Feynman sum of histories

[petrushka.googol]

As we are aware Richard Feynman proposed that a particle can take any path in a double slit experiment (albeit hypothetically) but ultimately probabilities resolve to a deterministic pattern (interference pattern).

 

What we know for certain is:

a) Interference exists irrespective of the number of slits (should be greater than 1)

b) Interference exists for electrons, buckyballs etc in addition to photons

 

Then is this model not implicitly deterministic?

 

Although there exist an infinite number of potential pathways for a photon on the incident side of a slit,

the presence of a slit seems to ensure that at least 1 (actually several) photons pass through this?

 

Then how true is the need to consider n histories as opposed to a few more or less certain histories?

 

How indeterminate is this model in essence?

 

Please advise.

[ajb]

Then is this model not implicitly deterministic?

This is just one example of the more general Feynman path integral approach to quantum mechanics. Here all possible paths are included in the calculation of the quantum amplitude, but those closest to the classical path count for more.

[Enthalpy]

The interference pattern has a deterministic prediction, but its observation is statistic. One particle is detected at one place (in the traditional experiment) and shows no pattern at all because it gives a single point, many particles make fringes more recognizeable but always noisy.

 

Interferences exist with a single aperture as well. It's called diffraction, and limits the angle resolution of telescopes for instance.

 

Light interferences were computed before Feynman by summing complex amplitudes - that is, including the phase - over all possible paths; there was no need then to add: paths "of the particle". QM added that other particles behave that way, and Feynman (or someone else?) that this holds if the particles transform meanwhile.

 

To the formulations "the particle can take any path" or "we ignore which one it has taken", I prefer "the particle takes them all" and "indetermination appears when the context forces a particle to decide" for instance at a detector. I'll change my opinion if reading of an experiment that needs it.

[decraig]

As we are aware Richard Feynman proposed that a particle can take any path in a double slit experiment (albeit hypothetically) but ultimately probabilities resolve to a deterministic pattern (interference pattern).

 

Actually, he doesn't. Feynman's QED is about fields, not particles.

 

Now, it is also true that he admits to thinking in terms of particles and talks about particles, then tells us that he has made a slip and that he is prone to do this noticing his mistake.

Edited December 21, 2013 by decraig