Sum over histories and double slit?

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Discussion Overview

The discussion explores the relationship between Feynman's sum-over-histories approach to quantum probability and the double slit experiment. It addresses concepts such as probability waves, interference, and the nature of quantum particles in relation to classical paths.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions how Feynman's sum-over-histories approach integrates with the double slit experiment, particularly regarding the nature of probability waves and their interference.
  • Another participant suggests that the sum over histories can be applied by adding classical paths and calculating the amplitude, noting the importance of the absolute square of the amplitude for determining probabilities.
  • A subsequent reply clarifies that the absolute square of the amplitude represents the probability of the electron arriving at a specific spot on the detector, not the electron passing through both slits.
  • Further contributions affirm that the interference pattern observed can still occur even when electrons are fired one at a time, emphasizing that summing over paths does not imply the electron physically traverses both slits.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of the probability associated with the electron's behavior in the double slit experiment, particularly regarding the concept of the electron "going through both slits." The discussion remains unresolved with multiple competing interpretations present.

Contextual Notes

There are unresolved aspects regarding the normalization factor in the sum-over-histories approach and the definitions of proxy waves versus Feynman's probability waves. The discussion does not clarify these limitations fully.

Who May Find This Useful

Readers interested in quantum mechanics, particularly those exploring foundational concepts in quantum probability and the implications of the double slit experiment.

beatlemaniacj
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I was recently studying Feynman's sum-over-histories approach to quantum probability. I also was reading an interesting paper on the double slit experiment. How do these two work together. Do some of the probability waves not have a out of phase partner to interfere with itself?

On a related not, what's the difference between the proxy wave, and Feynman's probability waves.

If the proxy wave is fictitious, how do atoms resist other atoms passing through it.

I know this is a lengthy question but please try to answer.
 
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The easiest way to do the "sum over histories" for the 2 slit experiment, is to take the classical paths (2 of them) and just simply add up e^iS/h for the 2 different paths to get an amplitude. The probability is of course the absolute square of the amplitude. There is of course a normalizing factor, but that can be sometimes annoying to get, and I can't remember the details of that for the 2-slit experiment at this moment.
 
And that value (absolute square of the amplitude) would be the probability of the electron going through both slits?
 
No, the probability that the electron arrives at that spot in the detector. There is no probability for the electron "going through both slits".
 
This still applies in the case of an interference pattern when only one electron is fired.
 
Yes it does. You sum over both paths, but that doesn't mean the electron physically moves through both slits.
 

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