Speed of light

[xud]

I am interested to know why it not possible for an object to travel faster than c.
I am well aware of the formula called Tau, the factor by which mass, length and time are altered and you increase speed.
Suppose we have our imaginary spaceship which is travelling at c/2. To accelerate to this speed requires a certain amount of energy. If we want to accelerate further we need more energy, but also there is an increase in mass because the spaceship is travelling faster, so it requires yet more energy - and so on.
Where does the factoer Tau come from and how is it derived?

[jake-the-peg]

I think you're talking about the relatavistic mass increase formula from special relativity m=mo/sqrt(1-v squared / c squared)) - [I've not heard it called Tau before]

It was first discoverred that the speed of light in a vacuum was constant and a maximum as a consequence of the famous Michelson Morely experiment in 1887 http://en.wikipedia.org/wiki/Michelson-Morley_ experiment.

From this and the principal that physical laws are the same in all inertial frames of reference ( you can't tell you're moving if you're moving at a steady speed) Einstein arrived at, relatistic mass increase, length contraction and time dilation in the Special Relativity paper of 1905

Put very simply momentum is conserved but when you then factor in time dilation you get mass increase as a consequence.

Richard Feynmann wrote some brilliant undergraduate level lectures on Science and chapter 16 of the first volume covers this wonderfully, it's also in his book 6 not so easy pieces (but it's not that hard really)

There's a variation based on it here:
http://www.wbabin.net/harrison/derive.htm

[2complicated]

The best book I have ever read giving answers to these questions is 'The time and space of Uncle Albert'. It is written for children, which may be why I liked it so much, but describes most of Einsteins theories in an easy to understand way.

[fo3nix]

Jake of course gives a good explanation, but I would disagree with him on the Feynman book recommendation. The three volumes of his lectures are some of the best physics books ever written, but I (and I've read others too) think that the special relativity chapter isn't all that great. I'm sure I read once that he had to rush those few lectures for some academic reason at the time and didn't go into the depth he wanted to. Maybe that accounts for it?

A great, perhaps slightly advanced treatment, is Spacetime Physics by Taylor and Wheeler.

xud: to get a proper understanding you'd be better reading a book on SR; the length of these answer sections isn't long enough to explain it properly, especially with the lack of good mathematical typesetting.

Finally, note that SR is for zero acceleration. If you want to properly take into account acceleration (near c), you'll need the full might of General Relativity.

[mibn2cweus]

Relativistic mass (mass dilation) need not be considered to understand why C is a brick wall for velocity. Time dilation should satisfy this requirement. If you find you need to consider mass in an equation use ress mass as this leads to less confusion.

On the other hand, here's a little something to add to the mix . . . time limits C

[mibn2cweus]

D'oh! Sorry about that, "ress" should be "rest"