>I understand. I was trying ask about whether or not, if there were say
> 10^10^10 slits, would the electron go through all of them. Do we know for
> sure?

You can perform the experiment with a thin grid instead of slits and get 
similar patterns.  But 10^10^10 in the traditional top-down way is a googol, 
which is more than we can measure.  I mean, if you're asking "can we measure 
unbelievably large numbers directly", then no, of course we can't.  But 
theories would be pointlessly complicated if we restricted things that have 
no apparent limit to some arbitrary finite number.

> Also, I want the inside of time answer. Right now, in the multiverse, it
> seems like the number of differentiated states may be a very large number,
> but is it infinite? I expect the answer to be no, but I'm no expert.

The answer would not be infinite iff spacetime and mass were both quantized. 
This would restrict the possible number of states of a particle to a finite 
number.  Most theories of spacetime (with the exception of general 
relativity) quantize spacetime entirely, and in doing so quantize velocity 
(independent of relativistic movement), but the theory is inconsistent with 
relativity.  Mass is not known to be quantum, and we may never prove it one 
way or the other.  It is possible, though.

However, I don't understand your objection to an infinite number of states. 
The universe in which we live appears by current measurements to be infinite 
in size (because it is geometrically flat), and will last forever (because 
its expansion is hastening).  Trying to eliminate infinite numbers from math 
is like trying to keep the sun moving around the earth in physics.  It 
complicates prediction, and has no benefit.

I don't agree with the prevailing belief on this list that one can only 
define probability mass over an discrete domain, just in case that's part of 
your objection.


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