I thought this might bring you out.
But break that down a bit mire, will you?
No, it’s told from one twin’s point of view. There’s no ‘outside’ frame other than what’s needed for storytelling.
One twin goes to the stars, the other stays home. During the journey they communicate telepathically. One twin ages faster than the other, hilarity ensues.
Nice writeup, Jonathan.
I first read Time for the Stars in high school and loved it (I had an older sister who enjoyed her dominance over me in our family, although she wasn’t my twin, so that part of the book in particular spoke to me). I re-read it again about four years ago and found that it held up pretty well. A very satisfying ending when Tom returns home to (a) firmly tell his aged twin brother just how things are gonna be from then on, and (b) find his lovely (and red-haired, natch) true love waiting to marry him.
I still like the idea of the Long-Range Foundation (“Bread upon the waters…”), funding pure science just for the hell of it, and becoming - almost accidentally - filthy rich in the process.
And therein lies the problem. Which twin ages faster? The one who remains at rest. But, at rest relative to what? One could just as well say that Tom remains at rest aboard the stationary spaceship, while Pat zips away on the fast-moving planet. So why isn’t Tom the old one, while Pat remains young?
This paradox doesn’t show up in the actual Twin Puzzle (sometimes mistakenly called the Twin Paradox), because there, either the twins never meet up again (in which case one genuinely cannot say unambiguously which one ages more), or at least one of the twins must change reference frame at some point to meet up again, and that change introduces an asymmetry into the problem.
You know, Chronos, while you’re absolutely right about the mathematics I think it’s a lost battle, at least for storytelling purposes. We the readers need an unambiguous frame of reference and the general literary effect is that the person moving close to c does not age biologically compared to the person on the planet. Even though Heinlein got the equations wrong that is how time dilation works in culture (even if it isn’t proper physics.)
One twin leaves Earth, travels fast, and returns to Earth. Using Earth as the reference makes logical sense even if there’s no mathematical justification for choosing one or the other.
But let me ask this- if Heinlein is wrong, what actually would happen? One twin is older than the other when they meet up again, is that much true?
Yeah, I suppose that’s the real issue. What would the real world effects be of traveling near-c for 75 years? Certainly from a literary narrative standpoint RAH got to show the aging/non-aging thing and it allowed for the character to grow.
Also, can anyone find a book earlier that used this so well, or as such a central point of the story?
Actually, just to nitpick, the starship didn’t travel near-C for that entire time. It sped up and slowed down as it went from planet to planet.
I think you’ve got the wrong end of the stick on this one. The twin who stays on earth remains in the stationary frame (ignoring the acceleration of the earth around the sun, etc.) His twin, on the starship, accelerates several times – when he starts moving away to the stars, going from planet to planet, tyhen coming back. He is clearly NOT in a stationary frame, but one that has accelerated at least twice. So the twins aren’t “identical”, and one certainly has a preferred frame of reference, so one can be older than the other.
So, I don’t think heinlein screwed up in that aspect. In fact, I’ve had physics professors point out that, in such a situation, the acceleration of one twin is what breaks the symmetry. This is, after all, a realizeable experiment – you CAN take two ultra-accurate clocks and send one on a journey, then compare them when you re-unite them. (In fact, haven’t they done this?)
A more valid question is "which twin thinks the other is moving faster when they communicate telepathically? Since each is in a valid reference frame at that time, moving relative to the other at constant velocity. But, of course, it’s using instantaneous communication not subject to the laws of relativity, so it’s an unphysical situation to start out with.
Probably more than you ever wanted to know about the Twin Paradox (“so-called”, per Chronos)
Not in Heinlein’s story. The traveling twin never turns around and comes back: When they eventually meet up again, it’s through the use of a magic FTL tech that’s been invented since the ship left.
And while the traveling twin does accelerate, it’s in such a way that he’s always moving away from the other twin, so the acceleration doesn’t qualitatively change anything about the problem.
Wait. The direction of the acceleration changes the relativistic effect?
What?
Wait, he got the math wrong? Or got the math right but told the story wrong?
(Because yeah, you’re right about the return trip being by magic FTL.) If he’d written it as one twin leaves and then comes back, it would be correct then?
His calculations were correct, in the sense that went through the formulas to get the numbers, but his applications of the math were incorrect, in that the numbers he got out don’t mean what he thought they do.
And even without the magic FTL transportation at the end, the magic FTL telepathy still introduces the same problem. Basically, I think his thought process was something like “What would the Twin Paradox look like if we could look at what’s happening with both twins at the same time?”, but didn’t realize that “at the same time” isn’t meaningful in relativity.
Of course, it being a science fiction story, one can also posit that relativity is wrong and there really is some preferred reference frame… But if relativity is wrong, then where’s the time dilation coming from to begin with?
This is why I gave up on a physics degree and switched to a soft subject. It just made me the history major with the most math and science EVER.
Incidentally, Heinlein also showed a very poor understanding of relativity in other books: Citizen of the Galaxy and Methuselah’s Children come to mind. But in those other books, it was mostly just a background detail, sufficiently minor that I could sweep it under the rug of my suspended disbelief, and still enjoy the book overall. In Time for the Stars, though, it’s the major premise of the book, which makes such sweeping impossible for me.
I’m glad you picked this book as one of the better juveniles. It’s always been one of my favorites, but it always seems to be pretty far down the list when others list their favorite Heinlein books.
It seems clear to me that Heinlein knew all about the twin paradox, and he probably wrote this book by thinking, “Hey, what if I put actual twins in a story, put one in a relativistic spaceship, and then write a plot on the ramifications of that?”
The problems with the math go further than the time dilation between the twin on Earth and the Twin in the spaceship. There are also communications between twins in different spaceships, and there the reference frame issue gets a mite fuzzier. Heinlein’s basic formulation was that all that matters is how fast you’re going relative to the speed of light. He could work the time dilation formulas and come out with the right answers, but he never got the implications of them.
The most egregious example of this in Heinlein’s writing was his belief that all you had to do was keep accelerating and at some point you’d ‘break through’ the light barrier. In one of the juveniles (I can’t remember if it was “Time for the Stars”), there’s a scene where a ship’s engineer tells the protagonist that faster-than-FTL speed is not possible, and that they have to time the shutdown of the engines carefully to get as close as possible to the speed of light. The kid then asks, “Well, what happens if you don’t, and just keep on accelerating?” The engineer then gets a worried look on his face and wanders away to ponder such a deep question. The whole exchange betrays a lack of real understanding of how relativity works.
I believe “Starman Jones” also posited regions of space that had mapped ‘discontinuities’ - essentially wormholes - and that FTL travel involved ‘twisting the tail’ of a ship and accelerating past light speed at exactly the spot of a discontinuity so you’d pop out instantly in another part of the universe. And ships that ‘twisted their tails’ (accelerated past light speed) in the wrong spot would simply be lost forever - perhaps deposited in another part of the universe because their discontinuity had an unknown exit point.
Heinlein never got the fact that it requires infinite acceleration to exceed C, and therefore there’s no way you could accelerate past it.
I think this passage is frequently misquoted and misunderstood. I won’t argue RAH’s shaky grasp of relativity overall - although I will say it’s something I can set aside in the framework of a good story - but the passage in which the kid is asking the engineer questions doesn’t stand as evidence that Heinlein misunderstood the topic.
First, the careful timing of the ship’s speed is navigational, not related to exceeding c. At the speeds and time slippage postulated (whether factually correct or not), the turn from accelerating to decelerating needs fairly fine timing in order to arrive where they expect to without wasting additional travel time and fuel. I don’t recall any discussion of exceeding c.
As for the kid’s questions, I don’t recall the engineer giving a bad answer; he realizes the discussion has gone beyond what he can explain in non-mathematical terms and so tosses out a Heinleinism to cover it: “I guess you’ll just have to try it and find out!”
I’m not sure which book you mean by “this book”, but I don’t rank Time for the Stars as “one of the better juveniles”. In fact, it’s my least-favorite of them, for the reasons I described. If you mean Citizen of the Galaxy (leaving aside the question of whether it’s technically a juvenile), yes, I liked that one well enough, though it’s not my personal favorite.
And the scene you refer to, “but what if you then turn on the engines”, is from Methuselah’s Children. Or at least, that’s one of the places it showed up: I wouldn’t swear that there’s not a similar scene in some other book. And IIRC, it’s Lazarus Long that asks it, not an uneducated kid, so the captain isn’t just patronizing him with a non-answer.
It allso comes into Farmer in the Sky when Bill asks the Chief Engineer of the Mayflower what would happen if they got up to near c and then the Captain stepped up the drive and held it there. The CE claims he truthfully doesn’t know what would happen but he’d give a pretty to find out.