RiddlerA said:
Assume an object which is moving relative to everything else in the universe...
The object was never at rest in any frame... And its speed is lower than 'c'...
So now can i say that the object has no rest mass?
No. The object is always at rest in a frame that is moving along with the object, which is to say the frame of an observer who happens to be riding along with that object. (It would only be very slightly sloppy to call that frame "the object's frame"). Whatever mass the object has in that frame is its rest mass. So we can define the rest mass of an object as the mass it would have if measured by some observer not moving relative to that object.
And I also need to know why speed of light is assumed to be the cosmological speed limit?
Not so - the speed of light is not ASSUMED to be the cosmic speed limit. "Nothing can travel faster than light" is not an assumption. It is a (somewhat oversimplified) summary of results derived by mathematics and logic from a much simpler and more natural assumption that also has substantial experimental evidence behind it.
The starting assumption is the Principle of Relativity, which basically says that the laws of physics won't change out from underneath you just because you're moving. If you do an experiment in a sealed, climate-controlled, vibration-isolated, not affected by anything happening outside the walls, no windows laboratory in December when the Earth and your lab is moving in one direction at about ten miles a second... And then do the same experiment in June, six months later when the Earth is on the other side of the sun and moving in the opposite direction at ten miles a second... You'll get the same results. Likewise, we don't expect experiments to give different results at different times of the day, even though the Earth's rotation means that we're constantly moving in different directions.
That's a very common-sense assumption, and it is supported by a huge amount of experimental evidence, including the famous Michelson-Morley experiment.
Now comes the twist... The speed of light can be CALCULATED from the laws of physics (specifically, Maxwell's equations of electricity and magnetism). Therefore, if the laws of physics don't change when the observer happens to moving, then all observers, regardless of their motion, must use the same Maxwell's equations and hence must calculate and see the same value for the speed of light.
That's kinda weird, because it says that if I see a beam of light moving at speed c, and I see you moving in the same direction at speed .4c... I'll see the difference between your speed and the beam of light as .6c, but you will see the difference between your speed and the speed of the beam of light as c, not .6c. Because speed is defined as distance traveled divided by time, the only way that can happen is if you and I are measuring distance and time differently.
Special relativity is about how two observers moving relative to one another measure distance and time differently, in such a way that all of the laws of physics, including especially Maxwell's equations and the speed of light, will hold for both observers. The math is actually not all that complicated; Einstein's book (Relativity: The Special and General Theory - pay special attention to appendix 1) manages to get through it with no calculus, just basic algebra. Time dilation, length contraction, and some other stuff follow from this math. And among the the "other stuff" that follows from the math is:
1) No amount of force will accelerate any object of non-zero mass that is moving at a speed below the speed of light relative to you to a speed greater than the speed of light relative to you.
2) If an object can move from point A to point B more quickly than a beam of light could make the same journey, then some observer traveling at some speed somewhere will see the object arrive at point B before it has left point A - and would be able to stop the departure from A even though the arrival at B is known to happen.
3) The equations all include a term that looks like \sqrt{1-{v^2}/{c^2}}, and that makes no real-world sense if v is greater than c.
#1 is a pretty convincing argument against any form of traditional transport working at speeds greater than light - a bigger better rocket motor won't ever do the job.
#2 excludes the standard science fiction hyperdrives and wormholes and space-warping mechanisms, unless you are willing to give up any sane notion of cause and effect.
#3 doesn't have to forbid anything. We could argue that it's just saying that the math of special relativity doesn't apply at speeds greater than light... But we'd still have to deal with #1 and #2, and propose some other theory that is consistent with the observed fact that the laws of physics don't change just because you're moving. No one has ever been able to come up with a such a theory, and even if someone could, we'd still have #1 and #2 to deal with.
So, until (and we can bet very long odds against this happening) some seriously compelling experimental evidence comes along to tell us that the Principle of Relativity is wrong... We can conclude that nothing with non-zero rest mass can travel faster than the speed of light.
