This thread was threatening to get hijacked by questions about the legitimacy of Heinlein’s portrayal of the twin paradox in Time for the Stars. The basic premise being that as the one twin continues to accelerate, they eventually lose telepathic contact because of the relative time dilation, but after the twin decelerates, even though they are far away, the telepathic contact resumes. One poster objected to this, saying that for as long as the one twin is still accelerating, which twin is aging faster and which slower is an open question - they are both the younger twin from their own perspective - and it is only when the one twin decelerates that he become the younger one. So:
Is this true? Is it only the final deceleration that makes him ultimately the younger one?
What if they came back in contact, but the one was still accelerating? Would they both think they were younger?
What if instead of the one twin decelerating, the earth twin decides to accelerate to match the traveling twin? Would this make a difference? Would he have to match just the acceleration, or would he also have to match the velocity?
What if the twins tried to communicate using a conventional EM signal? Assume that distance is not an obstacle - the one twin is not accelerating away from the the other, they are accelerating “in place”.
You can’t compare them to say one is younger unless they are brought together. When they are far apart, their relative time is ambiguous proportional to how far apart they are.
It wouldn’t matter that one was still accelerating, if they are brought together, their relative age can be compared.
Yes. No (see 2.).
Here it would depend on if they are accelerating towards/away from each other, or parallel to each other. It would be the same as if they were in a gravitational field.
Actually, you should look at simultaneity on the Wikipedia page on relativity, especially the figure. Points A and B can be simultaneous, or either one can be in the other’s past, depending on the frame of reference. Even if A and B are stationary WRT each other, and agree that the horizontal green line is constant time, they are not simultaneous in the blue or red frames of reference. On the other hand, for Science Fiction, it’s reasonable to say that the two beings have to agree on a frame of reference to be able to communicate.
By the way, Larry Niven had this also in, IIRC, World of Ptavvs. The relative velocity of the two beings, and not spatial separation, prevented telepathic interfacing. There, they were all within the solar system, so there was less ambiguity of simultaneity.
The problem is that the book “Time for the Stars” has as one of it’s premises that relativity doesn’t always hold and that faster than light communication is indeed possible. And so the author is free to brush Einstein’s theories into the trash. When you’ve got instantaneous telepathic communication over distances of multiple light years then it turns out you can indeed tell which twin is older and which twin is younger without the need to bring them together.
Of course, if you want to stick with what we currently think are the actual physical laws of the universe, it seems you can’t.
The two twins aren’t identical once one of them starts accelerating. This isn’t special relativity, where neither has a preferred rame of reference – the one that’s accelerating is clearly different from the one at rest – he’s accelerating. He has a force acting on him to make him accelerate. The other one doesn’t. You can’t switch to some other inertial reference frame in which the second twin is accelerating and the first one is stationary. So they are distinguishable, and the one that’s accelerating will seem to see time passing more slowly than the stationary one.
This. The basic issue with the ‘simultaneous’ telepathy described in the story, is that Heinlein doesn’t consider the question, ‘to whom does it appear simultaneous?’. If the communication appears to be sent and received simultaneously in one twin’s reference frame, then it will not appear to be simultaneous in the other’s, when they have a relative velocity (even if neither is currently accelerating). Einstein’s Special Theory of Relativity doesn’t say anything about the situation described in the story, because the situation as described is incoherent under the framework of that theory.
Heinlein has one twin accelerating. Special Relativity assumes inertial frames of reference, which must be at constant velocity. Read the Wiki on The Twin Paradox.
and
Because Heinlein’s traveling twin is under acceleration, he is not in two different intertial frames, but an infinite number of inertial frames. Each moment is a jump to a different frame.
Yes, Heinlein does propose a system of communication that is faster than light. Yes, that does violate our understanding of physics. It’s a game of “What If?”. But the effect is as if the two are repeatedly being brought back together to compare their differences. Heinlein only violates Einstein’s physics with the telepathy, he treats the rest of physics the same. It is effectively a different kind of thought experiment to show what is happening with near light speed travel.
IIRC Heinlein addresses two complications with the telepathic contact. The first is time dilation, and so as the traveling twin accelerates the communication becomes more difficult for the homebound twin because he has to spend longer and longer to receive and send the messages, and the messages they communicate get shorter and shorter as a consequence. Of course, for the purposes of the story, the traveling twin does “slow down again” at other points in the journey, making the communication easier. Okay, so there is a minor difficulty that the destination star probably is not at rest compared to Earth, still, the relative velocities between Earth and those systems are probably a lot closer than the relative velocity between Earth and the traveling, done and high fractions of light speed.
The second complication that Heinlein proposes is a kind of mental slip, that the fast aging twin loses the ability to remain in contact with the slow aging twin. IIRC he does suggest an reason, but I don’t recall the specifics. But Heinlein puts this in to push the next element of the story, that the telepathic ability is passed down to descendents, and the contact can be established with them. So the fast aging twin’s kid picks up the communication, then the grandkid. Again, that’s the author making up the rules as he goes.
Yes, the telepathy does violate what we know of the laws of physics, but no, the effect is not as if the two are repeatedly brought together, because it sidesteps the critically-important question of how they’re brought back together. If the stay-at-home twin is zipped out to meet the travelling twin, that’s completely different from if the travelling twin is zipped back home to meet the Earthbound twin, and there’s no reason to prefer one over the other.
I think you’re mixing up two different plot elements, here. Most of the telepathic pairs were twins, with the result that the one at home was geriatric (but hopefully not dead of old age) by the time the ship arrived. But one of the pairs was a grandfather and granddaughter, so of course the grandfather was chosen to be the one who went on the ship while the granddaughter stayed home.
Yes … but the complication I don’t see him addressing at all is the question of ‘simultaneous to who’ in the simultaneous communication. Although one twin seems to take longer to express the same thought, their conversation continues unbroken from statement to response–and it just can’t, given any consistent relativistic picture of the meaning of the term in this context.
Assume, for example, that what we mean by simultaneous communication is ‘transmission and reception are simultaneous from the point of view of the telepath sending the transmission’. Well, in that case, then when they’re traveling apart, the receiving twin will detect a time lag, because ‘simultaneous’ events lie along a different set of sets of coordinates in space-time in his reference frame. This has the interesting consequence that each twin will see the other twin’s transmissions as taking time, even though their own transmissions are instantaneous; there will be long gaps in their conversation, which each will see as the time needed for the other twin’s response to arrive.
The fun part of this actually happens when the twins are approaching each other, and the time lag from the reception end appears to be negative when the transmission appears instantaneous from the transmitter’s frame. If they are approaching each other quickly enough, or think fast enough, they can get their answers to their partner before the partner has asked their question. Physicists call this ‘causality violation’. Usually, this means you’ve made a bad assumption. But there’s no consistent assumption you can make for this situation that can’t be made to lead to this sort of result; when events are separated by a spacelike interval (which events separated in space but not in time–i.e. simultaneous events–must be), then there are reference frames in which event A precedes event B, in which event B precedes event A, and in which the two are simultaneous. So if there’s any way for one of those events to affect the other, then there’s a way to build a causally inconsistent model. Which then leads to any sort of time-travel paradox you care to think of.
To be fair, there is one consistent assumption you could make: You could establish some cosmically-prefered reference frame, and then say that all telepathic communications are instantaneous as measured in that prefered reference frame, no matter how the telepaths themselves are traveling. This, effectively, is what Heinlein did in Time for the Stars. But there’s no reason to expect that that prefered reference frame would be the one that Earth is in, as is the case in the book.
You don’t have to decelerate to detect who is older and who is younger… Just put one in a light speed circle around the other… He’ll be going near c, and yet will still be able to receive timely communications about his siblings life.
Unless the changing of direction counts as deceleration, i suppose… I’m not all that big on relativity.
Btw… I’ve got a question related to the speed of light. Due to time dilation, a person in a ship sees themselves going faster and faster, and theoretically, at c, a person would be going infinitely fast. So, at what fraction of c do they see themselves as going greater than 300,000 km/s? It has to happen sometime, but i’ve never been able to make the math work.
I’m not sure what you’re asking, here. If I’m in a ship, I always look perfectly normal, to myself. It’s everyone else outside the ship who is having their time and lengths screwed up. And I always see the Earth moving away from me at the same speed that the Earth sees me moving away from them.
I think the idea is to use the metersticks of the stationary frame to measure distance traveled as perceived by “stationary” observers, which makes sense if you’re trying to figure out the moving-frame time required to get to, say, Alpha Centauri: 4.2ly=v*t’, with 4.2ly measured in the “stationary” frame and t’ in the “moving” frame. This “speed” exceeds c if you’re moving faster than c/sqrt(2).
Usually, this means you’ve made a bad assumption. But there’s no consistent assumption you can make for this situation that can’t be made to lead to this sort of result; when events are separated by a spacelike interval (which events separated in space but not in time–i.e. simultaneous events–must be), then there are reference frames in which event A precedes event B, in which event B precedes event A, and in which the two are simultaneous. So if there’s any way for one of those events to affect the other, then there’s a way to build a causally inconsistent model. Which then leads to any sort of time-travel paradox you care to think of.