Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: MikeFontenot on 02/09/2018 21:27:13

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 wellknown "timedilation" 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 hometwin'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 "narrowlyfocused" as possible. Much more complete and wideranging information about the traveler's perspective in the twin "paradox" is contained in my webpage:
https://sites.google.com/site/cadoequation/cadoreferenceframe (http://"https://sites.google.com/site/cadoequation/cadoreferenceframe")

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

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

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.
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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 :)

Possibly, Michael Huemer resolves the issue.
http://www.owl232.net/papers/twinparadox.pdf

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 colocated 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 motionpicture 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.

Seems your link is not working.
Hopefully this one should. https://sites.google.com/site/cadoequation/cadoreferenceframe#References
Thanks for doing that. I think I haven't posted enough yet to be allowed to have a clickable link.

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 “turnaround” 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?

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 “turnaround” 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 commonlyproposed 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 timedilation 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 reunited. 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 noninertial 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.

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).

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.

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?

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 “turnaround” 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.

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.

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?

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.

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.

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/newsevents/news/2018/06/nistatomicclockcomparisonconfirmskeyassumptionseinsteinselevator
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?
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After all, 'gravity' equals to a uniform acceleration according to relativity, so you have a possibility there.

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.

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. " ?

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/c^{2}, 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)/c^{2} = 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.

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.

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”

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.
.

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.

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.

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.
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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

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.
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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".

[...]
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.

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.

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.

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 ?

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)
[ Invalid Attachment ]

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)
cadojump.gif (5.37 kB . 435x687  viewed 2302 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.

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'.
[ Invalid Attachment ]

[...]
The error: [...] There is no 'jump'.
[...]
We'll have to agree to disagree.