Re: How can a massless particle exist?

Andrew,

Good question. To begin with, massless particles do exist, and are certainly detectable. The one you are probably most familiar with is the photon, which makes up light and other electromagnetic radiation. In fact, your eyes are detecting photons right now as you read this message. The other massless particle that we know of is the gluon, which carries the strong nuclear force that holds quarks together.

You ask: "Becuase matter and energy are interchangable would it not also have to have no energy?"

The answer is, not exactly. Einstein's special theory of relativity states that the total energy of a particle with mass is:

           mc^2
E = -----------------
    sqrt[1 - (v/c)^2]

Here, m is the rest mass, i.e. the mass of the particle when it is at rest. v is the velocity, and c is the speed of light. When we do a series expansion of the above equation, we get:

E = mc^2 + 1/2 mc^2 (v/c)^2 + ...
 
  = mc^2 + 1/2 mv^2 + ...

What does this tell us? If v equals zero, the equation becomes the famous E=mc^2, which states that a particle at rest has a total energy equal to its mass times the speed of light squared. If you completely annihalated this mass, this is how much energy would be obtained.

Now, if you are familiar with Newtonian mechanics, the second term should look awfully familiar. It is the expression for the kinetic energy of a moving body. In relativity, we group the parts of the above equation into three terms, all in units of energy:

E = M + P

Where:

E                          : total energy
M = mc^2                   : rest energy (mass)
P = 1/2 m v^2 + ... = cp   : kinetic energy (momentum)

Now, if a particle (such as a photon) is massless, the term M goes to zero. So we end up with simply:

E = P

This means that all of the particle's energy goes into motion. There is no rest mass because it is impossible to ever view the particle at rest (becayse it travels at the speed of light, c).

It has taken a long time to get here, but what I hope you can see from this is that while a particle with non-zero mass must also have non-zero energy (even when P equals zero), it is possible for a particle with energy not to have any mass (i.e. M equals zero). I hope this helps clarify things for you.

A nice starting point on the web for further study of relativity is Dave's relativity page, which has a pretty good overview of special relativity topics, and links to other resources. Good luck!

Sam