Sum over histories and double slit?

In summary, the conversation discusses Feynman's sum-over-histories approach to quantum probability and its relation to the double slit experiment. The difference between the proxy wave and Feynman's probability waves is also mentioned, with a question about how atoms resist other atoms passing through it. The easiest way to calculate the probability in the 2 slit experiment is also briefly explained, with a clarification that there is no probability for the electron to physically go through both slits. The conversation concludes by mentioning that this method still applies in the case of an interference pattern with only one electron being fired.
  • #1
beatlemaniacj
49
0
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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  • #2
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.
 
  • #3
And that value (absolute square of the amplitude) would be the probability of the electron going through both slits?
 
  • #4
No, the probability that the electron arrives at that spot in the detector. There is no probability for the electron "going through both slits".
 
  • #5
This still applies in the case of an interference pattern when only one electron is fired.
 
  • #6
Yes it does. You sum over both paths, but that doesn't mean the electron physically moves through both slits.
 

1. What is the concept of "sum over histories" in relation to the double slit experiment?

The concept of "sum over histories" refers to the idea in quantum mechanics that all possible paths of a particle must be considered when calculating its behavior. In the double slit experiment, this means that the particle does not take a single path, but rather exists as a superposition of all possible paths. This superposition then interferes with itself, creating the observed interference pattern.

2. How does the double slit experiment demonstrate the principle of superposition?

In the double slit experiment, the particle exists as a superposition of all possible paths. This means that it simultaneously passes through both slits and interferes with itself, creating an interference pattern on the detector. This demonstrates the principle of superposition, where a particle can exist in multiple states or locations at the same time.

3. What role does observation play in the double slit experiment and the concept of sum over histories?

In the double slit experiment, observation collapses the superposition of all possible paths and forces the particle to behave as a single entity, either passing through one slit or the other. This is known as the collapse of the wavefunction. In the concept of sum over histories, observation is also important as it determines which path the particle takes, and therefore affects the overall interference pattern.

4. How does the double slit experiment support the idea of wave-particle duality?

The double slit experiment is a classic example of wave-particle duality in quantum mechanics. The experiment shows that particles, such as electrons, can exhibit both wave-like and particle-like behavior. The interference pattern observed on the detector is characteristic of a wave, while the particles themselves behave as discrete entities when they are observed or measured.

5. What are some real-world applications of understanding the concept of sum over histories and the double slit experiment?

Understanding the concept of sum over histories and the double slit experiment is crucial in the development of new technologies, such as quantum computing, where the principles of quantum mechanics are utilized. It also has applications in fields such as cryptography, medical imaging, and materials science. Additionally, the double slit experiment has been used to test the foundations of quantum mechanics and has played a significant role in our understanding of the nature of reality.

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