Generating energy with wormholes?

[Flight]

Let's say there's a wormhole entrance on the floor of my room, and the exit would be on the ceiling. If I drop a ball on it, it would "fall forever". Am I right on this one?

So, if it falls forever, I could throw some water, and use its motion to turn a gear that would generate electricity. In that case, I would have "endless free energy" being created.

I know it screams "troll-physics", but I honestly can't see the flaw in this plan (except the fact we don't have the technology to build it). Why is that not going to work?

Thanks in advance for any explanations, and sorry for my limited knowledge in physics!

PS: Yes, I got this idea while playing Portal.

 

[adjacent]

The water stream would have kinetic energy.It will be transferred to the turbine and the water stream would stop(eventually reaching 0 kinetic energy)

 

[Flight]

From my understanding, gravity would keep the water stream ever accelerating, "generating" more and more kinect energy, which could be transferred endessly to the turbine.

The key point here is that we don't have to spend any energy to transport the water from the floor to the ceiling back again, assuming the wormhole would take care of that. Or at least I'm hoping that the energy necessary to keep the wormhole working would be less than the amount we can harvest from such machine.

 

[ViperSRT3g]

I believe it would be safe to assume that the wormhole would probably shrink from objects traveling through it or become unstable and collapse.

 

[George Jones]

I believe it would be safe to assume that the wormhole would probably shrink from objects traveling through it or become unstable and collapse.

This is the correct answer, and is analyzed in mathematical detail on pages 245 - 247 of the technical monograph "Lorentzian Wormholes" by Matt Visser

Another interesting feature of locally-static traversable wormholes is that they appear, at first glance, to be perpetual motion machines ...

Back-reaction: Certainly the object gains (or loses) energy upon traversing the wormhole. It does so at the cost of altering the mass of the wormhole mouths themselves ...

[mathematical analysis snipped]

The total energy gained by the object is matched by a corresponding mass loss for the wormhole mouths ...

The wormhole cannot sustain this process.

The energy comes form the mouths of the wormholes, each of which can have an independent mass. Roughly, the "imprint at infinity" (one of the ways mass is defined in GR) of the mouths of the wormhole changes as the object cycles through the wormhole.

According to Visser, if M_1 and M_2 are the mass-energies of the mouths of the wormholes, and m is the mass-energy of the falling object, there is a nice conservation of mass-energy, $\Delta \left(M_1 + M_2\right) = -\Delta m$. He derives expressions for these changes for repeated passes through the wormhole.

 

[HarryRool]

Even if you assume that the wormholes are somehow stable, your scheme will still fail. The reason has to do with what happens inside the wormhole. [A portal-like wormhole is infinitesimally thin. So you assume that there is no "inside" (a finite region that objects would traverse). But there has to be, even if it's no longer than an atom.]

Here's a excerpt from this Wormhole FAQ:

Is a wormhole whose mouths are arranged vertically in a gravitational field a source of unlimited energy?
No. The argument in favor of such a wormhole being an energy source is this: An object falls from the upper mouth, gains kinetic energy as it falls, enters the lower mouth, reemerges from the upper mouth with this newly acquired kinetic energy, and repeats the cycle to gain even more kinetic energy ad infinitum. The problem with this is that general relativity does not permit discontinuities in the metric – the descriptor of the geometry of spacetime. This means that the gravitational potential of an object at the lower mouth must continuously rise within the wormhole to match the potential it had at the upper mouth. In other words, this traversal of the wormhole is “uphill” and therefore requires work. This work precisely cancels the gain in kinetic energy.

 

[bcrowell]

This is the correct answer, and is analyzed in mathematical detail on pages 245 - 247 of the technical monograph "Lorentzian Wormholes" by Matt Visser

Is this on arxiv?

Here's a post from a previous thread with some links to non-paywalled material:

https://www.physicsforums.com/showpost.php?p=819700

 

[pervect]

I believe it's a book - see for instance https://www.amazon.com/dp/1563966530/?tag=pfamazon01-20.

I believe it's pretty much "the" reference on wormholes. Visser has excellent credentials.

Unfortunately, perhaps due in large part to a semi-popular book that makes similar incorrect claims to the "wormhole FAQ" (which I'm not familiar with), there appears to be more confusion on this point than there should be :-(.

 

[George Jones]

Is this on arxiv?

No it is a book

https://www.amazon.com/gp/product/1563966530/?tag=pfamazon01-20

that, surprisingly, seems to be out of print.

 

[HarryRool]

Be aware that Visser is assuming a wormhole metric (gravitational field) that is discontinuous across an infinitesimally thin throat. This assumption naturally leads to a nonconservative gravitational field, which motivates his calculation. But the usual assumption in general relativity, as I understand it, is that the metric is never discontinuous across a surface (because the surface geometry would then be ill-defined) [See, for example, Gravitation by Misner, Thorne, and Wheeler (1973), p. 553]

If instead you assume that the metric changes continuously across a very thin throat of finite (i.e. non-infinitesimal) thickness, the gravitational field remains conservative. This, by definition, rules out the possibility of any closed paths along which a particle could have gained or lost energy after returning to its starting point (which agrees with the Wormhole FAQ excerpt).

Although the assumption of a metric discontinuous across the wormhole throat is mathematically convenient (see Visser's calculation on p. 246-7 of his book), I'm not sure it's physical. [Are there any examples of genuine, as opposed to approximate, discontinuities in nature?]