Creating speed more than light?

1. Aug 9, 2015

Auror

If we make a great voltage difference and let electricity flow , electron's kinetic energy will be equal to $eV$ . For some value of V (we wish to give) , won't the velocity be over speed of light ? What's wrong with such approach of thinking ?

Again , if we increase temperature of a system of gas , average speed,rms speed will increase and a some temperature it should cross speed of light . What's the bug in such idea ?

2. Aug 9, 2015

Orodruin

Staff Emeritus
You cannot accelerate an electron to the speed of light no matter how much energy you put in, the relativistic formula for total energy is $E = \gamma m$, where $\gamma$ is the gamma factor.

3. Aug 9, 2015

Borg

The problem is that you can't just add velocities in a simplistic manner to get something to go faster than light. It's more complex than that as you can see from the Wiki article on Special Relativity. It's a very long article but that's what it takes to understand why your not thinking about it correctly.

4. Aug 9, 2015

Staff: Mentor

The electron's KE is $KE = \frac{mc^2}{\sqrt{1-v^2/c^2}}-mc^2$. This goes to infinity as v goes to c.

5. Aug 9, 2015

bcrowell

Staff Emeritus
There are a nice educational paper and accompanying video in which exactly the experiment you describe was carried out:

Bertozzi, "Speed and kinetic energy of relativistic electrons," Am. J. Phys. 32 (1964) 551, http://www.scribd.com/doc/258743358/Bertozzi-Speed-and-kinetic-energy-of-relativistic-electrons-Am-J-Phys-32-1964-551 [Broken]

If you look at figure 3 in the paper, you'll see that the velocity approached c but never surpassed it, even when Newton's laws would have predicted it to go many times faster than c.

Last edited by a moderator: May 7, 2017
6. Aug 9, 2015

soothsayer

Simply put, your eV formula only applies for non relativistic electrons. As the electrons become relativistic, the rules change significantly. This is the same reason you can't just look at $\frac{1}{2}mv^2$ and say "if I put in enough energy, my velocity could exceed c!"

7. Aug 9, 2015

Orodruin

Staff Emeritus
The kinetic energy will still be eV. It will just not be enough to accelerate the electron to light speed or above because of how relativistic mechanics work.

8. Aug 9, 2015

soothsayer

Oh, you're right of course. My bad. I was somehow thinking it was a velocity equation and not energy...

9. Aug 10, 2015

Markus Hanke

This approach is based on the assumption that speeds ( kinetic energies ) add linearly; in Special Relativity however this is no longer true as you approach the speed of light. The faster you go, the less effect adding more energy will have, so it gets increasingly difficult to add to your speed. The speed of light itself is never reached - it would require an infinite amount of energy to get there, which is of course not possible. As others have pointed out, relativistic kinematics are based on hyperbolic geometry, not Euclidean geometry, so they work differently from what we might have learned back in high school.

10. Aug 10, 2015

Staff: Mentor

Kinetic energies do add linearly. It's just speeds that don't.

11. Aug 11, 2015

Markus Hanke

Apologies, you are right ! My bad
Thanks for pointing it out.