MarkB
Legend
The principle of Relativity is not "everything is relative to everything else." It could more accurately be stated as "everything is relative to the speed of light, which is a constant."
Physics for a friend....Twins Paradox
The principle of Relativity is not "everything is relative to everything else." It could more accurately be stated as "everything is relative to the speed of light, which is a constant."
tomBitonti
Adventurer
What I remember is that what differentates the twins is that one stayed in an inertial frame of reference, while the other does not.
In the looped universe case, wouldn’t the paradox still occur if both twins start in the same frame, then only one is boosted? (Edit: Hmm, but then again, what if the twins were put in the same frame at the end by boosting the second twin, instead of slowing down the twin that was initially boosted?)
But then, what if one of the twins is accelerated by a passing massive body four times, so to make a similar trip (as in the usual case, not the looped case)?
Thx!
TomB
In the looped universe case, wouldn’t the paradox still occur if both twins start in the same frame, then only one is boosted? (Edit: Hmm, but then again, what if the twins were put in the same frame at the end by boosting the second twin, instead of slowing down the twin that was initially boosted?)
But then, what if one of the twins is accelerated by a passing massive body four times, so to make a similar trip (as in the usual case, not the looped case)?
Thx!
TomB
Last edited:
Not really.
You can do the analysis considering two travelers - one who passes by Earth at 0.8 C on their way to Alpha Centauri, the other passing by Earth at the same moment going 0.9c for the same trip. They'll arrive at Alpha Centauri each having experienced a different amount of time dilation for that segment of trip, both of them moving at constant velocity - so both in inertial frames of reference.
The twin paradox requires that we get the two people in the same place, so that we can see how weird it is that one ages more than the other. But, you don't need it to show time dilation varies for different speeds.
freyar
Extradimensional Explorer
If I'm reading what you're saying correctly, yes. In the "looped" universe, the twin that stays on earth still ages more than the one that travels around the entire universe. The calculation works the same as in the usual "unlooped" case, except you only have an "outgoing" leg to the trip. It doesn't matter whether you stop the traveling twin at the end or have the earth-bound twin jump on the spaceship. What is going on here is that, in the loop universe, relativity works as normal on small scales, but there is a special frame for the universe itself if you know about the largest sizes.
Incidentally, people do try to measure if our universe has circle-like directions to it (the geometries, being 3D in space, are a bit more complex), or really a finite size. As you might guess, we basically just know that the size of the universe is at least a bit bigger than how far we can actually see in the universe, somewhere around 15 billion lightyears (I don't remember the precise results).
I think i recall the comoving distance to the edge of the observable universe (which takes into account expansion - where the edge of the universe is now, after that light was emitted), is currently best estimated as 14.3 billion parsecs, so 45 billion light years or so.
freyar
Extradimensional Explorer
Yes, I just had a minute to look it up. And it seems the 2003 limit on the size of any "loop" in the universe is just a bit less, though I think there are newer, slightly larger limits.
Is that a limit in the size of a loop in the universe, or in the observable universe?
freyar
Extradimensional Explorer
A loop in the universe. Although, if it were that small, the loop would just fit inside the observable universe. Like I say, I think the limits are now slightly better, maybe the loop has to be just bigger than the observable universe. I can't quite remember off the top of my head, and I'd have to do a real lit search to find it since wikipedia doesn't list anything more recent. But I'm pretty sure it's not possible to do much better than that (for pretty clear reasons, I think).
Similar Threads
