[Bill S]

You are forgetting the relativity of simultaneity.

This may be a bit off topic, but it's a chance to check my conclusion of a few years ago.

I wrestled for a long time with a scenario in which there were three craft in an expanse of empty space.  Two, piloted by Alice and Bob, were maintaining a separation of 20 light seconds.  Their clocks were synchronised.  The third craft, piloted by Charlie, was overhauling the other two at 0.8c. 

Eventually, I reached the following conclusion.

If two clocks, in the same RF, are synchronised and are separated by a distance “L”, then an observer in another RF who sees them as moving at speed “V”, will see the moving clocks as being out of synchronisation.  The rear clock will appear to be ahead of the front clock, and the difference in time will be given by the equation: VL/c², where V is the relative speed between the two inertial frames, and L is the distance between the two clocks.  In this scenario the relative speed between the two inertial frames is 0.8c, and the distance between Alice and Bob is 20 light seconds, in their RF.  This equation reveals how Charlie sees on Bob’s clock.

(0.8c)(20 ls)/c² = 16 seconds.

Thus, Charlie concludes that Bob’s clock is 16 seconds ahead of Alice’s and his at the point when his and Alice’s are synchronised.

[PmbPhy]

Possibly, Michael Huemer resolves the issue.

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

Its simple using GR. When the traveling twin "instantaneously" turns around he reckons that he is in that moment in a gravitational field and as such the gravitational aging is instantaneous too. Work it out and see for yourselves. Its a good exercise.

[Bill S]

Its simple using GR.

Heumer maintains that GR is not needed to resolve the twins paradox.

I would value your comments on:

“III. Two Wrong Responses to the Twin Paradox”

[yor_on]

Seems to me there are two ways of looking at this.

One is a 'jagged universe', a universe we see as being a whole universe, but relating to our own definition of a 'time', because that is our measurement, always locally made, From such a point of view, the twin accelerating can swear on a bible, although theoretically, that it was this turnaround that instantly aged the stay at home twin. It's jagged, because it imply that what counts for a time dilation is accelerations/decelerations. It breaks up the idea of what we see looking out into pieces of time relative ourselves, if that now make sense.

The other one is the one in where accelerations doesn't matter, although they still do of course. In that scenario a time dilation is about clocks, relative your wristwatch, too. But it keeps the universe you see in a fluid state relative your own 'time'.

Myself I prefer the second one as it then (the universe) doesn't break up into 'instants', but both scenarios present you with the same golden standard for what 'time' it is.

It's local.
.

[yor_on]

Actually that's the most interesting part of it. That we all share this local definition, and that the only thing you need to do to be 'in sync' is to be there, in a 'same frame of reference' as they say. That's the deepest part of the twin paradox to me.

[Bill S]

 Have to say I prefer the second option, too, for a number of reasons.

The idea of gaining, or losing, large chunks of time, in whatever RF, by an “instantaneous” action in one RF might work in theory; but in the physical world??

If you can achieve your objective by using SR, why involve GR unnecessarily?  It seems a bit like having a ladder that reaches your roof, then grumbling because it isn’t 20 ft longer.

[yor_on]

Well, the stay at home twin won't agree to him instantly jumping in time, aka aging, and neither scenario expect him too, as far as I got it Bill. That's how I read it anyway, rereading it :). You might say that the scenario where he 'instantly age' is the one really defending (pointing out) the view of 'time' being purely local, but it still leaves you to define where and how it happened. It's once again questioning what a 'whole universe' really means, and that's a pretty deep question.
=

both scenarios expect the stay at home twin to have aged more 'for real' so it's actually more of a matter of taste which one you prefer, to state a truth. It's just that taking it to its limits leave you wondering what happens when you blink, cause that's an acceleration too. And if we take the photographical 'proof' of electrons orbiting (orbitaling?) a nucleus then that too is a orbit of sorts :) And as Newton pointed out, all orbits are accelerations (unless we're discussing things like Earths motion which is a geodesic according to relativity, instead of a orbit.)

That's actually interesting too, because defining electrons to be in a 'orbit' instead of a 'orbital' crave them to surpass the speed of light if I remember right. Maybe you could create a scenario in where anything surpassing that speed automatically become superpositions? Heh :)

wonder what that would make a black hole :)
And, thinking some more about it, indeterminism, aka 'virtual photons', zero point 'energy/HUP' etc

[guest4091]

This is the same answer he got on another forum.
In fig.1, A is the stationary twin and B is the wandering twin. B moves at .6c relative to A outbound and inbound, with an instantaneous reversal* at B4. The light signals (blue) are sent at unit intervals (tick marks) from A. B receives 2 signals in 4t outbound and  8  signals in 4t inbound. All A events are observed by B in a continuous sequence with no gaps, and all B events (shown only as tick marks for clarity) are observed by A. This must be the case for signals emitted from one boundary of a closed path to the opposite boundary.
The interpretation of a time jump for A events observed by B is based on the axis of simultaneity (aos) (red). The aos is defined by the SR clock synch convention. If B pings A for a clock reading, (events B1, A2, B4), the clock reading is assigned to half the round trip transit time, B 2.5. If B pings A for a 2nd clock reading, (events B4, A8, B7), the clock reading is assigned to half the round trip transit time, B5.5.
Since B cannot assign a time to the A clock readings until after they are detected, the aos is irrelevant to B observations of A.
The 'time jump' is the result of a poorly rendered drawing.
Fig.2 shows a more realistic reversal which rotates the aos clockwise between the two positions shown in fig.1.
Each observes clock rates as doppler effects while diverging or converging, since clocks are frequencies. Aging is the accumulation of time, and determined by a comparison of clocks at reunion. Mutual observations are irrelevant.
This is a case of making a simple problem unnecessarily complicated. Even as a 1st  approximation, it still serves the purpose of illustrating time dilation and aging.
In the 3rd drawing, using the ct scale of A, draw an arc at 5 centered on 0 that meets the x coordinate of the reversal point. That point projected horizontally indicates ct=4, the same value resulting from the red hyberbolic calibration curve (as labeled by Max Born). It's simpler to draw an arc! Rotate the drawing 180 and apply the same method from ct=10.
The net result B loses 2t and ages 8t. 

twin jump.gif (7.99 kB . 512x606 - viewed 4330 times)
twin-jump2.gif (3.67 kB . 286x573 - viewed 4343 times)

[MikeFontenot (OP)]

BTW, have you read Heumer’s paper?

I read enough of it to know that I don't agree with him at all.  He says acceleration isn't important.  I say it is vital in resolving the twin "paradox".

[MikeFontenot (OP)]

[...]
 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.
[...]

I prefer to reserve the term "time dilation" for INERTIAL observers only.  I don't like to use it for accelerating observers.  The reason is that sometimes an accelerating observer will conclude that the observed person's age is increasing much FASTER than his own ageing.  And for other accelerations, the observed person's age can even be DECREASING as the observer gets older, so her ageing rate is negative.  That makes the term "dilation" not appropriate, since "dilation" is meant to convey that the observed clock is running slower to some extent.

Another reason I don't use the term "dilation" for anything other than the current ratio, of the ageing of the observed person, to the ageing of the inertial observer, is that it is sometimes used by people to refer to the OUTCOME of the twin "paradox", not as a "rate ratio" at all.  So the term can become ambiguous, and prone to misinterpretation.

[Bill S]

I read enough of it to know that I don't agree with him at all.  He says acceleration isn't important.  I say it is vital in resolving the twin "paradox".

Then perhaps you didn't read enough.  Surely, if someone disagrees with you you want to know why.

[yor_on]

I don't see why you think that a time dilation always must be slower Mike. As long as the arrow of time goes in one same direction for both.

[Bill S]

Re #27.

This is not my strong point, and it would take more time than I have available to do the comparison.

How do the outcomes from the Figs in #27 compare with those from  http://www.owl232.net/papers/twinparadox.pdf ?

[guest4091]

Mike;

I don't know how you derived the expression, but here is one method from a spacetime graphic. The axis of simultaneity is red and light path is blue. The angle ( provides similar triangles because the t and x axes are symmetrical relative to light path.

j=time jump

j/x = x/t = v, thus j=xv

since x is the same for outbound and inbound,

j1+j2 = x(v1+v2)

cado-jump.gif (5.37 kB . 435x687 - viewed 4696 times)

[MikeFontenot (OP)]

I don't know how you derived the expression, but here is one method from a spacetime graphic. The axis of simultaneity is red and light path is blue. The angle ( provides similar triangles because the t and x axes are symmetrical relative to light path.

j=time jump

j/x = x/t = v, thus j=xv

since x is the same for outbound and inbound,

j1+j2 = x(v1+v2)

cado-jump.gif (5.37 kB . 435x687 - viewed 4696 times)

That diagram looks similar to the Minkowski diagram in my derivation, and the equation looks similar to my CADO equation.  I've recently added to the end of Section 11 a detailed description of how I originally derived the CADO equation from the Minkowski diagram.  The CADO equation can also be derived in a purely analytical manner from the Lorentz equations, but I did that only in my original paper, not in the webpage.

[guest4091]

The finale;
The graphic shows the popular 'twin paradox' with the (red) axis of simultaneity (aos) for the outbound and inbound paths of B. The aos is the basis for the 'time jump' from the lower to the upper position. Supposedly B observes A age instantly from t=3 to t=7 upon reversal. The error: the (blue) light signals originate at A and are not round trip signals originating at B, which is required for the SR clock synch convention. The aos does not apply to the drawing, which is only a case of doppler effects. Notice that the image received by B at the reversal is A2, and the next to be received is A3. There is no 'jump'.

twin vs aos.gif (4.47 kB . 293x592 - viewed 4120 times)

[MikeFontenot (OP)]

[...]
The error: [...] There is no 'jump'.
[...]

We'll have to agree to disagree.