# Feynman's every possible trajectory theory

feynman's "every possible trajectory theory"

does feynman's "every possible trajectory theory," where quantum particles travel through all pths before reaching an endpoint, mean that they also travel into the past?

or faster than light ??

I believe all such cases give small contributions to the action S so that we can teach/learn this in classical enviroment.

nate808 said:
does feynman's "every possible trajectory theory," where quantum particles travel through all pths before reaching an endpoint, mean that they also travel into the past?
The path integral formalism incorporates the 'moving back in time' aspect of anti matter compared to matter.

But you cannot really say that a particle follows every possible trajectory though. It is just that there is a possiblility that the particle has followed a certain tajectory. For each trajectory there is such a probability.

marlon

Hi everybody,

as far as I know, in Feynman' s non-relativistic version of path integral quantum mechanics, travelling back in time is simply prohibited by postulating that these trajectories have zero probability. As for travelling faster than light, it is actually possible in Feynman's theory : consider the case of a free particle whose position x_i is exactly known at an initial time t_i=0. If you calculate the probability of it's being at any other point x at a time t say t= 1 sec, you'll find that it's uniform in space, that is the particle has an equal chance of having drifted away a 1cm from it's starting point or some few hundred parsecs away, thus violating any reasonable physical speed limit. This is esssentialy nothing more than the Heisenberg uncertainty principle : knowing the exact position, you have total uncertainty on the momentum, which thus takes a value from 0 to infinity with equal probability.

We hereby showed that non relativistic quantum mechanics is ... non relativistic :-). I however have no idea whatsoever of the generalization of path integral methods to the relativistic case (quantum field theory), but I' d be curious to here about the "remedy" used in this case.

Bye,

Nicolas

PS : is there a simple way to fit in sketches or equations ? it's my first message on this forum, it feels awkward not to be able to scribble a small graph or something...

Hi Nicolas. Good first post. You can add attachments, thumbnails and write equations in something called Latex or something weird, but I'm not sure how or whether they are available to non-contributors (except attachments - I've done that myself). I should look into it but I'm lazy.

The one question I have in regards to your answer: as far as I see that if [delta]x is zero then [delta]p is undefined, rather than infinite. That is [delta]x * [delta]p cannot be said to be h/2pi any more than any other number. Can the exact position or momentum (i.e. with zero uncertainty) be measured and, if so, is it correct to take 'undefined' to mean 'infinite'?