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?
Gravity is a conserved vector field. Any closed path through a gravitational potential leaves you with the same energy you started with. And if it doesn’t you’ve stolen energy that was creating the gravity in the first place leaving less for the next circle to take and are thus just transforming energy from one to another.
Does that apply when the space isn’t simply connected? It could be conservative at every neighborhood, but not conservative over all if you allow portals.
Gravity would propagate through the connected space. The potential would probably be very VERY weird shaped but i see no reason it wouldnt be conservative or otherwise consistent with GR (the math of which is far beyond me). Though keep in mind in GR space curvature IS gravity and can change over time, I doubt you could maintain a knife edge thin aperture, it would all smooth out.
What’s really fun though are gravetomagnetic effects.
These are to gravity what magnetism is to the electric field. Both the electric field and gravitational field are conservative. But changing or accelerating charges generate magnetic fields which are NOT conservative hence how an electron spinning around a coil in a field in a generator gains energy even though it returns to its starting point. However in doing so it accelerates up to velocity as well generating a counteracting field that cancels out some of the field accelerating it, the motion moving it, or both. Thus the nonconservative fields have a potential energy associated with them that can be extracted from them or used to couple two phenomena that are both coupled to them.
To get gravetomagnetic effects you need huuuuuge mass flows and accelerations. But you can similarly steal the energy that drives them. Think frame dragging and extraction of black hole rotation.
but i see no reason it wouldnt be conservative or otherwise consistent with GR
I’m assuming GR holds. Does it actually prove the field is conservative, or just irrotational? If it’s irrotational and simply connected, then it’s conservative, but if you stick a portal in it, it might not be.
I doubt you could maintain a knife edge thin aperture, it would all smooth out.
Portals don’t need a knife edge. For example: Flight Through a Wormhole. You do need negative energy density or it will collapse, but that on its own shouldn’t break conservation of energy.
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.
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.
I have a PhD in Physics and my thesis was, in part, related to wormholes, so here it goes. (Squark covered most of your question already, though.)
If something falls into a black hole, it increases the black hole mass. If something escapes a black hole (such as Hawking radiation), it decreases the black hole mass. Same with white holes. A wormhole is basically two black/white holes connected by a throat. One pass through the portal would increase the mass of the entrance and decrease the mass of the exit by the mass of the passing object.
A portal with two ends having opposite masses would behave rather strangely: they sort of repel (the equivalent of Newton’s law of gravity), but the gravitational force acting on the negative-mass end propels it toward the positive-mass end. As a result, the portal as a whole will tend to accelerate toward the positive end (entrance) and fly away, albeit rather slowly.
In addition, due to momentum and angular momentum conservation, the portal will start spinning to counteract the motion of the passing object.
At a glance, it seems like you’re asking for extrapolation from a “suppose X—therefore X”—type statement, where X is the invalidation of conservation laws.
I don’t quite understand this statement. The only real premise I can see in my original comment is
suppose humanity one day developed the ability to create wormholes.
(Please feel free to correct me if you were in fact referring to some other premise.)
Wormholes are generally agreed to be a possible solution to Einstein’s equations—they don’t, in and of themselves, violate conservation of energy. The scenario I proposed above is a method for generating infinite energy if physics actually worked that way, but since I’m confident that it doesn’t, the proposed scenario is almost certainly flawed in some way. I asked my question because I wasn’t sure how it was flawed. Whatever the flaw is, however, I doubt it lies in the wormhole premise.
I am just taking wormholes to mean “altered connectivity of space” and leave out the “massive concentrations of mass” aspect.
The curious thing about portals portals is that they somehow magically know to flip gravity when a object travels thourht. If the portal is just ordinary space there shouldn’t be a sudden gradient to the gravity field but it should go smoothly from one direction to the other. And in additon gravity ought to work throught portals. that would mean that if you have a portal in a ceiling it ought to pull stuff throught it towards the ceiling (towards the center of mass beyond the portal). That is a standard “infinite fall” portal setup should feel equal gravity up and down midway between the portals. That kind of setup could be used to store kinetic energy but it doesn’t generate it per se.
However if portals aftected the gravity fields it could be that the non-standard gravity environment could be a major problem and would work even when you didn’t want it to. That is since the net 0 gravity point of a infinite fall setup needs to transition smoothly to the “standard gravity environment” that likely means that quite a ways “outside” the portal pair there would be a reduced gravity environment.
You can probably think about it as the lines of a gravity field also going through the wormhole, and I believe the gravitational force would be 0 around the wormhole.
The actual answer involves thinking about gravity and spacetime as a geometry, which I don’t think you want to answer your question.
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?
Gravity is a conserved vector field. Any closed path through a gravitational potential leaves you with the same energy you started with. And if it doesn’t you’ve stolen energy that was creating the gravity in the first place leaving less for the next circle to take and are thus just transforming energy from one to another.
Does that apply when the space isn’t simply connected? It could be conservative at every neighborhood, but not conservative over all if you allow portals.
Gravity would propagate through the connected space. The potential would probably be very VERY weird shaped but i see no reason it wouldnt be conservative or otherwise consistent with GR (the math of which is far beyond me). Though keep in mind in GR space curvature IS gravity and can change over time, I doubt you could maintain a knife edge thin aperture, it would all smooth out.
What’s really fun though are gravetomagnetic effects.
These are to gravity what magnetism is to the electric field. Both the electric field and gravitational field are conservative. But changing or accelerating charges generate magnetic fields which are NOT conservative hence how an electron spinning around a coil in a field in a generator gains energy even though it returns to its starting point. However in doing so it accelerates up to velocity as well generating a counteracting field that cancels out some of the field accelerating it, the motion moving it, or both. Thus the nonconservative fields have a potential energy associated with them that can be extracted from them or used to couple two phenomena that are both coupled to them.
To get gravetomagnetic effects you need huuuuuge mass flows and accelerations. But you can similarly steal the energy that drives them. Think frame dragging and extraction of black hole rotation.
I’m assuming GR holds. Does it actually prove the field is conservative, or just irrotational? If it’s irrotational and simply connected, then it’s conservative, but if you stick a portal in it, it might not be.
Portals don’t need a knife edge. For example: Flight Through a Wormhole. You do need negative energy density or it will collapse, but that on its own shouldn’t break conservation of energy.
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.
I have a PhD in Physics and my thesis was, in part, related to wormholes, so here it goes. (Squark covered most of your question already, though.)
If something falls into a black hole, it increases the black hole mass. If something escapes a black hole (such as Hawking radiation), it decreases the black hole mass. Same with white holes. A wormhole is basically two black/white holes connected by a throat. One pass through the portal would increase the mass of the entrance and decrease the mass of the exit by the mass of the passing object.
A portal with two ends having opposite masses would behave rather strangely: they sort of repel (the equivalent of Newton’s law of gravity), but the gravitational force acting on the negative-mass end propels it toward the positive-mass end. As a result, the portal as a whole will tend to accelerate toward the positive end (entrance) and fly away, albeit rather slowly.
In addition, due to momentum and angular momentum conservation, the portal will start spinning to counteract the motion of the passing object.
At a glance, it seems like you’re asking for extrapolation from a “suppose X—therefore X”—type statement, where X is the invalidation of conservation laws.
I don’t quite understand this statement. The only real premise I can see in my original comment is
(Please feel free to correct me if you were in fact referring to some other premise.)
Wormholes are generally agreed to be a possible solution to Einstein’s equations—they don’t, in and of themselves, violate conservation of energy. The scenario I proposed above is a method for generating infinite energy if physics actually worked that way, but since I’m confident that it doesn’t, the proposed scenario is almost certainly flawed in some way. I asked my question because I wasn’t sure how it was flawed. Whatever the flaw is, however, I doubt it lies in the wormhole premise.
EDIT: Also see the replies from shminux and Squark.
I am just taking wormholes to mean “altered connectivity of space” and leave out the “massive concentrations of mass” aspect.
The curious thing about portals portals is that they somehow magically know to flip gravity when a object travels thourht. If the portal is just ordinary space there shouldn’t be a sudden gradient to the gravity field but it should go smoothly from one direction to the other. And in additon gravity ought to work throught portals. that would mean that if you have a portal in a ceiling it ought to pull stuff throught it towards the ceiling (towards the center of mass beyond the portal). That is a standard “infinite fall” portal setup should feel equal gravity up and down midway between the portals. That kind of setup could be used to store kinetic energy but it doesn’t generate it per se.
However if portals aftected the gravity fields it could be that the non-standard gravity environment could be a major problem and would work even when you didn’t want it to. That is since the net 0 gravity point of a infinite fall setup needs to transition smoothly to the “standard gravity environment” that likely means that quite a ways “outside” the portal pair there would be a reduced gravity environment.
You can probably think about it as the lines of a gravity field also going through the wormhole, and I believe the gravitational force would be 0 around the wormhole.
The actual answer involves thinking about gravity and spacetime as a geometry, which I don’t think you want to answer your question.