, meaning the other room becomes inaccessible to you, but it still exists. |
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But shouldn't there be a me in both rooms?
Otherwise I'd expect to end up in a universe with exceedingly less people (and matter in general). Or is it a non-physical me that's making the path through the continuum of adjacent universes? (Which has it's own set of problems).
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Wikipedia, Google, Mathworld, Integer sequence DB
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