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thunderchicken
2005-Feb-25, 12:24 AM
Can anyone explain in simple terms the principals of special relativity? Why can’t a “spaceship” traveling away from earth continue accelerating until it reaches the speed of light? If we on earth see it traveling away from us the speed of light, can’t we say it’s traveling at the speed of light?

Vilim
2005-Feb-25, 01:28 AM
Can anyone explain in simple terms the principals of special relativity? Why can’t a “spaceship” traveling away from earth continue accelerating until it reaches the speed of light? If we on earth see it traveling away from us the speed of light, can’t we say it’s traveling at the speed of light?

There are quite a few intros to relativity which go into the math behind the derivation of the basic equation (the best analogy I know of involves a hypothetical light clock). But in any case, the special relativity correction usually comes in the form of


gamma=1/((1-(v^2)/(c^2))^1/2)


The reason that a spaceship cannot accelerate to the speed of light is because the relatavistic equation for its kinetic energy is


E=(mc^2)*gamma-(mc^2)=(mc^2)(gamma-1)


where mc^2 is from Einsteins famous equation E=mc^2 which is the rest energy of an object. That is, if I have a ball that weighs one kilogram and it is converted into energy, it would yield the equivalend of 21.48 Megatonnes of TNT (if I didn't make a mistake in my calculation).

As you can see


lim (gamma) = infinity
v->c

so in reality it would take an inifinite amount of energy to accelerate even an electron to the speed of light.



If we on earth see it traveling away from us the speed of light, can’t we say it’s traveling at the speed of light?

But the thing is that we on earth will never see it going at the speed of light, even if it is going 99.9999% of the speed of light and we get in our spaceship going the opposite direction, we will never see the other spaceship going the speed of light due to velocity addition.

The previous equations are off the top of my head, they might be wrong, but in any case, this is the best job I can do explaining it[/img][/code]

Sam5
2005-Feb-25, 01:43 AM
Can anyone explain in simple terms the principals of special relativity? Why can’t a “spaceship” traveling away from earth continue accelerating until it reaches the speed of light? If we on earth see it traveling away from us the speed of light, can’t we say it’s traveling at the speed of light?

According to the electrodynamics theory of H.A. Lorentz, as published in “Versuch Einer Theorie Der Elektrischen Und Optischen Erscheinungen In Bewegten Körpern,” 1895, the “ether” of space would put up a resistance to the motion of mass through it. The electrodynamical reaction of the atoms of the mass would cause the atoms to compress in the line of motion, and they would “length contract” and also gain mass due to the rapid motion. Seems that he thought that “c” would be an unattainable speed of mass when forced through the “ether” at very high speeds. He thought the atoms would compress to flat disks and gain infinite mass. Einstein explained the theory in a different way in 1905. The Einstein version is more well known than the original Lorentz version, and several people here will be happy to explain it to you.

worzel
2005-Feb-25, 02:18 AM
I don't think the Lorentz version had time dilation in it Sam5, so the Einstein version is different, and the one that agrees with observation.

Back to the OP: just to add to what Vilim said - from your point of view, in your spaceship you could accelerate away from earth at a constant rate forever and thus seemingly go faster that c. But if you then measured the distances between all those stars you were whizzing by you'd find that they were closer together than they were when you set out resulting in you never actually exceeding c afterall.

thunderchicken
2005-Feb-25, 02:54 AM
Back to the OP: just to add to what Vilim said - from your point of view, in your spaceship you could accelerate away from earth at a constant rate forever and thus seemingly go faster that c. But if you then measured the distances between all those stars you were whizzing by you'd find that they were closer together than they were when you set out resulting in you never actually exceeding c afterall.

So, relative to earth is the spaceship going c? If not, why does it "seemingly" do so to someone on earth...or does it. I understand that the ship is not going c relative to other stars or whatever, but why is the speed measured from earth not credible? [/quote]

Kristophe
2005-Feb-25, 03:04 AM
Measured from Earth, it still wouldn't be seen as going at c. As measured from anywhere, it can never quite reach c.

As viewed from Earth, we'd see time on the ship getting slower and slower, and as the ship approached c we'd see it's acceleration approaching 0. We'd never see the fuel required to accelerate it to or past c ever get burnt.

worzel
2005-Feb-25, 09:22 AM
Back to the OP: just to add to what Vilim said - from your point of view, in your spaceship you could accelerate away from earth at a constant rate forever and thus seemingly go faster that c. But if you then measured the distances between all those stars you were whizzing by you'd find that they were closer together than they were when you set out resulting in you never actually exceeding c afterall.

So, relative to earth is the spaceship going c? If not, why does it "seemingly" do so to someone on earth...or does it. I understand that the ship is not going c relative to other stars or whatever, but why is the speed measured from earth not credible? [/quote]
The relative speed between the ship and the earth would always be the same for people on the ship and on earth, and it would always be less than c. My point was that you don't feel like you can't go any faster just because you're near c (from earth's perspective), you can keep on accelerating forever just as you imagined, it's just that time and space conspire to keep you below c no matter how long you accelerate for.