Dark Energy, Faster-Than-Light Travel, and Fine Structure Bombs

Last week’s talks were using sci-fi space travel as a hook to talk about relativity, and my original idea for the talk was to explain how faster-than-light travel ultimately ends up violating causality. Some observers will see effects happening before the events that cause them, and that’s just weird. In How to Teach Relativity to Your Dog, the illustration I use is a stationary dog watching a cat moving by at half the speed of light and a space alien zipping past at four times the speed of light. In that scenario, the dog can hand a water balloon to the passing alien to soak the cat, and everything makes sense, but from the cat’s point of view (shown by the slanted grid of lines in the “featured image” above), the alien passes at the cat first, and the dog later, and thus the origin of the water balloon is kind of mysterious.

I didn’t end up using this, because I thought it was probably too subtle for the target audience, but I did spend some time thinking about it, and about faster-than-light (FTL) travel in a sci-fi context, and whether there is really any plausible way to make it work. And the causality thing is a big roadblock– even the ability to send messages faster than light allows you to create paradoxes, and that’s not a good thing. If you want FTL to work, you need some way to avoid that problem, which has mostly been ignored by SF writers (though Charlie Stross in Singularity Sky and Iron Sunrise at least acknowledges it, in that the godlike transcendant AI of those stories explicitly enforces a rule against doing anything that would create paradoxes).

I did hit on a goofy idea for a causality-preserving FTL scheme, though, inspired in part by a bit from Alastair Reynolds’s House of Suns. The source of the paradoxes, after all, is having parties on both ends of the trip interact in some way, mixing faster-than-light and slower-than-light frames of reference. You might arguably be able to avoid this problem by blocking that sort of contact– Reynolds does this via magical and unexplained means, but modern cosmology offers a quasi-real method.

That is, thanks to inflation right after the Big Bang, and the dark-energy-driven accelerating expansion of the universe, there are vast regions of space that will never be causally connected to Earth– galaxies so far away that their light can’t have reached us yet, and that are being pushed away from us so fast that their light will never reach us. There’s no way to make a paradox from those places.

So, the goofy idea is this: FTL travel that’s only good over really huge distances. Like, the radius of the observable universe. You can instantaneously jump from some points in the Milky Way to points in galaxies beyond the visible horizon, with causality being preserved by the accelerating expansion of the universe keeping those points from contact with each other. But each of those transfer points goes to a completely different galaxy, out of causal contact with any of the other points you can reach from points within reach of the first one.

(You might reasonably complain that if these are points that will never be connected at slower-than-light speeds, there shouldn’t be any way to connect them to enable the FTL travel in the first place. But you traditionally get one free bit of utter hand-wavey magic per SF story, so I’ll cash that in there.)

I have no idea how you’d build a plot around that, which is why I’m throwing it out in a blog post rather than trying to put it in a story to sell to somebody. But you could probably twist that in some fun ways– if the ultra-long-range FTL is relatively easy, it’s a novel explanation of the Fermi paradox, for example: we don’t see interstellar empires in the Milky Way, because those empires exist, but consist of one solar system per Hubble volume; if you can hop to a distant galaxy easily, it’s not worth the hassle to go to the next star over. Or if you want to do the “deep time” thing, you could play with the fact that over billions of years, as dark energy speeds up the expansion, you’ll be able to reach galaxies that are closer to your starting point. I’m sure somebody with some plotting skills could have fun with this; if you do, name something after me.

Another oddball idea that came to mind as I was thinking about this (there were a bunch of annoying delays on my flights down to Houston and back) was to throw in the changing fine structure constant business. The fine structure constant, as you may or may not know, is a dimensionless constant consisting of a ratio involving Planck’s constant, the speed of light, and the fundamental charge. This tells you something about the strength of electromagnetic forces in quantum mechanics, and gets its name because it turns up in calculations of the “fine structure” of atomic energy levels.

There are exotic theories in which the fine structure constant changes over time, and some observations that I don’t entirely believe that claim to see it changing at different rates in different parts of the sky. Which means that if you were to put the ultra-long-range FTL scheme into a story, you might include trips to places where the constant has a different value.

But then, you have to ask, what would the effect of that be? That is, if you moved something via magic FTL means from one place to another, what would happen to it when it arrived in a place with a different value of the fine-structure constant?

This is the kind of thing that lends itself to back-of-the-envelope Fermi problem stuff, so we can try to estimate the effect. Basically, a change in the fine-structure constant would lead to a shift in the energy levels of all the atoms and molecules making up an object moving from one place to another. the details of this would be kind of complicated, but you might reasonably guess that after a fairly short time, any excess energy produced would go into heat. Because thermodynamics.

So, how much heat are we talking? Well, the general energy scale for atomic energy levels is around an electron volt, or about 10^-19 joules. The fine structure constant is a bit less than 0.01 (very close to 1/137, a fact that drove some famous physicists a little crazy), so we could maybe say that 1% of that energy is associated with the fine structure, or about 10^-21 joules per atom. But if you change the fine structure constant by too much, you would rule out the formation of stars as we known them– this is one of the things that always comes up in Anthropic Principle arguments– so any change would need to be much less than that. Let’s call it 1% again, so you could get maybe 10^-23 joules/atom out of moving stuff from one galaxy to another.

So, how much total energy is that? Well, if you’re talking something like a person, you’ve got maybe 100 kg of mass, and the average mass of an atom making up a person is probably around 10 atomic mass units, so that’s 10²⁸ atoms/person, or a total energy of around 10⁵ joules. The canonical scale for sudden release of thermal energy is the TNT equivalent, with 1 ton of TNT giving up an energy of 4×10⁹ joules, so this would be about one ten-thousandth of a ton of TNT, or tens of grams. Somewhere short of a stick of dynamite, I guess. Which would probably be kind of unpleasant for the person arriving at the end of their trip, but maybe not fatally so.

Of course, I pulled all those numbers out of thin air, other than the unit conversions, so if you wanted to play with this, you’d have wiggle room. Having people and objects making an FTL transition arrive either badly chilled or sweating could be a reasonable detail. Or if you want a weapon, you could imagine connecting to something with a much greater difference, and making a bomb out of it (though anywhere with a fine-structure constant different by enough to make a big boom probably won’t contain stars and planets that we would find useful).

Anyway, that’s the kind of idle noodling around you get from somebody with a little knowledge of physics and astronomy who’s stuck in an airplane thinking about sci-fi space travel. Which ought to be enough to prove a point of some sort.