THE ACCELERATION PROBLEM IN RELATIVITY
The basic essence of relativity is that no object can travel faster than the speed of light.
Let us suppose that there is a bat with which you can hit any object and make it go at the speed of light. Simple and straight.
Next thing to thing about is what would be the repercussions if an object already moving at the speed of light is hit by this bat?
I) Now that object cannot move faster than the speed of light so if we try to calculate the transfer of momentum from the bat to the body (product of the mass and velocity of an object), the speed of that object cant increase so the only possible explanation would be that the mass of that body should increase to balance, if any, change of momentum.
Now the density of that object would be obviously known and the density of an object to its truest forms cant change until we add more mass per unit volume which is quite a task.
As the mass of an object is Density x Volume and surely the density cant change, but the mass is changing so the volume will have change to balance the equation. Therefore if the density of an object is unique only that substance will be added to change the volume.
Which leads to the conclusion that if you do this experiment with an object its SIZE WILL INCREASE that also by the same material of which its made of.
II) Now lets suppose we want the calculate the force applied on that object. The force on an object is the product of the mass of that object and the acceleration that force produces on the body.
That object which we are hitting is already going at the speed of light and according to general relativity its velocity wont increase even after the hit so the initial velocity of that object and the final velocity are same which means that the acceleration would be zero and the force would also be zero.
As the force is zero the work done and energy implied would also be zero therefore where would the muscular energy applied by you go ?
A close example to this phenomenon is pushing of a wall. When you push a wall no work is done as in the case above but we observe an equal and opposite reaction which essentially means that we would be thrown back at velocity proportional to the energy that particle possesses.
This of course might look unrelated as in the wall case displacement in 0 while in the particle case the force is zero.
if we call the reaction due to the bat "crappy" where would the muscular energy of our arm go ?
This would be in no relation with the law of conservation of energy.
This explanation can also be extended to how photons will move if the clash into one another. if the wall example is right then a photon will come to a standstill after hitting another photon which is at the speed of light as the force will cancel out its velocity as the mass of both is same itself.
Enlighten Me Now.
