Feynman and Time

[prj45]

Can I run something by you all please?

Feynman asks us to believe that calculating where a photon goes involves us suspending our perception of nature, and that only by working out every path it could take are we able to actually work out where it will end up.

We're also told that time slows down the faster things go, so photons travelling near the speed of light experience no time.

Is this why we have to consider every possible path a photon travels to work out where it ends up? Is it because it's got all the time in the universe, and actually does go everywhere, interfering with itself in the world as we perceive it?

[selfAdjoint]

The path integral method of Feynmann is not connected to the time dilation of special relativity. In fact when Feynmann first published his method, it "didn't do" relativity; it applied to non-relativistic quantum mechanics. It was a German physicist, Wick, who showed how to use a mathematical device (replacing t by i\tau plus analytic continuation), to make Feynmann's integrations converge in relativistic spacetime.

[turin]

... time slows down the faster things go, so photons travelling near the speed of light experience no time.

Is this why we have to consider every possible path a photon travels to work out where it ends up?I suspect not. It is my understanding that the photon actually takes all possible paths due to uncertainty. First, we need to decide what we're talking about when we say "photon." If this is an amount of propagated electromagnetic energy, then what is the spread we allow? If we require that the energy is at a definite value, then we arrive at a definite magnitude for momentum. This leads to quite an uncertainty in position. I don't know all that much about it, though.

[jnorman]

you cannot say or know anything about a photon in between the time it is emitted and the time it is absorbed. it is a crazy world.

[TeV]

The path integral method of Feynmann is not connected to the time dilation of special relativity. In fact when Feynmann first published his method, it "didn't do" relativity; it applied to non-relativistic quantum mechanics. Yup!The Feynmann method is excellent for calculation of the result of processes.That was trully example of a quantum physicist's work motto "shut up and calculate!". But if one starts think about details and what happens underneath ,nasty question arrive to his mind.
time-emit-time-emit/emit-time-time-emit/emittime/
This is a little english word palindrom game appropriate to introduce when thinking over Feynman method (read backwards) :smile:

[kurious]

What if the photon physically splits into smaller photons which really do take all the Feynman paths simulataneously?

[ZapperZ]

I think that the one thing that is missing in this discussion about Feynman's path integral method is that this technique has very strong underpinnings based on the CLASSICAL mechanics principle of least action. The Lagrangian/Hamiltonian approach to classical mechanics came logically out of this principle. Unless one spend time to understand that first, then Feynman's path integral method may appear odd or as if it came out of nowhere.

http://www.eftaylor.com/pub/FmaAJPguest5.pdf

Zz.

[selfAdjoint]

Huygen's principle in fact, was said to be its inspiration.

[ZapperZ]

Huygen's principle in fact, was said to be its inspiration.

Actually, the "action" in least action principle can have several meanings. It depends on what quantity in a particular problem that you want to "minimize". In Huygen's and Fermat's least time, it is the time quantity that you want to find the stationary solutions for. Thus, the principle of least action when applied to optics now becomes the principle of least time. This then gives you the classical trajectory of light paths across various index of refraction materials.

Zz.

[prj45]

What if the photon physically splits into smaller photons which really do take all the Feynman paths simulataneously?

Don't think it needs to do that. If it travels at the speed of light through space, but the speed of zero through time then it could go on every path; it's got all the time in the universe to do so. ... ?