Does Feynman's path integral ignore alternative histories?

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Summary:

Does Richard Feynman's multiple histories ignore alternative histories?
Summary: Does Richard Feynman's multiple histories ignore alternative histories?

Did Richard Feynman's multiple histories (https://en.wikipedia.org/wiki/Multiple_histories) ignore the existence of other alternarive histories or paths?

I ask this referring to this comment from this page: http://sciencechatforum.com/viewtopic.php?f=46&t=16239

"The Feynman path integral assumes that only where you don't observe it the particle could be trying all different ways to get from A to B. If it INTERACTS with anything along the way, like a detector or a barrier with slits to pass thru or just another particle then where it went is NAILED DOWN. The alternatives do not exist --- the path integral formula ignores them"

But is this completely right? Are alternative histories completely eliminated in Feynman's sum up over histories?
 
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  • #2
PeterDonis
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Are alternative histories completely eliminated in Feynman's sum up over histories?
You seem to be confusing yourself by using the term "histories" in two different ways.

A path integral is an integral over all the possible paths that lead from a given starting point to a given ending point. So if by "histories" you mean "different possible paths from a given starting point to a given ending point", then obviously the path integral includes multiple histories. That's where the term "sum over histories" comes from, after all.

However, when doing a particular path integral, you hold the starting and ending points fixed. That means any particular path integral is computing the amplitude for some particular starting state to turn into some particular ending state at some particular event in spacetime. Those starting and ending points are direct observables--for example, you might compute the amplitude that an electron and a positron, created in an accelerator with such-and-such energy, will annihilate each other and turn into a pair of gamma rays with such-and-such energy going in such-and-such directions. So if by "histories" you mean "different possibilities for direct observables", any particular path integral does not allow for multiple histories in that sense, because to even define the integral you have to specify the starting and ending points.

You can consider "alternate histories" in the sense of different possible starting or ending points. For example, you could compute the amplitude that an electron and positron will annihilate each other and turn into various possible things: a pair of gamma rays, a pair of muons, a pair of D mesons, etc. Each of these different possibilities will be a different path integral, so you can consider "multiple histories" in this sense by doing multiple path integrals.
 

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