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.

Comments

  1. #1 Matthew McIrvin
    May 6, 2014

    I’m not sure the super-long-range jump on its own really eliminates paradoxes, if it’s two-way, because the FTL jump is itself another kind of causal connection. You have to have some reason why you can’t jump way outside your light cone, then jump back into the past of your original light cone.

    You could make all the superluminal jumping happen along a preferred foliation into spacelike surfaces, for instance: it would violate relativity, but maybe in a gentle enough way to not break existing physics too badly. A lot of SF treatments are sort of implicitly doing this whether or not the author realizes it.

    But if you do that, I think you don’t even need to specify that you can only jump to causally disconnected regions.

  2. #2 Chad Orzel
    May 6, 2014

    I apparently wasn’t clear enough about this, because I got the same basic question on G+, too. I was thinking something location-specific for this– that is, you could go back and forth between two specific points at a very wide separation, but not from a point in our solar system to a point in a distant galaxy and then back to a point near Alpha Centauri, for example. That would allow FTL in a local area, and open up paradoxes, I agree. But if you had a 1:1 mapping between points, or something like that, then you would need to travel multiple light-years at STL speeds to make a trip to a nearby star, and causality would be safe. Or safer, anyway.

    If you wanted to drag classic SF elements in, say that it works via wormholes that are only stable when connecting points separated by Hubble-volume quantities of space.

  3. #3 Steve
    May 6, 2014

    Doesn’t the fine structure constant affect radioactive decay rates and neutron capture cross sections? Maybe somebody could make a ball of plutonium that is subcritical in our galaxy but explodes when it’s mailed through your portal.

  4. #4 Uncle Al
    May 6, 2014

    FTL commuting to causally disconnected regions has boojums. Nothing dictates one shape of space during all creations. Local vacuum temperature of 1000 C or a universe filled with dilute neutral hydrogen (early after a Big Bang) would be inconvenient immediately after arrival.

    Open a wormhole to obtain an unlimited energy source or sink. The trick, as with piercing an aperture into a tightly inflated balloon, is not to shatter the membrane during or after.

  5. #5 Matthew McIrvin
    May 6, 2014

    The jumping between regions with physical constants reminds me of Asimov’s novel “The Gods Themselves,” in which a limited exchange between universes with different physical constants gets exploited as an energy source, but eventually turns out to pose a danger to the universe as the different physics “leaks through”.

  6. #6 Matthew McIrvin
    May 6, 2014

    “I was thinking something location-specific for this– that is, you could go back and forth between two specific points at a very wide separation, but not from a point in our solar system to a point in a distant galaxy and then back to a point near Alpha Centauri, for example.”

    OK, so it’s really a more limited version of the “special foliation” case. You’ve got two timelike worldlines (for the two different “places”) that are mapped onto each other, with the events on one mapped to the events on the other with a consistent temporal order.

  7. #7 z
    May 6, 2014

    I was more thinking it was similar the old cliche of “dream worlds”. In that the vehicle of FTL (dreaming), allowed the user to travel (or rather teleport as I tend to view travel as continuous) to a “far off world” that is completely separated from the origin. Though once he arrives back (back to the original or “back” to the dream world), his place and time would still fall in line with what if he were a non-FTL user.

  8. #8 Lyle
    May 6, 2014

    With your comments on the fine structure constant you are approaching Eddingtons fundamental theory, which is a throughly confusing work, He is one of the folks you are referring to about the value of 1/137. He had a nice theory when it looked like the fine structure constant was 1/136 but then experiments destroyed that beautiful theory. So he just said we will add one because it seems a nice thing to do. making it 1/137.

  9. #9 Stephen
    May 7, 2014

    I am not too clued in around the physics of causality, but to me it seems that the extent of the problems that come with broken causality would be dependant on how the universe would deal with paradox’s and then you would have to wonder if there could be such a thing as a paradox as for all we would know is that once a person has done a thing during time travel, that thing will always happen and said travellers were always there and are incapable of changing any order of events up to when they originally left. Such a temporal loop was made substantially , for me anyway, in the Warhammer 40k novel Desert Raiders which, despite the phenomena being used as book ends to the story, displays a temporal loop well and how said causality disreprancies would not change the timeline.

  10. #10 Mu
    May 7, 2014

    Even if it’s possible to construct examples where FTL travel seems to subjectively violate causality, does that make it impossible? If I’m hit by an artillery round fired from beyond visual range at supersonic speed, I die before I’ve been subjectively able to register the boom, but that doesn’t mean that overall causality has been violated. Unless FTL travel actually reverses the arrow of time, and I can arrive at my point of origin before I started, I might end up highly confused but not in true violation of causality.

  11. #11 Eric Lund
    May 7, 2014

    @Mu: I think the prohibition is not against FTL travel per se, but rather crossing the speed of light barrier. If you cross that barrier, then you are not in an inertial frame, and somebody who is (and is therefore privileged over your non-inertial frame) will see your arrow of time reverse. That means you could return to the same point in space time, violating causality. A tachyon does not necessarily violate causality as long as it does not interact with anything in the subluminal universe.

  12. #12 Sili
    May 8, 2014

    10^5 joules would heat 10^5 grams 1 deg C, so if that’s all, arrival would be like a bad fever (or hypothermia on the return).

  13. #13 wereatheist
    Berlin, Germany
    May 8, 2014

    @Sili, #12: you are off by a factor of 4.16 or so.
    Heating would be less than by a quarter of K.
    So no bad fever only some sudden feeling of internal heat :)

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