Why can't an object move at the speed of light

[emperrotta]

I have looked through some of the threads which discuss the fact that an object cannot move at the speed of light because it would require an infinite amount of energy. What allows us to state that it requires an infinite amount of energy? Is it because if an object were moving at the speed of light, then for:

E=\gammamc²

where \gamma=1/\sqrt{1-(v/c)^{2}

v=c. With v=c, there is no defined value for E.

You'll have to forgive me. I have not taken Calculus in 10 years. I am probably not stating this correctly.

Thanks for any further explanation people are willing to give me.

 

[ZikZak]

The problem is not really that it takes infinite energy. The problem is that c is constant in all reference frames. Regardless of your speed relative to other bodies, light rays still pass you at c, so you can never catch up to them no matter how fast you fly.

 

[JesseM]

I have looked through some of the threads which discuss the fact that an object cannot move at the speed of light because it would require an infinite amount of energy. What allows us to state that it requires an infinite amount of energy? Is it because if an object were moving at the speed of light, then for:

E=\gammamc²

where \gamma=1/\sqrt{1-(v/c)^{2}

v=c. With v=c, there is no defined value for E.

For v exactly equal to c, E is undefined. But if you remember the idea of "limits" from calculus, it's also true that in the limit as v approaches c, \gamma approaches infinite, so E must approach infinity too (meaning that you can make E become arbitrarily large by allowing v to get arbitrarily close to c).

 

[JesseM]

The problem is not really that it takes infinite energy. The problem is that c is constant in all reference frames. Regardless of your speed relative to other bodies, light rays still pass you at c, so you can never catch up to them no matter how fast you fly.

We've discussed this before, but I disagree that you can explain why it's impossible to reach c without considering energy issues--if anyone's interested in seeing the previous discussion, look at this thread (ZikZak's post #5, my response in post #10, and more discussion from post #13 onward)