Determination of past vs future probability

[Loren Booda]

How is estimating the probability that a future event might happen different from estimating the probability that a past event might have happened?

 

[Pythagorean]

I haven't taken a full fledged quantum class (that's next year for me),
but I know that if I answer, someone will tell me I'm wrong and thus, answer your question, so I'll conjecture purely for your sake...

There's two ways I can think of to look at this. If we look at it theoretically, like say, take a time-dependent schroedinger equation, that it should be exactly the same, just at a different time, t. In this case, you'd have two t's for your limit of integration, t future, and t past.

I think, however, in reality, if an event has already occured, than the probability wave has already collapsed. The event has already occured, so there is no probability attached to it, just a definite.

Unless of course, you haven't observed the event, than it still exists as a probability until you observe it.

 

[Loren Booda]

Both quantum mechanics (concerning microscopic probability) and general relativity (concerning macroscopic probability) are time symmetric. I would guess that excludes wavefunction collapse. Could wavefunction collapse ever occur in reverse?

 

[selfAdjoint]

Quantum mechanics, as the formalism is normally presented, has two kinds of development. The development of the wavefunction when not observed is smooth ("unitary", preserving probability measures). It is therefore reversable.

The other development is the "collapse of the wavefunction" as a result of observation. This is NOT reversable or unitary. Some people are offended by the existence of this awkwardness, and would seek to eliminate it and have an all-unitary physics. To do this leads to the Everett many-worlds theory.

 

[Pythagorean]

Quantum mechanics, as the formalism is normally presented, has two kinds of development. The development of the wavefunction when not observed is smooth ("unitary", preserving probability measures). It is therefore reversable.

The other development is the "collapse of the wavefunction" as a result of observation. This is NOT reversable or unitary. Some people are offended by the existence of this awkwardness, and would seek to eliminate it and have an all-unitary physics. To do this leads to the Everett many-worlds theory.

Have you ever read "In search of Schroedinger's Cat" by Jon Gribbins?

He supports the many-worlds theory. Interesting book.

 

[Loren Booda]

Could memory and prediction be processes time-reversed relative to each other?

 

[moving finger]

The other development is the "collapse of the wavefunction" as a result of observation. This is NOT reversable or unitary. Some people are offended by the existence of this awkwardness, and would seek to eliminate it and have an all-unitary physics. To do this leads to the Everett many-worlds theory.

the many-worlds model is not the only time-symmetric attempt at an interpretation of QM (and not all many-worlds interpretations are necessarily time-symmetric). There are time-symmetric Bohmian models also. Here is just a couple of such papers :

http://arxiv.org/PS_cache/quant-ph/pdf/0210/0210207.pdf#search=%22time%20symmetric%20bohmian%20mechanics%22

http://arxiv.org/abs/quant-ph/0601095

and from a paper entitled "Arrows of Time in Bohmian Mechanics" by Shelly Goldstein and Roderich Tumulka :

Bohmian mechanics is a theory about point particles moving in space according to a law of motion (an ordinary differential equation) involving a quantum mechanical wave function. It is a consequence of this law of motion that in a typical world governed by Bohmian mechanics, observers would observe for the results of their experiments exactly the frequencies predicted by quantum mechanics. Since the theory is time symmetric, arrows of time are grounded in the specialness of the initial wave function. A more complex situation arises in some recently studied relativistic variants of the law of motion: they imply backwards causation, though only in a very special and limited way that is free of causal paradoxes.

And in a time-symmetric deterministic interpretation, estimating probabilities of future events is essentially the same as estimating probabilities of past events - limited only by our epistemic perspective.

Best Regards