# Speed of light and quantum question?

1. Dec 28, 2006

### smileandbehappy

Sorry if I am asking the most stupid question but I am only an a-level student in the UK so don't have that a deep an understanding of physics. However my teacher says that the speed of light is always constant in a vacuum and this can be explained using curved space time and special relativity. I have no problem with this however.

In another part of my course my teacher says that light travels as particles or photons. These photons can take an infinite number paths to get from A to B - however if the particles do not go in a straight line how do they go at a constant velocity? Surely the speed may appear to take longer if the path is a greater one that if the photon takes a more direct path.

If you could explain this to me it would be appretiated.

2. Dec 28, 2006

### StatMechGuy

The first statement, that the speed of light is constant, can be read as "Two people in different inertial reference frames will, when attempting to measure the speed of light, measure the same value." This is where you start getting into Minkowski space and such.

Now, in the other part of the course, they don't take an infinite number of paths, because in the quantum world saying "a particle followed this path" is meaningless. What can be said is that each path contributes to the probability of traveling from one point to another. When you add up the contributions of these paths, they interfere with each other. The photon does not actually travel down every path, but every path that it could possibly take contributes to how the photon actually propagates.

Of course, a photon is not a particle in the same sense as an electron. I would recommend you read the opening section of Rodney Loudon's book "The Quantum Theory of Light" (you can find the actual text on Amazon.com) and maybe this might help you a little.

3. Dec 29, 2006

### Jheriko

You have to be careful when dealing with curved spacetimes, the curvature can make an object which is moving at the speed of light in one place look like it is moving faster or slower from another place. It doesn't actually move any faster though, its an "optical illusion" if you like, created by curved space.

As StatMechGuy states, every possible path contributes to the final distribution for the photon position. I think it is important to note that "every possible path" does not imply any physical limitations for these paths, such as "not exceeding the speed of light", "only going forwards in time" and "always taking the shortest path" etc..

The confusion with this method originates from the word "path" I think. This method employs a functional integral, which conveniently, can be identified with a summation over all possible paths. So there are no real paths and nothing travels down them, they are just tools for computation and visualisation. AFAIK photons don't really go anywhere, its the probability of it being somewhere which moves and changes.

BTW, the question is not stupid. AFAIK lots of people struggle with these concepts... myself included.

Last edited: Dec 29, 2006