[MikeFontenot (OP)]

The apparent paradox in the twin "paradox" scenario arises because it would seem that each twin should conclude that the other twin is ageing more slowly, due to the well-known "time-dilation" result, during the entire trip, except for the single instant at the instantaneous turnaround ... "surely" nothing could happen to peoples' ages during a single instant.  But that assumption is wrong: the traveling twin must conclude that the home twin's age instantaneously increases during the instantaneous turnaround.  There are various ways to obtain this result, but by far the easiest and quickest way is to use the equation described in this posting.

The change in the home-twin's (her) age, before and after an instantaneous velocity change at some instant t in the traveler's (his) life, is given by the very simple "delta_CADO_T equation":

  delta_CADO_T(t)  =  - L(t) * delta_v(t),

where

 delta_v(t)  =   v(t+)  -  v(t-),

and where t- and t+ are the instants of his life immediately before and immediately after his instantaneous velocity change at t.  The quantities v(t+) and v(t-) are their relative speeds at the instants t+ and t-, according to her. v  is positive when the twins are moving apart, and negative when they are moving toward each other.  The quantity L(t) is their distance apart when he is age t, according to her.

So, getting the change in her age during an instantaneous velocity change by him is very simple: you just multiply the negative of their distance apart (according to her) by the change in his velocity.  Couldn't be simpler.

For example, take a case where their relative velocity right before his turnaround is v = 0.9 ly/y (they are moving apart), and right after his instantaneous velocity change their relative velocity is v = -0.8 ly/y (they are moving toward one another). Then

 delta_v  =   ( -0.8 ) - (0.9)  =  -1.7 ly/y.

Suppose that their distance apart at the turnaround is 20 ly.  Then

 delta_CADO_T  =  - 20 * (-1.7)  =  34.0 years,

so he says that she instantaneously got 34 years older during his instantaneous turnaround. Couldn't be simpler.

Now, suppose that at some later instant t in his life, he decides to instantaneously change his velocity again, this time from -0.8 ly/y to 0.7 ly/y.  So this time, he is instantaneously changing from going toward her to going away from her.  In this case, we have

 delta_v  =   (0.7) - ( -0.8 )  =  1.5 ly/y.

Suppose their distance apart now 18 ly.  Then

 delta_CADO_T  =  - 18 * (1.5)  =  -27.0 years,

so he says that she instantaneously got 27 years younger during his instantaneous turnaround. Couldn't be simpler.

The above information was intentionally designed to be as concise and "narrowly-focused" as possible.  Much more complete and wide-ranging information about the traveler's perspective in the twin "paradox" is contained in my webpage:

 
 https://sites.google.com/site/cadoequation/cado-reference-frame

[Phillipz]

I do not know how many updates have been made so I can not help recommending them.

[yor_on]

Seems your link is not working.
Hopefully this one should.   https://sites.google.com/site/cadoequation/cado-reference-frame#References

[yor_on]

As long as you're not suggesting that it is the turnaround that 'instantly ages' the stay at home twin, instead pointing out the fluidity of time as related to different frame of references I agree. Time as a 'universal golden standard' doesn't exist as far as I can see. Locally though we all age, no matter how fast we speed away (or towards), or  at what mass we are, and that aging doesn't change pace using your wrist watch to define it from.
=

What's important to notice in any such scenario is how one then define other frames of references. One does it by comparing ones own wristwatch against whatever will count as the other ones frames 'clock'. So we have a golden standard of sorts, and/but, it's purely local. The same way we define repeatable experiments actually. And the most interesting thing to me there is that they do work, after all, they gave us physics (and my computer too :)

[Bill S]

Possibly, Michael Huemer resolves the issue.

http://www.owl232.net/papers/twinparadox.pdf

[MikeFontenot (OP)]

As long as you're not suggesting that it is the turnaround that 'instantly ages' the stay at home twin, [...]
[...]

That IS what I'm saying.  Her age IS instantaneously changing (either positively or negatively), in his reference frame, and that change is caused by his instantaneous velocity change.  But that doesn't mean that her instantaneous change in age is anything that can have any physical effect on her life.

There are two ways to see that.

One way is to realize that there could be multiple "travelers" who happen to be momentarily co-located at the turnaround point, and who each decide to change their velocities wrt the home twin at that instant in different ways.  So they would each legitimately and correctly say that their action has caused the home twin's age to suddenly change in their frame.  And these "travelers" would generally disagree with one another about how much her age has suddenly changed ... and whether she has suddenly gotten older or younger.  But it is obvious that she couldn't possibly be simultaneously experiencing all these different age changes.

But an even more important thing to realize is that it is in principle impossible for the home twin to experience any sudden change in her age, positive or negative.  At each instant of her life, her brain (and also the rest of her body) is in some specific, definite state.  Different instants of her life have different states, but the state of any particular instant can't ever change.  It is analogous to the image in each frame of a motion-picture reel of film: the image in each given frame is fixed.  The projectionist is free to vary the speed at which the projector is running, or even switch the direction in which the frames are being moved through the projector.  But the actors in each frame obviously can't perceive that.

[MikeFontenot (OP)]

Seems your link is not working.
Hopefully this one should.   https://sites.google.com/site/cadoequation/cado-reference-frame#References

Thanks for doing that.  I think I haven't posted enough yet to be allowed to have a clickable link.

[Bill S]

My reasoning may be wide of the mark, here, so I would value comments.

Acceleration involves a change in speed, direction or both, thus, the “turn-around” constitutes acceleration.

The “twins paradox” comes about as a result of time dilation and length contraction. 

The Lorentz equations, which gave mathematical veracity to time dilation and length contraction, feature only time, length, velocity and the speed of light.  There is no mention of acceleration.

Einstein incorporated time dilation and length contraction into SR, and SR is concerned only with uniform motion.  There seems to be no need to venture into general relativity.  So why do we have to use acceleration to solve this particular paradox? 

[MikeFontenot (OP)]

My reasoning may be wide of the mark, here, so I would value comments.

Acceleration involves a change in speed, direction or both, thus, the “turn-around” constitutes acceleration.

The instantaneous turnaround involves a special kind of acceleration: an infinite acceleration that only lasts an infinitesimal time.  Mathematically, it is a Dirac delta function.  It is an idealization of a very large acceleration that lasts only a very short time.

The “twins paradox” comes about as a result of time dilation and length contraction.

No.  Time dilation and length contraction both follow from the Lorentz equations, which describe how two inertial reference frames are related.  They don't apply to accelerated reference frames during periods or instants of acceleration. If there are no accelerated reference frames involved, no apparent paradox arises. The commonly-proposed scenario that uses an inertial "proxy" to take the place of the traveler who normally instantaneously turns around at the turnpoint is a red herring: no one in that contrived scenario is surprised by anything that happens during that scenario ... thus there is no apparent paradox in that scenario.

The cause of the apparent paradox in the traditional scenario where the traveling twin instantaneously turns around at the turnpoint, is due to an unwarranted assumption that is frequently made.  While the traveler isn't accelerating, he is an inertial observer, and is thus entitled to use the time-dilation result: he says that during his unaccelerated portions of his trip, the home twin (she) is ageing more slowly than he is.  The unwarranted assumption is that since the traveler is unaccelerated during essentially the entire trip (the whole trip except for a single instant), that he should find her younger than he is when they are re-united.  He mistakenly assumes that her age couldn't possibly increase during the single instant when he changes his velocity.  So when he finds her to be the older twin at the reunion, he is surprised, and confused ... thus the apparent paradox.  The resolution of the apparent paradox is that in the traveler's non-inertial reference frame, her age DOES suddenly increase by a large amount in the single instant of his turnaround.  And that increase is exactly enough to explain what he finds when they are reunited.

[yor_on]

Let me ask you.

would you agree to that in a uniform motion the same time dilation is existing?
Or do you expect it to come true only in accelerations?

Myself, I have no problem with different frames finding a same 'object' to have different time dilation's, relative their own local time (wrist watch).

[MikeFontenot (OP)]

Let me ask you.

would you agree to that in a uniform motion the same time dilation is existing?
Or do you expect it to come true only in accelerations?

I think I answered your question in my response above to Bill S.  If not, please elaborate on your question.

[yor_on]

Sorry, but no, No elaboration, it's a very simple question answerable by a 'yes' or a 'no'. I'll take away the question mark though if it helps you see it?

would you agree to that in a uniform motion the same time dilation is existing, or do you expect it to come true only in accelerations?

[Janus]

My reasoning may be wide of the mark, here, so I would value comments.

Acceleration involves a change in speed, direction or both, thus, the “turn-around” constitutes acceleration.

The “twins paradox” comes about as a result of time dilation and length contraction. 

The Lorentz equations, which gave mathematical veracity to time dilation and length contraction, feature only time, length, velocity and the speed of light.  There is no mention of acceleration.

Einstein incorporated time dilation and length contraction into SR, and SR is concerned only with uniform motion.  There seems to be no need to venture into general relativity.  So why do we have to use acceleration to solve this particular paradox? 

You are forgetting the relativity of simultaneity.  While time dilation and length contraction are only dependent on the speed difference between two frames,  the relativity of simultaneity is dependent on the velocity difference, which involves direction.
For example,  if you are traveling between two clocks A and C while passing a third clock B, and assuming that A, B, and C are synchronized in their own rest frame, then:
If you are traveling from A to C, then clock C will be, according to you, ahead of clock A in respect to what time it reads and if you are traveling from clock C to A then according to you, clock A will be ahead of clock B.

A numerical example:
You're traveling at 0.6c relative to the three clocks, for which the proper distance between the clocks is 1 light hour.
You pass clock B while it reads 12:00, while traveling towards A,  At that moment, according to you, Clock A reads 12:36 and Clock B reads 11:24
On the other hand, if you pass B at the same speed while going from A to C, then Clock A reads 11:24 and Clock C reads 12:36 at that moment.*
If you were to suddenly reverse direction as you pass B, while initially traveling from A to B, then clock A will "jump" from reading 11:24 to 12:36*

Acceleration comes into play with time dilation and length contraction when it involves a change speed, as changing speed changes the magnitude of these two effects.   Acceleration additionally effects the relativity of simultaneity when it involves a change of direction.


*Keep in mind that this is the time it "is" at these clocks and not the time you would "visually see" on these clocks.  In all these examples, when you are next to clock B when it reads 12:00, both you and an observer sitting by clock B would be visually seeing images of Both Clocks A and C reading 11:00.

[Janus]

Sorry, but no, No elaboration, it's a very simple question answerable by a 'yes' or a 'no'. I'll take away the question mark though if it helps you see it?

would you agree to that in a uniform motion the same time dilation is existing, or do you expect it to come true only in accelerations?

The problem with the question is that it assumes that time dilation is the only factor in consideration. Time dilation is difference in tick rate between an observer's clock and the observed clock at any given in instant in time as measured by the observer. This is different from "total difference in accumulated time" which relies on other additional factors.

[Bill S]

The Lorentz equations, which gave mathematical veracity to time dilation and length contraction, feature only time, length, velocity and the speed of light.  There is no mention of acceleration.

No. Time dilation and length contraction both follow from the Lorentz equations, which describe how two inertial reference frames are related.  They don't apply to accelerated reference frames….

There seems to be a similarity here that makes me wonder about the “No”.

BTW, have you read Heumer’s paper?

[Bill S]

You are forgetting the relativity of simultaneity.

I'll have to return to that when I have a bit more time and compare it with some of my past notes.

[yor_on]

No Janus, I don't agree to there being a difference. A time dilation is your wristwatch against some defined 'clock' of another frame of reference. What makes the twin experiment unique is the idea of it being measurable as a 'real time dilation' making one 'identical twin' younger than the other. and of course the need for an 'acceleration' if we want the thought experiment to work. But a time dilation is a time dilation.

[yor_on]

The problem with putting it the way you do Mike is that I see no way to test it other than theoretically. I doubt even NIST could do it https://www.nist.gov/news-events/news/2018/06/nist-atomic-clock-comparison-confirms-key-assumptions-einsteins-elevator

Then again, maybe they can :)

But as long as its not testable it will stay as a hypothesis,´and you still haven't told me if you think this type of time dilation differ from the ones we see through 'relative motion'. If you think it does, then how?
=

After all, 'gravity' equals to a uniform acceleration according to relativity, so you have a possibility there.

[Janus]

No Janus, I don't agree to there being a difference. A time dilation is your wristwatch against some defined 'clock' of another frame of reference. What makes the twin experiment unique is the idea of it being measurable as a 'real time dilation' making one 'identical twin' younger than the other. and of course the need for an 'acceleration' if we want the thought experiment to work. But a time dilation is a time dilation.

Then you are defining "time dilation" differently than SR does.

[yor_on]

Not sure what you think about there Janus, are you thinking of " Special relativity indicates that, for an observer in an inertial frame of reference, a clock that is moving relative to him will be measured to tick slower than a clock that is at rest in his frame of reference. This case is sometimes called special relativistic time dilation. " ?