I'm in a freshmen level physics class now, so I don't know much, but something I heard today intrigued me. My TA was talking about how at the research facility he worked at, they were able to accelerate some certain particle to "99.99% the speed of light". I said why not 100%, and I didn't quite understand his explanation, but he said it wasn't possible. This confused me. Since the speed of light is a finite number, why can we go so close to its speed but not quite?
Edit: I read all the answers, and I think I'm sort of understanding it. Another silly question though: If we are getting this particle to 99.99% the speed of light by giving it some sort of finite acceleration, and increasing it more and more, why cant we increase it just a little more? Sorry I know this is a silly question. I totally accept the fact we cant reach 100%, but I'm just trying to break it down. If we've gotten so close by giving it larger and larger acceleration every time, why cant we just supply it with more acceleration? And how much of a difference is there between 99.99% the speed of light, and the speed of light? (I'm not really sure if "difference" is a good word to use, but hopefully you get what I'm asking).
Answer
By special relativity, the energy needed to accelerate a particle (with mass) grow super-quadratically when the speed is close to c, and is ∞ when it is c.
$$ E = \gamma mc^2 = \frac{mc^2}{\sqrt{1 - (\text{“percent of speed of light”})^2}} $$
Since you can't supply infinite energy to the particle, it is not possible to get to 100% c.
Edit: Suppose you have got an electron (m = 9.1 × 10-31 kg) to 99.99% of speed of light. This is equivalent to providing 36 MeV of kinetic energy. Now suppose you accelerate "a little more" by providing yet another 36 MeV of energy. You will find this this only boosts the electron to 99.9975% c. Say you accelerate "a lot more" by providing 36,000,000 MeV instead of 36 MeV. That will still make you reach 99.99999999999999% c instead of 100%. The energy increase explodes as you approach c, and your input will exhaust eventually no matter how large it is. The difference between 99.99% and 100% is infinite amount of energy.
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