Comment by ars | Hacker News Reader

Comment by ars | Hacker News Reader

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No. Using them is the problem.

Say you are in a gravity well with one side of the wormhole, and the other side is outside the well.

You could "lift" matter outside the gravity well without spending energy.

There are other problems as well: Gravity has no discontinuities, as objects move, the gravitational field moves with it. You never have a situation where gravity just suddenly shows up. (The same is true for an electrical field BTW - you can never create one, you can only move an existing one (i.e. split up the positive and negative parts). A magnetic field can be created, but that's because you always create a north and south at the same time. If magnetic monopoles existed you could not create just one, you could only separate the two halves.)

Anyway, a wormhole would allow you to have a gravitational discontinuity and that's impossible, it would create a gravitational wave with an infinite frequency. As you know a true square wave is physically impossible - the fourier transform requires an infinite frequency - but that's what you are doing by moving matter via a wormhole.

> You could "lift" matter outside the gravity well without spending energy.

How is that? Wouldn't the gravitational force just propagate across the wormhole, making for a continuous gravitational gradient?

Maybe we're talking about separate conceptions of what a "wormhole" is here. For one example of what I'm picturing, you could have a one-wormhole universe as a three-dimensional hologram along the surface of a 4D hypertorus. You can go "through the doughnut hole" to get somewhere quicker than you could by going "around the doughnut", but that doesn't mean that there's a discontinuity anywhere on the surface of the hypertorus. Gravitational waves from one point-source would be propagating both "into" the wormhole (along the inside of the doughnut) and "through regular space" (along the outside of the doughnut) and eventually encountering themselves at the destination and maybe constructively or destructively interfering, but they wouldn't be forced into a square wave at any point.

> How is that? Wouldn't the gravitational force just propagate across the wormhole, making for a continuous gravitational gradient?

That would be even worse. Let a strong gravitational force go through the wormhole and drop something near it (not through it).

Then move the wormhole (and the gravitational force) elsewhere, lift the object, and bring the wormhole back.

Normally the thing that generates gravity has inertial mass, so it costs energy to move. Not with a wormhole. If you speculate that it should have inertial mass, then how much?

I'm kind of lost by your contruction. Is the something we drop the same as the object we "lift"? What does it mean to lift the object? Try removing the pronouns, and being more specific with your steps.

Is this a thought experiment you came up with on your own, or do you have a paper you're citing? If the latter, do you have a link?

> Try removing the pronouns, and being more specific with your steps.

That would be even worse. Let the strong gravitational force of the Earth go through a wormhole located on a small platform in deep space, and drop a rock near the wormhole (not through the wormhole).

Then move the wormhole (and the gravitational force) elsewhere, lift the rock off the platform, and bring the wormhole back.

Your thought experiment clearly implies energy is spent moving the wormhole. That would be the energy needed to spend to move your example rock.

The solution to this is almost certainly "moving the wormhole takes energy and solves this 'paradox'". The mass-energy of the wormhole could be from gravitational field energy, for example.

How much energy? The wormhole doesn't have an inherent mass, so how much energy does it take? After all you can put an arbitrary amount of mass through it.

I would guess that that would depend on the situation.

I would think that whatever method you have of moving a mouth of the wormhole, would have some interactions with the masses providing the gravitation.

Also, I'm not 100% sure that a wormhole would not have something like an inherent mass, because iirc there are solutions where a black hole mass is entirely because of the way spacetime is set up, without any particles needed? I'm not sure about that, but I think that is what I read..

You're looking at it the wrong way. If you can extract energy from dropping the rock through the wormhole, it takes energy to pull the rock away from the wormhole (and, by symmetry, it takes that much energy to move the wormhole away from the rock).

You're assuming the gravitational field can't permeate the wormhole. In your first scenario, the gravity well would extend out of the other side of the wormhole.

A wormhole is in no way a gravitational discontinuity, the toplogy for them is well defined. The creation of a wormhole would be a bit tricky, as this does require a discontinuity, but there's no reason to think that's impossible. After all, a gravitational singularity is also a discontinuity, and physicists have no problem with that.

Here's a concrete example:

https://en.wikipedia.org/wiki/Ellis_wormhole

That's a wormhole with a well-defined metric that satisfies the Einstein field equations.

> You're assuming the gravitational field can't permeate the wormhole. In your first scenario, the gravity well would extend out of the other side of the wormhole.

That would be even worse, I replied to the same thing here: https://news.ycombinator.com/item?id=12301858

> A wormhole is in no way a gravitational discontinuity

A movable one certainly is, and a non movable one doesn't make any sense from a relativity point of view.

> Ellis Wormhole

Did you read your own link? "and there is no gravity"

There's a reason they say that. And there is no place in the universe without gravity. It's a mathematical solution, not a representation of the physical world.

Can you define what you mean here by discontinuity? I meant that the function of the gravitational field is continuous everywhere under the topology of the manifold, the mathematical definition. I see no discontinuity, but perhaps you're using a different definition?

The "no gravity" line there means the stress tensor is zero, and this is a so-called "vacuum solution." Essentially all closed form solutions to the field equations are vacuum solutions because it's almost impossible to write a closed form solution otherwise.

> I see no discontinuity, but perhaps you're using a different definition?

Sorry. The gravitational field of the object you just sent through the wormhole, not the gravitational field of the wormhole itself.

> and a non movable one doesn't make any sense from a relativity point of view

Do you agree that you can't "leave the universe" in the sense of travelling past the information-propagation wavefront of the Big Bang—even in a case where our universe begins to shrink and that wavefront starts to come toward us?

If yes, then a non-movable wormhole can be justified exactly like that: it's part of that same wavefront—part of the topological outer surface of the universe, not an object "in" the universe.

You are implying absolute coordinates by saying that. It's similar to saying the universe has a center - the place where the big bang started.

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