# If an object accelerates for i

I have some question about relativistic features of objectswhich moves with speed of light.

If an object accelerates for infinite time, then it will in theend reach speed of light. Then, to make it clear, assume a rocketwith infinite power source (source is also assumed to be massless)that accelerates in space, or vacuum without any disturbance in itsmotion. Also assume that there is another rocket same as the onementioned above and, in vacuum, it moves with speed of lightwithout any force given to it. Both move with speed of lightrelative to an observer at rest.

Sums up: From t=0, rocket A is accelerated until it reaches thespeed of light and infinite and massless power source is assume tobe given even after the speed of rocket A = c. Rocket B, on theother hand, at t=0, it moves with speed of light and moves forwardin constant speed in vacuum.

What are differences in physical properties between twoobject?

Answer:

# If you have a rocket with non-zero mass and if it moves at aspeed of light (your 2nd rocket, Rocket B), then it’s energy would be infinite (which is practically impossible).But let’s assume you have that.

# Now you have an infinite power source and you are acceleratinganother rocket (Rocket A). You are saying that, at time, t =infinity, your Rocket A would reach the speed of light. That’s alsoa valid statement.

# Now, think carefully about what you mean by INFINITE (i.e. attime, t = infinity).

Infinity is not a number that you can reach there and you can gobeyond that if you try harder.

Infinity is basically a sensation which says that how much youtry you can never reach there (and going beyond that is out ofquestion).

# So, you can never reach t = infinity.

This means, you can never have your Rocket A at the light speed(no matter how long you accelerate). (If you defend yourself bysaying “ok, I will wait for infinite time and get my rocket at thatspeed”, then I would say, go back again through the arguments ofinfinity and convince yourself that you can’t.)

# So, you can never accelerate something and get it to the speedof light.

##### I think this will clarify your confusion and help youthink physically.

# Now the difference in physical property of Rocket A and RocketB:

[ I ] As Rocket B is in light speed, everything inside it don’tevolve with time (i.e. time stops there), whereas time will runslow but never stops in Rocket A.

[ II ] To an outside observer, Rocket B would be contracted to apoint whereas Rocket A always have finite length (which will tendto zero but never reaches zero). etc

## If you still stick to your question, then I would say therewill be no difference in physical properties between two bodieswith non-zero mass and light speed (which is again not physical).If they are of zero-mass then there property would depend on thereenergy, like photons with different energy have differentfrequencies.