Double Slit experiment and the path of least Action

In summary, the path integral formulation of quantum mechanics tells us that the photon takes all possible paths, and the amplitude of finding the particle at the detection screen is found by summing up the amplitudes of all possible paths. Even though the classical limit reduces to the principle of least action, this principle does not hold in the quantum realm. The assumption that the photon goes through one slit or the other leads to a contradiction with experiment, so the answer to the question of which slit it went through is "both". Feynman also explains that assuming the principle of least action, there could only be one right path, but this contradicts the fact that the photon takes all possible paths. Furthermore,
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sqljunkey
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Using the principle of least action can you figure out which path the photon took, or which slit it went thru given some initial condition. Or is this not possible and why.
 
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The path integral formulation of quantum mechanics tells you that the photon takes all paths. So to find the amplitude of finding the particle at the detection screen, you have to sum up the amplitudes of all possible paths for arriving there. As Feynman clearly points out in the Feynman Lectures, Vol 3, Chapter 1, the assumption that the photon goes through one slit or the other leads to a contradiction with experiment. So the answer to your question, "...which slit it went through..." is, "both". Feynman showed that the path integral formulation of QM reduces to the principle of least action in the classical limit, because only along the classical path do the amplitudes add up constructively. Everywhere else they cancel out.
 
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But assuming this principle, there could be only one right path. if the photon had to go through both slits that means one of these trajectories was longer than the other one and would take more time and more action. and we know light takes the path of least action and least time.

Unless we are assuming that the photon, when we aren't looking, breaks apart into this probability distribution wave-like glob and travels through these slits, while interacting with itself and then when it meets the screen collapses into a measurable quantity.

But also having all these possible trajectories traveled, and interacting destructively or constructively with each other violates some other principles, because some of these paths would be going to the end of the universe and back just to get eliminated by destructive interference.

What I am thinking about this principle of least action is that if I know the initial position and the final position of the photon i can calculate it's trajectory. And it's either going to be one of these holes, because I have to take the minima of the action.

Correct me if I'm wrong. :3
 
  • #4
sqljunkey said:
if I know the initial position and the final position of the photon...
You also have to know the times at which the photon is at these positions. It’s not enough to say “there’s a dot on the film here”, you also have to be able to say when that dot appeared. You can do that for the detection event but not the emission event.
 
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  • #5
so If I measure the photon at the source, way before it travels through those slits, I would still destroy the interference pattern ?
 
  • #6
sqljunkey said:
But assuming this principle, there could be only one right path. if the photon had to go through both slits that means one of these trajectories was longer than the other one and would take more time and more action. and we know light takes the path of least action and least time.
Let's say you shine a beam of light trough long cylinder of glass. Let's say that cylinder is so long that the path around cylinder trough the air would take less time for light to travel. Would you expect that light will go around cylinder just because this path takes less time to travel?
 
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zonde I'm not going to make physics up and tell you that the photon is going to knowingly make an effort to bend around that rod of glass to shorten it's trajectory in time. I don't know.

But it's certainly an alternative idea to a shy particle that quickly turns into a distribution wave-like glob when people aren't looking at it and then back into a particle again when people are looking.
 
  • #8
sqljunkey said:
But it's certainly an alternative idea to a shy particle that quickly turns into a distribution wave-like glob when people aren't looking at it and then back into a particle again when people are looking.
Idea that quantum particles are somehow switching between particle like behavior and wave like behavior is simply flawed. If this idea is hunting you, you can try to adopt Bohmian interpretation to get rid of it.
 
  • #9
sqljunkey said:
... And it's either going to be one of these holes, because I have to take the minima of the action.
Correct me if I'm wrong. :3

You're wrong. As I stated earlier, and Feynman eloquently explains, the assumption that the photon goes through either one slit or the other leads to a contradiction with experiment, so it cannot be true. Again quoting Feynman, "You'll have to accept it. It's the way nature works. If you want to know how nature works, we looked at it, carefully. Looking at it, that's the way it looks. You don't like it? Go somewhere else, to another universe where the rules are simpler, philosophically more pleasing, more psychologically easy."

The principle of least action (or least time) only holds in the classical limit.
 
  • #10
sqljunkey said:
But it's certainly an alternative idea to a shy particle that quickly turns into a distribution wave-like glob when people aren't looking at it and then back into a particle again when people are looking.
The quantum mechanical explanation for the double-slit experiment isn’t anything like that.
 
  • #11
sqljunkey said:
I don't know.

But it's certainly an alternative idea ...

The issue here is that you don't know enough about the physics to be coming up with fanciful ideas. There are a lot of variations around the double slit, and without being familiar with those, you will end up with "alternatives" that are contradicted by experiment.

For example: read up on the double slit with polarizers. In this variation, interference appears (or not) depending on the relative setting of polarizers over each slit. This contradicts the notion that a particle goes through one slit or the other fairly convincingly.

http://sciencedemonstrations.fas.ha...-demonstrations/files/single_photon_paper.pdf
 
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  • #12
sqljunkey said:
Using the principle of least action can you figure out which path the photon took, or which slit it went thru given some initial condition. Or is this not possible and why.
QED tells you that the idea of a "path of a photon" doesn't make sense. That's why the action principle is applied to fields rather than to "trajectories" in the evaluation of QFT path integrals: It's derived from applying the saddle-point approximation to the path integral, which provides a formal expansion in powers of ##\hbar##, i.e., is a systematic expansion around the "classical field-theory limit", i.e., in this case Maxwell classical electrodynamics.
 
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1. What is the Double Slit Experiment?

The Double Slit Experiment is a classic experiment in physics that demonstrates the wave-particle duality of light. It involves shining a beam of light through two parallel slits and observing the resulting interference pattern on a screen. This experiment has been used to study the nature of light and the behavior of particles at the quantum level.

2. How does the Double Slit Experiment relate to the path of least action?

The path of least action is a principle in physics that states that particles will follow the path that minimizes the action, which is a measure of the energy required to move the particle. In the Double Slit Experiment, the path of least action is observed as the interference pattern on the screen, where the particles take the path that results in constructive interference and the brightest spots on the screen.

3. What is the significance of the Double Slit Experiment in quantum mechanics?

The Double Slit Experiment is significant in quantum mechanics because it demonstrates the wave-particle duality of light and the probabilistic nature of particles at the quantum level. It also shows that the behavior of particles can be influenced by the act of observation, leading to the development of the famous observer effect.

4. Can the Double Slit Experiment be performed with other particles besides light?

Yes, the Double Slit Experiment has been performed with other particles such as electrons, protons, and even large molecules like buckyballs. The results have been consistent with the wave-particle duality theory, further supporting the principles of quantum mechanics.

5. What are some real-world applications of the Double Slit Experiment?

While the Double Slit Experiment is primarily used for scientific research and understanding the behavior of particles, it also has practical applications. For example, it has been used to develop technologies such as electron microscopes and particle accelerators. Additionally, the principles of the experiment have been applied in fields like optics and quantum computing.

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