ksz said:
You're making my head hurt again.
There are massless particles, aren't there? Force-exchange particles whether photons for mediating the EM force or gluons for mediating the strong nuclear force (correct me if I'm wrong) are usually listed as having zero mass. If I recall, the equation for momentum of a massful particle is:
p = mv (mass times velocity)
But for photons, momentum is:
p = E/c (energy of the photon divided by speed of light)
Wikipedia states that "massless objects such as photons also carry momentum..."
See:
http://en.wikipedia.org/wiki/Momentum
So are photons massless? It is not impossible for a massful object to attain light speed?
Pardon me, I should have spoken more clearly. Photons
can have mass, both real and imaginary. When a photon is acting as a mediator particle for the EM field, it can travel at just about any speed. These are more commonly called
virtual photons. The probability of it traveling at a speed other than the speed of light diminishes as it travels farther, though. When a photon is traveling at a speed other than the speed of light, that is when it has mass - real mass if it is traveling slower than the speed of light or imaginary mass if it is traveling faster than the speed of light. Now, this starts to sound like photons really act like the tachyons that we were discussing earlier, and therefore should exist. Well, yes and no. They are still just photons, but there are some processes that cannot be explained unless we assume that they are traveling faster (and in some cases much, much faster) than the speed of light, as least for short distances (and here I mean VERY short distances). This even gets into some of the quantum effects that make electronics at these very small process sizes so difficult. A 45nm process is drawing lines that are only about 400 atoms across. So effects that show up at distances around the diameter of the atom aren't necessarily being effectively canceled out when you get fewer and fewer atom diameters to work with. (Hey, how about that for bringing it back on topic!

)
But, of course, your equations are perfectly correct for photons and massful particles that aren't acting within this particular area of quantum probability. However, there are plenty of examples of force mediator particles that aren't massless, so don't go down the wrong path thinking that all mediator particles must be massless. Just a few examples of massive mediator particles include the W, the Z, the gluon and the pion.
~Shard~ said:
Partly due to E=mc^2 though, mass
increases as you approach the speed of light. If you look at it one way, if you broke the speed of light, you would have infinite mass!

Also, time dilation occurs as near-light speeds. In other words, time does in fact slow down as you approach the speed of light. Lots of fun discussion here!
A common misrepresentation. It's not a matter of your mass changing, at least not the way you would think of it. Your mass, as we commonly think of it, is simply your rest mass, which is the 'm' in that lovely formula that you quoted. Now, the E in that formula is really your rest
Energy. It also doesn't change. Now, what does change is your
total energy. This includes kinetic energy (so it's no wonder that your energy would increase as you go faster).
The catch is that most of us are familiar with the Newtonian form of kinetic energy KE=1/2 * mv^2. However, this only applies if your not moving at some significant fraction of the speed of light. Once you get going really fast, then it's far easier just to look at total energy, which is
E=(mc^2)/SQRT(1-(v/c)^2)
So, as your speed approaches the speed of light, v/c approaches 1, and energy approaches a divide by zero error, or infinity. The other way to say this is that the amount of energy needed to get to 90% of the speed of light would be needed again to get from 90% to 97.5% of the speed of light, and that same amount again would be needed to get to 98.9% from 97.5% of the speed of light, and again from 98.9% to 99.4%. The closer you get the smaller the step you make for the same amount of energy.
How does this tie into time dilation? Well, from your point of view, you're constantly moving faster at a constant acceleration. If that were the case, then you'd get to the speed of light a some finite time. But, due to time dilation, your clock is slowing down, so even though you think you'll get there, you never will. It's said that a photon's clock is stopped, i.e. no time passes for a photon.
Anyway, I'll stop before I make ksz's head explode.
