Why infinite?

[That Guy]

Why would it take an infinite amount of energy to propel an object at the speed of light?

 

I'm a layman so, as per usual, please correct me if I'm hopelessly misguided...

 

As one approaches the speed of light© the objects mass increases exponentially as it gets closer and closer to c. So the energy taken to move it faster than it is currently travelling increases exponentially as its speed increases(gets closer to c).

 

Light has a finite speed. And numbers have no end (are infinite) and can describe any numerical value, no matter how hopelessly large -->

Should the energy not then be finite but almost unimaginably emmence?

 

Is the energy taken simply stated as "infinite" because there isn't so much energy in the observable universe?

[Janus]

The amount of energy needed to accelerate a mass up to a given velocity can be found by:

 

[math]E = mc^2 \left( \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}-1 \right )[/math]

 

Notice what happens as v nears c. The bottom half of that fraction approaches zero, which means the energy approaches infinity.

[booker]

So the energy taken to move it faster than it is currently travelling increases exponentially as its speed increases(gets closer to c).

 

Correctly speaking, the energy acquired increases geometrically with velocity.

[D H]

Correctly speaking, the energy acquired increases geometrically with velocity.

 

Correctly speaking, the energy acquired increases exactly as Janus described in post #2.

[Sisyphus]

For a layman, you might think of it as sort of a "zeno's paradox" kind of thing. It takes a certain amount of energy to go halfway to C, then the same amount to go halfway from there (half to three quarters), then the same amount to go halfway from there, etc. Hence, you can keep putting in more and more energy forever, and you'll never actually get there. (Note, that is a NOT what it actually does. It's a mathematical simplification, but it's the same general idea. The real equation is in post #2.)

 

Also note that this is relative velocity, e.g. what the accelerating spaceship looks like from Earth. From the perspective of the spaceship itself, you never "gain on" C at all. No matter what velocity you have relative to Earth or anything else, the apparent speed of light will always be the same in all directions. It will always look as if you are standing still, and everything else is approaching C.

[booker]

Correctly speaking, the energy acquired increases exactly as Janus described in post #2.

 

right