# The Simplist Explanation of the Twin Paradox

Discussion in 'Physics & Math' started by Mike_Fontenot, Jan 25, 2023.

1. ### Mike_FontenotRegistered Senior Member

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445
The important thing in understanding the twin paradox is to start with the most trusted result of special relativity: the time dilation equation (TDE) for two inertial people moving at a relative speed "v". From that alone, we can easily determine how old she and he are at their reunion (by looking at it from HER perspective, since she is always inertial). He will be younger than she is, by a definite and calculable fraction.

THEN, we try to get the same answer, but this time using HIS perspective instead of hers. He can also use the TDE for each of the inertial legs of his trip for his analysis, and so he will say that she will be younger than he is at their reunion (by the same calculable fraction that she used). Something is clearly wrong: they MUST agree about their respective ages at their reunion, because they are standing right next to each other then, and looking at each other.

The only thing he could be leaving out in his analysis is that he has (perhaps unconsciously) been assuming that nothing happens to her age during his instantaneous velocity change. That's the only remaining time in his life where additional ageing by her could have occurred. So he then KNOWS that during his instantaneous velocity change, she MUST have instantaneously gotten older by exactly the amount that is required to make them agree about their respective ages when they are reunited.

3. ### mathmanValued Senior Member

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1,972
It seems from your description, he moves away and turns around to get back. Try working it out with both observing each other throughout the trip. Differences will show up without instant aging,

5. ### Mike_FontenotRegistered Senior Member

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Sorry, I don't understand your comment. I think you must have misunderstood what I said. The scenario I analyzed above IS the standard twin paradox. He leaves her at a constant speed, goes to his turnaround point, instantaneously reverses his course, and returns to her at the same constant speed as on his outbound leg. And I showed above that using only the time dilation equation (TDE) for an inertial person, it's possible to show that the only way to get a consistent outcome at the reunion (from her perspective AND his perspective) is for him to conclude that she instantaneously ages by a large amount during his instantaneous turnaround. If he assumes that she doesn't age at all during his instantaneous turnaround, he will conclude that HE is the older twin at the reunion, and that contradicts her conclusion (which is certainly correct) that SHE is the older twin at the reunion. The only way they can agree at the reunion (which they MUST do), is for him to conclude that she ages instantaneously during his instantaneous turnaround.

7. ### DaveC426913Valued Senior Member

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If they are both moving inertially (also known as not accelerating), how can they ever meet again?

8. ### DaveC426913Valued Senior Member

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17,620
So ... he accelerates.
Which is non-inertial.
Which breaks the symmetry.

9. ### billvonValued Senior Member

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20,987
Google Minkowski diagram. It will explain this for you graphically.

10. ### James RJust this guy, you know?Staff Member

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38,009
Mike:

What you wrote seems fine, for the most part, but you haven't spelled out the scenario very clearly.

It seems you're assuming that "he" only accelerates once, which is when he turns around. So, you're assuming that "he" and "she" don't start or end your scenario at rest relative to one another.

Also, you're obfuscating when you claim that all the motion is "inertial". The accelerating part of "his" motion is non-inertial.

Special relativity doesn't require trust. Like other scientific theories, it is supported by observational evidence.

Did you have a question at all, or did you just think it important to tell us all about the twin paradox for the n-th time?

11. ### Mike_FontenotRegistered Senior Member

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445
Because he instantaneously changes his velocity with respect to her at his turnaround. He is NOT inertial at that one instant.

He doesn't accelerate during his outbound leg, or during his inbound leg. I.e., he is inertial during those portions of his trip, and so he is entitled to use the time dilation equation for inertial observers (the TDE) during those two segments of his trip. That means that, during those two segments, he concludes that she is ageing more slowly than he is. But there is a single instant during his trip when he is NOT inertial ... at the single instant of his instantaneous turnaround. And THAT is the instant in his life when he must conclude that she instantaneously gets much older then.

If you read my previous posting more carefully, you'll understand what I'm saying.

12. ### DaveC426913Valued Senior Member

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It doesn't matter how quickly he accelerates. He accelerates enough to invert his velocity vector. Thus breaking the symmetry.

No. You can't claim that the outbound trip and the inbound grip are part of the same scenario without including the reversal.

If you discount the reversal then you are looking at two independent scenarios in which the two travellers do not have the chance to compare both their starting ages and ending ages.

Either there is one scenario, in which
- two travellers sync their ages,
- then one traveller undergoes acceleration, which breaks the symmetry,
- and then they compare their aging again when they meet.

or
there are two distinct scenarios,
- one outbound and one inbound
- but in neither scenario have they have had the opportuny to sync their ages,
- which means they can't compare their aging.

You can't have it both ways.

Last edited: Jan 26, 2023
13. ### Mike_FontenotRegistered Senior Member

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445
He DOES instantaneously change his velocity at the start of his trip and at the end of his trip. But that has no effect on her age when they are co-located. When they are instantaneously co-located, an acceleration by one of them has no effect on the age of the other ... it COULDN'T: they are face-to-face and looking at each other! The effect of an instantaneous change in his velocity relative to her is proportional to their distance apart (as shown most dramatically by Brian Greene in his "alien riding a bicycle in a distant galaxy" NOVA show, where their separation is so enormous that relativistic effects occur even at bicycle speeds!).

Also, the scenario doesn't actually REQUIRE the two "twins" to be at rest at the beginning and end of the scenario. Two pregnant mothers could be perpetually inertial, moving at the stated relative velocity, and happening to give birth simultaneously at the instant they pass each other. And at the end of the scenario, when the two "twins" reunite, the traveler doesn't have to stop ... at the instant they are co-located again, they can just look at each other at that instant, and ascertain what their two ages are at that instant.

I claimed no such thing. I said that he is inertial DURING his outbound leg and DURING his inbound leg, but he is certainly NOT inertial at the instant when he reverses course at his turnaround ... at that instant, he undergoes an infinite acceleration in her direction, with an infinitesimal duration.

14. ### DaveC426913Valued Senior Member

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17,620
Billvon is correct.
Find a Minkowski diagram on the twin paradox that you're comfortable reading.
At the very least, any Minkowski diagram will show you that the scenario isn't just asymmetrical during acceleration. The two legs themselves are asymmetrical:

15. ### billvonValued Senior Member

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20,987
Which is impossible. Thus it may be an interesting thought experiment but will never happen in reality.

16. ### DaveC426913Valued Senior Member

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17,620
Even if it were - even in an ideal thought experiment - it's irrelevant.

Minkowski diagrams, such as the one in post 11 routinely assume a zero turn-around time. It has no effect on the symmetry-breaking.

Mike is wrong when he thinks he can maintain an inertial and symmetrical scenario simply by making the acceleration duration short enough.

17. ### Mike_FontenotRegistered Senior Member

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445
In this thread, I originally gave a resolution of the twin paradox that was purely qualitative, not quantitative. That was intentional, because some people's eyes glaze over when they see any equation. I gave an argument that allowed the traveling twin to INFER that (according to him) she must instantaneously age by a large amount when he instantaneously reverses his velocity at the his turnaround.

In what follows, for continuity I'm going to first repeat what I said in that first post. But then, I'll follow that with a quantitative description, and finally end with a specific numerical example.

___________________________________________________________________

Qualitative Description:

The important thing in understanding the twin paradox is to start with the most trusted result of special relativity: the time dilation equation (TDE) for two inertial people moving at a relative speed "v". From that alone, we can easily determine how old she and he are at their reunion (by looking at it from HER perspective, since she is always inertial). He will be younger than she is, by a definite and calculable fraction.

THEN, we try to get the same answer, but this time using HIS perspective instead of hers. He can also use the TDE for EACH of the inertial legs of his trip for his analysis, and so he will say that she will be younger than he is at their reunion (by the same calculable fraction that she used). Something is clearly wrong: they MUST agree about their respective ages at their reunion, because they are standing right next to each other then, and looking at each other.

The only thing he could be leaving out in his analysis is that he has (perhaps unconsciously) been assuming that nothing happens to her age during his instantaneous velocity change. That's the only remaining time in his life where additional ageing by her could have occurred. So he then KNOWS that during his instantaneous velocity change, she MUST have instantaneously gotten older by exactly the amount that is required to make them agree about their respective ages when they are reunited.

_________________________________________

Quantitative Description:

What is the exact cause of the fact that the home twin is older than the traveling twin at their reunion?

It is caused by the change in velocity of the traveling twin (he), when he is separated from the home twin (she).

The simplest case is when his change of velocity is instantaneous (but the outcome is similar when his acceleration is finite for a finite duration). According to him, when he instantaneously changes his velocity with respect to her by delta_v, he says her age instantaneously changes by the quantity

- L * delta_v,

where "L" is their (positive) separation then, according to HER, and

delta_v = v(inbound) - v(outbound).

Velocities are taken as positive when the twins are moving apart, so delta_v is negative in the standard twin paradox scenario.

________________________________________________________

Numerical Example:

I'll give a specific example of how the above equation is used. Let the relative speed of the twins be 0.866, using units of lightyears and years. That gives a gamma factor of exactly 2. So we immediately know that, when he is not changing his speed (and she never does), they each conclude that the other is ageing half as fast as they themselves are. Suppose she says that he goes outbound for 40 years (of her time). So she says that he is 20 years old at his turnaround. His turnaround is an EVENT, so everyone (including him) must agree that he is 20 years old then.

Similarly, according to her, she ages 40 more years while he is returning home. He ages by 20 years during his return (and both she and he agree about that, because the turnaround and the reunion are both EVENTS, so everyone agrees about his age then). So at the reunion, she is 80 years old, and he is 40 years old. They HAVE to agree about that, because they are standing side-by-side and looking that each other at the reunion.

But while he was going at a constant speed on his outbound leg, HE says (using the TDE) that she was aging at half his rate, so HE says she only got 10 years older on his outbound leg, and likewise for his inbound leg. So he concludes that she should only be 20 years old when he gets home. But she's not ... she's 80 ... he can see that. So where did she age the additional 60 years, according to him? There's only one place that could have happened: she HAD to have aged (according to him) by 60 years during his instantaneous turnaround.

And that's exactly what the simple equation in the above quantitative description section gives. Their distance apart at the turnaround (according to her) is

L = 40 * v = 40 * 0.866 = 34.64 ly.

In the qualitative section, I said

"According to him, when he instantaneously changes is velocity with respect to her by delta_v, he says her age instantaneously changes by the quantity

- L * delta_v,

where delta_v is his velocity change at the turnaround (and it's negative, so her age change is positive). We know from the known results at the reunion that he must conclude that she instantaneously gets OLDER when he accelerates TOWARD her.

Specifically,

delta_v = -0.866 - (+0.866) = -1.732.

So he says she instantaneously gets OLDER during his instantaneous turnaround by

- L * delta_v = (-34.64) * (-1.732) = 60 years.

Therefore she is 80 years old at their reunion, according to his calculations (and according to what he sees with his eyes then).

______________________________________________________

18. ### Mike_FontenotRegistered Senior Member

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I've got one important addendum to my above post:

As I showed in the first section above, the instantaneous ageing of the home twin (her), according to the traveling twin (him), can be INFERRED (without needing the equation I gave above for her instantaneous age increase) in the standard scenario where he only changes his velocity ONCE, and DOES return home. But it is important to point out that for more complicated scenarios (such as multiple instantaneous velocity changes at different times in his trip, or scenarios where he never comes home it all), the equation I gave (or alternatively, a Minkowski diagram analysis) is indispensable.

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20. ### Mike_FontenotRegistered Senior Member

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Those monographs are too long to post in this forum ... they are over 20 pages long.

There ARE four monographs shown on Amazon, but the one with the brownish cover is just an old version of the one with the purple cover. (I had tried unsuccessfully to revise that brown one, but it never worked, so I asked them to remove it, and I submitted the revised version as a new monograph.) The one with the red cover is the one that proves that the exponential form of the gravitational time dilation equation is incorrect, because it is inconsistent with the outcome of the twin paradox.

The one with the green cover is the oldest one, and is a simultaneity method that does NOT have an instantaneous age change for her (the home twin), according to him (the accelerating twin). My more recent results have proved that the instantaneous age change IS the correct solution, so this old method is incorrect. It's only value (if there is any) is as a refuge for people who cannot stand the idea of her instantaneous ageing (and in particular, instantaneous NEGATIVE ageing, where she instantaneously gets YOUNGER), according to him, when he instantaneously changes his velocity.

All three of those monographs are available (as downloadable PDF's) for free in the online viXra repository, and there are two additional short followup papers that are also available on viXra for free. The last one I published is actually the best one to start with, because it is very short, and has references to the other longer papers. It's at

https://vixra.org/abs/2210.0072

and it is titled "A Proposed Experimental Test of My Gravitational Time Dilation Equation".

(If you ever want to search viXra for any my papers, the best way is to use my full name: Michael Leon Fontenot with quotes around it.)

21. ### Mike_FontenotRegistered Senior Member

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445
My Amazon book with the red cover (which corresponds to https://vixra.org/abs/2109.0076 ), titled
"An Inconsistency Between the Gravitational Time Dilation Equation and the Twin Paradox", shows that the exponential version of the gravitational time dilation equation is incorrect.

My Amazon book with the blue cover (which corresponds to https://vixra.org/abs/2201.0015 ), titled
"A New Gravitational Time Dilation Equation", shows the derivation of the new gravitational time dilation (GTD) equation that replaces the incorrect exponential equation.

The two short viXra papers (which aren't published on Amazon) serve well as summaries of the results of the two much longer papers.

The first of the short papers is https://vixra.org/abs/2206.0133 , titled
"Is the Equivalence Principle Schizophrenic ... And a Summary, and a Correction (Revised Edition)". It shows that in some cases, the equivalence principle works, and in some cases, it doesn't, so the user should beware. This paper also corrects a statement in my New Gravitational Time Dilation paper which doesn't affect my important conclusions, but which still should be corrected. The paper also emphasizes the especially important conclusion in the second paper that the new GTD equation allows the (conceptual) construction of an array of clocks and measuring rods that establishes a "NOW" moment, for the accelerating observer (him), that extends throughout (flat) space, and which GUARANTEES that the "NOW" moment MUST be considered to be fully meaningful and "real" by him. That "NOW" moment agrees with the "Co-Moving Inertial Frame (CMIF) simultaneity method, and it proves that the CMIF simultaneity method is the ONLY correct simultaneity method.

The second of the short papers is https://vixra.org/abs/2210.0072 , titled
"A Proposed Experimental Test of My Gravitational Time Dilation Equation". It shows that my GTD equation, and the incorrect exponential GTD equation, are VERY different QUALITATIVELY, as well as quantitatively, and thus shouldn't be too hard to distinguish experimentally. I suggest that UNSTABLE charged particles could serve as high-speed accelerating "clocks", in a laboratory experiment. That might allow my GTD equation to be either verified or falsified. (The latest version of that second short paper also corrects a "non-strategic" error I made in all of my earlier papers, in which I said that an acceleration of 1 ls/s/s is equivalent to about 40 g's. It's actually equivalent to about 32 MILLION g's! That ratio [between 1 ls/s/s and 1 g] is just the number of seconds in a year.)

22. ### Mike_FontenotRegistered Senior Member

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445
P.S.:

In the above, I said:

The paper also emphasizes the especially important conclusion in the second paper that the new GTD equation allows the (conceptual) construction of an array of clocks and measuring rods that establishes a "NOW" moment, for the accelerating observer (him), that extends throughout (flat) space, and which GUARANTEES that the "NOW" moment MUST be considered to be fully meaningful and "real" by him.

I want to add that there are many physicists who still believe, {since different momentarily co-located observers (moving in different ways, some inertial, some accelerating) will come to different conclusions about the distant home twin's (her) current age}, that any particular one of them should NOT consider his conclusion to be meaningful and "real". But the array of clocks I have described for an accelerating observer GUARANTEES that his conclusion is meaningful and "real". And likewise for an inertial observer, who also has HIS own array of clocks. If an inertial observer rejects the meaningfulness of his conclusion about the current age of the distant person, then he MUST reject the fundamental assumption of special relativity: that the velocity of light is exactly the same for any inertial observer, because that assumption was what enabled him to synchronize his array of clocks. So if he rejects the meaningfulness of the current age of the distant person (as given by his array of clocks), he must reject special relativity itself. In the case of an accelerating observer, the clocks in his array can't be synchronized (because they run at different rates), but since he knows at each instant in his life how all the other clock readings are related to the current reading on his clock, his array DOES establish a "NOW" moment for him that extends throughout all space, and thus guarantees that his conclusions about her age are meaningful and "real".

23. ### phytiRegistered Senior Member

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690
mike;

You are as persistent as global climate change!
1.
A simple logical argument for twins A and B.
A moves in space at speed a relative to U, our trusted ref. frame.
Relative to U, B departs from A at speed b1 outbound and moves at speed b2 inbound to rejoin A.
We assume elapsed A-time to equal elapsed B-time at reunion.
If B moved a greater distance than A in the same A-time, B would have to have moved faster than A for some portion of his trip. SR states time dilation is a function of speed.
Thus the B-clock would have less accumulated time than the A-clock, contradicting our assumption.
A has a constant clock rate. B's clock rate varies, < A outbound and > A inbound.
Each loses time, but B loses more than A. Lost time cannot be recovered.
Each clock functions independently of the other.
2.
The motion of an anaut in space cannot affect distant processes such as clock rates. When scientists accelerate particles to near light speed, astronomers do not notice any changes in space.
3.
Included a gif showing case 1. The red hyperbolic lines are 'calibration curves' as labeled by Max Born. Where they intersect a velocity profile such as A or B indicates the same time. So t1 is projected onto A and the outbound for B. Rotate the plot 180ยบ, and
t2is projected onto A and the inbound for B.
This accounts for all the B-time, but there is additional A-time (t?).