Why Can't We Break the Speed of Light?

Date: 12/10/1999 at 18:42:02
From: Ilias
Subject: Why can't we break the speed of light?

I'd like you to explain why we can't go faster than the speed of light 
with the equipment we have now. Will there be any possibility of doing 
it in the future? Theoretically, how could it be done?

I know that the answer comes from Einstein's equation: E = mc^2, but I 
don't know exactly how. So if you could explain that point, I would be 
grateful.

Date: 12/10/1999 at 20:10:06
From: Doctor Ian
Subject: Re: Why can't we break the speed of light?

Hi Ilias, 

Unless Einstein's theory of special relativity turns out to be 
incorrect (which is possible), we won't be able to make things go 
faster than the speed of light by making 'better equipment'.

An object that would have a mass of, say, 1 kg (its 'rest mass') if 
you were holding it in your hand, would have an 'apparent' (or 
'relativistic') mass of more than 1 kg if it were whizzing by you on 
its way to somewhere. In fact, you could compute this apparent mass 
with this formula:

                                         1
     apparent mass = rest mass * -----------------
                                 sqrt(1 - v^2/c^2)

where v is its speed relative to you and c is the speed of light.  

Do you see what happens to this formula when v = c? A baseball moving 
past you at the speed of light would have an infinite amount of mass - 
more mass than the rest of the universe put together.  

What this means in practice is this. If you build a spaceship, and 
start up the engine, at low speeds almost all of the energy from the 
engine goes toward increasing the speed of the ship. But once the 
ship is moving at a very high speed, an appreciable amount of that 
energy goes, not into increasing the _speed_ of the ship, but into 
increasing its _mass_ - that is, making the ship heavier.

By the time the speed of the ship is, say, 99% of the speed of light, 
virtually all of the energy from the engine is being converted to 
extra mass instead of extra speed.

It's a little bit like trying to get to zero by dividing by two:

     1, 1/2, 1/4, 1/8, 1/16, 1/32, ...

You can get as close as you want, but you're never going to get all 
the way there.

I hope this helps. Be sure to write back if you're still confused, or 
if you have any other questions. 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/