Feynman Path Integral - All Possible Paths - Relativity Conflict?

In summary, the conversation discusses the concept of an electron being able to take all possible paths in the two slit experiment and the idea of space/time and distance being treated differently in the path integral formulation. The question of whether this means only one electron is needed for all observations is also raised. The speaker is seeking an explanation for how this reconciles with the finite number of permissible paths in a given time limit.
  • #1
lovatto
3
0
Hello

I have not familiarised myself with the mathematics etc I merely have the conceptual idea that, for example, with the two slit experiement and electron is permitted to take "all possible paths" from the electron gun to the detector screen.

The thought occurred (and as will all thoughts like this it will have obviously occurred to everyone else, I am only after an explanation, I am not claiming to have found a flaw etc)that not all paths are permitted.

An electron is fired at t0 and hits the screen at t1. There is obviously a finite number of permitable paths as the time limit imposes constraints, in that it can't have gone to the andromeda galaxy and back to the screen as there is simply not enough time for the electron to propagate that distance.

Can somebody point out how this is reconciled in the path integral formulation, or whether this exposes a fundamental misunderstanding on my part?
 
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  • #2
I believe the formulation occurs in a four dimensional space/time which has some supporting features for this kind of thing.
The concept of "distance" in space/time is different, it includes time and the speed of light (both squared) subtracted from the sums of squares of the usual three space dimensions, all under the radical.

I'm probably mangling this explanation, but it is something like this means that the idea of space distance alone becomes zero between any two event points and time is treated as an imaginary number so the electron is free to travel "paths" through space/time forward and backward.

While I am mangling things, this raises another question... if one electron can truly take all paths, do we need to have more than one electron? With sufficient paths forward and backward in time and covering all possible paths might it only take a single electron to account for all observations and suggest a reason why they all look alike? Sort of like using a single straw to weave a basket; it might look like a lot of individual straws until you notice how it was made...
 

1. What is the Feynman Path Integral?

The Feynman Path Integral is a mathematical formulation used in quantum mechanics to calculate the probability of a particle moving from one point to another in space and time. It takes into account all possible paths that the particle could take between the two points, including those that may seem unlikely or even impossible. This approach was developed by physicist Richard Feynman in the 1940s and has become an important tool in modern theoretical physics.

2. How does the Feynman Path Integral take into account relativity?

The Feynman Path Integral is based on the concept of spacetime, which combines space and time into a single four-dimensional continuum. This is essential for understanding special relativity, which describes how time and space are relative to the observer's frame of reference. The Path Integral considers all possible paths a particle could take in this four-dimensional spacetime, taking into account the effects of relativity on the particle's motion.

3. What is the "conflict" between the Feynman Path Integral and relativity?

The "conflict" between the Feynman Path Integral and relativity refers to the fact that the Path Integral approach to quantum mechanics is based on a classical concept of spacetime, while relativity is a more fundamental and modern theory. This means that the Path Integral does not fully take into account the quantum nature of reality, which is better described by the principles of relativity.

4. How is the Feynman Path Integral used in practical applications?

The Feynman Path Integral has many practical applications in theoretical physics, including quantum field theory, statistical mechanics, and condensed matter physics. It is used to calculate the behavior of systems at the quantum level, such as subatomic particles, and has been instrumental in developing the Standard Model of particle physics. It is also used in quantum computing and has potential applications in areas such as cryptography and data encryption.

5. Are there any criticisms of the Feynman Path Integral?

While the Feynman Path Integral has been a valuable tool in theoretical physics, it is not without its criticisms. One major issue is that it is a purely mathematical approach and does not provide a physical interpretation of the quantum world. It also does not fully reconcile with other theories, such as general relativity, which describes gravity. Additionally, the Path Integral can be difficult to calculate and interpret, making it challenging to apply to certain systems. However, it remains an important and widely used tool in modern physics.

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