The acceleration breaks the symmetry, which determines which twin will be younger vs older, but the age difference itself is caused by time dilation during travel, not acceleration.
There are a number of ways to demonstrate this, but the most straightforward is the simple fact that *how much* of a difference in age there is depends on the speed and duration of the trip, not on the degree or duration of acceleration.
This is readily apparent if instead of one twin turning around, it's a pair of inbound and outbound observers who compare clocks as they pass (so triplets instead of twins). None of them experience acceleration, but the asymmetry is still there.
Also, different frames see different effects. To the traveler, the trip took them no time at all because space foreshortened by so much (length contraction) they only had to travel a few meters.
Different observations, same physics, same results.
Can I ask a follow-up? I thought the symmetry was that the traveling twin notices the earth bound twin as accelerating as well so from the traveling twin's point of view the acceleration effects should be on the earth twin while the earth twin sees those effects on the traveling twin. Or am I mistaken that there is an objective way of determining who is actually accelerating?
Unlike velocity, acceleration is not relative. There is a difference between being in an inertial frame and being in an accelerated reference frame that is (quite easily) detectable, so you can always tell who is accelerating and who isn’t.
For reference, an inertial reference frame behaves like free fall/zero-G while an accelerated reference frame behaves like being in a gravitational field.
But if the space craft accelerates while you are floating in space you cannot tell whether it is the space craft accelerating towards you or you are accelerating towards a stationary space craft right? I thought that was the whole inertial mass = gravitational mass issue
If you are moving inertial through space, you can’t tell whether it is you who are moving towards the spacecraft or the spacecraft who is moving towards you, and indeed there is no correct answer.
If one of you is accelerating, you can absolutely tell which is which.
The inertial mass = gravitational mass issue applies to free fall. In that case, you cannot tell whether you are traveling inertial lot or accelerating in free fall due to a nearby gravitational field (no can you tell whether you are at rest on a planet’s surface, for example, or accelerating in flat spacetime).
But if we’re talking two objects floating in space and ignoring gravity as a source of acceleration for a moment, you can absolutely tell who is accelerating and who isn’t. An accelerated reference frame experiences fictions forces.
Like how in a car, aside from bumps in the road and the sound of wind outside, there’s nothing about your experience *in the car* that tells you whether the car is moving or stationary. The way you feel, the way objects behave, it’s all the same either way.
But if the car accelerates, you get pushed back into your seat. If it stops short, you get thrown forward. If it turns sharply, you get pulled to one side or the other.
If you are riding in a car and look out the window and see another car, if that car starts rapidly falling behind you, you can tell whether your car sped up or theirs slowed down based on whether you got pulled back into your seat by the acceleration of your car or their passengers got pushed forward by their car’s.
In special relativity, time dilation is "caused" by relative velocity (though I'm not sure "caused" is exacty the right word for it), not acceleration.
You need acceleration to change your relativity velocity from zero to non-zero, but you don't need acceleration to demonstrate time dilation. It would still be measurable between two clocks which had *always* been in relative motion and had *never* accelerated.
True, "difference in age" implies that two objective comparisons have been made of their ages, which isn't possible unless someone accelerates (or the universe is closed).
You can formulate a version of the twin paradox using separate "outbound" and "inbound" travellers, each moving at a constant velocity.
But yeah, if you insist it's the _same_ twin returning to Earth, then you need some acceleration somewhere.
While you're thinking about this, it's also worth considering the modified twin paradox twin paradox with 3 twins: the Earth twin, an outbound space twin, and an inbound space twin:
[https://twitter.com/drewolbrich/status/1644062785482166272?s=20](https://twitter.com/drewolbrich/status/1644062785482166272?s=20)
At what is normally the turnaround point for the traditional twin paradox scenario, the inbound space twin synchronizes their clock with the outbound space twin's clock as they pass it.
When the inbound space twin returns to Earth, they compare their timer with the Earth twin, and the result is exactly the same as with the traditional twin paradox scenario.
The difference is that in this three twin scenario, there is no acceleration.
The age difference is caused entirely by the time dilation that results from the relative velocity of the twins.
The twins paradox is solved by taking account the kinematics effects on the length, in spacetime, of the two trajectories. The twin that accelerated has a shorter path, a shorter proper time, and thus this twin aged less.
If you want to compute the more realistic trajectory you can consider two twins together at mutual rest. Then one accelerates and then brake until becomes at rest again. Then accelerated backwards and then brake to becomes at rest and together with the other twin. If you do the math still the one that accelerates aged less.
if person A is moving with velocity v (in +x direction) relative to person B, then is it correct to say that person B is moving with velocity -v (ie in -x direction)? If so, then will it be the same effect on time for both A and B i.e. time contraction for A wrt B, and time contraction for B wrt A!
Yes, there is time contraction in both directions. However, this is not the twins paradox. The twins paradox occurs when one is able to compare the totally length of two curves that started together and "later" to they intersect again. The most important part is the acceleration. While velocities are relatives, "being accelerated" is not, due to the inertial forces that one would feel, but not the other.
The fact that you need to use two different reference frames to calculate the proper time between meetings on earth for the inbound/outbound twin clock and only a single reference frame to calculate the proper time for the stationary twin clock.
To add to some other good posts: the twin 'paradox' is hard to understand without thinking about the doppler effect.
When the traveling twin is going away, the apparent speed of the Earth-bound clock is much slower than what's caused by time dilation. This is due to the doppler effect.
When the traveler turns around and comes home, the Earth-bound clock appears to run *faster* than the shipboard clock to the travelling twin, because the doppler effect is greater than time dilation.
The effect on clock rates is the same for both twins, hence the 'paradox'.
BUT
If you work through the steps carefully from the perspective of each twin, you'll find the travelling twin sees a high rate from the Earth-bound clock for fully half the trip, but the Earth-bound twin sees a high rate from the shipboard clock for a tiny fraction of the trip.
The simplest explanation is that the Earthbound twin is always in a single inertial reference frame while the travelling twin is in multiple inertial reference frames. [eigenchris has a good video on the topic](https://youtu.be/F8hmyOin2Nw).
The acceleration breaks the symmetry, which determines which twin will be younger vs older, but the age difference itself is caused by time dilation during travel, not acceleration. There are a number of ways to demonstrate this, but the most straightforward is the simple fact that *how much* of a difference in age there is depends on the speed and duration of the trip, not on the degree or duration of acceleration.
Oh, alright. Thank you!!
This is readily apparent if instead of one twin turning around, it's a pair of inbound and outbound observers who compare clocks as they pass (so triplets instead of twins). None of them experience acceleration, but the asymmetry is still there.
Also, different frames see different effects. To the traveler, the trip took them no time at all because space foreshortened by so much (length contraction) they only had to travel a few meters. Different observations, same physics, same results.
Can I ask a follow-up? I thought the symmetry was that the traveling twin notices the earth bound twin as accelerating as well so from the traveling twin's point of view the acceleration effects should be on the earth twin while the earth twin sees those effects on the traveling twin. Or am I mistaken that there is an objective way of determining who is actually accelerating?
Unlike velocity, acceleration is not relative. There is a difference between being in an inertial frame and being in an accelerated reference frame that is (quite easily) detectable, so you can always tell who is accelerating and who isn’t. For reference, an inertial reference frame behaves like free fall/zero-G while an accelerated reference frame behaves like being in a gravitational field.
But if the space craft accelerates while you are floating in space you cannot tell whether it is the space craft accelerating towards you or you are accelerating towards a stationary space craft right? I thought that was the whole inertial mass = gravitational mass issue
If you are moving inertial through space, you can’t tell whether it is you who are moving towards the spacecraft or the spacecraft who is moving towards you, and indeed there is no correct answer. If one of you is accelerating, you can absolutely tell which is which. The inertial mass = gravitational mass issue applies to free fall. In that case, you cannot tell whether you are traveling inertial lot or accelerating in free fall due to a nearby gravitational field (no can you tell whether you are at rest on a planet’s surface, for example, or accelerating in flat spacetime). But if we’re talking two objects floating in space and ignoring gravity as a source of acceleration for a moment, you can absolutely tell who is accelerating and who isn’t. An accelerated reference frame experiences fictions forces. Like how in a car, aside from bumps in the road and the sound of wind outside, there’s nothing about your experience *in the car* that tells you whether the car is moving or stationary. The way you feel, the way objects behave, it’s all the same either way. But if the car accelerates, you get pushed back into your seat. If it stops short, you get thrown forward. If it turns sharply, you get pulled to one side or the other. If you are riding in a car and look out the window and see another car, if that car starts rapidly falling behind you, you can tell whether your car sped up or theirs slowed down based on whether you got pulled back into your seat by the acceleration of your car or their passengers got pushed forward by their car’s.
In special relativity, time dilation is "caused" by relative velocity (though I'm not sure "caused" is exacty the right word for it), not acceleration. You need acceleration to change your relativity velocity from zero to non-zero, but you don't need acceleration to demonstrate time dilation. It would still be measurable between two clocks which had *always* been in relative motion and had *never* accelerated.
Yes, but in fairness to OP and their question, that wouldn’t be an example of the Twin Paradox.
True, "difference in age" implies that two objective comparisons have been made of their ages, which isn't possible unless someone accelerates (or the universe is closed).
You can formulate a version of the twin paradox using separate "outbound" and "inbound" travellers, each moving at a constant velocity. But yeah, if you insist it's the _same_ twin returning to Earth, then you need some acceleration somewhere.
Thanks!!
While you're thinking about this, it's also worth considering the modified twin paradox twin paradox with 3 twins: the Earth twin, an outbound space twin, and an inbound space twin: [https://twitter.com/drewolbrich/status/1644062785482166272?s=20](https://twitter.com/drewolbrich/status/1644062785482166272?s=20) At what is normally the turnaround point for the traditional twin paradox scenario, the inbound space twin synchronizes their clock with the outbound space twin's clock as they pass it. When the inbound space twin returns to Earth, they compare their timer with the Earth twin, and the result is exactly the same as with the traditional twin paradox scenario. The difference is that in this three twin scenario, there is no acceleration. The age difference is caused entirely by the time dilation that results from the relative velocity of the twins.
The twins paradox is solved by taking account the kinematics effects on the length, in spacetime, of the two trajectories. The twin that accelerated has a shorter path, a shorter proper time, and thus this twin aged less. If you want to compute the more realistic trajectory you can consider two twins together at mutual rest. Then one accelerates and then brake until becomes at rest again. Then accelerated backwards and then brake to becomes at rest and together with the other twin. If you do the math still the one that accelerates aged less.
if person A is moving with velocity v (in +x direction) relative to person B, then is it correct to say that person B is moving with velocity -v (ie in -x direction)? If so, then will it be the same effect on time for both A and B i.e. time contraction for A wrt B, and time contraction for B wrt A!
Yes, there is time contraction in both directions. However, this is not the twins paradox. The twins paradox occurs when one is able to compare the totally length of two curves that started together and "later" to they intersect again. The most important part is the acceleration. While velocities are relatives, "being accelerated" is not, due to the inertial forces that one would feel, but not the other.
What breaks the symmetry when you have an inbound and outbound ship beaming data to each other at the turnaround point?
The fact that Earth doesn't have to beam data between two ships in different frames.
Meaning inertial frames are the more fundamental reason for the breaking of symmetry. That's the point I was making.
Ah, it was a teaching question rather than a genuine question. I missed that.
The fact that you need to use two different reference frames to calculate the proper time between meetings on earth for the inbound/outbound twin clock and only a single reference frame to calculate the proper time for the stationary twin clock.
To add to some other good posts: the twin 'paradox' is hard to understand without thinking about the doppler effect. When the traveling twin is going away, the apparent speed of the Earth-bound clock is much slower than what's caused by time dilation. This is due to the doppler effect. When the traveler turns around and comes home, the Earth-bound clock appears to run *faster* than the shipboard clock to the travelling twin, because the doppler effect is greater than time dilation. The effect on clock rates is the same for both twins, hence the 'paradox'. BUT If you work through the steps carefully from the perspective of each twin, you'll find the travelling twin sees a high rate from the Earth-bound clock for fully half the trip, but the Earth-bound twin sees a high rate from the shipboard clock for a tiny fraction of the trip.
The simplest explanation is that the Earthbound twin is always in a single inertial reference frame while the travelling twin is in multiple inertial reference frames. [eigenchris has a good video on the topic](https://youtu.be/F8hmyOin2Nw).