# Creating speed more than light?

## Main Question or Discussion Point

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 ?

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Orodruin
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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 ?
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.

Borg
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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 ?
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.

Dale
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If we make a great voltage difference and let electricity flow , electron's kinetic energy will be equal to eVeV . 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 ?
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.

bcrowell
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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 ?
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.

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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!"

Orodruin
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your eV formula only applies for non relativistic electrons.
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.

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

What's wrong with such approach of thinking ?
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.

PeterDonis
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the assumption that speeds ( kinetic energies ) add linearly
Kinetic energies do add linearly. It's just speeds that don't.

Kinetic energies do add linearly. It's just speeds that don't.
Apologies, you are right ! My bad
Thanks for pointing it out.