# New Arguments In A Possible Proof That Negative Ageing Doesn't Occur In Special Relativity

Discussion in 'Physics & Math' started by Mike_Fontenot, Aug 7, 2021.

1. ### Mike_FontenotRegistered Senior Member

Messages:
358
Yes, although in my example, it's going from zero to -0.866.

But the point is, in CMIF, once the duration of the acceleration gets fairly small, further reductions in the duration (with accompanying increases in the magnitude of the acceleration that keep the area under the curve constant) have negligible effect, and the age increase of the distant person quickly approaches a finite limit. That's what makes instantaneous velocity changes in CMIF so useful and simplifying. But in the "EPVGTD" simultaneity method, the age of the distant person doesn't approach a limit as the acceleration duration is decreased ... the distant person's age goes to infinity. That is an absurd result, and (in my opinion) it casts doubt on the validity of the gravitational time dilation equation.

3. ### SsssssssRegistered Senior Member

Messages:
265
It's almost as if you were using the wrong expression for gravitational potential isn't it?

5. ### Mike_FontenotRegistered Senior Member

Messages:
358
Actually, I AM starting to doubt its validity. I THINK the original source of that equation was Einstein, in his 2007 paper. In that derivation, Einstein didn't use the exponential exp(Ad), he used 1 + Ad. He did conjecture that the exact expression was exp(Ad), but he didn't use the exponential in his derivation. I may try using 1 + Ad instead of the exponential in my example, and see if the results are more reasonable.

It's possible that the gravitational time dilation equation has only been experimentally confirmed for very small Ad. Maybe it's not valid for large Ad.

7. ### SsssssssRegistered Senior Member

Messages:
265
As I've said several times the problem is that Einstein is assuming a uniform gravitational field and that isn't the same as a field in which observers stay at the same distance which is what you want. Either is a decent approximation to the other over a small range of heights and times but you are using a large range.

8. ### Mike_FontenotRegistered Senior Member

Messages:
358
The equation I've seen allows the gravitational field strength to vary with height, but certainly doesn't require it to vary. I'm just using the equation with a constant "g" force.

9. ### SsssssssRegistered Senior Member

Messages:
265
Not in flat spacetime anyway.

10. ### Neddy BateValued Senior Member

Messages:
2,274
Let's consider the case on the right here:

As the traveler accelerates at the double-turnaround, he remains 20 years old (assuming the double-turnaround is short enough in duration). Using the CMIF method, he says that his distant twin sister goes from being 10 years old, to being 70 years old, and then back to being 10 years old, give or take a few seconds. The question then is, how could we use the pseudo-gravitational field caused by his acceleration to account for this?

1. Just before the acceleration occurs, (and therefore just before the pseudo-gravitational field occurs), it is a given from SR that he must claim that she is 10 years old simultaneously with him being 20 years old. So, that is our given starting point.

2. At the first part of the double-turnaround, the change that accompanies the first acceleration (and therefore the first pseudo-gravitational field) is her changing from 10 to 70. This can be explained by him being so much higher in the strong pseudo-gravitational field that his clock ticks much slower than hers, which is the same thing as her clock ticking much faster than his. This results in her age accumulating many more seconds (60 years is about 1892160000 seconds) while his accumulates only a few seconds.

3. At the second part of the double-turnaround, the change that accompanies the second acceleration (and therefore the second pseudo-gravitational field) is her changing from 70 to 10. The question then is: How can this be explained by her being so much higher in the strong pseudo-gravitational field? Surely all that can mean is that her clock ticks much slower than his, which means she stays 70 but he gains the 1892160000 seconds, right? No, we know that has to be wrong, because it is a given that he is still 20 years old after the second turnaround, so he cannot get older like that. So the ages must change in a away that he gains 1892160000 seconds relative to her without his age changing from 20 years old. So we have no choice but to subtract the 1892160000 seconds from her age. That is the only way the pseudo-GR explanation can account for her age going from 70 years old back to 10 years old.

Last edited: Sep 1, 2021
11. ### Mike_FontenotRegistered Senior Member

Messages:
358
Instantaneous Velocity Changes in the Equivalence Principle Version of the Gravitational Time Dilation Equation - Revised Model (the LGTD Model)

_______________________________________________________

I repeated my previous analysis of the instantaneous increase in the home person's (her) age (according to the accelerating person, AO, him), according to the Equivalence Principle Version of the Gravitational Time Dilation Equation, (the "EPVGTD" equation), and replaced it with the new equation, which I'll call the "Linearized Gravitational Time Dilation Equation", (the "LGTD" equation). I simply replace the exponential exp(A d) with the quantity (1 + A d). (This is the same approximation that Einstein used in his 1907 paper). In what follows below, I'll repeat each affected calculation that I made in my last post, and show the revised calculation.

[...]

[Previous]:

The "EPVGTD" equation says that the acceleration A will cause the HF to age faster than the AO by the factor exp(A d), where d is the constant separation between the AO and the HF.

[Revised]:

The "LGTD" equation says that the acceleration A will cause the HF to age faster than the AO by the factor (1 + A d), where d is the constant separation between the AO and the HF.

(Both of the above are for the case where the AO accelerates TOWARD the unaccelerated person (her).)

[...]

[Previous]:

The change in the age of the HF, caused by an acceleration "A" that lasts "tau" seconds is just

tau [exp(d)] sup A,

because [exp(d)] sup A is the constant rate at which the HF is ageing, during the acceleration, and tau is how long that rate lasts.

[Revised]:

The change in the age of the HF, caused by an acceleration "A" that lasts "tau" seconds is just

tau (1 + A d),

because (1 + A d) is the constant rate at which the HF is ageing, during the acceleration, and tau is how long that rate lasts.

[Previous]:

But we earlier found that A = theta / tau, so we get

tau [exp(d)] sup {theta / tau}

[Revised]:

But we earlier found that A = theta / tau, so we get

tau (1 + [ ( theta d ) / tau ] = tau + (theta d)

[...]

It is still true that d = 7.52 lightseconds and theta = 1.317.

Therefore the revised result is that the change in HF's age during the acceleration is equal to

tau + ( theta d ) = tau + (1.317)(7.52) = tau + 9.904.

So, in the revised model, as tau approaches zero (to give an instantaneous velocity change), the change in the HF's age during the speed change approaches 9.904 seconds from above. So the HF's age increased by a finite amount, unlike the infinite increase that the EPVGTD equation gave.

Before the instantaneous velocity change, the AO, the HF, and the home twin (she) were all the same age. She and the HF were co-located. So after the instantaneous speed change, the AO hasn't aged at all, but the HF is 9.904 seconds older than he was before the speed change, according to the AO. And since she and the HF have been colocated during the instantaneous speed change, they couldn't have ever differed in age during the speed change ... it would be absurd for either of them to see the other have an age different from their own age at any instant. So after the instantaneous speed change, the AO must conclude that she and the HF both instantaneously got 9.904 seconds older than they were immediately before the speed change.

By comparison, the CMIF simultaneity method says that the AO will conclude that her age instantaneously increases by 6.51 seconds, so the LGTD and CMIF don't agree.

12. ### phytiRegistered Senior Member

Messages:
612
Neddy;

Not really.
If the reversal is instantaneous, the acceleration requires no time, thus there is no equivalent g-field.
Per SR clock synch convention for inertial motion, the B signal which gets the At=10 value returns at Bt=21.2. B assigns At=10 to Bt=12. (Only because B follows a fantasy speed profile.)
Drawing an imaginary line from A10 to B20 is meaningless unless you make a measurement.
The upper half is a mirror image so B assigns At=70 to Bt=28.

If the CMIF method results in zero transit time for images, then you are regressing about 300 years.

13. ### phytiRegistered Senior Member

Messages:
612
Neddy;

B's future observation:
Just after the reversal at Bt=21.2, B cannot see the A-clock change from 10 to 70.
The clock event At=70 hasn't happened yet.
B receives the images from A in the same order they are generated, continuing with At=20.
In summation, B will have received 80 units of time from A within his 40 units, and A will have received 40 units of time from B within her 80 units.
A and B have identical clocks but they function independently of each other. The only factor affecting clock rate in SR is speed in space relative to light speed.

The green simultaneity lines are established via light signals. They do not have a magical independent existence.

14. ### SsssssssRegistered Senior Member

Messages:
265
Actually by light signals and an unprovable assumption of the isotropy of lightspeed and you can get different simultaneity surfaces by making different assumptions which are more complicated mathematically but equally valid so your way is not the only way and the assumption it rests on makes it just as imaginary as all others.

15. ### Mike_FontenotRegistered Senior Member

Messages:
358
I just repeated my previous analysis of instantaneous velocity changes in the "linearized" (LGTD) version of the equivalence principle version of the gravitational time dilation equation, but for the case where the instantaneous velocity change is AWAY FROM the home twin (her). The result is exactly like the previous result, except that she instantaneously gets YOUNGER, not older. (This contradicts my previous possible proof that negative ageing doesn't occur.)

Below, I'll repeat the previous calculations, and show the changes.

[Previous]:

I simply replace the exponential exp(A d) with the quantity (1 + A d).

[New]:

I simply replace the exponential exp(-A d) with the quantity (1 - A d).

[Previous]:

The "LGTD" equation says that the acceleration A will cause the HF to age FASTER than the AO by the factor (1 + A d), where d is the constant separation between the AO and the HF.

(The above is for the case where the AO accelerates TOWARD the unaccelerated person (her).)

[New]:

The "LGTD" equation says that the acceleration A will cause the HF to age SLOWER than the AO by the factor (1 - A d), where d is the constant separation between the AO and the HF.

(The above is for the case where the AO accelerates AWAY FROM the unaccelerated person (her).)

[...]

[Previous]:

The change in the age of the HF, caused by an acceleration "A" that lasts "tau" seconds is just

tau (1 + A d),

because (1 + A d) is the constant rate at which the HF is ageing, during the acceleration, and tau is how long that rate lasts.

[New]:

The change in the age of the HF, caused by an acceleration "A" that lasts "tau" seconds is just

tau (1 - A d),

because (1 - A d) is the constant rate at which the HF is ageing, during the acceleration, and tau is how long that rate lasts.

[Previous]:

But we earlier found that A = theta / tau, so we get

tau (1 + [ ( theta d ) / tau ] ) = tau + (theta d)

[New]:

But we earlier found that A = theta / tau, so we get

tau (1 - [ ( theta d ) / tau ] ) = tau - (theta d)

[both Previous and New]:

It is still true that d = 7.52 lightseconds and theta = 1.317.

[Previous]:

Therefore the revised result is that the change in HF's age during the acceleration is equal to

tau + ( theta d ) = tau + (1.317)(7.52) = tau + 9.904.

[New]:

Therefore the revised result is that the change in HF's age during the acceleration is equal to

tau - ( theta d ) = tau - (1.317)(7.52) = tau - 9.904.

[Previous]

So, in the revised model, as tau approaches zero (to give an instantaneous velocity change), the change in the HF's age during the speed change approaches 9.904 seconds from above. So with an instantaneous velocity change, the HF's age INCREASED instantaneously by a finite amount.

[New]

So, in the revised model, as tau approaches zero (to give an instantaneous velocity change), the change in the HF's age during the speed change approaches -9.904 seconds from above. So with an instantaneous velocity change, the HF's age DECREASED instantaneously by a finite amount.

[Previous]:

Before the instantaneous velocity change, the AO, the HF, and the home twin (she) were all the same age. She and the HF were co-located. So after the instantaneous speed change, the AO hasn't aged at all, but the HF is 9.904 seconds OLDER than he was before the speed change, according to the AO. And since she and the HF have been colocated during the instantaneous speed change, they couldn't have ever differed in age during the speed change ... it would be absurd for either of them to see the other have an age different from their own age at any instant. So after the instantaneous speed change, the AO must conclude that she and the HF both instantaneously got 9.904 seconds OLDER than they were immediately before the speed change.

By comparison, the CMIF simultaneity method says that the AO will conclude that her age instantaneously increases by 6.51 seconds, so the LGTD and CMIF don't agree.

[New]:

Before the instantaneous velocity change, the AO, the HF, and the home twin (she) were all the same age. She and the HF were co-located. So after the instantaneous speed change, the AO hasn't aged at all, but the HF is 9.904 seconds YOUNGER than he was before the speed change, according to the AO. And since she and the HF have been colocated during the instantaneous speed change, they couldn't have ever differed in age during the speed change ... it would be absurd for either of them to see the other have an age different from their own age at any instant. So after the instantaneous speed change, the AO must conclude that she and the HF both instantaneously got 9.904 seconds YOUNGER than they were immediately before the speed change.

By comparison, the CMIF simultaneity method says that the AO will conclude that her age instantaneously decreases by 6.51 seconds, so the LGTD and CMIF don't agree.

16. ### phytiRegistered Senior Member

Messages:
612
S8;

All theories are based on ideas that can't be proven in any absolute manner, but you have to start somewhere.
I agree, in the SR environment of inertial motion, there is no way to detect any dependence of light speed on direction, because of symmetry.
Einstein avoided that issue by defining the speed of light to be constant, and its purpose was not about light propagation, but a consistent theory. The expectations in an inertial frame should be the same as in a rest frame.
I don't claim the space time graphics are the only way, but pictorial language does have an advantage over a page of text. Also the brain is an image oriented organism.
The x' axis/(axis of simultaneity) is the result of applying the clock synch convention. It is simple and does not require knowing your velocity in space.
The idea of clocks spontaneously changing time are flags that something is wrong.

17. ### phytiRegistered Senior Member

Messages:
612
Neddy;

left:

With a continuous transition for the reversal, all the x' axes are formed.
I.e. relying on simultaneity without it, B skips over the history of A events from At(4.2 to 75.8), a jump from 10 to 70.
All because the oversimplified triangle is not a real physical motion.
right:
An approximation to B's perception of A-events.

18. ### Neddy BateValued Senior Member

Messages:
2,274
It is true that there is no way to measure the one-way speed of light without first assuming a simultaneity convention. The simultaneity convention in SR is to simply assume the speed of light is the same in all directions. In a thought experiment, we can also assume there are hypothetical synchronised clocks conveniently located wherever we want them to be. The time coordinate of any event can be assigned the moment the event occurs, by simply using the time displayed on the hypothetical clock conveniently located at the location of the event. It does not matter how much time it might take for some remote observer to obtain that information.

So, in my scenario, there are hypothetical syncrhonised clocks located throughout the entire length of the long train. Of course it would take time to synch all those hypothetical "train-clocks", but we can assume that process was completed before the twins are born. And, in my scenario, there are also hypothetical synchronised clocks located along the entire length of the long tracks that the train rides on. It would take time to synch all those hypothetical "track-clocks" also, but once again we can assume that process was completed before the twins are born.

So an event in my scenario is assigned time coordinates the moment the event occurs. There can be a track-clock at that location, which gives the t coordinate of the event, and there can also be a train-clock at that location, which gives the t' coordinate of the event. Again, it does not matter how much time it might take for some remote observer to obtain that information.

Mike_Fontenot likes this.
19. ### Mike_FontenotRegistered Senior Member

Messages:
358
Good explanation, Neddy.

20. ### phytiRegistered Senior Member

Messages:
612
Neddy;
You are considering a local synchronized system, eg. like GPS. I referred to a long distance system. The example you used was on the order of 40 ly!
In B's ref. frame those synched A-clocks won't be synched.

21. ### Mike_FontenotRegistered Senior Member

Messages:
358
So, what to make of all these different and contradictory results?

The "EPVGTD Equation" (the one with the exponential), says that, if the AO (he) instantaneously changes his velocity in the direction TOWARD the home time (her), she instantaneously gets INFINITELY older, according to him. That's nonsense, because it gives incorrect ages for the twins when they are reunited.

On the other hand, when he instantaneously changes his velocity in the direction AWAY from her, the EPVGTD equation says that her age doesn't change instantaneously. While it's not certain that that result itself is incorrect, it seems to result in an inconsistency at the reunion. The EPVGTD equation says that, with zero acceleration, he and all the HF's age at the same rate. That seems to require that on the outbound and inbound legs, his conclusion about the correspondence between his and her ages must be the same. And clearly, on the OUTBOUND leg, he MUST say she is ageing SLOWER than he is, by the factor gamma. So he must say that, on the INBOUND leg, she is ageing slower by the factor gamma. But in that case, their conclusions about the correspondence between their ages at the reunion won't be consistent: she says she is the OLDER, but he says she is the YOUNGER. So his conclusions won't match her conclusions at the reunion, which is impossible since they are colocated then and they MUST agree about the correspondence between their ages then.

So much for the EPVGTD equation. What about the LGTD equation? The linearized equation (the LGTD equation) gives results that are qualitatively similar to the CMIF simultaneity method: her age instantaneously changes, according to him, during his instantaneous velocity change (instantaneously increasing when his momentarily infinite acceleration is TOWARD her, and instantaneously decreasing when his momentarily infinite acceleration is AWAY FROM her). But the AMOUNT of the instantaneous change is greater than CMIF says it should be. It is interesting that the amount of the instantaneous age changes would be exactly the same for CMIF and LGTD if the linearized equation multiplied the distance "d" by the velocity "v", rather than by the rapidity "theta". But, in determining the velocity effect obtained by integrating the acceleration "A", it IS necessary to use the rapidity "theta", not the velocity "v", as the variable of integration. (Taylor and Wheeler go over this in detail).

WHY does the EPVGTD equation fail so miserably in this example? Isn't the GTD equation a well-established result in general relativity? And the equivalence principle is certainly well-established. Is the GTD equation WRONG?

And WHY goes the LGTD work better than the EPVGTD, at least qualitatively? The LGTD should be a justified approximation of the EPVGTD only when the argument (A d) is small, and an infinite "A" (even though it lasts only an infinitesimal time) certainly isn't small! The LGTD equation shouldn't give results that are even qualitatively correct, but it does. Why?

22. ### SsssssssRegistered Senior Member

Messages:
265
I dunno maybe you should use the gravitational potential that reflects the symmetry of what you are doing and account for the changing altitude of the inertial observer or give up on the gravitational potential approach as a bad idea because it doesn't really work outside the Rindler wedge anyway. Just a thought.

23. ### Mike_FontenotRegistered Senior Member

Messages:
358
Can you give me a reference on "the Rindler wedge"? The only Rindler publication I've got is Rindler's "Essential Relativity", revised second edition.