Does Time Contraction Change Substance?

[Nugatory]

Can I get this reference frame thing sorted first?

I am in my own Inertial Reference Frame (IRF).

I am observing something moving at near light speed.

Is that thing within my IRF ?

The phrase "in my reference frame" should be read as "using a reference frame in which I am not moving". If some object is moving at a constant speed relative to me, then there is a reference frame in which I am rest and the object is moving ("my" frame), a reference frame in which it is at rest and I am moving ("its frame"), and an infinite number of others in which we are both moving at various speeds (but in which some observer moving relative to both of us is at rest).

 

[Ibix]

An analogy that might be useful: a red car and a blue car approach each other on a straight road, each doing 30mph. Two people stand, one on each side of the road.

One of the pedestrians will say: there's a person in front of me, a red car approaching from the left at 30mph and a blue car approaching from the leftright at 30mph.

The other pedestrian will say: there's a person in front of me, a blue car approaching from the left at 30mph and a red car approaching from the leftright at 30mph.

The driver of the red car will say there are two people in front of me, approaching at 30mph, and a blue car approaching at 60mph.

The driver of the blue car will say there are two people in front of me, approaching at 30mph, and a red car approaching at 60mph.

You can see that on the face of it, all of these descriptions are contradictory. Which car is traveling left to right? Is one of the cars stationary, the other, or neither? This is all because these descriptions use different frames of reference. One pedestrian is looking one way, one the other, so they don't agree on what "left" and "right" mean. Nevertheless, you can see that it all fits together when you account for the difference in perspective. It is a coherent description of what happened.

Relativity extends this somewhat. It tells us that terms like "now", "length" and "clock tick rate" are like "left" and "right". They are not universal descriptions. They depend on who is using them. That's what time dilation is; it's why the twins don't agree on whose clock is running slow. They have different perspectives.

Now, back to our cars. After they pass each other, they circle round the block and come back. You'll get the same circumstance as before - except that one of the cars will have been on the "outside" and one on the "inside" of the loop around the block. The "outside" car's odometer reading will be higher, and it'll get back a moment later.

All four observers agree on that, whatever their point of view. Differential aging, as in the twin paradox, is like this. Everyone will be able to agree who has aged more.

In the example of the cars, you can see how all the bits fit together because it's a situation you are familiar with. You've got the experience. With relativity, you haven't. Trying to expain it with language that was never developed for such circumstances is a chancy process, as you are discovering. Your best bet is to learn to manipulate the maths yourself. If not, you will have to accept our word that we are describing a consistent scenario, but trying to do it with language that doesn't fit the concepts well.

 

[Ibix]

Edit: This post is now irrelevant, since Nugatory kindly fixed the typo in my previous post. I've left it here as a grim warning to myself. :D

One of the pedestrians will say: there's a person in front of me, a red car approaching from the left at 30mph and a blue car approaching from the left at 30mph.

The other pedestrian will say: there's a person in front of me, a blue car approaching from the left at 30mph and a red car approaching from the left at 30mph.

*Sigh* Try again, Ibix.

One of the pedestrians will say: there's a person in front of me, a red car approaching from the left at 30mph and a blue car approaching from the right at 30mph.

The other pedestrian will say: there's a person in front of me, a blue car approaching from the left at 30mph and a red car approaching from the right at 30mph.

You can see that on the face of it, all of these descriptions are contradictory.

...and are, in fact, completely contradictory because I made a stupid typo. D'oh.

 

[Nugatory]

My internal autocorrector, the thing that makes me such an ineffective proofreader :) slid right over that one until you pointed it out... But I've taken the liberty of correcting it for you above.

 

[Ibix]

Thanks! I know what you mean about autocorrect - you work out what it must say and don't notice that it doesn't say that. I don't know how I missed this one this morning, though. It hit me the second I looked at it just now.

 

[docroc]

If I understand your question -- and I am not a physicist, only an avid reader of stuff about physics -- I think your concern can be stated basically as "why don't I experience the changes due to relativity while they are happening? Are they real?" The answers to this all are why relativity is so mind-bending.

I think the answer (real physicists can correct me) is that relativity necessitates having different reference frames. Within your reference frame, you are not aware of atoms vibrating any slower or you aging more slowly, because, within your reference frame, they don't. This is why it's so weird! It is also why Einstein's answer to the question "what is time?" is so profound; he said "time is what is measured by clocks." Since the clock on your spaceship will tick at the same old rate (from your point of view in the same frame as the clock) nothing is changing. Ditto for the people left on Earth, within THEIR frame. Thus the laws of physics within each frame remain unchanged.

I personally like PHINDS' explanation best.

 

[ghwellsjr]

Is that clear now?

Nope. It is not clear to me. And I did not 'read and understand' post #4. I read it.

It is hard to understand Special Relativity with just words. Diagrams help a lot. I will quote some of my comments from post #4 and illustrate them with spacetime diagrams to see if that will help you to understand.

In their own rest frames, atoms vibrate at their 'normal' frequencies. In other frames where they are moving, their vibrations are slowed but this doesn't make them different material atoms or atoms in a different state.

Let's assume that we have a particular species of atom that emits pulses of light at a rate of a billion times a second which is one pulse every nanosecond.

For example, if two atoms moving away from each other at some speed give off a frequency of light that can be observed by the other atom, they will each see the same Doppler shifted frequency of light, or a slowing of the frequency. But this is not Time Dilation. If they are moving towards each other at the same speed, they will each see a speeding up of the frequency but in both cases, the same Time Dilation is in effect.

Here is a spacetime diagram showing two of these atoms, one red and one blue, starting off separated from each other but approaching and passing at 0.8c:

Please note that this is the rest frame of the blue atom and the red atom is the one that is moving at 0.8c and so it is the one that is Time Dilated by the factor of 1.667. The dots mark off one-nanosecond increments of time for each atom.

At the bottom of the diagram, the red atom is moving toward the blue atom and during this time, the blue atom sees the frequency of the light pulses coming from the red atom Doppler shifted by a factor of 3 as you can see by the 3 thin red lines compressed into the one-nanosecond interval of time just before the red atom reaches the blue atom. Once the red atom passes the blue atom, the Doppler shift changes to a factor of 1/3 so it takes three nanoseconds of blue's time to see each one-nanosecond pulse coming from the red atom.

The first lesson to be learned here is that the blue atom cannot see the Time Dilation factor (1.667) of the red atom, it can only see the Doppler shift factors of 3 and 1/3.

Now let's look at another diagram showing what the red atom sees of the blue atom's pulses:

Note that this is the same IRF as the first diagram, the rest frame of the blue atom. However, the Doppler shift factors that the blue atom saw of the red atom's pulses are identical to the Doppler shift factors that the red atom sees of the blue atom's pulses.

Time Dilation is not observable, it is the result of assigning an IRF to both atoms which will determine the speeds of both atoms and that establishes the Time Dilation of each atom, the faster it is moving the more its Time Dilation. You can make one atom at rest in one IRF which makes the second atom have all the speed so only the second atom is Time Dilated. Or you can have a different IRF in which the second atom is at rest and the first atom has all the speed making it the only one with Time Dilation. Or you can have an IRF in which both atoms are moving in opposite directions at some intermediate speed which will make them both have the same intermediate Time Dilation. But in all cases, they both see the same Doppler shift in the observed frequency of light.

As stated, we can have an IRF in which both atoms are moving in opposite directions at the same speed, in this case 0.5c:

The Time Dilation factor for both atoms is 1.1547 and I show the pulses going from each atom to the other atom. Again, they each observe the Doppler shift factor of 3 while they are approaching and 1/3 while they are departing.

Finally, we look at the same situation but in the rest frame of the red atom:

Once again, the Doppler shift factors are the same as in the other IRF's. And as I stated, the red atom vibrates "normally" in its own rest frame.

Does this help you to understand post #4? Any questions?

 

[shounakbhatta]

Hello All,

I have been reading this thread and I personally thanks all the contributor who have given such great explanations; Phinds especially.

Well, I won't say I would contribute something to this thread but I would like to ask something, or may be re-verify:

(a) The confusion is due to aging and time dilation.
(b) When we talk of dilation, it means expanding (in literary terms). Time is expanding, that means can we consider in 365 days (1 yr.) one of my hair on my head grows white.If time is running slowly, say in 700 days one of my hair on my head grows white.
So, I am aging slowly.

(c) Aging slowly automatically would imply, the time which is measuring the age of of the atom in my body is running slowly hence I am younger than you.

So, can we say, when I am speeding close to c, time dilation is causing slow aging and hence I am younger than you?

Please correct me if I am wrong.

 

[phinds]

Hello All,

I have been reading this thread and I personally thanks all the contributor who have given such great explanations; Phinds especially.

Well, I won't say I would contribute something to this thread but I would like to ask something, or may be re-verify:

(a) The confusion is due to aging and time dilation.
(b) When we talk of dilation, it means expanding (in literary terms). Time is expanding, that means can we consider in 365 days (1 yr.) one of my hair on my head grows white.If time is running slowly, say in 700 days one of my hair on my head grows white.
So, I am aging slowly.

(c) Aging slowly automatically would imply, the time which is measuring the age of of the atom in my body is running slowly hence I am younger than you.

So, can we say, when I am speeding close to c, time dilation is causing slow aging and hence I am younger than you?

Please correct me if I am wrong.

Nearly as I can tell from your post, I'm afraid you've missed the point here. If it takes one of your years for one of your hairs to turn white, then it takes one year. Period. I'll got through it again:

To restate your statement "The confusion is due to aging and time dilation", I would say the problem is due to confusion between time dilation and the relative aging of things. You are conflating them when in reality they are totally different things.

Time dilation is not "real". You, right now as you are reading this, are MASSIVELY time dilated in one frame of reference, heavily time dilated in another frame of reference, mildly time dilated in another, barely in another, and not at all in the frame of reference in which you are stationary. Clearly this cannot be a "real" effect 'else how could all those things be happening at the same time? Time dilation is just something that remote observers see/calculate.

AGING, on the other hand is real. You age at one second per second. EVERYTHING ages at one second per second. Time dilation is apparent and is frame dependent. Actual aging is real and is frame independent.

The confusion comes from two objects starting with the same age but then taking different paths through space-time and then meeting up and finding that one of them has traveled more through space than the other and the other has traveled more through time, thus they are not the same age when they meet up even though they were when they started out. They have both been aging at exactly the same rate of one second per second, but they have not been doing it for the same amount of time.

 

[shounakbhatta]

Ok. Got it.
Let me re-verfy if I got it.
Biological ageing, metabolism , cell ageing, etc. do not affect as time runs slow.

I stay on Earth, time goes by and you go in space ship, you covered more space right? I covered more time right?
Meeting both of us (although we are aging exactly the same rate 1 second per second) the difference lies in the time that you covered and I. So you return younger as time for you is faster (as you travel close to c), I am old as time for me ran slowly relative to you.

Is this right?

 

[phinds]

Ok. Got it.
Let me re-verfy if I got it.
Biological ageing, metabolism , cell ageing, etc. do not affect as time runs slow.

I stay on Earth, time goes by and you go in space ship, you covered more space right? I covered more time right?
Meeting both of us (although we are aging exactly the same rate 1 second per second) the difference lies in the time that you covered and I. So you return younger as time for you is faster (as you travel close to c), I am old as time for me ran slowly relative to you.

Is this right?

Almost. It is not correct to say "time for me ran slowly relative to you". I will say it for the third time now. Time runs at the same rate for everyone/everything, and that is one second per second. It is AGING that changes but you can't actually measure that until you meet up again.

Relative aging is a function of the distance through space-time, which depends on speed and gravity and relative aging depends on the distance you have traveled through space-time vs how much has some other object traveled through space-time or if one of you has been in a gravity well.

So if you and I are the same age and I stay here on Earth and you travel away at relativistic speeds and then come back, we both age at one second per second but when we meet up again, we have aged by different amounts even though we have been aging at the same rate.

On the other hand, if there were a black hole not too far from the Earth and you could go there and somehow maintain position just above the event horizon for what amounted to a short time to you, when you came back to Earth, we would have the same relative aging as above. At first this seems odd since you have not traveled all that far in space and you have not traveled very fast in my frame of reference but globally, you have been in an area of heavily "curved" space-time which has the same effect on aging as traveling at relativistic speeds because locally you ARE traveling at relativistic speeds even though globally it doesn't look that way.

For the fourth, and I hope last, time: Things don't age at different rates, they only age by different amounts relative to each other. This is not "time slowing down" it's just things taking different paths through space-time.

 

[shounakbhatta]

Ok. Got it. Thanks.
So we have not got anything in science, which would create a difference in the biological age?

One last thing (may be out of the topic). All those relativistic mass, relativistic energy, relativistic momentum all those are again appearance in frame of references right? Mass as per the conservation of law remains the same, same as energy and others?

 

[phinds]

Ok. Got it. Thanks.
So we have not got anything in science, which would create a difference in the biological age?

One last thing (may be out of the topic). All those relativistic mass, relativistic energy, relativistic momentum all those are again appearance in frame of references right? Mass as per the conservation of law remains the same, same as energy and others?

No, now you are getting into general relativity and that is more complicated. For one thing, "relativistic mass" is a deprecated concept and for another "conservation of energy" is a local concept and doesn't work for cosmological scales, and to mention one final one, photons have no mass at all but do have relativistic momentum.

This is a all whole 'nother topic and you should read up on that stuff and start a new thread when you have questions.

 

[shounakbhatta]

I believe relativistic mass (although an out dated concept) comes from Special Relativity only (through Lorentz transformation).

Anyway...

Thanks for everything.

 

[phinds]

I believe relativistic mass (although an out dated concept) comes from Special Relativity only (through Lorentz transformation).

Anyway...

Thanks for everything.

Yeah, my blanket statement "now you are getting into general relativity" was a bit broad but I'm trying to keep this thread to a single topic, namely Does Time Contraction Change Substance?

 

[PeterDonis]

Biological ageing, metabolism , cell ageing, etc. do not affect as time runs slow.

As you state it, this is not correct; "time runs slow" means that aging, metabolism, etc. all run slow. All those processes run at the "rate of time flow".

I stay on Earth, time goes by and you go in space ship, you covered more space right? I covered more time right?

Not really. "Space" and "time" are frame-dependent; with reference to my frame, you "cover more space" and I "cover more time". But the difference in aging between us when we meet up again is not frame-dependent; we both agree that you have aged more.

What you are missing is that it is spacetime that is important. We age differently because we follow different paths through spacetime, and your path is longer than mine, so you age more.

 

[PeterDonis]

So we have not got anything in science, which would create a difference in the biological age?

Yes, we do. The scenario you described, where you stay at home and I fly off in my spaceship and come back, creates a difference in our biological ages.

 

[russ_watters]

As a non-scientist (engineer), I think I see some wording choices that are causing confusion. Let me see if I can focus-in on that and clear some of it up:

Time dilation is a perception/calculation of a remote observer. It has no effect on the object itself.

Time dilation is not observable, it is the result of assigning an IRF to both atoms which will determine the speeds of both atomas and that establishes the Time Dilation of each atom...

Though I think I know what you mean, the way those are worded implies to me that time dilation is nothing more than a perspective illusion, like the photography trick of keeping Tom Cruise in the foreground of all pictures to makes him look taller than he really is. I don't want the OP (or others) coming away with that false impression.

I think there are two issues of confusion here (and as I said, I'm an engineer, not a physicist, so if I get any of this wrong, of course let me know...):
1. Time dilation refers to the tick rate difference, not the accumulated number of ticks. The accumulated number of ticks is observed and from that the tick rate difference can be calculated (or vice versa). The tick rate difference disappers when you bring two clocks together, but the accumulated time difference remains. Same goes for length contraction: it is very real when the "length" (distance) is accumulated, and that doesn't go away when you change perspective.

2. Focusing on symmetrical and arbitrary time dilation examples instead of more realistic roundtrip travels gives people the false impression that time dilation is totally arbitrary and has no real connection with observed reality. IE, that when two objects approach from a distance, both will observe the other's clock ticking faster than their own and both would be right (even accounting for doppler effect). But while it is true that if you are dealing only with frames of reference or hypothetical snapshots of objects that magically appear from nowhere it can be viewed that way, but in real-world situations it is not at all arbitrary: Objects have histories and through those histories, the "true" time dilation - the one that is recorded on their clocks when they are brought together - is uncovered, even before you observe that reality is observed by comparing the clocks.

If an astronaut is traveling away from earth, both witness the other's clock ticking slower, but the reality is that only one of them fired a rocket to get away from the other. The astronaut is the one "actually" moving and when he returns, his clock will read a shorter elapsed time and he'll be younger than his twin because of it. You can't make that go away by arbitrarily changing reference frames.

 

[ghwellsjr]

As a non-scientist (engineer), I think I see some wording choices that are causing confusion. Let me see if I can focus-in on that and clear some of it up:

Time dilation is a perception/calculation of a remote observer. It has no effect on the object itself.

Time Dilation is not observable, it is the result of assigning an IRF to both atoms which will determine the speeds of both atoms and that establishes the Time Dilation of each atom, the faster it is moving the more its Time Dilation.

Though I think I know what you mean, the way those are worded implies to me that time dilation is nothing more than a perspective illusion, like the photography trick of keeping Tom Cruise in the foreground of all pictures to makes him look taller than he really is. I don't want the OP (or others) coming away with that false impression.

I don't think you know what we mean. I said Time Dilation is not observable. Therefore it cannot be a perspective illusion because it cannot be seen. Phinds said it was a perception/calculation. He didn't say it was just a perception. What can be seen is the Doppler effect and that remains the same in all IRF's. But different IRF's produce different Time Dilations. On a spacetime diagram where increments of Proper Time are marked with dots as I do in my diagrams, Time Dilation is directly observable to us as we view the diagram, but the observers that we are depicting in the diagram have no knowledge or awareness of any of the coordinate effects, including the coordinates themselves or coordinate related effects like Time Dilation or Length Contraction.

I think there are two issues of confusion here (and as I said, I'm an engineer, not a physicist, so if I get any of this wrong, of course let me know...):
1. Time dilation refers to the tick rate difference, not the accumulated number of ticks. The accumulated number of ticks is observed and from that the tick rate difference can be calculated (or vice versa). The tick rate difference disappers when you bring two clocks together, but the accumulated time difference remains. Same goes for length contraction: it is very real when the "length" (distance) is accumulated, and that doesn't go away when you change perspective.

You say Time Dilation refers to the tick rate difference but you don't say between what and what. I presume you mean it's the tick rate difference between two clocks in relative motion. This is a very common notion but it is wrong as stated and doesn't make sense because it doesn't provide any way for the Time Dilation to be reciprocal between the two clocks. A better way to say it is that it's a difference between the tick rate of two clocks where one is moving in the rest frame of the other one.

However, even that is not the best or even the correct way to say it because Time Dilation is not a relationship between two clocks. Rather, it is a relationship between the passage of Proper Time on a clock (or any other object) and the passage of Coordinate Time for which there is no clock. If the clock is inertial, then it is also the ratio of the accumulated Coordinate Time and the accumulated Proper Time on the clock. If you look at my diagrams on post #37 and just focus only on the thick blue line and its dots marking off Proper Time, you can see how the Time Dilation changes when we transform to different IRF's. This is such a simple concept, especially when looking at a marked spacetime diagram, I don't know why it engenders so much confusion, except for the fact that so many people keep promoting so many false notions.

2. Focusing on symmetrical and arbitrary time dilation examples instead of more realistic roundtrip travels gives people the false impression that time dilation is totally arbitrary and has no real connection with observed reality. IE, that when two objects approach from a distance, both will observe the other's clock ticking faster than their own and both would be right (even accounting for doppler effect). But while it is true that if you are dealing only with frames of reference or hypothetical snapshots of objects that magically appear from nowhere it can be viewed that way, but in real-world situations it is not at all arbitrary: Objects have histories and through those histories, the "true" time dilation - the one that is recorded on their clocks when they are brought together - is uncovered, even before you observe that reality is observed by comparing the clocks. If an astronaut is traveling away from earth, both witness the other's clock ticking slower, but the reality is that only one of them fired a rocket to get away from the other. The astronaut is the one "actually" moving and when he returns, his clock will read a shorter elapsed time and he'll be younger than his twin because of it. You can't make that go away by arbitrarily changing reference frames.

Of course, I can't make the difference in the accumulated times on two clocks that start off together and end up together go away, nobody ever said it would go away, but that is not Time Dilation. In different IRF's the Time Dilations are different and yet the accumulated Proper Times on each clock remain the same. And it has nothing to do with which clock accelerated away from the other one. Suppose that some time after the first astronaut accelerates away, a second one accelerates toward the first one at an even higher speed and when they pass, the second astronaut is the one who accumulated less time.

 

[PeterDonis]

Time dilation refers to the tick rate difference, not the accumulated number of ticks.

A big part of the problem is that this terminology, while I totally agree with it, is not consistently used. Many people use "time dilation" to refer to the accumulated number of ticks. I personally would prefer the term "differential aging" for the latter--in the standard twin paradox, for example, that would be the reason one twin is older than the other when they meet up again. If everyone used terms consistently this way, then it would be clear that "time dilation" is a frame-dependent concept, while "differential aging" is an invariant, direct observable.

This would also enable people to more easily understand the Doppler Shift Analysis in the Usenet Physics FAQ article on the twin paradox, which derives the differential aging between the twins solely in terms of the observed relativistic Doppler effect. This shows that the concept of "time dilation" is not even necessary; you can compute predictions without ever using it. Maybe that would help to reduce confusion.

 

[ghwellsjr]

2. Focusing on symmetrical and arbitrary time dilation examples instead of more realistic roundtrip travels gives people the false impression that time dilation is totally arbitrary and has no real connection with observed reality. IE, that when two objects approach from a distance, both will observe the other's clock ticking faster than their own and both would be right (even accounting for doppler effect). But while it is true that if you are dealing only with frames of reference or hypothetical snapshots of objects that magically appear from nowhere it can be viewed that way, but in real-world situations it is not at all arbitrary: Objects have histories and through those histories, the "true" time dilation - the one that is recorded on their clocks when they are brought together - is uncovered, even before you observe that reality is observed by comparing the clocks.

If an astronaut is traveling away from earth, both witness the other's clock ticking slower, but the reality is that only one of them fired a rocket to get away from the other. The astronaut is the one "actually" moving and when he returns, his clock will read a shorter elapsed time and he'll be younger than his twin because of it. You can't make that go away by arbitrarily changing reference frames.

I have made some spacetime diagrams showing an astronaut traveling away from Earth and returning. The first one depicts the Earth rest frame, the one you claim has the "true" Time Dilation for the Earth and the astronaut.

Of course it is true that this diagram depicts the "true" Time Dilation of the Earth and the astronaut for the rest frame of the Earth but after this I'll show some other IRF's which also show "true" Time Dilations for the Earth and the astronaut. Note in the above diagram that the astronaut, depicted in red, travels at a speed of 0.8c so he is Time Dilated by the factor of 1.6667 which is the ratio of the accumulated Coordinate Time to the accumulated Proper Time (depicted by the dots) and that after 3 years of Proper Time for the astronaut on his way out, 5 years (3 times 1.6667) of Coordinate Time has transpired and the same for the way back. People on the Earth (depicted in blue) are at rest so they are Time Dilated by the factor of 1 and they age by 10 years (10 times 1) while the astronaut is gone. Please note how I specifically referenced the Proper Times of the astronaut and the Earth separately to the Coordinate Time of the IRF rather than to each other. That's very important to a correct understanding of Time Dilation.

Now let's transform the above IRF to one in which the Earth and the astronaut are departing away from each other at the same speed, 0.5c:

At 0.5c, the Time Dilation factor is 1.1547 so after 3 years of Proper Time for both of them, 3.5 years of Coordinate Time has transpired. That's when the astronaut fires his rocket to return home exactly how he did in the first IRF but now it gets him to a speed of 0.929c with a Time Dilation of 2.7 and it takes him 8.1 years of Coordinate Time for his 3 year of Proper Time. The astronaut's total Coordinate Time for his trip is 3.5+8.1 = 11.6 years, the same as the Coordinate Time it takes for the Earth to progress through 10 years of Proper Time at 0.5c with a Time Dilation of 1.1547. This is the first example of where the Time Dilations are "true" but different than the Earth's rest frame.

Now we'll do the IRF in which the astronaut is at rest during the first part of his journey. This puts the Earth traveling at 0.8c and experiencing the Time Dilation of 1.6667 while the astronaut has none (actually 1):

During the second part of the journey, the astronaut reaches a speed of 0.9756c and a Time Dilation factor of 4.55 and so when he gets back to earth, after 13.667 years of Coordinate Time (3 times 4.55) for a total of 16.667 years, it matches the accumulated Coordinate Time for the Earth (10 times 1.6667), another "true" example of Time Dilations.

Let's do another one, the IRF in which the Earth and the astronaut approach each other at the same speed:

This one is similar to the second one in this post, so I'll let you out the details.

Finally, the IRF in which the astronaut is at rest while returning:

This one is similar to the third one in this post so I won't go into the details.

I hope these diagrams have helped to show the difference between Time Dilation and Differential Aging.

 

[ghwellsjr]

If an astronaut is traveling away from earth, both witness the other's clock ticking slower, but the reality is that only one of them fired a rocket to get away from the other. The astronaut is the one "actually" moving and when he returns, his clock will read a shorter elapsed time and he'll be younger than his twin because of it. You can't make that go away by arbitrarily changing reference frames.

I'd like to further disabuse you of the notion that the astronaut is the one "actually" moving because he is the one who fired a rocket and that automatically guarantees that he will be the younger one when they meet up together later on.

Let's consider an astronaut (red) leaving Earth (blue) at 0.8c but some time later, another astronaut (black) leaves Earth at a greater speed, 0.9756c to eventually catch up to the red astronaut:

In this case, it's the black astronaut that ends up younger when they meet up together.

The oft repeated "rule of thumb" that it's the twin who accelerated that ends up younger leads to misunderstanding because it leads people to believe that it's acceleration that is important in resolving twin-type scenarios even if is does work in some cases (those where only one twin accelerates). It's better to understand that Time Dilation, like speed, is frame dependent and that if you add up accumulated time for each segment of each twin's progress, you always get the correct answer.

 

[PeterDonis]

the reality is that only one of them fired a rocket to get away from the other. The astronaut is the one "actually" moving

As ghwellsjr points out, this rule of thumb doesn't generalize. It only works in flat spacetime, and only if one of the twins is inertial the whole time. The rule that generalizes, as he says, is to compute the proper time along each worldline and compare the answers.

It's true that the "standard" twin paradox is set in flat spacetime, and only one of the twins in that scenario accelerates, so the rule of thumb works in that case, and that's the case that's usually given as the "standard" example of differential aging. But given the number of threads we get here in which somebody assumes that that rule of thumb generalizes, and starts applying it to more complicated cases where it doesn't actually work, and then wonders what "really" causes the difference in aging if it isn't acceleration, there is at least a case to be made that, for pedagogical purposes, we should skip the rule of thumb and go straight to the general principle: add up the proper time elapsed along each worldline and compare them.