
Originally Posted by
Duelix
The concept of relativity indicates that as you approach the speed of light, things act very weirdly (to put it simply). You can add up velocities, but this is only in classical mechanics. However, when the velocities approach the speed of light, you cannot add them up. Here is an example of this:
Wrong. You can add up velocities but you must add them using the formula that Janus just used. For small velocities this is practically the same as regular addition but when the velocities get near the speed of light it is not like regular addition because two velocities less than the speed of light will always add up to a velocity less than the speed of light and if one of the velocities is the speed of light then the result will be the speed of light no matter what the other velocity is.
(10 kph + 1,079,252,849 kph)/(1+ 10kph*1,079,252,849 kph/(1,079,252,849 kph)^2)
= (10 kph + 1,079,252,849 kph)/(1+ 10kph/1,079,252,849 kph)
= 1,079,252,849 kph(10 kph + 1,079,252,849 kph)/(1,079,252,849 kph + 10kph )
= 1,079,252,849 kph

Originally Posted by
Duelix
The speed of the trains seem to be approaching the speed of light, but the smallest train will take infinite amount of energy to actually obtain such a speed. As objects reach enormous speeds, their velocities don't actually seem to increase, but their mass increases exponentially.
Well that depends on what you want to call mass. If you are talking about an innate property of a thing then you are talking about rest mass and this does not change. Frankly I think this relativistic mass that you are talking about is an invented quantity with too little usefulness to be worth the confusion it creates, for it is more intuitive to keep the energy of motion as a separate quantity rather than including it in a mass that is purely relative.

Originally Posted by
Duelix
To go back in time then, we would assume that we must go past the speed of light. Seeing that time dilation makes time stop (to the observer) at the speed of light, then to go above, the only logical answer would be that you would go back in time. This is true, but going past the speed of light is impossible.
There is nothing sensible about any of this except your last phrase: "going past the speed of light is impossible". But we can do even better. Regardles of the inertial frame of the observer, massless objects always travel at the speed of light, and objects with mass always travel at less than the speed of light.