Question #49736

1 Answer
Dec 11, 2014

According to Einstein's theory of relativity, as an object approaches the speed of light, the amount of energy needed to accelerate that object increases, ultimately requiring an infinite amount of energy to actually achieve light velocity.

Einstein's two postulates of relativity are;
1.) The laws of physics are the same in all inertial reference frames.
2.) The speed of light in free space has the same value, c, in all inertial reference frames

The first postulate means that the laws of physics cannot change based of location or velocity. The second postulate is an observational fact. Light is always measured to have the same speed in a vacuum, #~3 xx 10^8# m/s.

Using these two postulates, Einstein was able to derive the equation for relativistic kinetic energy;

#K = (mc^2)/sqrt(1-v^2/c^2) - mc^2#

The first term is the total relativistic energy, and the second is the rest energy, the amount of energy locked up as the mass of the object.

When you allow the velocity of an object to approach the speed of light, #v->c#, the total energy, and thus the kinetic energy, goes to infinity!

#(mc^2)/sqrt(1-v^2/c^2)=> (mc^2)/sqrt(1-c^2/c^2) =>(mc^2)/sqrt(1-1) =>(mc^2)/sqrt(0) => oo#

Since the amount of work required to accelerate an object is given by the work-energy theorem;

#W = Delta K = K_(f i nal) - K_(i nitial) = oo - K_(i nitial)#

it would require an infinite amount of work to accelerate an object to the speed of light.