I have already asked this question on quora, with difficulty but I have not yet obtained a "works for me" answer. Please discuss with me about this.:)
Q:Why can we not touch the speed of light?
As T increases,
1) If "F" is constant, "v" will keep increasing and slowly the mass will start increasing , thus making acceleration equal to zero at t=infinity.
2)If "F" increases along with "m", so as to maintain the acceleration constant, as velocity increases, mass increases and near the speed of light, "m" increases infinitely, so, "F" has to be increases infinitely to maintain constant acceleration.
The Point is this: First, the mass has increased by an amount to bring acceleration down.Then, F is increased be me, so acceleration goes up, velocity goes up and only after all this , the mass will get bigger.
That is, near the speed of light,
at t=0(say), apply more force t=0 , acceleration is increased, t=0+dt , velocity is increased t=0+dt+some more dt , mass increases
That is, the velocity has to attain a higher value first for the mass to increase., which implies, the speed of light will be touched before mass really becomes infinity, bringing acceleration then to zero.
So, have we not touched the speed of light?
Suppose you say that all changes are instantaneously done,i.e.,
t=0 F increases t=0 a increases t=0 v increases (unlikely) t=0 m has increased as well
Then, my force has produced an effect on the mass instantaneously and not with a delay of signal propagation,i.e., i have transferred information instantaneously, which is not possible.
So, theoretically, have we not reached( at least touched) the speed of light?