Suppose I have sphere of 1 kg made of pure gold; and I can give it a velocity of 90% of lightspeed. The relativity theory predics that the mass of the sphere will about
double. But of what matter will the ‘new’ sphere be made of ? Gold ? Plasma ?
Gold. The same, litterally, as already constitutes the shpere. There won’t be any new gold atoms, the existing ones will simply be more massive, from your point of view. This assumes the shpere has a velocity of 90% of the speed of light relative to you. If you and shpere accelerate together relative to something else, such as the sun, the sphere will mass, as you measure it, the same as it always did.
Relativistic changes in mass are kind of a crock. The only way you’d really observe the change in mass is that the apparent momentum of the object in the reference frame where it has a velocity of 0.9c would be greater than the classically predicted value. There are two ways of accounting for this: you can add a relativistic correction factor to the classical formula for momentum (p=mv becomes p=mv(1-v[sup]2[/sup]/c[sup]2[/sup])[sup]-1/2[/sup]), or you can keep the old formula and sweep the relativistic complexity under the rug by saying that the mass changes (in this case p=mv but m=m[sub]0/sub[sup]-1/2[/sup], where m[sub]0[/sub] is the “rest mass”). The latter is what’s commonly done. Keep in mind that, in the sphere’s reference frame (i.e. the moving one), there would be no observed change in mass.
Well, Bob, the change in mass happens when anything massive moves at any speed. Flicking a booger causes the snotwad and your finger both to gain mass. Of course, this interesting fact has rather disappointing side-effect: It means that you can never reach light speed. From a stationary reference frame, the spacecraft (or massive subatomic particle, physics plays no favorites) approaching the speed of light in a vacuum (commonly called c) gains so much mass its acceleration drops to null before it can hit c. So you can’t travel back in time using relativistic time dilation effects. Dang. 
(Besides, when you work out the relativistic acceleration equations for speeds of or greater than c you get divide by zero errors.)
I agree with Bobort. Mass is only really defined in the rest frame of the moving object, since you can’t measure the mass of something that is moving. You can define mass this way if you want, but it’s completely ad-hoc and doesn’t have any real meaning. (This was the explanation given by the professor of a relativity class I took in undergrad.)
Sure you can. Measure the curvature in space time that it creates.
Really? Could you please explain how?
Doesn’t the path of a charged particle in a magnetic field depend on its charge/mass ratio? Does that mean you can measure the mass of a particle traveling close to the speed of light by observing the path it takes through a magnetic field?
A question on the increasing mass of objects increasing the speed of light. It is known that the mass increases to anyone outside of the frame of reference of the speeding object, but to the people in the spaceship or whatever, their mass remains the same right? And everything outside of their frame of reference would appear to increase. As such, the rocket doesn’t gain any mass to the astronauts as their speed increases. So to them, it doesn’t get more difficult to go faster, because their mass isn’t increasing. What’s wrong with this?
Mike
Certainly. And if the real mass increases with relative velocity, there exist reference frames in which every object is a black hole, which is nonsense.
Well, nothing really. If you’re in the spaceship accelerating towards c, you’re not going to notice any obvious relativistic effects. Because of time dilation and length contraction, it’ll just seem like you’re going faster and faster without limit to your apparent velocity.
Exactly. Just to expand on that a bit- if you’re in the spaceship, you’ll seem like you’re going faster and faster, until you’re speed hits infinity, and you can travel anywhere in the universe in zero time (and since you ARE going at infinite speed, in a sense you ARE everywhere at once). The other way of looking at it is that the universe is whirling by at lightspeed, but due to length contraction it now has zero size, so it doesn’t take you any time to traverse it (or rather for it to whiz by you).
On the other hand, outside observers will think you’re moving at c, not infinity.
Let me know if I’ve mangle some of this
Arjuna34
Relative to the ship, the ship’s veolcity is zero and light still travels at c.
Er, giraffe…you’ve heard of gravity, right? How do you think we’ve determined the mass of the earth, by weighing it? 
You quantum guys always leave that out.