Probability over universe = 0 or 1?

[nomadreid]

If you were to extend Born's Rule to sum or integrate over all points in space-time, would you necessarily get only either zero or one? Otherwise put, is it true that "anything that can happen will happen"?

 

[rootone]

The fact that something is possible does not make it inevitable ... unless you happen to believe there are a infinite number of actual physical Universes.
I don't think there are an infinite number of actual physical Universes.
So, IMO ... this is not true.

 

[phinds]

Sinc

The fact that something is possible does not make it inevitable ... unless you happen to believe there are a infinite number of actual physical Universes.
I don't think there are an infinite number of actual physical Universes.
So, IMO ... this is not true.

I agree.

 

[StevieTNZ]

"Everything that can happen does happen" is the motto of Brian Cox and Jeff Forshaw's book "The Quantum Universe" in which they advocate the many-worlds interpretation (I believe): http://www.amazon.com/dp/0241952700/?tag=pfamazon01-20

 

[rootone]

I haven't read it, but I don't have any problem with the authors as being fairly good at pop-sci presentations.
I am guessing that the subtitle does not represent the content of the book that accurately , and is more of a catchphase inserted by the publishers as a selling point.

Think about it though.
It is certainly possible that an as yet unknown asteroid could strike Earth in 10,000 years time and cause a mass extinction.
It is more probable that this will not happen.

Either it does happen or it doesn't.
The only way to be sure for certain that this possibility does in fact occur is that there would be an infinite amount of actual Universes.
Not hypothetical mathematically possible Universes, but actually real physical ones.

I think Occam's razor can then be applied (although it's not a law), but it does suggest to me anyway, that a proposal which requires infinite copies of nearly identical physical universes is getting a bit excessive as an explanation for what we see around us.

 

[phinds]

Again, I agree.

 

[nomadreid]

Thanks to all who responded. The consensus is clear... Not many MWI proponents out there, apparently. Would the answer have been the same if I had restricted the question more -- say, to pure states?

 

[bhobba]

Would the answer have been the same if I had restricted the question more -- say, to pure states?

Extend Born's rule to integrate or sum all points in space-time? Born's rule has nothing to do with integrating or summing all points in space time so what you mean by extending it has me beat.

Here is the statement of Born's Rule - Given an observable O there exists a positive operator of unit trace P, by definition called the state of the system, such that the expected outcome E(O) is Trace (PO).

Its a law of nature applying to all points of space time - nothing to do with integrating or summing over them.

Thanks
Bill

 

[nomadreid]

Thanks, Bill. Interesting that you are the first one to address the first sentence, rather than the second one, of my question.
Born's rule gives E(O) of the state at a single point in space-time. However, one can also ask what the probability is for the observable with respect to a given eigenvalue inside a given interval (that is, what is the probability that a given value will occur in that interval), and/or the expected value for that observable inside the interval. Granted, these would no longer Born's rule, but would be extensions of it. These calculations would involve a sum over the points in the interval.

 

[bhobba]

However, one can also ask what the probability is for the observable with respect to a given eigenvalue inside a given interval (that is, what is the probability that a given value will occur in that interval),

If that what you are thinking of then no extension is required. One can in general find observables for that sort of thing. But that is external to the system - you are considering the universe which, by definition, has nothing external to it.

Thanks
Bill

 

[nomadreid]

Hm... Very good point, Bill. Then, to modify (fudge) the question: for one of these observables is it the case that either
there exists a sequence of intervals I_i so that for all j, I_j⊂I_j+1 , and the corresponding sequence of probabilities (P_iover I_i) converges to 1,
Or
All such sequences of probabilities for that observable are uniformly equal to zero (e.g., as in the case of a contradiction).

Or a similar formulation that would permit the consistent formulation -- whether or not one agrees with it, or whether or not it is the case--of those many worlds interpretations who claim that anything that is possible is also necessary.

 

[tzimie]

Check this:
http://arxiv.org/abs/1008.1066
Born in an Infinite Universe: a Cosmological Interpretation of Quantum Mechanics

 

[nomadreid]

Thanks, tzimie. Looks interesting; I have downloaded it and will be reading it soon.