Science and Science Fiction: “The Old Equations”

March 1st, 2012

Jake Kerr’s Lightspeed story, “The Old Equations,” has been nominated for the Nebula Award for best novelette.  It’s thematically related to Tom Godwin’s famous story “The Cold Equations” which I’ve written about at Lightspeed and on this blog.

I basically got the gig to write a non-fiction article about “The Cold Equations” because the editor of Lightspeed, John Joseph Adams, knew of my interest based on the blog post.  He was running Jake Kerr’s new story and the original Godwin story, and wanted another article to go with them.  When I got the assignment, I asked to see Jake’s story so I could link my article between the old and the new (or the original and the “old,” depending how you look at it).

They sent it to me and I started reading it and stopped…cold.  (Couldn’t resist.)

The relativity in the story was WRONG.

I wasn’t totally surprised.  Relativity isn’t well understood, even by many physics students, and one common example used in special relativity is the twin paradox.  Basically one twin making a relativistically fast round trip to a nearby star ages less quickly than his brother remaining on Earth.  It isn’t quite special relativity because there are accelerations involved.  On the outward journey, EITHER twin communicating with the other would think that the other was experience time dilation, a slowing down.

That wasn’t how Jake wanted things to go.

The story was good, moving, and I liked it.  I didn’t immediately see a fix, but I was concerned it would be a fundamentally flawed story if published as it was.  So I let the editors know my issues with the science, and they put me in touch with Jake.  He was concerned, and really cared about getting things right.

Jake describes his side of things in this article.

Here was my email to him:

> This is a case of the well-known “twin paradox” of relativity.  BOTH twins should see the other’s clock moving slower.  There is no preferred frame of reference.  The traveler does become special, however, because he winds up accelerating and changing reference frames.  I studied this as a physics major, and nearly had to teach it as a professor (avoided it!), but did have to work with it for my science fiction.  Here’s my take.
>
> The instantaneous communication is dangerous and can be used to make a time machine of sorts.  Sticking with just radio communications both Earth and the traveler (let’s call him James) will see time dilation and everything slowing down.  It will be a factor of 3 for 94% lightspeed as measured by Earth.  In James’s frame of reference, the distance to his destination is essentially contracted and from his point of view he can indeed travel to his destination effectively faster than the speed of light.  Traveling at the speed of light you could travel any place in no time, effectively (see e.g., Poul Anderson’s novel Tau Zero).  There’s a change to a new frame of reference for James coming back and he would receive messages from Earth at an accelerated rate, rapid fire.  He returns to Earth younger.  This is verified by experiment in various ways.
>
> For the astronaut, it is indeed effectively faster than light travel, although it is also time travel into the future as the price.
>
> G. David Nordley has a couple of old articles on his website about these issues if you want a free source of followup.  There’s a long and detailed wiki article, too: http://en.wikipedia.org/wiki/Twin_paradox
>
> I admit, it’s still a bit hard to understand, especially at first, but that’s how it works.
>
> OK, working within that limitation…I think there are a couple of possible ways to go.
>
> If this alternate universe didn’t develop relativity, maybe they don’t understand lightspeed as the limit.  I strongly suspect that many tests would have led to it if Einstein had been ignored, but that can still be a premise.  Maybe there’s a fuel source based on something they’ve learned about that we don’t know that can provide constant acceleration.  (There’s a relativistic rocket equation you can find to calculate speeds/times based on this idea.)  But they can only use it once.  And they don’t understand that there’s a speed limit, so James never gets up to the speed intended, but only some fraction.  He personally won’t suffer so much time passing, but a lot more time will pass on Earth.  We can run some numbers to find a scenario that works if you like.  Magnetic fields could be used to turn the ship around at Alpha Centauri.  This is probably the way to go to get something similar to your intended story, but the timescales will have to be altered somewhat.  I think this can work.
>
> There’s another possibility that I think can work, although this may be harder to do, and more the story I imagined reading than your intended one.  Basically, James and the scientists have to discover and solve the twin paradox!  BOTH frames suffer time dilation on the outbound trip, much to everyone’s concern, and the asymmetry is not so clear.  With Einstein being ignored and dying early I thought maybe only special relativity was known and issues of acceleration and general relativity were unknown.  This is more of a puzzle story solution.  James is always going to end up younger than his round-trip time as experienced on Earth, but it can be fun and surprising.
>
> Anyway, maybe do some more thinking and we can chat on the phone soon if you like.
>
> As I wrote to John, the theme of losing communications and the trip feeling like an eternity may work well:
>
> “Put your hand on a hot stove for a minute, and it seems like an hour. Sit with a pretty girl for an hour, and it seems like a minute. THAT’S relativity.”  — Einstein
>
> OK, those are some of my thoughts and ideas.  I think there are ways to rework this to keep your nice ideas, themes, and emotions, without violating relativity.  I don’t think you want to change the rules of physics for this story, but just envision a world where this one branch was neglected but not wrong.
>

So we went back and forth a bit after that. Jake was open to my suggestions and game to make them work. I went on:

> OK, I think you can make this work. A comparison of the classical and relativistic rocket equations will give you the time difference for a trip of different distances/times. James and his wife think they’ll age at the same rate and he’ll be gone for a particular length of time. In truth, it will be a much longer time, and he’ll come back aged less than her. Maybe they can be played by Demi Moore and Ashton Kutchner. 😉
>
> Radio communications will work fine, I think, as the problem can be discovered and worked out on the journey out. BOTH sides will see time dilation.
>
> One suggestion for your constant acceleration drive is zero point energy, which has been used before, but really we’re clueless about it. Maybe scientists in an alternate universe can get it better than us Einsteinians. Some other areas of speculation would be fine, too, I think. The premise is really an ignorance of Einstein, and knowledge of other branches of science. It just has to be good enough to sound plausible, I think.
>
> The return trip is constant deceleration.
>
> You could also do it with something that just makes everything move really fast, right away. Simpler math.
>
> Well, your story. I’ll let you sweat the details, and be happy to help with making the relativity work out.

Making progress.  Jake replied with:

> Okay, Mike, here’s my takeaway:
>
> They use a newly discovered (fictional) power source that can fire him to the destination at constant acceleration. The speed goal is FTL travel, but they discover that the speed of light is a constant upper limit they hadn’t considered. As a result, the trip will take MUCH longer than they expected (I can use the 30 year/10 year scenario here, I’m thinking, so I don’t need to change much). Because of this, the underlying tension is the same (he arrives home in 10 years as expected, she seems him in 30), but the underlying problem is made a bit more complicated—it’s not just time dilation; it’s the discovery of the speed of light constant cap on speed along with time dilation.
>
> I’m thinking that’s some pretty freaking cool science juju to layer on top of what is an emotional story.
>
> Things that would make my life easier, so let me know if this works in your head: He is anticipated to surpass the speed of light in his first month. This way his first sail calibration (from Earth’s pov the THIRD month—which is to say the month when there is two way communication) throws off a major speed error that can be used to create a pretty neat dramatic irony, as the reader can see what’s going on while the characters are scrambling to figure it out.
>
> Does the above make sense to you?

It mostly did…


> That sounds plausible, except the combination of speeds, times, and distances are not arbitrary and must be self-consistent.
>
> I can run some numbers tomorrow and see if I can get something close to your desired parameters, ok?

I did after Jake gave me a green light:

> OK, so I looked at the classical and relativistic cases of constant acceleration.
>
> Let me propose the simplest, easiest scenario that’s not too different from what you’d like, but not quite what you’d like either.  Maybe it will work.
>
> First, classic Newtonian physics:
>
> At one Earth gravity (9.8 m/s^2) acceleration, accelerating to halfway to alpha centauri then slowing down the second half to arrive there at low velocity (to drop probes there, etc.), classically the trip would take about 4.1 years each way, or 8.2 years total.  The maximum speed halfway would be 2.25 times lightspeed.
>
> Now, relativistically:
>
> Constantly accelerating to the halfway point would leave the spaceship at 97% lightspeed, with time slowing down by a factor of 4 at that point.  From the perspective of our spaceship, that would take 3.6 lightyears years and total roundtrip time of 7.2 years.  Close to your ten, again.  Now, from the perspective of Earth, the roundtrip will be 16 years.
>
> Spending 1-2 years at the destination will make the totals 9 years subjective time for the voyager and about twice as long, 18 years on Earth, compared to the original plan of 10 years total mission time.  This isn’t so far of 10/30 (10/18).
>
> If we speed up the ship, the ratio gets larger and closer to 10/30, but the overall trip gets shorter and the times are quicker.  If we slow down the ship, the ratio gets farther away from 10/30, although the overall times increase.
>
> (The relativistic equations are not simple, and you need to use inverse hyperbolic trig functions.  One good reference online for these can be found at: http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html if you want to look for yourself.)
>
> Anyway, I don’t think this is a bad solution.  Trip takes twice as long as originally planned from Earth’s perspective, a little quicker from our voyager’s.  Time dilation peaks at a factor of four 1/4 the way through the trip.  (If you go beyond that be careful because the frames changes, but up until that point everything slows down from both perspectives, starting from nothing and building up gradually.)  Maybe our voyager made promises to kids to be back in time for graduations, etc, and an extra 8-10 years is a big deal.
>
> Hope this is all clear.  I can do some other scenarios, but we’re not going to do a lot better than this.

Jake liked this, but the solution wasn’t perfect yet.

> So I did extensive edits with the Glies planet timeline. The editors at Lightspeed felt that a 20 year mission was unrealistic for a couple, which in hindsight I have to agree with. Oh well, back to the drawing board.
>
> So I’m going back to the scenario you outlined below. What I’d like to do is have the following goal:
>
> The age spread between the ship and earth be about 20 years when it returns. I can’t lose the tragic image of an old woman and a young man on the return when they were both young when he left.
>
> With that in mind, this could be 5 years for the ship, 25 for earth, or something similar. Below you mention that if we speed the ship up the ratio get’s larger. So, my question for you: can you give me a speed and ratio that puts them roughly 20 years apart for a trip to alpha centauri?
>
> (Note: We can actually change the destination if it makes the math easier).

Yeah, headed that way!

> Hmmm,  I gave you a scenario that provided 10 years RT using classical mechanics.  Let me restate it just in case there has been a miscommunication:
>
> Original plan: 3.3 gee acceleration for 2.5 years, deceleration at 3.3 gee for 2.5 years, arrival at Gliese 581 — 5 years to get there, and the same thing and 5 years back, using non-relativistic equations.  Classically that’s 10 years round-trip flight time plus some time at the destination.  Classically, that’s a 10 year mission from Earth’s perspective, too.
>
> Relativistically, only a little over 5 years will pass on the ship, with 41 on Earth, give the acceleration, times, and distances.
>
> Before I spend more time on this, let’s confirm why this doesn’t work for you.  41 years is a little longer than you originally wanted, but works as well as 25 or 30 to my mind.
>
> Was there a misunderstanding, that it was 10 years to get to Gliese 581, and 10 years to get back, at an acceleration of 3.3 gee?  It’s only 10 years round trip, classically.  I set the time as 2.5 years to get halfway there, breaking the trip into quarters, accelerating and then decelerating after the halfway point.  Same thing coming back.
>
> OK, please confirm.  I think the original Gliese scenario is good.

If you’ve read Jake’s story, you might notice that we’re getting longer messages, not shorter ones, as the communications continue! 😉  From Jake:

>
> Yes! That may end up working. The goal is for the the round trip planning be for a ten year mission (or slightly shorter) with the assumption that they’ll surpass lightspeed on the trip, with ignorance of relativistic effects.
>
> So that works perfectly from what you’re describing. If that’s what you said before, then I just screwed up and assumed it was a 20 year classical round trip mission. Mea culpa.
>
> Relativistically, 5 years for the round trip from James’ perspective and 41 from Kate’s is freakin’ harsh, but I don’t think that’s bad. If they’re both 30 years old when he departs, he’ll be 35 and she’ll be 71 on his return. Ouch. Double ouch.
>
> If we agree on that, then I have to do only very minor edits at this point.

A bit more back and forth, some more details, and from me:

> For each month of subjective time on the ship, you want the equivalent time interval on Earth?

Yes, that’s what he wanted.  We worked up some stuff with some detailed timestamps, and decided to ignore some issues with instantaneous communication that is very tricky and confusing to handle (leads to time travel/causality issues).

Hope I haven’t missed any key exchanges above and it makes sense.  JJA did step in at one point to suggest the destination star system, since the discovery of an Earth-like planet had been announced recently (although its existence is still in dispute).

I spent more time helping Jake with the science than I spent on writing “The Cold Legacies” article to accompany the story.

If you’re hardcore enough to have read this far, let me wrap up.  The above, with only minor editing, are the actual exchanges Jake and I had.  I was really impressed with his desire to get the science right, and if you’ve read his side of things, you know it’s true.  It’s “science” fiction and the science should be taken seriously.  It’s a good, touching story, “The Old Equations.”  Ignorance of the rules of physics creates a tragedy as the frontier is explored.

It’s a nice follow up to “The Cold Equations” and I’m pleased to have been part of its creation.  Let me encourage you to take a look at it and consider voting for Jake’s story if you’re eligible.

 

Share/Bookmark

Tags: , , , , ,

You can follow any responses to this entry through the RSS 2.0 feed. You can skip to the end and leave a response. Pinging is currently not allowed.