We're used to the notion of the relativity of speed. If you're driving fast, a relatively slow-flying insect will go "splat" on the windshield. Some sort of "absolute speed" is meaningless; all that matters is the bug's speed relative to the car's speed. So something like a mile per hour doesn't mean anything absolute; it's only meaningful when comparing the motion of one thing relative to another.
Well, in relativity it turns out that a lot of things are like that. Not only is a mile per hour relative, but a mile is relative, and an hour is relative. There is no absolute hour sitting somewhere; it's relative to the observer. Other relative things include energy, momentum, and (relativistic) mass. That's most of the Special Theory of Relativity; the rest is some math and the observation that the speed of light (c) is always the same. (GR adds the idea that gravity and acceleration are equivalent, and a hell of a lot more math.)
When people start to understand this, if they're smart, they'll usually come up with the same question and ask, "Does time really slow down for the guy in the spaceship, or does it just seem to do so to us?" That's actually a very deep question, but the answer is simple: There is no really. There is no absolute time such that one can say that this one is real and that one is seeming. The only meaning of times and distances are what can be measured, what seems to an observer.
When people don't get relativity, it's often because of inability or unwillingness to understand that. So when you try to explain time dilation or Lorenz contraction, they think there's something about speed that somehow makes the time go slower or squashes the object. Then they reject the idea as ludicrous. (That idea actually existed in theories of the luminiferous aether that predated relativity, and it was ludicrous.) But that's not what relativity is saying at all.
Sometimes, to make people happier, I point out that there are things in relativity that might be called absolute, and so relativity just shifts our ideas of what is relative and what is not to other things. The speed of light, c, is always the same. It's the only speed that is always the same, prompting some people to say that maybe we shouldn't think of it as a speed. Distances and times are different for different observers, but when you put distances and times together in a particular way, you get something called the interval that all observers can agree upon. Similarly, while energies and momenta differ, if you put those two together in the same way, you get something called the rest mass which does not change. If you solve that equation for objects with a momentum of 0, you get the famous E=mc^2
Which leads us to a perspicacious (though not quite accurate) comment in the OP.
Well, sort of. At c, the aforementioned equation gives a rest mass of 0. So light doesn't have a rest mass and is what you might call "pure" energy and momentum.dj357 wrote:It follows from Einstein that as you approach the speed of light your mass increases, but is this actually true? e = mc2 tells us that for an object to reach 'c', the speed of light, you need infinite mass or infinite energy, but would it be possible for light to simply be mass that exists as pure energy...?
This indicates another way of seeing that you can't accelerate an object with rest mass to c. No matter how fast you go, when you combine the energy and momentum in that way, you'll always get a rest mass that is constant and not zero (well, if it's a rocket, your rest mass will go down as you throw mass out the rockets, so let's just imagine a capsule in a really big rubber band). In order to go at the speed of light, the rest mass has to be zero. So not only will going faster and faster not get you to c, but in an important way will not get you any closer to c.
