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Squark comments on Open Thread, May 11 - May 17, 2015 - Less Wrong
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To any physicists out there:
This idea came to me while I was replaying the game Portal. Basically, suppose humanity one day developed the ability to create wormholes. Would one be able to generate an infinite amount of energy by placing one end of a wormhole directly below the other before dropping an object into the lower portal (thus periodically resetting said object's gravitational potential energy while leaving its kinetic energy unaffected)? This seems like a blatant violation of the first law of thermodynamics, so I'm guessing it would fail due to some reason or other (my guess goes to weird behavior of the gravitational field near the wormhole, which interferes with the larger field of the Earth), but since I'm nowhere close to being a physicist, I thought I'd ask about it on LessWrong.
So? Any ideas as to what goes wrong in the above example?
Wormholes don't quite behave like portals in the game.
When something drops into a wormhole with zero velocity, the apparent mass of the entry end increases by the mass of the object and the apparent mass of the exit end decreases by the mass of the object. At some point one of the ends should acquire negative mass. I'm not sure what that means: either it literally behaves as a negative mass object or this is an indication of the wormhole becoming unstable and collapsing.
Similarly, when something with momentum drops into a wormhole, the momentum is added to the apparent momentum of the entry end and subtracted from the apparent momentum of the exit end. The apparent masses change in a way that ensures energy conservation. This means that the gain in energy of the "cycling" object comes from wormhole mass loss and transfer of mass from the high end to the low end. Again, if it's true that the wormhole becomes unstable when its mass is supposed to go negative, that would be the end of the process.
If you already postulate having enough negative energy to create a wormhole, there is no extra issues due to one of the throats having negative mass, except the weird acceleration effect, as I mentioned in my other reply.
Maybe. However, how will the geometry look like when the sign flip occurs? Will it be non-singular?
There isn't as much difference between negative- and positive-mass wormholes as between negative- and positive mass black holes. Negative-mass black holes have no horizons and a naked repulsive timelike singularity. A negative- (at infinity) mass wormhole would look basically like a regular wormhole. The local spacetime curvature would, of course, be different, but the topology would remain the same, S^2xRxR or similar.