Schrödinger's cat and many world interpretations

[nouveau_riche]

In the Schrödinger cat's experiment if the observer decide not to interact with cat directly by opening the box but rather by bringing the interaction of Geiger counter and radioactive substance to see if the cat's alive then why the de-coherence will occur?

 

[Simon Bridge]

Because you've made an observation ... the method of the observation does not matter.
You can get a robot to do it - the sentience of the observer does not matter.

Note - the Geiger counter won't detect the disintegration that kills the cat - the radiation from that event gets absorbed by the hammer that breaks the vial. But even if you could put the cat on a heart monitor, probe the box with x-rays, anything - it's all observing the cat.

 

[nouveau_riche]

Because you've made an observation ... the method of the observation does not matter.
You can get a robot to do it - the sentience of the observer does not matter.

Note - the Geiger counter won't detect the disintegration that kills the cat - the radiation from that event gets absorbed by the hammer that breaks the vial. But even if you could put the cat on a heart monitor, probe the box with x-rays, anything - it's all observing the cat.

but in the other case i haven't had a direct interaction with cat's wavefunction

 

[Simon Bridge]

Doesn't matter.
You don't have to have a direct interaction with the cats wave function.

I think you need to explicitly state what you think decoherence means in this context.

 

[Ken G]

To add to that, the reason you don't need to interact with the cat's wavefunction is that the cat doesn't have a wavefunction. Wavefunctions are qualities of entire systems (and that only holds if you break from the Copenhagen interpretation and hold that cats can participate in wavefunctions in the first place, because it is not so easy to demonstrate this)-- so includes anything you could measure about that system. That's the wavefunction you are interacting with. If you project that wavefunction onto the "cat" substate, you don't have a wavefunction any more, you have what is known as a "mixed state", described by a "density matrix." This matrix will reflect various entanglements between the cat and the other things you can measure, and it is through those coherences that your understanding of the cat is affected by your understanding of its environment. Put simply, if you choose to treat the cat as a quantum system, then it is entangled with the things you are measuring, and if you choose to treat it as a classical system, then the issue doesn't even come up (which is the purpose of the Copenhagen interpretation).

 

[StevieTNZ]

Fundamentally the whole system will be described by Schrödinger equation, which doesn't entail any form of collapse.

 

[Ken G]

If that is "fundamentally" true actually depends quite sensitively on your preferred interpretation! For example, Bohr would most likely say that the Schroedinger equation was never meant to apply to the whole system, and there is no experimental evidence that it does. The problem with it is that if you never get collapse, you have a real problem explaining the perceptions of the observer.

 

[bohm2]

The problem with it is that if you never get collapse, you have a real problem explaining the perceptions of the observer.

Yes, unless the wave function, as given by the Schrodinger equation, is not everything, as suggested by de Broglie/Bohm.

 

[StevieTNZ]

If that is "fundamentally" true actually depends quite sensitively on your preferred interpretation! For example, Bohr would most likely say that the Schroedinger equation was never meant to apply to the whole system, and there is no experimental evidence that it does. The problem with it is that if you never get collapse, you have a real problem explaining the perceptions of the observer.

Yes indeed, in regards to Bohr's interpretation. GianCarlo Ghirardi does a nice job of offering a thought experiment to differentiate whether collapse occurs at the macroscopic apparatus or not.

Perhaps when we perceive a definite state, the system is still in superposition? After all, to calculate the correct probability of a future state - if it can come from either state1 or state2 - then you need to calculate it as if it evolved from both state1 and state2 - at least that is Brian Cox's stance on the matter, in his quantum book.

 

[Ken G]

GianCarlo Ghirardi does a nice job of offering a thought experiment to differentiate whether collapse occurs at the macroscopic apparatus or not.

Can you summarize or link to it? It sounds interesting.

Perhaps when we perceive a definite state, the system is still in superposition? After all, to calculate the correct probability of a future state - if it can come from either state1 or state2 - then you need to calculate it as if it evolved from both state1 and state2 - at least that is Brian Cox's stance on the matter, in his quantum book.

I'm not aware of a probability that requires we calculate it as if it evolved from both state1 and state2 in any situation where state1 has been observed. What you refer to sounds more like a two-slit kind of situation?

 

[Simon Bridge]

iirc you can get it with particles that can decay into each other cyclically: the observed particle is understood as a composite state so that observation just puts the wavefunction in a particular superposition rather than collapsing to a unique substate.

 

[Ken G]

It sounds like you are talking about the interesting case of a neutrino with a measured flavor (say, a muon neutrino or some such thing). As this is not a state of definite energy, it will not be stationary, and will oscillate among the various flavor eigenstates. But that doesn't mean that when we observe a definite flavor state the particle is "still in a superposition"-- at that moment it's in a definite flavor state, not a superposition of flavors. However, it will evolve into a flavor superposition, as time passes. To make future predictions, we only need that it is in state1 now, not a superposition of state1 and state2, even though it will later on be in a superposition of state1 and state2. So I don't think that says much about the MWI approach, where the initial state1 is not really all there is to it-- we don't need any of state2 in that initial state, we only expect the superposition to appear at a later time, and the Copenhagen interpretation would just say it evolves from a state of flavor definiteness to a state of flavor indefiniteness (and back again).

 

[Simon Bridge]

I think the first mention I had of it was with K mesons.
There is a standard treatment of neutral particle oscillations which represents the flavor-state as a composite of virtual states.

How it evolves from a state of flavor definiteness to a state of flavor indefiniteness (and back again), appears well modeled by evolving the virtual particle states... which would provide an example to your query end of post #10 wouldn't it?

This is a bit different from preparing a system in a superposition of eigenstates where a measurement collapses the system to one and all subsequent measurements yield the same result.

I'd like to point out that this sort of argument just keep coming up with respect to Schrödinger's Cat ... it's kind-of the point. I don't think we can come up with the one right path i a forum discussion when so many reams have already been written on the subject. The best we can do is attempt to illustrate the different positions.

 

[Ken G]

How it evolves from a state of flavor definiteness to a state of flavor indefiniteness (and back again), appears well modeled by evolving the virtual particle states... which would provide an example to your query end of post #10 wouldn't it?

I don't think it does, but I understand what you are saying. To me, the issue is what has been established by experiment (the term "observed" was used in post #10), versus what remains fundamentally indeterminate. You are invoking a more sophisticated version of this principle, involving virtual states, but I don't necessarily see a fundamental difference there than with something like the simple example of a two-slit experiment that does not determine which slit the particle goes through. Then we can treat "going through slit A" as a type of virtual state as well, and we certainly agree that the result of the experiment will involve a superposition of slit A and slit B virtual states. But those slit states have not been observed, so that's why they can remain in superposition-- in post #10, I was asking about a reference to a situation where we do have an observation, yet we still need to include a superposition that includes elements that are contradictory to that observation (such as people talk about in MWI). Even with virtual states, I don't think that's ever necessary.

I'd like to point out that this sort of argument just keep coming up with respect to Schrödinger's Cat ... it's kind-of the point. I don't think we can come up with the one right path i a forum discussion when so many reams have already been written on the subject. The best we can do is attempt to illustrate the different positions.

I agree, and that's why I was trying to distinguish between essentially philosophical debates about the meanings of superpositions, versus an actual calculation of a probability of a future event that requires invoking a superposition. The latter is pretty concrete, so if there was actually a calculation that required we include a superposition of state1 and state2 (at some given time) even though we had actually observed state1 (at that time), then we would be forced to adopting an MWI-type view of the situation, it would no longer be an issue of philosophical priorities. But that's just what I don't think has ever been found to be the case.

 

[jasonjbaker]

Who is watching us watch the cat, again?

 

[DougW]

I still didn't see anyone really comment on the Many World Interpretation, so I'm going to give it the layman's try. In Many Worlds, there is no wave or decoherence at the particle level. Instead, all results actually happen. So in this case, there are Universes where the cat lives and Universes where it does not. 'You' have access to all these universes up until the moment that the information about which universe you are in reaches you. That information is bound by the laws of Physics and can not travel faster than the speed of light. David Deutsch describes it as a 'Decoherence Wave', if I remember correctly from his latest book 'The Beginning of Infinity'. Anyway once the information reaches you, there becomes more than one you, each belonging to a different universe. You'll have to read one of the experts to learn how this happens without violating conservation of mass, energy, etc. The way I understood it, all the universes split and merge all the time, but it is a bit confusing.

Anyway, what gets Duestch all riled up all the time is that no one wants to buy into the Many Worlds Interpretation because (in his opinion anyway) it makes us feel less important if there are near-infinite versions of each of us experiencing all these different outcomes. We all want to feel 'unique' so we dismiss the evidence of MWI. His explanation of this evidence includes things like Quantum Computing calcuations that have already been performed; i.e. we know the calculation requires x number of bits, yet in our universe fewer than x bits exist, so where is the rest of the calculation being performed? His answer: another universe. Same thing with the double-slit experiment. We see evidence of two photons interfering, but since only one exists in our universe where is the other? He hates that we 'made up' a wave to explain the dilemma, when the simpler explanation (the extra photon is in another 'very close' universe) is abandoned because again we don't like the idea that multiple copies of us exist in these Universes. Reading Duestch is fascinating stuff, and the politics of the Physics/Science community is also fun to read about. I get the impression that most other popular scientific authors don't like Deustch because among other things he is constantly telling other authors that they are wrong (in The Beginning of Infinity he hammers some of the theories of Dawkins and Jared Diamond among others...)

 

[Ken G]

We see evidence of two photons interfering, but since only one exists in our universe where is the other? He hates that we 'made up' a wave to explain the dilemma, when the simpler explanation (the extra photon is in another 'very close' universe) is abandoned because again we don't like the idea that multiple copies of us exist in these Universes.

I admit that there's a certain lure to the idea that photons in other universes are what is interfering there, but here are some of the problems with Deutsch's argument:

1) He dislikes saying that a "wave" is doing the interfering, rather than copies of the same particle, but this suggests that he feels it is natural for particles to interfere with themselves-- where does he get that? Nothing about particles suggests that they "should" interfere, so it's not like saying "oh, as soon as you recognize there are copies of this particle, it is obvious why they should all interfere." The entire idea that a particle can undergo interference comes from its wave nature, as waves are the way physics treats interference, and classical waves exhibit interference in a perfectly natural and easily mechanistically understandable way (that's what motivates the wave language in the first place). So it seems misplaced to me to want to replace the wave concept with the particle-interfering-with-itself concept, there's just no improvement there and we certainly lose contact with the nice classical analogies.

2) I don't think anyone actually dislikes MWI because it makes us seem less important in all those universes. Rather, it is the complete absence of empirical evidence of the existence of those other universes! I know a lot of astronomers, and we have all come perfectly well to terms with the idea that we are a very very tiny part of a very very large, possibly even infinite, universe, yet none of them are favorably inclined toward MWI. It has nothing at all to do with our place in the cosmos, it's all about the absence of evidence. Absence of evidence is not evidence of absence, but it is a good reason to reject an interpretation that seems unnecessarily bizarre.

 

[jasonjbaker]

If the there is a photon heading towards the slits, but it exists in two universes, what would cause the copy in universe A to interfere with the copy in universe B? I thought these universes cannot communicate?

 

[DougW]

What Duestch is saying is not that the particle is interfering with itself, he is saying that there are two particles interfering with each other. From my understanding, it is possible to recreate the results of the double-slit experiment simply by having multiple photon-sources. The photons from the different sources will interere with each other. (At least that is what I gathered from what Deustch said). So his explanation is that there are multiple sources, even when we think there is only 1. The universes CAN communicate as long as local coherence is in place. In his model decoherence is a local phenomenon that 'spreads' at the speed of light (or near) as information is spread. He also postulates that local decoherence can be 'undone' and the universes can be sort of 're-entangled' by loss of information, or additional information that 're-aligns' or 'merges' the universes. I'm sure if he read this he would say I'm not expressing it exactly right, again this is a lay interpretation of his theory.

In the end, it comes down to the idea that 'knowledge' has physical properties and a physical impact on environment. Also you need to be willing to accept that our consciuosness is a result of a physical paradigm, and thus can be duplicated. Tough stuff to digest. If Deustch weren't such an angry bugger, he wouldn't get ignored by the rest of the popular scientific community. I'm in the middle of Lisa Randall's new book 'Knocking on Heaven's Door', and while many of the concepts she is pushing are very similar to what Deustch presented in 'Beginning of Infinity' there is literally no mention of him or his work, whereas she notes the work of Dawkins and others several times...

 

[jasonjbaker]

Well, I have no doubt that consciousness is a physical manifestation or 'brain state.'

It's a pretty simple thing to test: put a human into a medically induced coma, and they are no longer conscious. Return the brain function, and voila, consciousness returns.

Anyway, clarify this: how are there 'multiple sources' to interfere with one another? If I fire one photon out of a gun at two slits, what mechanism would cause that photon to simultaneously exist in another parallel universe according to the MWI?

Further, how many other worlds does the photon exist in, and what determines that number? Are there three other copies of that photon in 3 other worlds, 3 trillion, infinite?

Finally, when we measure where the photon is in our world and collapse it's wave function, what happens to the copies in the other worlds? Our measured photon can no longer interfere with them, so we must be changing their reality as well.

 

[DougW]

Again, according to MWI, There are multiple universes, thus multiple everything. Multiple photon emitters, multiple photons being emitted, multiple cards with 2 slits cut in them, etc. Any time anything happens at a quantum level which can have varied outcomes, all of the outcomes occur in proportion to the probability. So in the case of the double-slit, a roughly equal number of photons go through the left slit and the right, and they interfere with each other. There is no 'collapse' as described in Copenhagen Int. (In fact one of Deustch's big pet peeves about MWI doubters is that they will never explain where the 'collapsed' particles go in the Copenhagen theory). Instead, there is decoherence locally between the universes. SO, once we have a measurement of some kind, the information spreads and decoheres the various universes so that further contact between then can not occur. So, if we observe prior to the photons hitting the photographic plate, then we have already decohered the universes, there is then no interaction of the photons in the different universes after passing through the slit and thus no interference pattern is seen. If we don't measure until the photographic plate (the reaction of the photon hitting the plate is an observation in itself), then we get the interference between the time when the photons pass through the slits and when they arrive at the plate, and we can see the interference pattern.

 

[Ken G]

From my understanding, it is possible to recreate the results of the double-slit experiment simply by having multiple photon-sources. The photons from the different sources will interere with each other.

But why? What is it about multiple photons that Deutsch thinks it is natural to say they should interfere with each other? Interference makes total sense if light is a wave, and no apparent sense at all if light is a particle, it makes no difference how bright the light is or how many photons there are. That was never really the issue with the two-slit experiment, because there is no kind of interaction between photons in any of our theories of light that could explain how two photons might interfere with each other. It's true that if we have lots of light, we know we can use the classical limit, but the classical limit is a field theory about electromagnetic waves, i.e., it is a wave theory, not a particle theory. Hence, Deutsch is not explaining anything by passing from the quantum to the classical limit by invoking multiple worlds-- how the quantum limit passes to the classical limit remains the question that the multiple worlds have shed no light on (literally).

 

[Simon Bridge]

And between you, you have pretty much covered the debate.

Feynman's wave-particle duality lectures have a wonderful description of what the description is telling you - the particle is what you see, but the wave governs the probabilities ... it's not like a physical wave in a medium like with water.

And that's the problem conceptually - these are just rules that allow us to make calculations much like how the Mayans could calculate eclipses. We are not doing much more than moving stones from one clay pot to another.

We can make the rules what we like as long as the math comes out with the right result - but that does not mean that we know what is going on.

So on the one hand we can understand the results of these experiments in terms some kind of wave made up of probabilities and we add up the probability amplitudes for every possible path to get the result - on the other hand we end up with these virtual particles. We could accept that they are just artifacts of the calculation process, and thus wholly imaginary, except that particles just like them can be made in a laboratory. Are the force mediators really there? If so then where do they come from and if not, then how come they are so reliably created.

Similarly with the refection example - the calculation requires summing amplitudes for every path a photon may have traveled - kind-of encouraging a picture where the photon must travel every possible path. But of course the photon only travels one path ... so the many paths in the sum are, perhaps, virtual paths ... paths not really followed. Except that we can selectively remove some paths and get a brighter reflection. So we can prove that even quite wild paths are in fact followed - they are real paths in the sense that an actual physical photon does actually travel that way.

I think every student has to struggle, and come to an accommodation, with these ideas. In the end, these are all inadequate ways of thinking about and describing the phenomena. They are crutches for the mind as we adjust to the way things are. Teaching it is like trying to describe fire to someone who has never seen it before.

Learning it is like learning to whistle - you spend ages not knowing how, the descriptions of what to do don't seem to be working, and then you get it. And what you get is that whistling is like the descriptions but not exactly, and you face the same problems if you try to teach someone how to whistle.

But, of course, you have to try.

 

[Ken G]

But of course the photon only travels one path ... so the many paths in the sum are, perhaps, virtual paths ... paths not really followed. Except that we can selectively remove some paths and get a brighter reflection. So we can prove that even quite wild paths are in fact followed - they are real paths in the sense that an actual physical photon does actually travel that way.

What works for me is to interpret one of the main "lessons" of quantum mechanics as telling us that we need to stop imagining that nature has an answer to every question we can ask but aren't smart enough to understand. Maybe we just aren't smart enough to ask the right questions-- and many of the questions we do ask don't really mean anything and so nature has no idea what the answers are (like what path does a particle follow when the path is not established).

 

[jasonjbaker]

With respect, I totally reject the notion that there are aspects of nature that we are simply not smart enough to understand as non-sequitur.

That's what people said in Newton and Galileo's day too.

 

[Ken G]

With respect, I totally reject the notion that there are aspects of nature that we are simply not smart enough to understand as non-sequitur.

That's what people said in Newton and Galileo's day too.

So you hold to a syllogism that says if people thought there were specific things we would never be smart enough to understand, and it turned out they were wrong about those things, this principle by necessity extends now to everything? This is the fallacy of the excluded middle. More likely, there are things we didn't think we could understand, yet we did, and there are things we think we will understand, yet we won't. Often I observe a kind of "selective reasoning", where any time we understand something, it gets classified as science, and every time we don't, it gets classified as philosophy. This is quite convenient for allowing us to imagine that science can figure out anything (and philosophy, nothing), but it's really just a form of creative accounting.

 

[jasonjbaker]

no, i simply don't believe there are things that we are not capable of understanding, given enough time to reason them out through the process of the scientific method.