Question

I'm in a freshmen level physics class now, so I don't know much, but something I heard today intrigued me. My TA was talking about how at the research facility he worked at, they were able to accelerate some certain particle to "99.99% the speed of light". I said why not 100%, and I didn't quite understand his explanation, but he said it wasn't possible. This confused me. Since the speed of light is a finite number, why can we go so close to its speed but not quite?

Edit: I read all the answers, and I think I'm sort of understanding it. Another silly question though: If we are getting this particle to 99.99% the speed of light by giving it some sort of finite acceleration, and increasing it more and more, why cant we increase it just a little more? Sorry I know this is a silly question. I totally accept the fact we cant reach 100%, but I'm just trying to break it down. If we've gotten so close by giving it larger and larger acceleration every time, why cant we just supply it with more acceleration? And how much of a difference is there between 99.99% the speed of light, and the speed of light? (I'm not really sure if "difference" is a good word to use, but hopefully you get what I'm asking).

Answer 1

There are (at least) two explanations, kinematical and dynamical.
Dynamics

When you want to make an object accelerate you have to use energy to produce force on the object. The force is (this equation is not really correct in SR but it suffices for our purposes) Now the point of SR is that the mass that the object seems to be having when it is moving with respect to you is not constant. It goes like where is the objects invariant mass (as seen from its own rest frame) and is the Lorentz factor. Now . So this means that the (apparent or relativistic) mass of the object becomes arbitrarily large and you would need an infinite amount of energy to get to the speed of light.
Kinematics

From the kinematical point of view it all boils down to relativistic concept of velocity. In SR when you want to change particle's speed you have to boost it. This is described by a certain Lorentz transformation.

Now its useful to move to the dual point of view. Instead of saying that you boost the particle you can just change your reference frame in the opposite way. So instead of giving the particle speed in direction you will look at the particle at rest from a reference frame that has speed in direction . This transformation is also described by a Lorentz transformation.

Now every Lorentz transformation preserves the relations , and (the middle one is actually Einstein's postulate on invariance of speed of light in every inertial frame). That means that if your velocity is less than speed of light it will be so in any reference frame. And also that if some particle was once going slower than speed of light, it will always do so