According to theory of relativity the speed of light in vacuum is ultimate. But since objects move relative to each other, with respect to what can't we travel at the speed of light?
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This is the fundamental postulate of special relativity:
Light (in vacuum) moves at the same speed no matter what you measure it relative to.
Pretty much everything in SR is just a mater of figuring out the deductive consequences of this basic fact. It is an experimental fact that it is so, and it was so even before Einstein -- in particular, light had been found to have the same speed no matter whether we measure it relative to Earth-in-July or to Earth-in-January (at which times our planet moves in different directions along its orbit around the sun).
The fact that light has the same speed for everyone means that if a light signal is sent from one particular time and place (an "event" in relativity jargon) and is received at a different time and place, then two observers will agree what the speed of the signal was - even if the two observers move relative to each other. They will then disagree about how far the two events were from each other -- so, inescapably, in order to agree about the speed they have to disagee abouth how long it took for the signal to move. So two observers do not necessarily agree about how long intervals of time there is between the same two events.
Similar more involved thought experiments lead to the "classical" relativistic effects of time dilation, length contraction and so forth, as necessary consequences of the fact that all agree about what the speed of light is.
In particular, the fact that matter or information cannot move faster than light is one of those consequences -- so it doesn't depend on what we measure the speed relative to, because the premise of the entire fact is that light moves at the same speed no matter what we measure it relative to.
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The simple answer is 'with respect to anything'.
For instance if I am standing somewhere and you are in a spaceship then we will always measure our relative speeds to be less than $c$. Equally, if I am standing somewhere and two spacecraft are passing me in opposite directions, then I will always measure the speeds of the spacecraft to be less than $c$, and they will also measure their speed relative to each other to be less than $c$ (as well as their speeds relative to me of course). This is true even if, for instance, I measure the speed of each spacecraft to be greater than $c/2$, in opposite directions.
What this means is that velocities do not add in the simple way that we expect from everyday life: if I stand by the side of the road and observe two cars approaching me from opposite directions, both at 30 mph, then I know that their speed relative to each other is 60 mph and when they collide the drivers will almost certainly be killed. If, however, I am standing on a spaceport and I observe two space-cars approaching in opposite directions at, say, $0.8c$ then I know that their speed relative to each other is still less than $c$: it is in fact about $0.98c$. I'm still pretty confident the drivers will be killed though.
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The Lorentz transformation may shed some light on this... $$\gamma = \frac{1}{{\sqrt {1 - \frac{{{v^2}}}{{{c^2}}}} }}$$
Assume one body is, dare I say, "stationary" and the other is traveling away at velocity v. If the relative velocity between these two bodies moving apart is equal to the speed of light, then the denominator in the Lorentz transformation would be equal to zero. Then gamma would be equal to one divided by zero which is utterly absurd. Nor is it possible for two bodies moving apart to travel faster than the speed of light, because then the denominator would consist of taking the square root of a negative number which introduces complex numbers.
Michael Lee
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Lets imagine for a moment that for some reason or other only one object was left existing within the universe, and it was a spaceship. It can accelerate and decelerate, thus movement is in effect here, movement across space. However, whether it is alone in the universe or not, it has a maximum speed of which it can move across the vacuum of space. That being of course, the speed of light.
Light itself has no control of the spaceship. In fact, no matter what speed the spaceship moves across the vacuum of space, those on board the spaceship would still measure the speed of light as being 300,000 km/s.
Thus if they tossed a light beacon out of the spaceship, and moved toward or away from the beacon, and did so at a variety of different speeds, they would still measure the speed of light being emitted from the beacon to be the very same 300,000 km/s.
This consistent outcome of the measuring of light speed can only happen if the spaceship itself was constantly in motion across the 4 dimensional space-time environment, and did so with the very same magnitude of motion that is also known as the spatial magnitude of motion of light, a.k.a. the speed of light.
And so overall, the spaceships spatial speed is relative to the 4D space-time environment. Meaning, the spaceships velocity of motion across space only, is merely determined by the spaceships direction of travel across the 4D space-time environment.
Sean
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