B Relativity: Twin Paradox - Is Age Determinable?

[Nugatory]

How does one decide when to switch "instantly" from one IRF to another in determining the solution to the twins paradox?

Everything is always in all frames and you can switch which frame you use to analyze the problem at any time and you will get the correct answer, or you can analyze the problem without ever switching frames.

Frame-changing only appears in the discussion of the twin paradox because there is no inertial frame in which the traveling twin is at rest; therefore any attempt to use such a frame to calculate the time elapsed on either clock must yield bogus results (and indeed the “paradox” is the result of taking the bogus result at face value).

 

[FactChecker]

No. The aging occurs during any time spent at relativistic velocities - whether for 1 second or for a month.
And the time spent getting to that speed can be arbitrarily short.

In SR, when two observers are moving inertially with respect to each other, each observer thinks that the other is aging slower. In that situation, when does the stationary twin get to age faster in the eyes of the traveling twin, as you propose?

 

[DaveC426913]

In SR, when two observers are moving inertially with respect to each other, each observer thinks that the other is aging slower. In that situation, when does the stationary twin get to age faster in the eyes of the traveling twin, as you propose?

But we're not talking about what they observe in-transit - we're talking about what they measure once planetside, and checking their clocks.

@Ibix offered to try to draw some Minkowski diagrams. That will illustrate what they see in-transit, and how the observation of each other's slowing is resolved.

 

[phinds]

In SR, when two observers are moving inertially with respect to each other, each observer thinks that the other is aging slower. In that situation, when does the stationary twin get to age faster in the eyes of the traveling twin, as you propose?

That's not what he said. He is pointing out that the age DIFFERENCE, that you don't see until they get back together, is greater the longer the time that the traveler travels.

EDIT: I see Dave beat me to it.

 

[FactChecker]

In SR, consider two IRFs whose clocks are Einstein synchronized. In SR, when two observers are moving wrt each other, the other frame's Einstein-synchronized clocks are always drifting off so that the trailing clocks indicate ahead of what you think they should and the farther back, the worse the error. The leading clocks indicate behind of what you think they should. If the traveling twin instantly turns around, the Earth IRF clock suddenly switches from a trailing position to a leading position. So it appears to the traveling twin that the Earth IRF clock has jumped from indicating behind to indicating ahead. That is, the Earth IRF clock suddenly ages a great deal. The farther away the Earth is, the greater its jump in age is. This is the SR mathematical treatment of an instantaneous change of direction of the traveling twin. It coincides exactly with the turn around of the traveling twin. So the aging of the Earth twin occurs at the instant of the turnaround. The amount of aging is determined by the distance of the traveling twin from Earth.

 

[FactChecker]

That's not what he said. He is pointing out that the age DIFFERENCE, that you don't see until they get back together, is greater the longer the time that the traveler travels.

EDIT: I see Dave beat me to it.

No. He didn't talk about the amount of aging. He talked about when the aging occurs. The amount of aging is determined by the distance between the twins. The aging occurs when the twin turns around. In Einstein-synchronized IRFs we can assume that observers all along the path can observe and reliably report back what they see. In such IRFs, they will always see the other frame's clocks running slow and aging slow. It is only at the moment of turn around that the traveling twin can record that the Earth twin ages too fast.

 

[DaveC426913]

In SR, consider two IRFs whose clocks are Einstein synchronized. In SR, when two observers are moving wrt each other, the other frame's Einstein-synchronized clocks are always drifting off so that the trailing clocks indicate ahead of what you think they should and the farther back, the worse the error. The leading clocks indicate behind of what you think they should. If the traveling twin instantly turns around, the Earth IRF clock suddenly switches from a trailing position to a leading position. So it appears to the traveling twin that the Earth IRF clock has jumped from indicating behind to indicating ahead. That is, the Earth IRF clock suddenly ages a great deal. The farther away the Earth is, the greater its jump in age is. This is the SR mathematical treatment of an instantaneous change of direction of the traveling twin. It coincides exactly with the turn around of the traveling twin. So the aging of the Earth twin occurs at the instant of the turnaround. The amount of aging is determined by the distance of the traveling twin from Earth.

Well, there's nothing "instant" about the change from a distant observer moving slowly to moving quickly. You will not see the clock "jump". The transition is smooth, even if distorted and asymmetrical.

Again, let's wait for the Minkowski diagrams. That will make it all easy to discuss.

 

[FactChecker]

Well, there's nothing "instant" about the change from a distant observer moving slowly to moving quickly. You will not see the clock "jump".
As the traveling twin decelerates, he will see his counterpart speed up to normal, so that, when he reaches rest wrt to Earth (even if only instantaneously), the twin on Earth will now be aging at a normal rate.

Again, let's wait for the Minkowksi diagrams. That will make it all easy to discuss.

This is all true and it shows that the Earth twin aging process can only occur when velocity changes. I have been discussing an instantaneous turnaround, but the same thing applies here. This is the SR way of mathematically handling changes in velocity. When there is no change in velocity, there can be no observed fast aging of the Earth twin. The length of the inertial flight only determines what amount of aging there will be when the traveling twin turns around. It does not determine when that aging occurs. The aging happens when the traveling twin turns around.

 

[DaveC426913]

Here's a simple one.

It's overly simplified because it illustrates infinite acceleration. (the traveling twin's path is not curved, as it would be with realistic acceleration).

That's important, because realistic acceleration means that in reality, the red and blue lines will not intersect at the midpoint - so there will be no "jump" from blue to red - it is smooth, if rapid.

 

[DaveC426913]

Ah. This one is more realistic:

 

[FactChecker]

Here's a simple one.

It's overly simplified because it illustrates infinite acceleration. (the traveling twin's path is not curved, as it would be with realistic acceleration).

That's important, because realistic acceleration means that in reality, the red and blue lines will not intersect at the midpoint - so there will be no "jump" from blue to red - it is smooth, if rapid.

View attachment 245235

Notice that the change from red to blue EDIT: blue to red occurs exactly when the traveling twin turns around. That is when he is accelerating. This is the Minkowski diagram representation of acceleration.

 

[DaveC426913]

Notice that the change from red to blue occurs exactly when the traveling twin turns around. That is when he is accelerating. This is the Minkowski diagram representation of acceleration.

See second diagram. Acceleration is not instant.

Note also that deceleration and negative acceleration (back toward Earth) are the same thing.

Mars-bound traveler actually beings accelerating at point 3, not at the midway point 4.5.

 

[FactChecker]

I am trying to say that all these approaches fit together and are not in conflict. When something is true, it can often be looked at in many consistent ways. The Minkowski diagram includes representations of changes in velocity (accelerations). To say that accelerations do not play a role is to say that these Minkowski diagrams are wrong.

 

[DaveC426913]

To say that accelerations do not play a role is to say that these Minkowski diagrams are wrong.

The first diagram is indeed wrong. It illustrates infinite acceleration (for simplicity).
The second diagram is the correct one.

And his acceleration (toward Earth) actually begins at point 3, not the midpoint.

 

[FactChecker]

The first diagram is indeed wrong. It illustrates infinite acceleration.
The second diagram is the correct one.

Or the first one is just on a scale where one can not see the smooth turnaround. The difference is less important than the similarities: when the motion is inertial, nothing unusual happens. It is only during the turnaround acceleration that the Earth twin can indisputably age more. The amount of aging is determined by the distance between the twins. The timing of the aging is determined by the timing of the turnaround acceleration.

 

[Dale]

If you are saying that they can choose to disagree by picking other methods of synchronization, then I will not argue. But I think that Einstein-synchronization has some serious logical advantages in this application.

The point isn’t whether or not to use Einstein synchronization. The point is in which frame to use it. In the earth-mars frame you get one answer, but in other frames using Einstein synchronization gives you a different answer.

It is only during the turnaround that the Earth twin can indisputably age more.

Well, that depends on the details of the specific non-inertial reference frame used. In my favorite coordinates the aging of the Earth twin is accelerated in the traveling twin over a longer period of time. Specifically, the time from when a light signal from the Earth twin will reach the traveler during the acceleration until the time when a light signal from the traveler during the acceleration will reach the Earth twin.

 

[DaveC426913]

The net effect is thus:

1. M and E age at the same rate while at Earth.
2. As M accelerates away from Earth, he will observe E aging slower.
3. If he shuts off his engines, E will continue to age at the same slow rate.
4. As he begins his decel (acceleration toward Earth) nearing Mars, E's slow aging will lessen until he is aging at a normal rate.
5. As M continues to accelerate (toward Earth) it reverses his course and E's aging will accelerate, now starting to appear slightly older.
6. As M continues to accel toward Earth, E will continue to age rapidly until M starts his decel.

The upshot is that, when M begins his acceleration, E continues to age slowly, even though the slowness begins to decrease.

 

[FactChecker]

The point isn’t whether or not to use Einstein synchronization. The point is in which frame to use it. In the earth-mars frame you get one answer, but in other frames using Einstein synchronization gives you a different answer.

I agree. I was wrong.

Well, that depends on the details of the specific non-inertial reference frame used. In my favorite coordinates the aging of the Earth twin is accelerated in the traveling twin over a longer period of time. Specifically, the time from when a light signal from the Earth twin will reach the traveler during the acceleration until the time when a light signal from the traveler during the acceleration will reach the Earth twin.

I think this will take me a while to grasp. It this moment, I am happy with anything that ties it to the velocity change for the twin to turn around.

 

[DaveC426913]

I agree. I was wrong.I think this will take me a while to grasp. It this moment, I am happy with anything that ties it to the velocity change for the twin to turn around.

Yes. Velocity change (specifically, sign from + to -). Not acceleration change.

 

[FactChecker]

The net effect is thus:

1. M and E age at the same rate while at Earth.
2. As M accelerates away from Earth, he will observe E aging slower.
3. If he shuts off his engines, E will continue to age at the same slow rate.
4. As he begins his decel (acceleration toward Earth) nearing Mars, E's slow aging will lessen until he is aging at a normal rate.
5. As M continues to accelerate (toward Earth) it reverses his course and E's aging will accelerate, now starting to appear slightly older.
6. As M continues to accel toward Earth, E will continue to age rapidly until M starts his decel.

The upshot is that, when M begins his acceleration, E continues to age slowly, even though the slowness begins to decrease.

I really like that.
Just to make it more complete, I would add a step 7 where the return is inertial and E appears to M to age slower. But that will not make up for the aging of the prior steps 4 and 5.
There should also probably be a step 8, where M decelerates to Earth speed. This will cause E to lose relative age, but not much since the distance between E and M is relatively small.

 

[DaveC426913]

Just to make it more complete, I would add a step 7 where the return is inertial and E appears to M to age slower.

mm. On the return, E will still appear to age rapidly. (See straight segment between 6 and 7).

There should also probably be a step 8, where M decelerates to Earth speed. This will cause E to lose relative age, but not much since the distance between E and M is relatively small.

E will still appear to age rapidly, but the rapidity will decrease until they are both aging at the same rate.

The diagram shows this.

As long as M is closing the gap with Earth, E will appear to age rapidly.

All lines on the return trip are diagonally going NW to SE (i.e. E is aging faster than M):

(I see that there is a "missing feature" in this diagram. It's not wrong, it's just not easy to plot it on a timeline).

I was writing up a description:
"Earth-Mars Return trip, 12 months Earth time, 9 months ship time"
and planned to describe each point of the traveller's journey as if they are months.

But The traveller is not checking his clock at regular intervals! His checks (0,1,2,3,4,5,6,7,8,9) are not evenly spaced. eg. the passage of time between traveller's 4 > 5 and 6 > 7 are of quite different durations.

 

[phinds]

No. He didn't talk about the amount of aging.

Hm ... I can only think that we are interpreting the following VERY differently:

(A ship that accelerates at 5gs to .9c and then immediately decelerates back to rest may have a very small discrepancy, whereas a ship that accelerates at 5gs to .9c and stays there for a month will have a much larger discrepancy.)

I am only able to interpret that as being about the amount of aging.

EDIT: By the way, I feel that my posts in this thread are likely coming across as being overly argumentative. That is not my intent.

 

[Nugatory]

It is only during the turnaround acceleration that the Earth twin can indisputably age more.

Indisputably? We cannot say without ambiguity when the turnaround happens, which makes it rather easy to dispute that proposition (and any other claim that anything not colocated must have happened at the the time of the turnaround).

If the traveling twin is receiving continuous time broadcasts from the Earth twin (say the Earth twin broadcasts the time on their clock once every second) they will find no discontinuity during the turnaround acceleration; instead the faster aging of the Earth twin is spread out across the entire return leg. Surely that is sufficient reason for the traveling twin to dispute the proposition that the Earth twin's excess aging happened during the turnaround?

What's really going on here: Any attempt to assign the age difference to anyone part of the journey is going to be pretty much arbitrary. It's as if you were to drive directly from Paris to Berlin while I took a longer route through Livorno; certainly I covered more kilometers than you, but there's no non-arbitrary way of saying which specific kilometers on my route were the "extra" ones.

 

[FactChecker]

During inertial flight, the clocks and people in other, relatively moving IRFs always appear to have slow clocks and be aging slower. So if there are unaccelerated flight segments, the traveling twin thinks that the Earth twin is aging less rapidly. The only time when the traveling twin can think that the Earth twin is aging faster is when he is accelerating toward Earth.

 

[PeterDonis]

It seems like this thread could benefit from a link to the Usenet Physics FAQ article series on the twin paradox:

http://www.math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html
Many of the issues raised in this thread are discussed there.

 

[PeterDonis]

relatively moving IRFs always appear to have slow clocks and be aging slower

It depends on what you mean by "appear". If you read the "Doppler Shift Analysis" from the Usenet Physics FAQ article series I linked to, you will see that (as @Nugatory pointed out), if the traveling twin is watching the stay at home twin through a telescope, he will see the stay at home's clock running faster throughout his return leg (i.e., as soon as he turns around). So as far as what actually "appears" in the telescope image, the statement of yours quoted above is simply wrong.

What you really mean by "appear" is that, after adjusting for light travel time, the traveling twin will calculate that the stay at home twin's clock is running slow compared to his own during both legs (outbound and return). But this calculation also involves a simultaneity convention, and that convention changes from the outbound leg to the return leg. (The "Time Gap Objection" page in the FAQ talks about this.) Not to mention that it's a strange use of language to use the word "appear" to refer to something calculated, while what actually appears in the telescope image is the opposite. (Unfortunately this abuse of language is so common in discussions of relativity that it comes naturally to anyone.)

 

[PeterDonis]

The equivalence principle has no relevance to the twin paradox. That is a fundamental misunderstanding.

This is too extreme. The Usenet Physics FAQ I linked to has an "Equivalence Principle Analysis" page that discusses this issue.

 

[FactChecker]

What you really mean by "appear" is that, after adjusting for light travel time, the traveling twin will calculate that the stay at home twin's clock is running slow compared to his own during both legs (outbound and return).

This is close to what I meant. I think it's equivalent. But my thinking is that all IRFs have their set of Einstein-synchronized clocks and recorders everywhere that report what is happening where the other moving IRF observer is. My use of "appear" was careless, but I meant that someone/something in the "stationary" IRF directly beside the moving observer records and reports the moving clock and aging with a time tag of the stationary IRF.

But this calculation also involves a simultaneity convention, and that convention changes from the outbound leg to the return leg. (The "Time Gap Objection" page in the FAQ talks about this.)

Certainly. I always assume that an IRF with no acceleration has a set of clocks everywhere which have been Einstein-synchronized at all times. The clock times would need to be re-Einstein-synchronized immediately after any acceleration.

Not to mention that it's a strange use of language to use the word "appear" to refer to something calculated, while what actually appears in the telescope image is the opposite. (Unfortunately this abuse of language is so common in discussions of relativity that it comes naturally to anyone.)

Yes. Again, I apologize. I'm sure that there is a lot of more precise terminology that I do not know.

 

[FactChecker]

It seems like this thread could benefit from a link to the Usenet Physics FAQ article series on the twin paradox:

http://www.math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html
Many of the issues raised in this thread are discussed there.

At first glance, this link looks excellent. I will study it.

 

[PeterDonis]

The clock times would need to be re-Einstein-synchronized immediately after any acceleration.

Yes, but then your claim that the stay at home twin ages during the turnaround turns into the claim that re-synchronizing clocks can cause the stay at home twin to age. Which seems unusual, to say the least.