Can Wormholes Be Stabilized Using Negative Energy Density?

[Christofer Br]

Could we hypothetically use it to create a region of space with the magnitude of the stress component of stress energy tensor greater than magnitude of mass denisty component?

 

[mfb]

No.
To make it worse, all solutions (I know of) need negative energy densities, and we have no idea if these can exist at all.

 

[ComplexVar89]

No.
To make it worse, all solutions (I know of) need negative energy densities, and we have no idea if these can exist at all.

Not speaking to the feasibility of wormholes, per se, but doesn't the Casimir effect count as experimental proof of the possibility for negative energy densities? Or am I missing something?

 

[pervect]

Could we hypothetically use it to create a region of space with the magnitude of the stress component of stress energy tensor greater than magnitude of mass denisty component?

No, in classical General Relativity you need a negative energy density to stabilize wormholes. See for instance the Moris-Thorne-Yurtsever wormhole paper, https://authors.library.caltech.edu/9262/1/MORprl88.pdf, "Wormholes, time machines, and the weak energy condition".

The B-level "explanation" of this is that adding more positive energy just increases the gravity, causing the throat of the wormhole to collapse, rather than keeping it open.

If you can find a copy at the library, "Lorentzian Wormholes" by Visser is a good source that's not too technical.

 

[mfb]

Not speaking to the feasibility of wormholes, per se, but doesn't the Casimir effect count as experimental proof of the possibility for negative energy densities? Or am I missing something?

It is just an attractive force between two things of (high) positive energy density.

 

[pervect]

The casimir force violates the weak energy condition, so it's a promising candidate, but I'm not sure if it violates the average weak energy condition, which is what you really need to stabilize a wormhole according to the Morris-Thorne-Yurstserver paper.

To possibly oversimplify, the plates of known conductorshave a positive energy density, the space between two conductive plates can have a negative enregy density due to some strange quantum weirdness, the supression of certain frequencies in the quantum vacuum.

To violate the average weak energy condition, as I understand it at least, the negative energy between the plates has to be greater in magnitude than the positive energy density of the plates themselves.

 

[PeterDonis]

To possibly oversimplify, the plates of known conductors

have a positive energy density, the space between two conductive plates can have a negative enregy density due to some strange quantum weirdness, the supression of certain frequencies in the quantum vacuum.

I think a better way to put this is that the energy of the vacuum between the plates is slightly lower than the energy of the vacuum outside the plates. Whether this means the vacuum inside the plates has "negative energy" depends on how you pick the zero point of energy, which in the absence of gravity, i.e., in flat spacetime, is an arbitrary choice.

The problem is that, if we are talking about trying to stabilize a wormhole, we aren't in flat spacetime. That complicates the whole issue; see below.

The casimir force violates the weak energy condition, so it's a promising candidate, but I'm not sure if it violates the average weak energy condition, which is what you really need to stabilize a wormhole according to the Morris-Thorne-Yurstserver paper.

Strictly speaking, the quantum vacuum in general violates the weak energy condition. That's because the effective stress-energy tensor that you get when you try to calculate one for the quantum vacuum looks like a cosmological constant, and a cosmological constant violates the weak energy condition.

The problem is that, if we "naively" calculate the stress-energy tensor of the quantum vacuum, we find that it not only violates the weak energy condition, but its energy density is so large--by something like 120 orders of magnitude--that it produces a huge spacetime curvature that we do not actually observe. So clearly we are missing something basic about what the "actual" energy of the quantum vacuum is.

If we assume that, whatever the something basic is that we're missing, it will turn out to assign exactly zero energy density to the quantum vacuum in flat spacetime, then that would make the energy density between a pair of conducting plates slightly negative. This corresponds to a slightly negative cosmological constant, which produces attractive gravity, hence the tiny attractive force between the plates. This is one way to heuristically understand the Casimir force. (Note that on this view, spacetime between the plates is not flat, but slightly curved--basically it's a small piece of anti-de Sitter spacetime.)

To check whether the average weak energy condition is violated, as you note, we have to take into account the stress-energy of the plates. In real Casimir experiments that we have conducted, of course, the plates have a huge positive energy density that swamps any negative contribution from the quantum vacuum inside the plates. But that does not mean that any possible configuration of this sort must have that property; the Morris-Thorne-Yurtsever paper basically tries to investigate the implications of a "Casimir" configuration with plates whose energy density is small enough that the AWEC is violated, so that a wormhole can be held open. Their conclusion appears to me to be that we don't know enough about quantum field theory to know whether such a configuration is possible or not.