Thinking about superconductance

[pete5383]

Hey everyone. It's summer, and I'm thinking, mostly about superconductors for some reason, and I have a question.

For this, I'm going to pretend we have a room temperature superconductor pulled into a wire (I know, doesn't exist, but just thinking here). If a DC voltage was applied to a circuit with 0 ohms of resistance, the amps would be huge right? The way I figure it, the electron flow speed would only be limited by Relativity, that is, by the speed of light. (Stop me any time if I'm wrong about something). But with a voltage continuing to accelerate the electrons to higher and higher speeds, eventually they'll near c and then start to gain mass, right? And I don't see how this mass gain would be limited, so after enough time, the mass would be very large, and I don't see what would prevent it from collapsing into a black hole or something of the like (ok, maybe not a black hole, but collapsing due to its gravity).

This seems wrong (maybe because I'm assuming room temperature superconducting wire). Can anyone tell me where I'm a skew?

 

[berkeman]

Happy to. You don't need room temp superconductors, you can just talk about free electrons. Think about your common CRT TV. The electrons that light up the phosphur dots on the screen are boiled off the cathode in the back of the tube (in the neck), and then are accelerated toward the anode by the large +25kV or so anode voltage that is pumped by the flyback transformer. This acceleration gets the electrons up to a substantial fraction of c, so their mass increases a little, and that affects the deflection a little that they obtain due to the vertical and horizontal deflection coils.

The problem with your scenario is how much energy you need to put into the accelerated electrons to get their mass up to where you would make them into micro black holes. The equation for mass as a function of velocity is pretty simple, so just calculate how much energy you would need to put into an electron to get its mass up to micro black hole levels. I haven't done the calc, but I'm guessing it's way more energy than we can generate at SLAC or other existing particle accelerators. Kind of a funny idea, though. Maybe I'll do the calc when I have some spare time.