Absolutely nothing that Superhal said is correct. We know exactly what would happen, and it doesn’t involve the mass of anything changing. The bullet would move forward relative to the gun at the same speed that it always does, and this would not cause the bullet to exceed c. In fact, in a sense it’s just as far from c as you and I are right now: Everything is at rest, in its own reference frame.
Damn, I thought I was making good time.
Imagine the OP being about a magical gun being fired at 10MPH less than the speed of light, and endless arguments about how the specific magical properties of the gun make a difference.
I’m never hip.
The thing with relativity is that there is no fixed reference, fixed time, fixed distance - it’s all relative to the observer.
So from the view of the guy on earth, everything in the spaceship is going real slow (time is “dilated” and distances are shrunk in the direction of motion, and to balance the equations of speed and distance, mass is also increased.
paradoxically, from the view of the guy in the spaceship, exactly the same is happening to the Earth reference. Earth’s time is running slower, eath is a flat cookie not a globe because distances shrink in the direction of earth’s motion viewed from the spaceship, and earth masses are really big.
But, you say… how is that possible? What happens if we compare clocks? This is the key mind-bender of special relativity - you can’t. There is no such thing as “simultaneous” over distance. If I set off a flash or set off an explosion in two places, separated by, say, a million miles, the spaceship observer will not see them as simultaneous (even after back-calculating for when he saw them vs. speed of light from his point of view…)
Remember, to simplify we were talking about two frames of reference in steady, fixed velocities. To come back and compare clocks side by side again later, one or both of the observers - the rocket or the earth - have to accelerate/decelerate by a huge relativistic amount. That acceleration changes your frame of reference and allows you to reconcile apparently contradictory points of view. The math for that is even more complex.
Actually, Earth still will be a globe; you’re correct in saying that it undergoes length contraction, but that’s only the instantaneous picture of the spherical Earth, which you would only see if light travelled at infinite velocity. But of course, light travels at a finite velocity, and since the Earth, relative to you, travels at a velocity comparable to that of the light reaching you from the Earth, parts that would ordinarily be invisible for you become visible (the Earth ‘moves out of the way’, so to speak), and you’ll see a distorted, delayed, but still spherical image of it. This effect is known as Penrose-Terrell rotation: if you go fast enough, objects appear rotated, such that you’ll be able to see their backs before having passed them.
Again, the masses aren’t changed, by any sensible definition of “mass”. One only gets the notion of mass changing in relativity if one assumes, for no particularly good reason, that the formula for momentum remains the same as Newton posited, and further assumes, for even less reason, that any inconsistencies must be attributed to the mass rather than to the velocity.