Are The Odds Regarding Particles Definitely Independent Events?

[David Sklansky]

I might be exposing my ignorance here, but I have often wondered whether the randomness associated with subatomic particles, 50% chance they will decay in 13 microseconds, 50% chance they spin up rather than down, etc. etc. is independent. I know there is no "cause" for this randomness. But does that also mean that the randomness is totally independent? Or might it be like a deck with a few octillion cards in it. So that if we find one paricle up there is a teeny extra chance that the next one is down. Because half of all particles are up and half are down. Cards rather than coin flips.

Does Bell's Theorem or something else prove this idea wrong?

[Duke]

Locality is the first issue that I see.

[inlemur]

This seems to me like a philosophical question rather than one that can be proven or shown empirically. A similar situation occurs in statistical mechanics, where the fundamental postulate is that all microstates occur with equal probability. This assumption leads to models that accurately describe real physical systems, but the postulate itself is unproven.

[Duke]

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This seems to me like a philosophical question rather than one that can be proven or shown empirically. A similar situation occurs in statistical mechanics, where the fundamental postulate is that all microstates occur with equal probability. This assumption leads to models that accurately describe real physical systems, but the postulate itself is unproven.

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There are big differences between "can't be proven," "can't be proven yet," and "can't be proven because we currently have a fundamental misunderstanding." I see absolutely no reason to cite likely ignorance as a reason to relegate something to long discussions about nothing. I spend my life trying to avoid that trap.

[chezlaw]

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[ QUOTE ]
This seems to me like a philosophical question rather than one that can be proven or shown empirically. A similar situation occurs in statistical mechanics, where the fundamental postulate is that all microstates occur with equal probability. This assumption leads to models that accurately describe real physical systems, but the postulate itself is unproven.

[/ QUOTE ]

There are big differences between "can't be proven," "can't be proven yet," and "can't be proven because we currently have a fundamental misunderstanding." I see absolutely no reason to cite likely ignorance as a reason to relegate something to long discussions about nothing. I spend my life trying to avoid that trap.

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This is a simple can't be proven.We can't prove that apparant randomness isn't in fact deterministic and it immediately follows that apparantly random events could be dependent.

chez

[inlemur]

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[ QUOTE ]
This seems to me like a philosophical question rather than one that can be proven or shown empirically. A similar situation occurs in statistical mechanics, where the fundamental postulate is that all microstates occur with equal probability. This assumption leads to models that accurately describe real physical systems, but the postulate itself is unproven.

[/ QUOTE ]

There are big differences between "can't be proven," "can't be proven yet," and "can't be proven because we currently have a fundamental misunderstanding." I see absolutely no reason to cite likely ignorance as a reason to relegate something to long discussions about nothing. I spend my life trying to avoid that trap.

[/ QUOTE ]

When I say can't be proven, I mean that to the best of my understanding it is non-falsifiable and indistinguishable from a simpler model. Using the previous example, it could be that different microstates occur with different probabilities. However, if this is the case, the variation in probability with which they occur is so slight that systems can be modeled as though each microstate occurs with an equal probability. I don't exclude the possibility that either of these models could be more representative of the actual physical phenomenon, but one of them is sufficient to describe any system we have yet encountered and is simpler than the other.

All that aside, as we all know, nothing can be truly proven; the best we can do is develop models which most accurately predict physical phenomena. When a model makes a prediction that is unobservable (and we're kidding ourselves if we think that we can observe the effect of a single particle's quantum state on every other particle in the universe) in addition to all the predictions of some other model, we stick with the simpler model, for reasons that should be obvious.

[m_the0ry]

Yeah this is the locality debate and believe me a lot of words can be said about it.

From what I've been reading there is increasing evidence showing that locality is in fact false and that action at a distance is possible. There have been a few experiments devised to test this hypothesis. You'll never guess what they're waiting on - the LHC. (/joke)

[flipdeadshot22]

[ QUOTE ]
This seems to me like a philosophical question rather than one that can be proven or shown empirically. A similar situation occurs in statistical mechanics, where the fundamental postulate is that all microstates occur with equal probability. This assumption leads to models that accurately describe real physical systems, but the postulate itself is unproven.

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You should probably attempt to learn a little basic QM before handing off such a question to philosophy. Determining probabilities for quantum mechanical systems to undergo a given set of transitions has a fundamental connection to the commutivity of the operators that define such transitions or "events" as DS put it. Commutivity is basically a mathematical statement that expresses our ability to 'observe independent quantum events' (none of this is standard QM terminology, since i'm trying to keep this simple and avoid making my post 5 pages and filled with Latex coding.)

A good example of this is the non-commutivity of the momentum (p) and position (x) operators, which can mathematically be expressed as [x,p]=ihbar. The fact that the right side of the equation is nonzero means that the two operators do not commute, and that once you have performed a measurement and determined the exact position of the particle, you cannot subsequently measure its momentum with any certainty. So getting back to what david was asking, the odds regarding the measurement of position and after that, the measurement of momentum are not independent.

Contrast this to the measurement of the spin of a particle. Spin is a 3 dimensional property of many quantum systems, and has the property that the measurement of the spin in the x, y or z direction, followed by another measurement in a different direction than the first measurement CAN BE considered independent or, mathematically stated for instance [Sz, Sx] = 0. This shows the commutivity of the spin in the z and x directions (this can be generalized to all directions). This means that if we measure the spin of a particle to be up with 100% certainty, we can follow this up with another measurement to see what the spin is in the x direction and obtain a 0% probability that it exists in this state.

[flipdeadshot22]

Just to correct myself in my above post before metric jumps on me, the commutation relation for the Sz Sx spin operators [Sz, Sx] = 0, is incorrect (these operators actually anti-commute)

Also, in case my post was tl;dr, it applies only to scenarios in which we measure two distinct properties of a system, rather than running multiple trials of measuring a single property (such as that of spin in davids OP.) In the case we are determining whether a system is in a spin up or spin down with a 50/50 chance, then yes this is your basic coinflip with no "hidden variables" or deterministic causes.
The usual form of QM does not say anything about these actual deterministic causes that lie behind the probabilistic quantum phenomena. This fact is often used to claim that QM implies that nature is fundamentally random. Of course, if the usual form of QM is really the ultimate truth, then it is true that nature is fundamentally random. But who says that the usual form of QM really is the ultimate truth? (A serious scientist will never claim that for any current theory.) A priori, one cannot exclude the existence of some hidden variables (not described by the usual form of QM) that provide a deterministic cause for all seemingly random quantum phenomena. I think a good example of this is the Bohm interpretation (check out wiki).

[PairTheBoard]

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A priori, one cannot exclude the existence of some hidden variables (not described by the usual form of QM) that provide a deterministic cause for all seemingly random quantum phenomena.

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I thought that was the whole point to Bell's Theorem. That if you assume such a hidden variable it leads to contradictions that can be observed.

PairTheBoard