Sum of Histories Simultaneous Paths

[PhanthomJay]

OK I'm just starting to read Hawking new book, and am confused already. I'll never get through the book if I don't understand this:

Feynman apparently claims that particles (photons, electrons, carbon molecules), when traveling from A to B, take every possible path to get there...simultaneously.

I've probably misunderstood this, because would this not imply that a photon, traveling at lightspeed from A to B in a 'straight' line (shortest path), would travel faster than the speed of light when taking another path, because it takes a longer path in the same time? I know this is not something new, but can someone clear this up for me?

Thanks.

 

[PhanthomJay]

Bump? I'm just trying to find out if a photon violates its own finite speed when it simultaneously probablistically takes all possible paths to reach its destination, paths that are longer than the geodesic path. Thanks.

 

[tom.stoer]

What Feynman did (and what Hawking repeats) is to translate (his own) rigorous mathematical formulation into colloquial language. But that does not mean that one can invert this procedure and translate blindly eveything back b/c this is somehow like playing Chinese whispers.

In your case I would say that in the exact quantum mechanical formulation the "speed" of the photon is not defined. If you try to play Chinese whispers then 'yes', the photon would "move" with speed unequal c", but again "moving" is not defined as well.

If you calculate expressions for physical processes then you will find that photons always travel with speed = c.

For a better understanding I recommend Feynmans books:
"QED: The Strange Theory of Light and Matter": http://en.wikipedia.org/wiki/The_Feynman_Lectures_on_Physics
"The Feynman Lectures on Physics": http://en.wikipedia.org/wiki/QED:_The_Strange_Theory_of_Light_and_Matter

(it is not my place to criticize Hawking but I am not a fan of his popular writings; I miss statements like "one has to be careful taking this too literally ..." - which would be not a good advertisement, of course :-)

 

[PhanthomJay]

Tom..thank you for the response. I'll have to agree that sometimes Hawking does take a lot of liberties in his writings, without qualifying his statements.

Thanks again.