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.

[jason1990]

I think it would be fair to say that the standard notion of independence does not typically apply to quantum phenomena. The standard notion is that A and B are independent if

P(A and B) = P(A)P(B).

But in a quantum setting, P(A and B) is not well-defined in general. The uncertainty principle prevents us, in many cases, from measuring quantum properties simultaneously. Moreover, the statistical properties of sequential measurements depend, in general, on the order in which the measurements are done.

[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]

[ 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.

[oe39]

it seems like a global hidden variable theory would be hard to disprove?

[chezlaw]

[ QUOTE ]
[ 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 ]
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]

[ QUOTE ]
[ 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.

[Metric]

If two systems are quantum mechanically entangled, then probabilities will be dependent on one another. If two systems are "seperable" (not entangled), then there exist at least some observables for which probabilities will be independent.

For increasingly large (multi-part) systems, an increasingly large fraction of the state space is dominated by entangled states. The universe as a whole is certainly described by an entangled state.

[yukoncpa]

[ QUOTE ]
If two systems are quantum mechanically entangled, then probabilities will be dependent on one another. If two systems are "seperable" (not entangled), then there exist at least some observables for which probabilities will be independent.

For increasingly large (multi-part) systems, an increasingly large fraction of the state space is dominated by entangled states. The universe as a whole is certainly described by an entangled state.

Post Extras


[/ QUOTE ]
Doesn’t entanglement entail action at a distance? If so, Metric, I thought this was something that you are arguing against.