Neil's News

Perpetual Motion

19 October 2008

Like most eight year olds I dreamed of using an electric generator connected to the front wheels of a vehicle to drive an electric motor connected to the back wheels of the vehicle. Thus once the vehicle was started, it would power itself.

There are three approaches for debunking perpetual motion machines (or more accurately, free energy or overunity machines):

  1. "It violates the laws of thermodynamics." This dismissive statement allows one to know that the machine won't work -- regardless of its details. But it is an unsatisfactory answer because it doesn't tell you why it won't work. Essentially it is a statement of faith that somehow the universe won't allow it.
  2. "Friction will stop it." This dismissive statement is actually flat wrong. One can always reduce friction through better engineering. Friction is not a valid explanation with which to offset apparently excess energy.
  3. "There's an unaccounted energy sink here that exactly equals the surplus." This is the way to properly answer a perpetual motion challenge. There is always some overlooked energy sink. It's just a matter of finding it.

In the case of the generator on the vehicle, the missing insight is that turning the generator will cause more work for the motor -- exactly the same amount of work as the generator will produce. There's always a gotcha, but finding it can sometimes be tricky.

Here's a more challenging one: Take a 1kg mass (probably half of which is antimatter) at sea-level. Use a magic E=mc2 machine to convert the mass to energy. Assume perfect efficiency. Send that energy up a tower using (take your pick) a laser beam, a rotating vertical axle, or an electric wire. Use another magic E=mc2 machine to convert the energy back into 1kg. Drop the mass off the top of the tower and collect the excess kinetic energy from the fall (using a water wheel or some such). Rinse. Repeat.

[Perpetual Motion Machine]

Where's the flaw? Don't say it violates the laws of physics; of course it does, that's the point. Don't say friction would kill it; granted with existing technologies the loss for a single cycle would be measured in many orders of magnitude, but improving efficiency is 'just' an engineering problem. The correct answer is that somewhere there's an overlooked energy sink exactly equal to the altitude of the drop.

Perpetual motion machines are fun gedanken experiments for exploring the completeness of one's understanding of Physics. Clearly there's a hole in my understanding of physics because I can't close the gap.

Liam Morland writes:

Here is my best guess: A 1 kg mass would convert into a huge amount of energy. If only a tiny fraction of that energy were lost while it travelled up, it would account for the energy coming from the 1 kg of falling mass. Perhaps there is some kind of quantum gravity effect or something like that which steals tiny amounts of energy when it travels against gravity.

Yes, this is undoubtedly the flaw's location, though the exact nature of how a gravitational field steals energy from a rotating axle is somewhat mysterious. A physicist mentioned a few years ago (I've been kicking this idea around since high school) that if I were transmitting the energy using a laser/photocell combination, the light would red-shift as it climbs out of the gravity well. Red light carries less energy than blue light. This makes sense, though a consequence of this is that the universe must look slightly blue-shifted for Earth-based telescopes.

Chris Jones points out the curiosity that the spinning axle version would seem to violate Newton's 3rd law since the whole Earth (dragging the solar system behind it) would slowly inch-worm its way across the universe. Whereas the laser version would not since the upwards laser has a slight recoil.

Temple Keller writes:

It took me awhile to think through it, and here's the reason: in classical mechanics, the set up with the axle really is a free energy source. I kept looking for a Newtonian solution, and there just isn't one. But with general relativity, time runs slower at sea level than it does up high. So from the perspective of a person at sea level, that axle is rotating slightly more quickly... and to make it rotate more quickly, he has to put more energy into it. It struck me as strange that this problem required the heavy machinery of relativity, until I realized that relativity is already implicit in the problem statement, since we're converting mass and energy back and forth.

The question that's not clear to me is, What the hell is happening to that axle in the long term? Is it getting twisted up? I think it must be. I know other thought experiments involving perfectly rigid bodies run into trouble when you think about them relativistically. Anyway, that's all I got.

Indeed, the gravitational time dialation at sea-level goes hand-in-hand with the gravitational red-shift, mentioned above. I think you've just hit the answer. There won't be any twisting, since the motor is running in a slower time frame than the generator. The number of rotations at the bottom will match the number of rotations at the top. But the motor might be running at 100rpm, whereas the generator might be running at 99rpm. Thus energy is lost. Nicely done!

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