Question

Ok, I've stumbled onto what I think is a bit of a paradox.

First off, say you had some computer in a very fast(near light speed) centrifuge. You provide power to this computer via a metal plate on the "wall" of the centrifuge's container, so it works similar to how subways and streetcars are powered.

If the computer normally would consume 200 watts, how much power would it consume at say 1/2 of light speed? Would it consume 400 watts from our still viewpoint?

Also, what if you were to be capable of communicating with this computer? Would the centrifuge-computer receive AND transmit messages faster from our still viewpoint? I'm a bit lost in even thinking about it.

Answer 1

One thing to be aware of is that the principle of relativity would not apply to this computer--rotating reference frames are not inertial, and therefore, will not be related to 'stationary' reference frames by simple Lorentz transformations. Also note that if there are any capacitors or anything along those lines in the computer, then they would be accelerating with respect to a rest frame, and this acceleration would produce electromagnetic waves (and even failing this, accelerating current-carrying wires would have a similar effect), which would create a potentially measurable difference between the frame of the computer and the rest frame.

My instinct for this problem, though, is that the power consumption of the computer would go down, not up--the computer uses energy in its rest frame, which has a slower clock than the lab frame. So, it would go on using 200 J every second of ITS proper time, which would correspond to more time in the lab frame.