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wormholes, part V

Since my last post on this topic, several new interesting things related to this have come to light. And some of the things I mentioned last time I wanted to get to seem less important, so I'm not sure whether I will get to everything. And this whole series may be longer than I thought or veer off in another direction.

Recently, some friends at work and I have been discussing the possibility of making a low budget sci-fi film related to the Many Worlds Interpretation of quantum mechanics. And this seemed like a pretty independent topic, but somehow in discussing the physics issues behind what we envision the plot of our film to be, there have been some crossovers. So I have had some new and interesting thoughts about why wormholes should be impossible from thinking about that. But I've also learned some new things in the course of reading some more papers on wormholes while trying to get the details right for this part V post.

First, there's a pretty good popular-level reference online which summarizes most of what I've already discussed plus a few important other things about wormholes. It comes from a Scientific American article written by Ford and Roman in 2000:
http://www.bibliotecapleyades.net/ciencia/negativeenergy/negativeenergy.htm

(A good bit of what I wrote in my previous posts was based loosely on what I found in Thomas Roman's 2004 review of this subject http://arxiv.org/abs/gr-qc/0409090, but the popular link above is more readable for a general audience.)

I said that I wanted to try and give some examples of the kinds of restrictions the QEI's and what we know about the Casimir Effect put on the construction of wormholes. Rather than doing the work myself, I'll just quote from the SciAm article above since they provide some numbers:

When applied to wormholes and warp drives, the quantum inequalities typically imply that such structures must either be limited to submicroscopic sizes, or if they are macroscopic the negative energy must be confined to incredibly thin bands. In 1996 we showed that a submicroscopic wormhole would have a throat radius of no more than about 10-32 meter.

This is only slightly larger than the Planck length, 10-35 meter, the smallest distance that has definite meaning. We found that it is possible to have models of wormholes of macroscopic size but only at the price of confining the negative energy to an extremely thin band around the throat. For example, in one model a throat radius of 1 meter requires the negative energy to be a band no thicker than 10-21 meter, a millionth the size of a proton.

Visser has estimated that the negative energy required for this size of wormhole has a magnitude equivalent to the total energy generated by 10 billion stars in one year. The situation does not improve much for larger wormholes. For the same model, the maximum allowed thickness of the negative energy band is proportional to the cube root of the throat radius. Even if the throat radius is increased to a size of one light-year, the negative energy must still be confined to a region smaller than a proton radius, and the total amount required increases linearly with the throat size.

It seems that wormhole engineers face daunting problems.


So hopefully this gives you a sense for what an advanced civilization would need to do in order to make a wormhole such as that depicted in Interstellar, assuming it were even possible. They would need to be able to harness amounts of negative energy that were on par with the total (positive) energy output of billions of stars (like, the energy of an entire galaxy). But on top of that, they would need to find a way to concentrate all of that energy into an extremely tiny space much smaller than the size of a single proton. This is obviously something that, if it worked, would require a very "post singularity" civilization. But there's a catch-22 here in that, it's hard to imagine a civilization which could harness all of the energy in an entire galaxy (even if we were talking about positive energy rather than a kind of energy not known to exist in such quantities) without imagining that they had first been able to colonize a galaxy. But if they haven't been able to build a wormhole yet (the most plausible way anyone has come up with for traveling faster than light) then how would they be able to colonize a galaxy? Even if they had lifespans long enough to live for the hundreds of thousands of years it would take to make a roundtrip journey like that, they wouldn't be able to communicate back to their home planet or with other pioneers exploring other regions of the galaxy, while they were traveling. But all of this of course is pure science fiction, since we're not talking about positive energy, we're talking about negative energy which, as I've explained in previous posts, can only exist momentarily in very tiny quantities microscopically.

This leads in to my next important point: why couldn't an advanced civilization figure out a way to somehow mine negative energy, picking up little tiny quantities of it here and there from different microscopic effects, and store it or concentrate it somehow, building up a vast resource of negative energy which they could use to build wormholes?

There are a couple reasons they can't do that. One of course is that in doing so, it would violate the quantum energy inequalities. But even so, given that the full extent of these inequalities is still being worked out and we don't know exactly where or when they apply (for example, it has been proven for flat space and for various curved spaces, but if you add extra dimensions or other weird modifications of gravity, there are still some cases where it remains unproven), is there any more solid reason to think this couldn't be done? The answer is yes, there's a big reason which I had left out of previous posts but which is highlighted in this SciAm article and I've seen reference to in a few other places. The reason is, violating the QEI's would also allow you to violate the 2nd law of thermodynamics, one of the most sacrosanct laws of physics ever discovered, even more sacred (I dare say) than the absoluteness of the speed of light.

One of the unique things about gravity as opposed to other forces is that, as far as we know, it only acts attractively not repulsively. This is because the charge associated with this force (mass/energy) is believed to be always positive. (With other forces, such as electromagnetism, the charge--electrical charge--can be positive or negative, and therefore you can get either attraction or repulsion.) A repulsive force (or "antigravity") is what's needed in order to stabilize a wormhole. That's why you need negative energy. And because of quantum uncertainty, you do have a combination of positive and negative energy fluctuations in the vacuum, which average out to zero (or very slightly above zero) over the long run or over large regions of space. But by "long run" and "large regions of space" here we mean compared to the Planck length or the Planck time which are both very very tiny. Because the average has to be zero, if you take away the negative energy and beam it off into deep space, you would be left with a bunch of positive energy. In other words, you would have extracted positive energy out of the vacuum that you can then use to do useful work. This would be a free and infinite energy source, which is the holy grail for many crackpots who have made it their life's work to try and build perpetual motion machines (and often claim falsely to have succeeded). Negative energy, antigravity, perpetual motion, and breaking the 2nd law of thermodynamics (which implies that you need to expend energy to do useful work, you can't just do it for free) are all directly connected to each other. A firm disbelief in this by the physics community is why all of the people who claim to have harnessed "zero point energy" are ignored. The 2nd law of thermodynamics is something which should almost not even be regarded as a law of physics, but as a law of mathematics/statistics. It's pretty much a direct consequence of statistics, with only very minimal mathematical assumptions going in (such as ergodicity). If it were broken, it wouldn't just mean the laws of physics don't work, it would mean statistics and basic mathematics doesn't work.

In the next part, I'd like to connect up some of the issues here with the issues we've been discussing in the development of our low budget sci-fi film. As a teaser, I will say that a big thing I realized after writing all of this is that I've been thinking of "traversable wormhole" the whole time as mostly meaning "something big enough that a human being could pass through it". This is the type of wormhole portrayed in Interstellar. And as I hope you'll agree after reading this far, it seems like one can say with a very high degree of certainty that it would be impossible, even for an infinitely advanced post singularity civilization. However, there is another class of traversable wormholes I wasn't thinking about much when I started writing this series. And that's microscopic wormholes that could allow a single particle or some other small piece of matter or information to pass through, from one point in space to a very distance point in space. If this were possible, then you would have faster than light communication but not faster than light travel (unless you could scan every atom of the body, convert it to pure information, beam it through, and reconstruct the body--similar to Star Trek teleportation). It would still give rise to all of the same paradoxes of time travel, but it seems much more difficult to rule out just based on the physical restrictions on negative energy densities. I think it's pretty likely that this type of traversable wormhole is also impossible to build, although in focusing on the big kind of wormhole featured in Interstellar, I was missing what is surely the more interesting question (of how or why we can't build a microscopic traversable wormhole that could be used for communication). This will get us into issues of computational complexity, revisiting Hawking's chronology protection conjecture, and seeing the 2nd law of thermodynamics come up again in a different way.

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