Imagine you are on a spaceship traveling 10 miles per hour less then the speed of light. If you fired a gun in your direction of travel, what would happen?
Probably shouldn’t be in GQ because there can’t be a factual answer. But my guess is that somewhere in the barrel the bullet will suddenly achieve near-infinite mass, destroying the ship you are traveling on.
From your viewpoint it would look exactly as it would on Earth or anywhere.
From the viewpoint of someone who saw you moving 10 mph below c you use the special relativity addition of velocities formula
w = (u+v)/(1+uv/c[sup]2[/sup])
where u = c-10 mph and v = the velocity of the bullet (as measured relative to the gun)
It will be less than c which is I assume what you were asking about.
Since the gun/bullet are, relatively speaking, standing still - the bullet will move within the spaceship at its ‘normal’ speed - it would not accelerate in excess of its containers speed.
damn, ninja’d by an oldguy!
You’ll see the bullet leave the gun at the speed you would expect. A stationary observer would see everything on the ship happening in slow motion so it would seem like the bullet is barely travelling faster than you are.
Why couldn’t there be a factual answer?
No completely wrong. It will have very large mass as viewed by someone at rest, but so will the rocket ship. And it will seem to take much longer to reach the shops wall so the difference in momentum will be very small.
Relativity tells us there are no special inertial frames of reference. If your reasoning were true, then someone who was flying past the Earth at a very high speed in a rocket would conclude that a bullet shot on Earth would destroy any room in which it were shot – and we know this doesn’t happen.
Nobody knows what happens at the speed of light. Even 10mph under the speed of light there should be all sorts of weird stuff happening, and I don’t believe we’ve come even close with anything manmade with mass.
The key point is “10 mph under the speed of light.” Flying a rocket really really fast probably wouldn’t even be a 1/100 of that.
Superhal, I have a question for you. You have a person on a spaceship that is moving at c-10mph. You also have a stationary observer. From the reference point of the person on the spaceship, how fast is the stationary person moving?
We’ve accelerated particles close to that speed and their behavior accords exactly with the predictions made by relativity.
The OP’s question has been answered correctly by everyone else.
What if we put it on a treadmill? 
We do know what it’s like to move with a speed close to that of light, because relatively to innumerably many places in the cosmos, we’re moving at that speed right now. Speed is a relative quantity; as long as one isn’t accelerating, physics always works the same, independently of speed.
And even if that weren’t true, for situations where we genuinely don’t have any first-hand experience, that nevertheless wouldn’t mean that what we could say about that situation would be no better than guesswork. As long as we have a theory covering the appropriate situation, we can at least make predictions substantiated by all the evidence in accordance with our theory. These predictions may be false, in principle, but they’re still the most reasonable answer.
By this statement, you seem to be under the mistaken belief that the bullet will exceed the speed of light. But, of course it can’t and won’t. From the perspective of an outside observer, they will see time on the spacecraft dilated to the point that the bullet will scarcely move at all (and will also appear to be be squashed flat), while from the perspective of the person firing the gun (or on the receiving end of the bullet) they will perceive it to be moving at normal speed but the outside universe to be very slow.
There is nothing outside of what normal physics in this example, and we see objects moving at large fractions of the speed of light regularly, both in terrestrial particle accelerators and from cosmic rays entering the atmosphere. These objects have properties which are predictable within the framework of Special and General Relativity, and there is nothing weird about it, or at least, weird in any way that we cannot deal with mathematically.
Stranger
Imagine there are three clocks. One on Earth, one on the spaceman firing the bullet, and one on the bullet itself. What do they all read? I think the answer is that: the Earth one is undilated, the spaceman’s is dilated quite a bit, and the one on the bullet is dilated quite a bit plus a smidge. In other words, the time dilation prevents the paradox.
Ah - that’s clear then. I am just a tad confused about the units of measurement though. Is a *smidge *some fraction of a nanosecond - come to that, what about a tad?
Yeah…also where is the observer of the clocks? On earth?
Is this by now an Official SD Meme? If so, gotta add it to the others and alert that website.
And by “meme” I mean “inside joke,” but I’m net-hip.
It’s way past that. There is nothing hip about it anymore.