Why can't you reach the speed of light?

[Antuanne]

I get why it is impossible to accelerate faster that the speed of light, because at the speed of light and object has infinite mass and so need infinite force to accelerate it. But, I don't get why you can't accelerate to the speed of light. So what I'm saying is I get why you can't accelerate >c but why can't you even hit c at all?

 

[Drakkith]

I get why it is impossible to accelerate faster that the speed of light, because at the speed of light and object has infinite mass and so need infinite force to accelerate it.

Incorrect. The mass of the object does not change after accelerating. The confusion comes from something called "Relativistic mass". In this badly worded term an objects total "mass" comes from both the invariant or rest mass of the object, plus the kinetic energy it possesses. It is far more accurate and less confusing to leave mass meaning the invariant or rest mass of an object.

Imagine this. If the true mass of an object increased as your velocity increased, we would get the peculiar effect of anything turning into a black hole when it gets up to a high enough velocity! The problem is that there are no preferred frames of reference. This means that to an extremely high energy proton, EVERYTHING ELSE is traveling at more than 99% the speed of light and from its frame of reference the Earth and the Sun should collapse into a black hole! Obviously this does not happen.

But, I don't get why you can't accelerate to the speed of light. So what I'm saying is I get why you can't accelerate >c but why can't you even hit c at all?

I can't tell you WHY you cannot accelerate to or past light speed, as I don't know the fundamental laws well enough to explain them, but I can assure you that mass doesn't increase as you accelerate and it would take infinite energy to accelerate you to light speed thanks to relativistic effects.

 

[Simon Bridge]

Welcome to PF;
You have to think about it carefully - what do you mean by "speed"? Relative to what?

You will never observe yourself traveling any speed other than zero - you are at rest with respect to yourself. You can, however, do work to change the relative speed between yourself and other objects.

You will always measure the speed of light in a vacuum to be c - no matter what relative speed the emmitting object has. Therefore you can never be in a situation where light is stationary to you... so you cannot reach lightspeed that way.

The amount of work you need to do to change your relative speed with respect to something becomes very large as you approach a relative speed of c. At c, the math diverges and you need infinite energy.

You can, however, get arbitrarily close to it.

Note: mass increase has nothing to do with it - you will measure your own mass to be the same as always no matter what the relative speed.

 

[harrylin]

I get why it is impossible to accelerate faster that the speed of light, because at the speed of light and object has infinite mass and so need infinite force to accelerate it. But, I don't get why you can't accelerate to the speed of light. So what I'm saying is I get why you can't accelerate >c but why can't you even hit c at all?

Hi, welcome to physicsforums

In fact you already gave the answer yourself: infinite relativistic mass corresponds to infinite energy. It would require infinite energy to accelerate something to exactly the speed of light.

 

[russ_watters]

Key word: asymptote: http://en.wikipedia.org/wiki/Asymptote

 

[Antuanne]

OK, I understand the fact that it is impossible to exceed the speed of light because the relativistic mass would be infinite which would require infinite force, but shouldn't it be possible to go the speed of light, just not over? What I'm saying is that I get you can't go faster than c, but why couldn't you go at c?

 

[harrylin]

OK, I understand the fact that it is impossible to exceed the speed of light because the relativistic mass would be infinite which would require infinite force, but shouldn't it be possible to go the speed of light, just not over? What I'm saying is that I get you can't go faster than c, but why couldn't you go at c?

I'll try once more: if you go at c you already have infinite kinetic energy. That is not possible. For every fraction of getting closer to that unreachable limit, increasingly more energy must be spent, so that it can never be reached - that's what is meant with asymptotic.

See also the same here:
"en.wikipedia.org/wiki/Speed_of_light#Upper_limit_on_speeds"

 

[DrGreg]

I'll try once more: if you go at c you already have infinite kinetic energy.

Antuanne

To spell it out even more clearly:

• If you had infinite relativistic mass you would also have infinite energy (via E = mc²)
• That infinite energy would consist of your initial energy when at rest plus added kinetic energy.
• The added energy would have to be transferred to you from somewhere else.
• There isn't an infinite amount of energy available in the rest of the universe to be transferred to you.

Therefore none of the above is possible.

 

[Simon Bridge]

OK, I understand the fact that it is impossible to exceed the speed of light because the relativistic mass would be infinite which would require infinite force, but shouldn't it be possible to go the speed of light, just not over? What I'm saying is that I get you can't go faster than c, but why couldn't you go at c?

Perhaps we have misunderstood the question? Why would you think that it should be possible for you to travel at c? Perhaps if we knew that we'd have a better chance of giving you an answer you understand? Otherwise your question has already been answered: eg.

You have to think about it carefully - what do you mean by "speed"? Relative to what?

You will never observe yourself traveling any speed other than zero - you are at rest with respect to yourself. You can, however, do work to change the relative speed between yourself and other objects.

You will always measure the speed of light in a vacuum to be c - no matter what relative speed the emmitting object has. Therefore you can never be in a situation where light is stationary to you... so you cannot reach lightspeed that way.

The amount of work you need to do to change your relative speed with respect to something becomes very large as you approach a relative speed of c. At c, the math diverges and you need infinite energy.

You can, however, get arbitrarily close to it.

I don't know what other sort of answer you are expecting?

If you could accelerate to the speed of light and then no further - like you have been speed-governed by the Universe ... then you'd reach a point where, no matter how hard you worked, you'd not increase in speed at all.

However - all speed is relative.
Relative to someone else, you are not traveling at the speed of light.
According to them, you may have quite a bit of accelerating left.
Who is right?

Relative to yourself, you are stationary. Speed is zero. This is no different from you being stationary at any other time in your life. So you should be able to get some increase in speed for a bit of work - just like always.

It follows that you must never actually hit the speed of light.

When you talk about speed, in future, try to say what the speed is relative to.