To say that a

particle with rest mass can travel

*at the speed of light* is

incorrect. If you consider a

force that is acting on this particle,

classical physics says the particle will simply gain

kinetic energy, and therefore move more and more quickly.

Einstein's

theory of special relativity showed this to be a 'low-velocity

approximation'. The relation

E=mc^2 illustrates that

energy and

mass are the same thing (they're both energy! ..so rest mass is just bound-up energy!). The reason classical physics never caught on is because c^2 is

LARGE, and at low

velocities, the kinetic energy (divided by c^2) of things never measured up to the rest mass of things.

*But,* as you get closer to the

speed of light, the KE/c^2 is beginning to be

comparable to the particle's rest mass, and the description of the particle's

motion set down in classical physics becomes more and more

inaccurate. What's actually happening is that as you're watching the force act on the particle, it appears that instead of increasing the particle's kinetic energy, the particle simply

appears to grow more massive, and what you see is a particle that is growing in apparent mass while its velocity is increasing at a rate less and less given that same force. The

limit (which is

approached, and NOT HIT) of the particle's increasing velocity is the speed of light. When the particle is very (very, very, very) close to the speed of light, its rest mass is extremely small compared with its 'kinetic mass' or KE/c^2. In this case, the particle is starting to act more like a

massless particle (but not quite), and to talk about the old notions of mass and kinetic energy really doesn't serve our purposes anymore. In this situation,

physicists simply talk about 'the energy' of the particle, for instance, the people at a certain

particle accellerator might boast that they can produce beams of 20

GeV electrons (GeV, or giga-

electron-volt is simply a measure of 'the energy', and 20 of those is much much bigger than the humble rest mass of the electron, about a half MeV or mega-electron-volt, and in this case, the electron is moving damned fast, almost-but-not-quite the speed of light). Perhaps the particle is going 99.99999% the speed of light. In fact,

particle physicists sometimes talk about 'how many nines' there are in that above

percentage. For a particle with rest mass, the percentage can gain nines on the end, but never equal 100%.

So, the energy at which this classical-is-OK to classical-is-WRONG transition happens is given as the ratio of 'the energy' to the rest mass grows large. Consider that with a massless particle, that ratio is ALWAYS

infinite, no matter what the energy of the particle is, and that's why its spedometer always seems to be pegged at the speed of light. Also consider that for particles with rest mass, it would take an infinite amount of 'the energy' to make the rest mass completely

negligible, and the particle's velocity equal-to the speed of light.

I don't know about you, but I don't have an infinite amount of energy lying around.. I don't even thing

the Universe could get its act together for that. So, particles with rest mass are forever reveled to the LESS THAN AND NOT EQUAL TO

c classification.