Darren New wrote:
> summing in smaller and smaller and 
> smaller probabilities of something happening. 

BTW. By this, I mean that you say "How can the electron get from A to B?"

Well, it could go in a straight line. That's the main factor.

Or it could absorb some photon from somewhere else on the way at point C in 
between, change direction, and end up at B.

Or it could emit a photon at point C, and end up at B.

Or it could absorb a photon at C, emit one at D, and end up at B.

Etc etc etc.

Each emit/absorb interaction happens with about the probability of 1/137, 
which is the "charge" of the electron. So you don't have to go too far to 
get a good number of decimal places. That last step adds about one part 
error per 18,000, so one decimal place out of 5 or so. (Quarks have a much 
higher "charge", like 1/8 IIRC, so you have to run the calculation out lots 
of steps before you get similarly good results arithmetically.)

But if you add up *all* those probabilities, for *every* possible C or D or 
etc, everything goes to infinity. If you stop after any number of 
interactions (i.e., assume space is discrete), the math says you get a 
really close answer. But if you add up *all* theoretical interactions 
(taking the limit as the distance between C and D goes to zero), the answers 
make no sense.

Now I know what you're saying. Even if space was quantitized to one inch, 
assuming an open universe, there should be places sufficiently far away from 
your starting point that the probability is arbitrarily close to zero.

However, it all works out OK if space is both quantitized and finite; then 
you get quantitized probabilities as well.

Or maybe the probability actually does go to zero far enough from the 
electron. I'm not sure what relativity says about electrons moving faster 
than light over significant distances. It may be that sufficiently far from 
the atom, the probability of the electron being there is absolutely zero, 
just like the probability of two electrons in the same quantum state being 
in the same place is absolutely zero.

I'll have to ask a friend I know who is a practicing theoretical physicist.

-- 
Darren New, San Diego CA, USA (PST)
   Serving Suggestion:
     "Don't serve this any more. It's awful."

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