Grey Area on Apr 14 2008, 07:16 PM, said:
So to calculate the energy required to accelerate to a certain speed you take the mass (m) x velocity (c (usually sol)) squared. Its a bit more complex than that and the actual calculation would be differential but for a simple explanation It'll do, until someone corrects me its been ages since I have dealt with that.
Actually, the mathematics involved with Special Relativity are elegantly simple.
Above, a little ways, I discussed the speed limit of "C":
(1 / square root of (1 - velocity squared / speed of light squared))
We cannot attain the speed of light because if velocity in the relation above is = the speed of light, the relation becomes the square root of zero...which of course is zero...meaning something would have no length and time would cease to exist, which of course isn't possible for an object in space. Thus, "c" is unattainable. And of course, making velocity > "c" would result in the square root of a negative number, which is not a real number...thus, you can't attain or exceed the speed of light, according to Special Relativity...
Of course, none of the changes would be perceptible to the person who was actually moving!
...wierd stuff, eh?
It's really that bottom-line simple....of course, understanding the derivation of that relation takes a little more than basic algebra. Einstein wrote a popular exposition on Relativity in 1916, in which he said that it assumed a level of education which corresponded to that of a college matriculation exam. I think today perhaps that might be a little shy of the real requirement.
If you're actually interested, the book is called, oddly enough , RELATIVITY, Albert Einstein (1916) (c. 1961, the estate of Albert Einstein). It's relatively short (no pun intended), at about 155 pages or so, but it will take some patience and effort, and a knowledge of algebra at least to get through it. It's elegantly simple, really!
If you actually take the time to study Einsten's own work, and you get down to the bottom line of this cosmic speed limit stuff...you just kind of sit there with your mouth agape and say, "Holy crap...of course!"
It's alot of fun!