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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?

F=ma; m=m0/sqrt(1-(v^2/c^2))

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?

Sidarth
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1 Answers1

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The reason that we can't reach the speed of light is that, no matter how much we accelerate, when we stop accelerating to measure the speed of light, we will still find the speed of light is the same as it was before. [1] In other words, no matter how fast we go, we are still as far from the speed of light as we started.

It would seem (correct me if I'm wrong) that you believe that acceleration produces a change in velocity which THEN produces a change in mass an instant later. If so, this is a misunderstanding of how the mathematics works with these equations. The change in velocity and the change in relativistic mass occur in conjunction with each other. (PS I nearly said at the same time, but that would have been confusing given we are talking about time. But it is a perfect pun given the question.) So there is no instant when the velocity changes and the mass doesn't.

By the way, these changes in mass are only apparent to an onlooker. To the spaceship doing the acceleration, it doesn't feel like its mass is getting heavier.

[1] That is a key postulate of special relativity.

matscienceman
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