wavefunctions problem

[Andeh]

Please correct me if I don't have my facts straight at any point in this...

 

>an object's wavefunction expresses the probability of finding that object in a particular location.

 

>the probability of finding an object in a particular location increases when that location is observed longer. I.e. the probability of me teleporting to Mars at some time in the next ten minutes is very low, compared to the probability of me teleporting to Mars some time in the next ten million years.

 

>Therefor, the shape of a wavefunction (and general behavior of it's object) will vary dramatically depending on the length of the time-frame. Across an infinate time-frame, all events, no matter how improbable, would have the same probability. This is clearly not true. Does this imply that there is something confining wavefunctions to a certain timeframe. Or does it imply that our model of wavefunction is incorrect, or that our model of time is incorrect?

 

Basically, how can you have just raw probability without the element of time--and so what dictates that element of time.

[timo]

>an object's wavefunction expresses the probability of finding that object in a particular location.

By definition the WF contains all information about the particle; that does indeed include probabilities for finding it at certain locations

 

the probability of finding an object in a particular location increases when that location is observed longer. I.e. the probability of me teleporting to Mars at some time in the next ten minutes is very low, compared to the probability of me teleporting to Mars some time in the next ten million years.

The probability for any event to happen within the next 20 minutes is larger or equal to the probability for the same event to happen within the next 10 minutes. That has nothing to do with quantum mechanics and wave functions, though. The probability for location of an object is to be understood as an instantaneous one, not an integrated one.

 

Therefore, the shape of a wavefunction (and general behavior of it's object) will vary dramatically depending on the length of the time-frame.

Not sure what you mean there. Certainly, the characteristic behavior of cheese on the time scales of minutes (lay around, do nothing) qualitatively differs from that on the time scale of years (rot).

 

Across an infinate time-frame, all events, no matter how improbable, would have the same probability.

No.

 

This is clearly not true.

Yes.

 

Does this imply that there is something confining wavefunctions to a certain timeframe.

Dunno, I didn't understand your argument.

 

Or does it imply that our model of wavefunction is incorrect, or that our model of time is incorrect?

I think it means that your line of reasoning, which I cannot really follow, is flawed.

 

Basically, how can you have just raw probability without the element of time.

The wave function is (often) given as a function f(x,t). That does include time. I don't quite see how the statement "the chance to roll two equal numbers with two dice is 1/6" would require the element of time, though.

[Andeh]

 

 

The probability for any event to happen within the next 20 minutes is larger or equal to the probability for the same event to happen within the next 10 minutes. That has nothing to do with quantum mechanics and wave functions, though. The probability for location of an object is to be understood as an instantaneous one, not an integrated one.

 

Doesnt it have to do with quantum mechanics and wave functions, since wavefunctions are probability amplitudes, and probability (at least regarding location) is dependant on the timescale?

 

And what do you mean by instantaneous vs. integrated?

[timo]

Forget about "integrated vs. instantaneous". I was assuming you were having a particular form of experiment in mind. The key problem is: The wave function f(x) at some instant tells you the probability to find a particle at a certain location in case you look for it in this instant. You, however, are speaking about probabilities over a period of time - which is why I said "integrated", since that is usually what you do in some way if you extend something instantaneous over a time interval. The process of "observing" a particle in the context of QM is -to my knowledge- an instantaneous event (*), not a process that extends over some time interval. Therefore, it has no duration. Therefore, you'd have to define what you mean by "observe longer"

 

(*) There is an interesting issue with this statement: QM is supposed to end in classical physics provided one looks at it in the proper limit. Since observations in classical physics are intervals that extend over some time, this raises the question how you'd get from the instantaneous event to the time interval. This is in fact exactly the point that is most unclear in your post. As indicated, I don't know the answer to this question. Since the measurement process is QM is not understood very well (at least according to the people of our mathematical physics group) it may be that this is in fact unknown - but it is more likely that I just don't know the answer.