Q&A with James R and Tony on the Twin Paradox Experiment

It looks like your answer is also the exact opposite of James R's.

A and B are twins on the earth, they left the earth on the same day, and A and B were exactly the same young when they left.
A and B have exactly the same acceleration and deceleration process, but A returns to the earth after reaching a speed of 0.1 c. B maintains a constant speed after reaching 0.1 c, and flies forward for another 10 ly, and then returns to the earth . May I ask, when A and B meet again on the earth, which one will be younger?
A and B have exactly the same acceleration and deceleration process, the only difference is that B flies 20 ly more than A at a constant speed. Do you still have questions about the scene I proposed now? If there is no doubt, please tell me when A and B meet, which one is younger?

The above is the question I asked, and James R gave a clear answer: "I think that in this case they will be the same age when they meet up at the end."
Judging from James R's answer, he was very clear about my question and had no objection to the scene I proposed.

Then according to James R, we can draw the conclusion that acceleration is the key factor affecting time dilation. Because A and B have exactly the same acceleration and deceleration process, the only difference is that B flies 20 ly more than A at a constant speed. But James R has clearly told us "I think that in this case they will be the same age when they meet up at the end.” . This means that the difference in B relative to A does not cause B's time to become slower than A's.

"according to James R, we can draw the conclusion that acceleration is the key factor affecting time dilation"

Acceleration is the key factor affecting time dilation when trying to resolve the traditional Twins Paradox. That does not mean that velocity is not a factor at all.
Also, the problem I was addressing was a variation of the traditional Twins Paradox, sort of a Triplets Paradox. Since time dilation is a function of both velocity and acceleration, one or the other may take a key role. Or, they may have equal roles. It depends upon the problem. There is no single answer.
I expect James R knows that. He was probably too exasperated from dealing with so many astronauts from so many different threads that, for this "Triplets" case, he misread the problem and jumped to the wrong conclusion.

You misunderstood.

I am surprised to see you holding the misconception that SR does not deal with acceleration. You are not alone. Many members on many science forums would agree you. When they post, they usually get corrected but the misconception continues. See my post, #9 above.

I don't want to appear condescending to someone with your level of proficiency, but I will repeat.
If time dilation is a "Function Of" velocity and velocity is a "Function Of" acceleration, then time dilation must be a "Function Of" acceleration (albeit indirectly).
That's basic algebra. Time dilation for an inertial/accelerating observer/observed pair requires a different equation from the one required for inertial observer/observed pairs, but it is still part of SR.
In fact, time dilation for accelerating/accelerating observer/observed pairs is also part of SR. But I have never seen the equation for that last condition.

That being said, I do not agree with phyti's analysis. He does not seem to be aware of the time dilation equation for an inertial/accelerating observer/observed pair.
Thanks for this. I was indeed under a misapprehension of the limits to the scope of SR. We chemists never studied it in much depth, I’m afraid, so what you kindly refer to as my proficiency is not that great. I’ve learnt something. On checking it seems the “special” indicates a restriction to flat spacetime. Is that right?

"according to James R, we can draw the conclusion that acceleration is the key factor affecting time dilation"

Acceleration is the key factor affecting time dilation when trying to resolve the traditional Twins Paradox. That does not mean that velocity is not a factor at all.
Also, the problem I was addressing was a variation of the traditional Twins Paradox, sort of a Triplets Paradox. Since time dilation is a function of both velocity and acceleration, one or the other may take a key role. Or, they may have equal roles. It depends upon the problem. There is no single answer.
I expect James R knows that. He was probably too exasperated from dealing with so many astronauts from so many different threads that, for this "Triplets" case, he misread the problem and jumped to the wrong conclusion.
SR cannot withstand logical analysis.
I started a dialogue with GPT, and GPT's initial views are completely consistent with SR's mainstream views. But after my debate with it, GPT overturned the original point of view.
I can do the same thing to mess with the logic of James R and his apprentices, and as you can see, James R's answer throws them into a mess. The chemist here is like a clown, he brings me a lot of joy.

I started a dialogue with GPT, and GPT's initial views are completely consistent with SR's mainstream views. But after my debate with it, GPT overturned the original point of view.
That's because it is a chatbot that just makes stuff up to chat with you.
SR cannot withstand logical analysis.
Demonstrably false.

I started a dialogue with GPT, and GPT's initial views are completely consistent with SR's mainstream views. But after my debate with it, GPT overturned the original point of view.
That's because ChatGPT is designed to lie to you and tell you anything you want to hear.

Try asking it for a proof that the moon is made of cheese. It will make a strong argument.

It appears that GPT is a good diversionary innocent. Let's go back to the triplet paradox.

A and B are twins on the earth, they left the earth on the same day, and A and B were exactly the same young when they left.
A and B have exactly the same acceleration and deceleration process, but A returns to the earth after reaching a speed of 0.1 c. B maintains a constant speed after reaching 0.1 c, and flies forward for another 10 ly, and then returns to the earth . May I ask, when A and B meet again on the earth, which one will be younger?
A and B have exactly the same acceleration and deceleration process, the only difference is that B flies 20 ly more than A at a constant speed. Do you still have questions about the scene I proposed now? If there is no doubt, please tell me when A and B meet, which one is younger?

The above is the question I asked, and James R gave a clear answer: "I think that in this case they will be the same age when they meet up at the end."
Judging from James R's answer, he was very clear about my question and had no objection to the scene I proposed.

Then according to James R, we can draw the conclusion that acceleration is the key factor affecting time dilation. Because A and B have exactly the same acceleration and deceleration process, the only difference is that B flies 20 ly more than A at a constant speed. But James R has clearly told us "I think that in this case they will be the same age when they meet up at the end.” . This means that the difference in B relative to A does not cause B's time to become slower than A's.

Tony;
So during t1----2t1, A and B have different time dilations.
At t1 the change in direction for A is instantaneous, thus no f=ma. Only the discontinuous linear path segments are compared.

The small triangle from 0 to 2t1 is the typical example used in the 'twin' scenario.

Both A and B follow the same triangular course, one is larger than the other, so they both could have the same curvilinear transitions between constant velocities.

Any differences in accumulated time would have to be during the straight line segments.

A and B are twins on the earth, they left the earth on the same day, and A and B were exactly the same young when they left.
A and B have exactly the same acceleration and deceleration process, but A returns to the earth after reaching a speed of 0.1 c. B maintains a constant speed after reaching 0.1 c, and flies forward for another 10 ly, and then returns to the earth . May I ask, when A and B meet again on the earth, which one will be younger?
A and B have exactly the same acceleration and deceleration process, the only difference is that B flies 20 ly more than A at a constant speed. Do you still have questions about the scene I proposed now? If there is no doubt, please tell me when A and B meet, which one is younger?

The above is the question I asked, and James R gave a clear answer: "I think that in this case they will be the same age when they meet up at the end."
Judging from James R's answer, he was very clear about my question and had no objection to the scene I proposed.

Then according to James R, we can draw the conclusion that acceleration is the key factor affecting time dilation. Because A and B have exactly the same acceleration and deceleration process, the only difference is that B flies 20 ly more than A at a constant speed. But James R has clearly told us "I think that in this case they will be the same age when they meet up at the end.” . This means that the difference in B relative to A does not cause B's time to become slower than A's.

B will be younger than A when they meet up again.

From the Earth Frame:
A and B travel outward, accelerating until they reach a speed of 0.1c relative to the Earth. Since you did not specify, to keep things simple, I will assume an extremely high value of acceleration, so that neither craft is far from the Earth upon reaching 0.1 c. This will allow us to avoid the headaches of some complicated math by making the time differences between Earth and ships during the acceleration( as measured from an Inertial frame) insignificant to the scenario as a whole.
IOW, according to Earth, A is gone for only an extremely short period of time and returns having accumulating just a tiny bit less time on its clock. So small, that we can effectively say it is 0. From this point on, A's clock ticks at the same rate as the Earth clock.
B continues on for 10 ly at 0.1c, taking 100 yrs by the Earth's clocks to do so. During which time, B clock accumulates ~99.5 years. B turns around and returns,taking another 100 years to do so, and accumulating another 99.5 years on its clock. B returns to Earth having aged ~1 year less than both Earth and A, have aged 200 yrs.

According to A:
As it accelerates away from Earth, Earth's clocks tick just a tiny bit slower than its own. Now here is where A's acceleration comes into play. Because A is in an accelerated frame of reference, this adds an additional component to what it determines as happening to clocks. It no longer can just consider its speed relative to other clocks, but what direction they are in, how far away they are, and the magnitude of the acceleration. Clocks in the direction of the acceleration run fast by a factor that increases with distance and acceleration magnitude. and clock in the opposite direction run slow by a factor in the same way. Since we set up things so that the distance between A and Earth is this only adds a tiny difference.
While A is accelerating away from Earth, the Earth clock ticks even slower according to A, but when A brakes and then accelerates back to Earth, it means that according to A, during that period, Earth clocks run fast by a tiny bit, so that by the time the two join up again the Earth will have aged a bit more than A. (during the turn-around B will be determined to run slow, but again due to the extremely small change in distance during this period, the accumulated difference will be tiny)

According to B: During the initial acceleration, A's clock runs the same speed as B, and Earth clocks run slow, accumulating just a tiny bit less time. Once it enter the coasting stage, and A's relative velocity increases, A's clocks starting ticking slow, and since A will eventually reach a speed of -.198c relative to B, it will for some time tick slower than Earth's clocks, and end up accumulating just a tiny bit less time than the Earth clock upon returning to Earth.
B continues to coast for 99.5 yrs by its clock, during which time, just over 99 yrs pass on Earth and A's clock due to the relative velocity.
B starts its turnaround acceleration. At this point B is light-years from Earth and A, so this becomes a huge factor in what B determines happens to Earth's and A's clock. So even though the acceleration last for an very short time, the magnitude of that acceleration combined with the distance has has the Earth/A clocks run very fast and accumulate ~2 years in time.
B starts a new coasting phase, taking 99.5 yrs to get back, during which time the Earth/A clocks run slow and accumulate an additional 99 yrs, for a total of 200 yrs for the 199 yrs it took according to B.

When is it said that acceleration is important in these scenarios, it isn't because it has any effect on clocks being accelerated as measured from an inertial frame other than the change in speed, it is because it how the behavior of clocks are measured from within an accelerated frame, and how this causes the observer that undergoes the acceleration to come to the same end conclusion as those that didn't.

B will be younger than A when they meet up again.

From the Earth Frame:
A and B travel outward, accelerating until they reach a speed of 0.1c relative to the Earth. Since you did not specify, to keep things simple, I will assume an extremely high value of acceleration, so that neither craft is far from the Earth upon reaching 0.1 c. This will allow us to avoid the headaches of some complicated math by making the time differences between Earth and ships during the acceleration( as measured from an Inertial frame) insignificant to the scenario as a whole.
IOW, according to Earth, A is gone for only an extremely short period of time and returns having accumulating just a tiny bit less time on its clock. So small, that we can effectively say it is 0. From this point on, A's clock ticks at the same rate as the Earth clock.
B continues on for 10 ly at 0.1c, taking 100 yrs by the Earth's clocks to do so. During which time, B clock accumulates ~99.5 years. B turns around and returns,taking another 100 years to do so, and accumulating another 99.5 years on its clock. B returns to Earth having aged ~1 year less than both Earth and A, have aged 200 yrs.

According to A:
As it accelerates away from Earth, Earth's clocks tick just a tiny bit slower than its own. Now here is where A's acceleration comes into play. Because A is in an accelerated frame of reference, this adds an additional component to what it determines as happening to clocks. It no longer can just consider its speed relative to other clocks, but what direction they are in, how far away they are, and the magnitude of the acceleration. Clocks in the direction of the acceleration run fast by a factor that increases with distance and acceleration magnitude. and clock in the opposite direction run slow by a factor in the same way. Since we set up things so that the distance between A and Earth is this only adds a tiny difference.
While A is accelerating away from Earth, the Earth clock ticks even slower according to A, but when A brakes and then accelerates back to Earth, it means that according to A, during that period, Earth clocks run fast by a tiny bit, so that by the time the two join up again the Earth will have aged a bit more than A. (during the turn-around B will be determined to run slow, but again due to the extremely small change in distance during this period, the accumulated difference will be tiny)

According to B: During the initial acceleration, A's clock runs the same speed as B, and Earth clocks run slow, accumulating just a tiny bit less time. Once it enter the coasting stage, and A's relative velocity increases, A's clocks starting ticking slow, and since A will eventually reach a speed of -.198c relative to B, it will for some time tick slower than Earth's clocks, and end up accumulating just a tiny bit less time than the Earth clock upon returning to Earth.
B continues to coast for 99.5 yrs by its clock, during which time, just over 99 yrs pass on Earth and A's clock due to the relative velocity.
B starts its turnaround acceleration. At this point B is light-years from Earth and A, so this becomes a huge factor in what B determines happens to Earth's and A's clock. So even though the acceleration last for an very short time, the magnitude of that acceleration combined with the distance has has the Earth/A clocks run very fast and accumulate ~2 years in time.
B starts a new coasting phase, taking 99.5 yrs to get back, during which time the Earth/A clocks run slow and accumulate an additional 99 yrs, for a total of 200 yrs for the 199 yrs it took according to B.

When is it said that acceleration is important in these scenarios, it isn't because it has any effect on clocks being accelerated as measured from an inertial frame other than the change in speed, it is because it how the behavior of clocks are measured from within an accelerated frame, and how this causes the observer that undergoes the acceleration to come to the same end conclusion as those that didn't.
Janus58, my old friend, it's great to see you speak again. Apparently you gave a different answer than James R.
Your answer can be simply stated as: In the earth reference system, B's speed (0.1c), let B's time slow down. Do you agree?

Janus58, my old friend, it's great to see you speak again. Apparently you gave a different answer than James R.
Your answer can be simply stated as: In the earth reference system, B's speed (0.1c), let B's time slow down. Do you agree?
No, my answer cannot be simply stated as such, as it ignores the important point that who's time is running slower at any given point of the exercise depends on which of the three is making that determination and that none of these determinations are any more valid than the others. The answer has to be taken as a whole and not piecemeal.

No, my answer cannot be simply stated as such, as it ignores the important point that who's time is running slower at any given point of the exercise depends on which of the three is making that determination and that none of these determinations are any more valid than the others. The answer has to be taken as a whole and not piecemeal.
What you mean, I can simply understand that consciousness determines the final result. What do you think of James R's answer, his conclusion is different from yours.

What you mean, I can simply understand that consciousness determines the final result. .
No, that is not what I mean, consciousness plays no role.

No, that is not what I mean, consciousness plays no role.
Janus58, according to your analysis, taking the earth as the reference system, B's speed is 0.1c, which causes B's time to be slower.
Then with B as the reference frame, the speed of A is 0.1c, which will cause the time of A to be slower.
So in the end, whose time will be slower?
Janus58, you told us that the time of B will be slower in the end. Did you use the people on the earth as the reference system to give the conclusion?

Janus58, according to your analysis, taking the earth as the reference system, B's speed is 0.1c, which causes B's time to be slower.
Then with B as the reference frame, the speed of A is 0.1c, which will cause the time of A to be slower.
So in the end, whose time will be slower?
Janus58, you told us that the time of B will be slower in the end. Did you use the people on the earth as the reference system to give the conclusion?
I said that at the end of the scenario( when A, B and the Earth are all together again*), B will have accumulated less total time than A or the Earth. All frames of reference will agree with this conclusion*, They just will not agree as to which one's time was running slower at various points of the exercise. Time dilation, which is a measure of how fast another clock is ticking compared to your own at that moment, is only one factor that produces the end result, there is also length contraction( case in point: While in the Earth reference frame, B traveled to a distance of 10ly before returning, In B's reference frame, B never got more than 9.95 ly from Earth), and the relativity of simultaneity.
A reference system is not something that requires people or any object, it is a "framework" against which events are measured. While it is common to say, "the Earth's reference frame", this is just because this is less cumbersome than saying the more correct: "The reference system that the Earth is considered to be at rest with respect to". Working from the particular reference frame that a given object or clock is at rest with respect to is simply a convenience which helps keep things simpler, but is is not requirement.

* The rejoining of the Earth with A and B is vital to this agreement across all frames of reference. If they had not done so,( for example, B simply comes to rest with respect to the Earth while still some 10 ly away), there will be no such agreement between frame of references. You'll have frames which say that A and the Earth are the ones that accumulated less total time.

Experimental evidence here:

[Physics FAQ]

· Bailey et al., “Measurements of relativistic time dilation for positive and negative muons in a circular orbit,” Nature 268 (July 28, 1977) pg 301. Bailey et al., Nuclear Physics B 150 pg 1–79 (1979).

They stored muons in a storage ring and measured their lifetime. When combined with measurements of the muon lifetime at rest this becomes a highly relativistic twin scenario (v ~0.9994 c), for which the stored muons are the traveling twin and return to a given point in the lab every few microseconds. Muon lifetime at rest: Meyer et al., Physical Review 132, pg 2693; Balandin et al., JETP 40, pg 811 (1974); Bardin et al., Physics Letters 137B, pg 135 (1984). Also a test of the clock hypotheses (below).

The Clock Hypothesis
The clock hypothesis states that the tick rate of a clock when measured in an inertial frame depends only upon its velocity relative to that frame, and is independent of its acceleration or higher derivatives. The experiment of Bailey et al. referenced above stored muons in a magnetic storage ring and measured their lifetime. While being stored in the ring they were subject to a proper acceleration of approximately 1018 g (1 g = 9.8 m/s2). The observed agreement between the lifetime of the stored muons with that of muons with the same energy moving inertially confirms the clock hypothesis for accelerations of that magnitude.
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Velocity has two components, speed and direction.
The word 'acceleration' is confusing when used in changing speed and changing direction. The two results are different. One component can change independently of the other.
An object can be redirected into an orbit without a change in speed.
An object can be boosted in speed without a change in direction.
Acceleration/deceleration pertaining to speed is well established.
I would substitute 'redirection' for change in direction.
From Einstein's 1905 paper, par.4:
"If we assume that the result proved for a polygonal line is also valid for a continuously curved line, we arrive at this result: If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at rest the travelled clock on its arrival at A will be
.5tv^2/c^2 second slow."

* The rejoining of the Earth with A and B is vital to this agreement across all frames of reference. If they had not done so,( for example, B simply comes to rest with respect to the Earth while still some 10 ly away), there will be no such agreement between frame of references. You'll have frames which say that A and the Earth are the ones that accumulated less total time.
Janus58, your answer finally made exchemist give "like". Your answer may have reflected the current situation of SR, such an answer can win "like", which is very abnormal. I don't want to destroy your SR Paradise, but I really hope that you can limit yourself within your own circle and not harm people outside your circle.