B Relativity: Twin Paradox - Is Age Determinable?

[PeroK]

But 1) and 3) do not take place at the same position relative to A as the acceleration in the simple case, assuming the same total space time intervals for both scenarios.

I really don't see why not. We're assuming that B executes some sort of periodic motion: half a cycle in the simple case and 1.5 cycles in the next case.

The difference in differential ageing between the scenarios must be less than the time for the periodic motion. As with all twin paradox scenarios, there are small variations based on how many acceleration phases B has.

To clarify: Are you assuming that A will age the same amount in B's frame during these two accelerations?:
S1: Single acceleration in the simple scenario
E3: 3rd acceleration in the extended turnaround scenario

Yes, of course, these are physically identical.

 

[A.T.]

But 1) and 3) do not take place at the same position relative to A as the acceleration in the simple case, assuming the same total space time intervals for both scenarios.

I really don't see why not. We're assuming that B executes some sort of periodic motion: half a cycle in the simple case and 1.5 cycles in the next case.

We also assumed the same total space time interval (path length) for all cases, so with more periods the amplitude (maximal separation has to be less).

To clarify: Are you assuming that A will age the same amount in B's frame during these two accelerations?:
S1: Single acceleration in the simple scenario
E3: 3rd acceleration in the extended turnaround scenario

Yes, of course, these are physically identical.

The aging of A in B's non-inertial frame depends on the spatial separation of A and B. Since the separation is less for E3 than for S1, A will age less in B's frame during E3 than during S1, even if B's proper acceleration and acceleration duration are the same for E3 and S1.

 

[PeroK]

The aging of A in B's non-inertial frame depends on the spatial separation of A and B. Since the separation is less for E3 than for S1, A will also age less, even if the proper acceleration and duration are the same.

You keep saying that but what prevents B from executing the same acceleration when he reaches the same distance from A? Why does B have to be closer? And why does be have to be significantly closer? If I specify the turnaround distance for B as $1m$ and I concede that E3 takes place $2m$ closer to Earth. I have no idea why, but let's accept that E3 must take place $2m$ closer to Earth than S1. These distances are negligible in the context of 4 light years. That is going to make a negligible variation to the $6.4$ years.

Please tell me why B cannot execute SHM as many times as he pleases? Back and forward the same mean distance from A? Why is SHM impossible in the twin paradox?

I only posted this idea to highlight an issue with the "acceleration causes ageing" interpretation. I didn't expect an argument on the physical feasibility of B changing direction more than once.

You must be fundamentally misunderstanding what I'm saying.

 

[PeroK]

The aging of A in B's non-inertial frame depends on the spatial separation of A and B. Since the separation is less for E3 than for S1, A will age less in B's frame during E3 than during S1, even if B's proper acceleration and acceleration duration are the same for E3 and S1.

Can you provide your analysis of the differential ageing assuming that A ages 6.4 years as a result of the first turnaround? What happens quantitatively if B changes direction linearly twice more? Why do subsequent changes of direction have mininal effect on the ageing of A?

Assume that any subsequent changes of direction of B take place in less than 1 day (in A's frame). Please show why no further significant ageing of A takes place, unless the overall journey itself is significantly extended (in A'a frame).

Please, let me see your analysis.

 

[A.T.]

You keep saying that but what prevents B from executing the same acceleration when he reaches the same distance from A? Why does B have to be closer?

I explained that here:

We also assumed the same total space time interval (path length) for all cases, so with more periods the amplitude (maximal separation has to be less).

 

[Dale]

That can't be right. The differential ageing relative to Terence can't depend on the number of changes of direction.

But it can depend on the distance between them at the turnaround.

 

[PeroK]

But it can depend on the distance between them at the turnaround.

What stops B making repeated changes of direction (over a relatively short time) in the vicincty of the initial turning point?

 

[PeroK]

I explained that here:

Obviously it's the same give or take a day or two for the various acceleration phases - as it always is for the twin paradox. It's a proper time of $6$ years (give or take an arbitrary variation for the turnaround(s)).

Obviously, if B does additional accelerations that will take a small amount of proper time. But that cannot explain additional differential ageing of 6.4 or 6.3 years or whatever.

 

[vanhees71]

But for the one way example here, there is no way to avoid a synchronization assumption, because that is the sole determinant of what the start event is for the Mars clock. There is only one incident of colocation. The interval beginnings are determined solely by a synchronization decision, which can be a physical procedure, thus invariant, but it is still a choice, and effectively defines a frame.

Then the problem is insufficiently defined. You have to clearly define everything in physical terms, i.e., in terms of physically defined events to begin with.

 

[A.T.]

Obviously it's the same give or take a day or two for the various acceleration phases - as it always is for the twin paradox. It's a proper time of $6$ years (give or take an arbitrary variation for the turnaround(s)).

Obviously, if B does additional accelerations that will take a small amount of proper time. But that cannot explain additional differential ageing of 6.4 or 6.3 years or whatever.

Where does this "additional differential ageing of 6.4 or 6.3 years" come from?

 

[PeroK]

Where does this "additional differential ageing of 6.4 or 6.3 years" come from?

This is getting just silly now. I've explained a simple scenario in excruciating detail and all you're doing in nitpicking the details.

I don't know what this is all about now.

 

[jbriggs444]

Where does this "additional differential ageing of 6.4 or 6.3 years" come from?

I've lost track. I think it was part of a reductio ad absurdum argument to the effect that one should not attribute differential aging to acceleration.

The following narrative is how I reconstruct it:

There were two claims. One was that the progress of the stay-at-home twin from the point of view of the traveling twin would always be in the forward direction. The other is that the "point of view" of the traveling twin is always accurately reflected by an instantaneously co-moving inertial frame.

If we accept the former claim then, during periods of forward acceleration (by B away from A), A's clock advances. In effect the former claim acts as a ratchet. [This claim is arguably correct -- in any valid coordinate chart, it will hold].

If we accept the latter claim then, during periods of reverse acceleration (by B toward A), A's clock advances by 6.3 or 6.4 years each time. [This claim is also arguably correct. If we look at the "time now" on A's clock in the after-acceleration frame, it will be 6.3 or 6.4 years advanced from the "time now" on B's clock in the before-acceleration frame]. I think that @PeroK proposed trip details to arrive at those numbers.

If one accepts both claims together, then one might conclude that the stay-at-home twin's elapsed time will have advanced by a total proper time equal to the number of turnarounds multiplied by 6.3 or 6.4. That conclusion is obviously false -- so something has gone wrong.

One way of looking at what went wrong is that the sequence of instantaneous tangent inertial frames do not fit together to create a valid coordinate chart covering A's world line. The first claim only holds for valid coordinate charts. The error in the analysis is pretending that the "traveler's frame" both covers A's world line and uses a synchronization convention that matches B's sequence of tangent inertial frames.

One can build an accelerated frame around B's world line and extend it to encompass A's world line. But the attribution of differential aging based on using that frame will come as much from the details of the frame as from B's acceleration profile.

 

[PeterDonis]

Ok, so it looks like I'm going to have to point out what @jbriggs444 predicted I would point out.

It seems logical that if the first turnaround caused A to age by 6.4 years, then so must the third change of direction.

It might seem logical, but it's not valid, because the implicit reference frame you are using is not valid. Once you have multiple turnarounds, or orbits, or whatever, the reference frame you are implicitly using to make statements like "A ages 6.4 years during the first turnaround) is not valid for such statements because it no longer validly covers A's worldline: the mapping from the frame's time coordinate to events on A's worldline is no longer one-to-one. (It is for the case of a single turnaround with no orbits, but only for that case.)

The deeper root cause of this problem is being unwilling to give up the intuition that there should be some fact of the matter about A's "rate of aging" relative to B. There isn't. That's what relativity tells us. The only invariant in the problem is the comparison of elapsed times when the twins meet again. There is no invariant that corresponds to A's "rate of aging" relative to B (or B's relative to A, for that matter). So statements like "A ages 6.4 years during the turnaround" aren't statements about physics; they're statements about some human's choice of coordinates. (And if the choice of coordinates isn't a valid coordinate chart, they're not even well-defined statements.) You can do all the physics without ever having to make such statements, so why make them at all?

 

[PAllen]

Then the problem is insufficiently defined. You have to clearly define everything in physical terms, i.e., in terms of physically defined events to begin with.

Well, you can use a physical procedure to define a frame. Einstein clock synchronization is a physical procedure, and if you specify two bodies with attached clocks performing it, the result of the procedure is frame independent, but at the same time, it effectively defines a frame based on those two bodies. The beginning events in a one way scenario are defined by a choice of bodies to perform this operation.

 

[PeterDonis]

It's about answering the question: "How does the whole process look like in the rest frame of the traveling twin?",

And if you insist on asking that question, even though, as I pointed out in my previous post just now, you can do all the physics without doing so, then you first have to construct a consistent "rest frame of the traveling twin" that covers all of A's worldline during the trip. And the frame @PeroK is implicitly using when he talks about A "getting younger" in a scenario with multiple turnarounds or orbits does not. There are multiple ways of doing so that do cover A's worldline, but none of them will have the property that "A gets younger" during any part of the trip.

 

[PeterDonis]

Einstein clock synchronization is a physical procedure

But it only works for a pair of bodies that are (a) in free-fall inertial motion, and (b) at rest relative to each other. That's a severe limitation.

 

[metastable]

The deeper root cause of this problem is being unwilling to give up the intuition that there should be some fact of the matter about A's "rate of aging" relative to B. There isn't. That's what relativity tells us. The only invariant in the problem is the comparison of elapsed times when the twins meet again. There is no invariant that corresponds to A's "rate of aging" relative to B (or B's relative to A, for that matter). So statements like "A ages 6.4 years during the turnaround" aren't statements about physics; they're statements about some human's choice of coordinates. (And if the choice of coordinates isn't a valid coordinate chart, they're not even well-defined statements.) You can do all the physics without ever having to make such statements, so why make them at all?

I’m confused on this point. If A and B are both radioactive, won’t their relative compositions differ when they meet again? Won’t this problem now affect A & B’s invariant mass in addition to their elapsed time?

 

[PeterDonis]

If A and B are both radioactive, won’t their relative compositions differ when they meet again?

Yes, that's a consequence of the invariant I described: the comparison of elapsed proper times. But you're adding an element to the problem that nobody in this thread was including. See below.

Doesn’t this now affects A & B’s invariant mass?

This is just quibbling. Nobody has been talking about radioactive objects, or indeed objects undergoing any kind of change. We're just talking about the twin paradox. Throwing in a complication like what will happen to radioactive substances is irrelevant to the topic of the thread. If you want to know what happens to the invariant mass of a radioactive object over time, start a separate thread.

 

[PeroK]

Ok, so it looks like I'm going to have to point out what @jbriggs444 predicted I would point out.
It might seem logical, but it's not valid, because the implicit reference frame you are using is not valid. Once you have multiple turnarounds, or orbits, or whatever, the reference frame you are implicitly using to make statements like "A ages 6.4 years during the first turnaround) is not valid for such statements because it no longer validly covers A's worldline: the mapping from the frame's time coordinate to events on A's worldline is no longer one-to-one. (It is for the case of a single turnaround with no orbits, but only for that case.)

The deeper root cause of this problem is being unwilling to give up the intuition that there should be some fact of the matter about A's "rate of aging" relative to B. There isn't. That's what relativity tells us. The only invariant in the problem is the comparison of elapsed times when the twins meet again. There is no invariant that corresponds to A's "rate of aging" relative to B (or B's relative to A, for that matter). So statements like "A ages 6.4 years during the turnaround" aren't statements about physics; they're statements about some human's choice of coordinates. (And if the choice of coordinates isn't a valid coordinate chart, they're not even well-defined statements.) You can do all the physics without ever having to make such statements, so why make them at all?

I thought that was my whole point. That A's rate of "ageing" (it was always in quotes in my earlier posts) relative to B is meaningless.

I still think the whole idea that "acceleration of B causes A to age" is not a valid concept. Even if you can justify it with a caveat that "it only works once". It's not an explanation for differential ageing that has any physical significance, as far as I can see.

Perhaps my argument against it overlooked deeper problems with coordinate systems. But, if B makes an elaborate interstellar journey then the differential ageing can still be simply computed by the integral of the speed in A's frame. Attempts to attribute differential ageing to acceleration and time dilation in B's frame are fundamentally flawed.

 

[PAllen]

But it only works for a pair of bodies that are (a) in free-fall inertial motion, and (b) at rest relative to each other. That's a severe limitation.

So what? That is exactly what is needed to specify the OP scenario to make it fully defined.

 

[DaveC426913]

What I was attempting to analyse was the "acceleration causes ageing" interpretation of the twin paradox. I was trying to highlight an issue with this interpretation.

Ah. Then we are in agreement.

 

[Dale]

What stops B making repeated changes of direction (over a relatively short time) in the vicincty of the initial turning point?

Nothing

 

[Bruce Wallman]

It only depends on the velocity of the traveling twin. If that person gets anywhere near the velocity of c (compared to the universe), that person will suffer from time dilation and will lose some heartbeats, etc in aging. So that person will be younger. However, the twin on Earth is also traveling at a decent speed within the universe. So it needs to be that the one going to Mars has a much faster velocity relative to the universe and something significant against c. I do not think acceleration has anything to do with time dilation directly.

 

[Ibix]

If that person gets anywhere near the velocity of c (compared to the universe)

This is not correct. In a standard twin paradox, where one twin is inertial and one twin travels out-and-back then it's the speed of the traveller relative to the inertial observer that matters. In the "one-way" version under discussion here there is no unique answer.

"Speed compared to the universe" is not a well-defined concept.

 

[Herman Trivilino]

If that person gets anywhere near the velocity of c (compared to the universe), that person will suffer from time dilation and will lose some heartbeats, etc in aging.

All that matters is the relative speed of the twins. And the speed need not be anywhere near $c$. Modern clocks are precise enough to see the effect when the speed is a very tiny fraction of $c$.

 

[JArnold]

I'm just joining this long discussion, and it may be inevitable that my contribution will only be annoying. But there are basic and well-established principles that should guide the discussion: Uniform motion is relative; inertial acceleration and gravitational effects are absolute. In the former case, observers will mirror each other's experience of retarded clock speeds; they will each say the other's clock is moving more slowly. In the latter case (and our GPS system relies on actual time dilation): clocks move more slowly according to the intensity of their location in a gravitational field and according to their subjection to a force (as can be experimentally confirmed).

 

[SiennaTheGr8]

... Uniform motion is relative; inertial acceleration and gravitational effects are absolute. ...

I'd rephrase that: your velocity is relative, but whether you're moving inertially isn't.

 

[Ibix]

actual time dilation

"Actual" isn't a sensible word here. No time dilation is any more actual than any other. Some circumstances lead to symmetric time dilation and others lead to asymmetric time dilation (and some to differential aging) , that's all.

clocks move more slowly according to the intensity of their location in a gravitational field and according to their subjection to a force

Location in a gravitational field yes (more precisely, the gravitational potential difference between two clocks governs their rate). But force does not cause any time dilation.

 

[1977ub]

re: acceleration "causing" aging.

Here is a scenario with no acceleration. It involves 2 travelers and one stationary observer. One traveler passes Earth moving toward a distant star 4 light years distant, synchronizing clocks with Earth observer as it passes very closely. Another traveler leaves the distant star toward earth. Both outgoing & incoming travelers are traveling near to c as measured by the Earth observer. For Earth observer the first traveler moves away for 2 years and then passes the other traveler closely - information is swapped between the travelers so that the toward-earth traveler finds that all observers and instruments on the outward-traveling ship have aged less than one second since they passed earth. Less than a second later, the earthward ship arrives at earth.

 

[hutchphd]

Less than a second later, the earthward ship arrives at earth.

I'll save everybody else the trouble: whose clock are you referring to?

 

[1977ub]

I'll save everybody else the trouble: whose clock are you referring to?

inward ship - experiences almost no time after passing the outward ship.

 

[hutchphd]

re: acceleration "causing" aging.

I'm sorry but I don't see how this recitation relates to the intro. Nobody is questioning time dilation.

 

[JArnold]

I'd rephrase that: your velocity is relative, but whether you're moving inertially isn't.

Velocity is just motion in a particular direction. Inertial motion isn't relative? Don't tell Einstein.

 

[JArnold]

"Actual" isn't a sensible word here. No time dilation is any more actual than any other. Some circumstances lead to symmetric time dilation and others lead to asymmetric time dilation (and some to differential aging) , that's all.

Location in a gravitational field yes (more precisely, the gravitational potential difference between two clocks governs their rate). But force does not cause any time dilation.

Actual time dilation is "actual" when A observers the clock of B moving more slowly, while B observers the clock of A to be moving more quickly. It is not actual when each observes the other's clock to be moving more slowly.
Force causes time dilation because it causes acceleration, and time dilation corresponds with acceleration.

 

[SiennaTheGr8]

Velocity is just motion in a particular direction.

I'd rephrase that: velocity is the derivative of position with respect to coordinate time.

Inertial motion isn't relative? Don't tell Einstein.

If by "inertial motion" you mean "velocity," then yes, it's relative. If by "inertial motion" you mean "whether one's motion is inertial," then no, it's not relative. Agreed?

 

[SiennaTheGr8]

Actual time dilation is "actual" when A observers the clock of B moving more slowly, while B observers the clock of A to be moving more quickly. It is not actual when each observes the other's clock to be moving more slowly.
Force causes time dilation because it causes acceleration, and time dilation corresponds with acceleration.

This is incorrect. I suggest brushing up on time dilation.

 

[SiennaTheGr8]

To elaborate, @JArnold :

At the very least your terminology is off. What you've described sounds more like "differential aging" than "time dilation," and when you say "actual" perhaps you mean "invariant." (But even so, there are still problems with the post.)

 

[JArnold]

I'd rephrase that: velocity is the derivative of position with respect to coordinate time.
If by "inertial motion" you mean "velocity," then yes, it's relative. If by "inertial motion" you mean "whether one's motion is inertial," then no, it's not relative. Agreed?

I think I agree. Uniform velocity, speed, and rest are relative. Whether a body is inertial or accelerating is not. Yes?

 

[SiennaTheGr8]

I think I agree. Uniform velocity, speed, and rest are relative. Whether a body is inertial or accelerating is not. Yes?

Yes, although you can drop the word "uniform," and you needn't mention "speed" or "rest" (they're both covered by "velocity").

 

[JArnold]

To elaborate, @JArnold :

At the very least your terminology is off. What you've described sounds more like "differential aging" than "time dilation," and when you say "actual" perhaps you mean "invariant." (But even so, there are still problems with the post.)

To elaborate, @JArnold :

At the very least your terminology is off. What you've described sounds more like "differential aging" than "time dilation," and when you say "actual" perhaps you mean "invariant." (But even so, there are still problems with the post.)

"Time dilation" is a standard term. "Actual" is not-relative, and can be measured variously from different reference frames.

 

[SiennaTheGr8]

"Time dilation" is a standard term.

Yes, but you're using it incorrectly.

"Actual" is not-relative, and can be measured variously from different reference frames.

The word you're looking for is invariant.

 

[JArnold]

Yes, but you're using it incorrectly.
The word you're looking for is invariant.

You seem to have your own dictionary. "Velocity" doesn't substitute or include "speed" and "rest"; velocity is speed in a particular direction, and a body that is considered to be at-rest thereby has neither speed nor velocity. A clock-speed that can be considered more-or-less dilated from other reference frames isn't invariant, it is very much variant.

 

[Ibix]

Actual time dilation is "actual" when A observers the clock of B moving more slowly, while B observers the clock of A to be moving more quickly. It is not actual when each observes the other's clock to be moving more slowly.

You seem to be inventing your own term here. The underlying reason for time dilation, always, is that the interval along a given worldline between planes of simultaneity in a particular coordinate system depends on the chosen worldline. I would not use "actual" to describe this in any case. "Symmetric" and "asymmetric" is better since it describes what's happening without taking a position on whether one coordinate-dependent effect is more "actual" than another.

Force causes time dilation because it causes acceleration, and time dilation corresponds with acceleration.

It most certainly does not. Time dilation in special relativity depends purely on the velocity of a clock compared to your choice of "at rest". In general relativity you can, in some spacetimes, divide the effect into one depending on relative velocity and one depending on gravitational potential. In general spacetimes I think the only available definition relates to the angle between the clock's worldline and the worldline of constant spatial coordinates, and the result may be nonsensical since the latter needn't be timelike.

Note that "acceleration" appears nowhere in any of that.

 

[Ibix]

"Velocity" doesn't substitute or include "speed" and "rest"; velocity is speed in a particular direction, and a body that is considered to be at-rest thereby has neither speed nor velocity.

It doesn't substitute, but it does cover. If you know the velocity you know the speed and you know whether or not the object is at rest. I'd suggest that regarding an object at rest as having zero velocity is better than it not having a velocity since it is more consistent with the mathematical description (for example, an object with velocity $\vec v$, when transformed into a frame with velocity $\vec v$, has velocity $\vec v-\vec v=0$, not "doesn't have velocity"), but either is unambiguous.

A clock-speed that can be considered more-or-less dilated from other reference frames isn't invariant, it is very much variant.

Agreed. I believe @SiennaTheGr8 was proposing "invariant" in place of your "actual", but I don't think it covers what you mean by "actual", which is indeed coordinate dependent. Which is why "actual" is a bad word to use.

 

[JArnold]

Time dilation in special relativity depends purely on the velocity of a clock compared to your choice of "at rest". In general relativity you can, in some spacetimes, divide the effect into one depending on relative velocity and one depending on gravitational potential. In general spacetimes I think the only available definition relates to the angle between the clock's worldline and the worldline of constant spatial coordinates, and the result may be nonsensical since the latter needn't be timelike.

The underlying reason for time dilation is real-world physics. With relative uniform motion it is observer-dependent, and yes, there is no “actual.” With gravitation and inertial acceleration different clocks actually move at different speeds, and one twin will actually age more than another.

When results become “nonsensical” it may be because one’s formalisms have lost contact with physics — physical effects like “acceleration”, for example. An observer, in uniform motion (or “at rest”), and at an infinite distance from two clocks, can observe one clock actually moving more slowly than the other if one of the clocks is more affected by a gravitational field and/or the application of a force. (Note that “infinite” and “uniform” or “at rest” means sufficiently free of objective influences, as can be determined by a test-particle floating freely in a vessel in the observer’s lab.)

 

[Ibix]

The underlying reason for time dilation is real-world physic

Actually, no (edit: Dale, below, prefers to call your statement "meaningless" rather than saying "no" - I don't have a problem with his wording, although I - obviously - wouldn't have picked it). Time dilation isn't a direct observable and depends on the choices you make in your interpretation of things you actually can observe.

With gravitation and inertial acceleration different clocks actually move at different speeds, and one twin will actually age more than another.

This isn't correct. It's trivial to construct variants on the twin paradox scenario in which both twins undergo acceleration and either do or do not age differently. And it's possible to do the same in a gravitational field, although the maths needed to determine the course is more complicated.

When results become “nonsensical” it may be because one’s formalisms have lost contact with physics

Or it may be because an interpretation of results that works ok in flat spacetime does not generalise well to curved spacetime.

An observer, in uniform motion (or “at rest”), and at an infinite distance from two clocks, can observe one clock actually moving more slowly than the other if one of the clocks is more affected by a gravitational field

No. They will observe the two Doppler shifted. To what extent they attribute this to the clock "actually" ticking slowly and how much to effects on the light of its passage through the curved spacetime (edit: or, indeed, different coordinate velocities) is an interpretation. In a static gravitational field there's an obvious way to do this, but not in general. And you are not obligated to use the obvious interpretation even when it's available

the application of a force

A force does not have any effect on the tick rate of a clock except inasmuch as it changes the path of a particle. The elapsed time is $\int\sqrt{|g_{ab}dx^adx^b|}$ (and this has been experimentally tested), which depends only on the first derivative of coordinates, not the second. Velocity, not acceleration.

 

[Dale]

The underlying reason for time dilation is real-world physics.

While true, this statement is so broad that it is meaningless. What specifically in the real-world physics does it depend on?

In general time dilation is given by $\frac{d\tau}{dt}$. In an inertial frame that simplifies to $\sqrt{1-v^2}$, but that is not a general rule for all situations. Note that $d\tau$ is invariant but $dt$ is not.

 

[Bruce Wallman]

All that matters is the relative speed of the twins. And the speed need not be anywhere near $c$. Modern clocks are precise enough to see the effect when the speed is a very tiny fraction of $c$.

Yes, we see slight effects at micro levels in current astronauts. I was thinking about a more noticeable age difference. To answer two replies at once, the twin staying on Earth is still moving relative to the universe or cosmos. We know it is in the thousands of km/s range. This reduces all of our aging by a slight amount over 100 years. The faster moving twin might save 10 days of lifetime while the one on Earth saves 1 second. The age difference would then be 9 days, 23 hours, 59 minutes, and 59 seconds. The thing that we move relative to is the universe or cosmos - this is an easier way to understand the twin paradox than our motion relative to one another. When reduced to movement relative to one another, then both twins are always moving at the same velocity and acceleration relative to one another, so there would be no difference in aging. There needs to be a common ground to measure against. I look at that as the gravitational center for all things and call it the universe. This is a hard concept to point at since the big bang or bounce happened everywhere relative to us, but such is life.

 

[Ibix]

The thing that we move relative to is the universe or cosmos - this is an easier way to understand the twin paradox than our motion relative to one another.

Easier or not, it's wrong.

When reduced to movement relative to one another, then both twins are always moving at the same velocity and acceleration relative to one another, so there would be no difference in aging.

The whole point of this scenario is to make students realize that this analysis is naive and, ultimately, incorrect.

 

[Dale]

The thing that we move relative to is the universe or cosmos - this is an easier way to understand the twin paradox than our motion relative to one another.

Easier or not, it's wrong.

Well, I wouldn’t say it is wrong, but it is certainly not easier. While you can choose any reference frame, the velocity wrt the local frame where the CMB is isotropic is irrelevant. It drops out of the equations, so determining it has no bearing on the result and simply adds additional and unnecessary complication. The local CMB frame is as superfluous to this problem as the aether.