Naked Science Forum
On the Lighter Side => New Theories => Topic started by: Le Repteux on 26/10/2018 20:08:42

I repeat to anyone who wants to listen that acceleration is absolute, and that we thus shouldn't change reference frames when acceleration is involved, but @David Cooper does the contrary in his Relativity page (http://www.magicschoolbook.com/science/relativity.html), which probably means that many readers here think the same, so I thought it might be useful to discuss it.
Here is the exert I'd like to discuss from David's page:
For example, if a rocket leaves the Earth and flies away into space for a year at 0.866 of the speed of light, then turns round and comes back at 0.866 of the speed of light, that trip will take two years from the point of view of the people in the rocket, but four years will have run through on the Earth before the rocket comes back. If we do our analysis from the "frame of reference" in which the Earth is considered to be stationary, then the rocket was moving and its clocks were ticking at half the normal rate throughout both legs of its voyage. However, if we use a different frame of reference instead, we could then imagine that it's the rocket that is stationary during the first leg of its voyage while the Earth is moving away from it at 0.866 of the speed of light, and that would mean that the clocks on the rocket can now be thought to be ticking twice as fast as the clocks on the Earth throughout this half of its trip. During the second half of the rocket's journey though, the rocket will be calculated to be chasing the Earth at 0.99 of the speed of light to catch up with it, and its clocks will be reckoned to be ticking about three and a half times as slowly as clocks on the Earth. The end result will still be that the whole journey will take two years for the rocket (as recorded by its clocks) while four years will still have gone by on the Earth (as recorded by clocks there). So, while we have accounts of events that contradict each other as to when the different clocks were running faster or slower than each other, the most important numbers about how long the whole trip takes will always agree at the end of the process when the two parties are reunited  all accounts determine that the rocket records two years while the Earth records four.
I think that changing reference frames in this case simply adds a useless complexity to the problem. When we feel an acceleration, we know we are accelerating, and we know the direction, so changing reference frame is like refusing to admit that we are accelerating even if we can feel it. To me, the only use of denying it is to extend the reference frame principle to acceleration, and I think it's not a good way to improve our knowledge of relativistic phenomenon. The earthbound observer that starts moving away knows it is not accelerating, and the one that knows he is accelerating is not moving away: where does this happen in real observations? In my simulations on motion, I show the way light could travel between two accelerated particles (http://motionsimulations.com/Acceleration%20with%20two%20particles). There might be other ways, but it's one of them. It links acceleration to relativity instead of sweeping it under the rug like this switching of reference frames does. It's based on the idea that a particle that belongs to a system of two bonded particles necessarily accelerates before the other one knows about it, because that information cannot travel at more than the speed of light.
It is a very simple idea but it has many interesting issues. One of them is that the system contracts during acceleration, one of the features of relativity. The other is that it goes on moving at constant speed once acceleration has stopped, and that this motion is still due to the direction and the speed of light. And the third one is that the first particle resists to accelerate since it is already informed that the second one is not actually moving, a resistance that we can probably attribute to its mass, an hypothesis that looks more promising than the Higgs' one. As I said, there may be other ways to apply acceleration to particles, but why not start with this one? Even if it is not the right way, discussing it might raise up better ones, and at least, we will have something else to do than denying the observations.

I repeat to anyone who wants to listen that acceleration is absolute, and that we thus shouldn't change reference frames when acceleration is involved, but @David Cooper does the contrary in his Relativity page (http://www.magicschoolbook.com/science/relativity.html), which probably means that many readers here think the same, so I thought it might be useful to discuss it.
I found David’s page to be accurate in this respect. He describes the same thing from different reference frames, but doesn’t mix them in any particular description, so one is as good as the next. David is also an absolutist, so the wording sometimes comes across in that light.
Yes, it is true that in the frame of the spaceship going out, Earth clocks are the ones dilated to half their normal rate. That is straightup relativity theory.
I think that changing reference frames in this case simply adds a useless complexity to the problem. When we feel an acceleration, we know we are accelerating, and we know the direction, so changing reference frame is like refusing to admit that we are accelerating even if we can feel it.
David’s description (in any frame) does not deny who is doing the accelerating. The comparison of clocks comes out the same each time, as evidence of this.
Considering a situation from a different frame does not add complexity, but is instead essential to understanding relativity, that physics works the same in any frame.
The earthbound observer that starts moving away knows it is not accelerating, and the one that knows he is accelerating is not moving away: where does this happen in real observations?
Who ever said the Earthbound observer accelerates? You’re reading it wrong.
One of them is that the system contracts during acceleration, one of the features of relativity.
Things contract due to speed, not acceleration. I can have two objects with identical speed but one accelerates 1000 times as much as the other, and they’ll both still have matching times on their clocks when compared. If your simulation doesn’t show this, it is wrong.

I repeat to anyone who wants to listen that acceleration is absolute, and that we thus shouldn't change reference frames when acceleration is involved, but @David Cooper does the contrary in his Relativity page (http://www.magicschoolbook.com/science/relativity.html), which probably means that many readers here think the same, so I thought it might be useful to discuss it.
[...]
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. For example, the most basic way is to use Lorentz equations. But by far the easiest and quickest way to obtain the same result is to use the delta_CADO_T equation (which can be derived from the Lorentz equations, or from the Minkowski diagram). The following is a brief description of the delta_CADO_T equation.
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

Things contract due to speed, not acceleration. I can have two objects with identical speed but one accelerates 1000 times as much as the other, and they’ll both still have matching times on their clocks when compared. If your simulation doesn’t show this, it is wrong.
The simulation shows the same contraction if the resulting speed is the same. The contraction is due to the distance traveled by the accelerated particle before the photon issued from that acceleration accelerates the second one. If that first particle would suffer more acceleration, it would simply travel more distance in the same time before the second particle would start to accelerate, so the distance between them would be more contracted. If it would take more time to reach that speed, it would be less contracted each time it would increase its speed, but the total contraction would be the same once it would have reached the same speed. I've put the acceleration at .01c to get a noticeable effect. While the photon always moves by steps of 1 unity, the particle starts moving with a step of .01 unity, and it increases its speed by the same amount only when the photon is back from the second particle, and only if the acceleration is still on. There might be a different way to increase the speed of such a system, but I didn't find any yet. Acceleration has to be limited, as if it was quantized, otherwise it seems impossible to simulate.
Contraction is thus due to speed, not to the rate at which speed increases, but it certainly happens because speed increases. For instance if we stop the acceleration, the particles go on making steps with respect to one another to move on the screen, but the contraction doesn't increase even if the steps are not executed at the same time. Contraction happens because the first particle is forced to move towards the second one during its acceleration, and because the second one has not accelerated yet. It's obviously a relativistic phenomenon since it is due to the limited speed of light, to the idea that no information can travel faster than light, and to a particle's steps being executed relatively to the other particle's steps since it uses the data from the light of the other particle to execute its own step.
Who ever said the Earthbound observer accelerates? You’re reading it wrong.
If he doesn't accelerate, then he cannot write down that he is the one that starts to move away from the other observer, otherwise he would be falsifying the observation.
Considering a situation from a different frame does not add complexity, but is instead essential to understanding relativity, that physics works the same in any frame.
That works fine as far as only constant motion is concerned, but when acceleration is involved, it only serves to universalize the reference frame principle. Relativistic phenomenon are not due to reference frames, they are due to the speed of light being limited. I don't need that principle to build my simulations, only that the speed of light stays the same in any direction on the screen, and that the particles move with regard to the screen.
Yes, it is true that in the frame of the spaceship going out, Earth clocks are the ones dilated to half their normal rate. That is straightup relativity theory.
It is true only if we sweep acceleration under the rug, otherwise the traveling twin knows he has to reverse the data, and he also knows how much younger he will be when he gets back if he has accelerometers on board. That would be current applied physics, and people wouldn't have to question that part of the Relativity theory anymore.

Who ever said the Earthbound observer accelerates? You’re reading it wrong.
If he doesn't accelerate, then he cannot write down that he is the one that starts to move away from the other observer, otherwise he would be falsifying the observation.
That’s fine since David never said that Earth ‘starts to move’. In the frame of the other observer, Earth was always moving and never started to move. There is no acceleration implied.
In that frame, Earth clocks are dilated to half the rate of the ship clock. Your simulation should be able to show this.
That works fine as far as only constant motion is concerned, but when acceleration is involved, it only serves to universalize the reference frame principle.
Not sure what that means, but it is perfectly valid for things to accelerate in any frame.
Relativistic phenomenon are not due to reference frames, they are due to the speed of light being limited. I don't need that principle to build my simulations, only that the speed of light stays the same in any direction on the screen, and that the particles move with regard to the screen.
That doesn’t sound like relativity. It sounds like your screen is the preferred frame.
Yes, it is true that in the frame of the spaceship going out, Earth clocks are the ones dilated to half their normal rate. That is straightup relativity theory.
It is true only if we sweep acceleration under the rug, otherwise the traveling twin knows he has to reverse the data,
Reverse what data? He does no such thing.
and he also knows how much younger he will be when he gets back
He doesn’t get back. He is stationary for the first halp (never left home), and then he accelerates hard for the second half to catch up to Earth that has been moving the whole time, and never comes back.

He doesn’t get back. He is stationary for the first half (never left home), and then he accelerates hard for the second half to catch up to Earth that has been moving the whole time, and never comes back.
If he has an accelerometer and he calculates its future acceleration while thinking it is the earth that is moving away, I'm afraid he will accelerate too much to get back at the same speed he got away.
Reverse what data? He does no such thing.
If the twin knows he is the one to move away, he knows the earth only seems to do so, so he has to reverse the relativistic calculation if he wants to know his true relativistic aging, otherwise he will have a surprise when he will meet his twin, and so will his twin if he thinks the contrary.
That doesn’t sound like relativity. It sounds like your screen is the preferred frame.
It is the only way light can move at the same speed in any direction on the screen. Without that assumption, no simulation using light is possible, which means reality is impossible to simulate, and if inversely relativity is true, then it means that we live in an unrealistic world that is impossible to simulate, a world that we will never be able to understand more than what we already understand with Relativity.
That’s fine since David never said that Earth ‘starts to move’. In the frame of the other observer, Earth was always moving and never started to move. There is no acceleration implied.
In that frame, Earth clocks are dilated to half the rate of the ship clock. Your simulation should be able to show this.
There is no relative motion without previous acceleration. A twin cannot appear to be moving away from another one without neither of them having previously accelerated away from the other, and since he only appears to be moving away, there is no need to simulate anything to consider it is the earth that is moving away.

But that assumption is wrong: the traveling twin must conclude that the home twin's age instantaneously increases during the instantaneous turnaround.
Hi Mike,
Unfortunately, the relativity principle is based on the assumption that instantaneous stuff is not part of this world. That's what happens when we use only the reference frame principle to predict relativistic outcomes. On the contrary, if the traveling twin can use his accelerometer to know he is turning around, then he can also use it to start calculating when he starts accelerating away from the earth, and he will need no instantaneous stuff to predict the outcome.

But that assumption is wrong: the traveling twin must conclude that the home twin's age instantaneously increases during the instantaneous turnaround.
Unfortunately, the relativity principle is based on the assumption that instantaneous stuff is not part of this world.
The instantaneous age change of the home twin (according to the traveling twin), caused by an instantaneous velocity change by the traveling twin, is qualitatively quite similar to the very rapid age change of the home twin (according to the traveling twin), caused by a short finite acceleration by the traveling twin. So the instantaneous velocity change scenarios are quite valuable as good approximations to what happens when the accelerations are finite.
The "delta_CADO equation" given in my previous posting is based on a more general "CADO equation" that can be used for both instantaneous velocity changes, and for finite accelerations, by the traveler. The "CADO equation" allows the determination of the quantity "CADO_T(t)", which is the current age of the home twin, according to the traveler, for any specified instant t in the traveler's life.
The CADO equation can handle any kind of accelerations by the traveling twin. An example is given in Section 7 (entitled "Some CADO Equation Results for Finite Accelerations") of my webpage:
https://sites.google.com/site/cadoequation/cadoreferenceframe
for a sequence of +/ 1g accelerations by the traveler, and an "agecorrespondence" diagram is described which shows the current age of the home twin (she), for each instant t of the traveler's (his) life, according to him. Specifically, the diagram gives CADO_T(t) during a 1g acceleration that lasts two years of his life, followed immediately by a +1g acceleration that lasts for another 2 years of his life. (The negative acceleration means that he points the nose of his rocket toward her, and the positive acceleration means that he points the nose of the rocket away from her.)
At the beginning of the 1g acceleration, they are separated by about 40 lightyears (according to her), which took 26 years of his life for him to reach, at a constant speed of 0.774 ly/y (constant except for a short initial 1g acceleration to get him up to the 0.774 ly/y speed) . She is 17 years old then (according to him). At the end of the 1g acceleration, he is 28 years old, and she is 81.24 years old (according to him). During that 1g acceleration, she gets 64.24 years older (according to him), whereas he only gets 2 years older. Her rapid age increase is smooth and continuous during that acceleration.
Then he does the two year +1g acceleration. At the end of the +1g acceleration, he is 30 years old, she is 21.75 years old (according to him). During that +1g acceleration, she gets 59.49 years younger, whereas he gets only two years older. Her rapid age decrease is smooth and continuous during that acceleration.
In my paper:
"Accelerated Observers in Special Relativity", PHYSICS ESSAYS, December 1999, p629,
a plot of the her age (according to him) vs his age, during those backtoback accelerations, is given. The webpage gives a qualitative description of the shape of that plot, but the plot itself isn't given. (The scenario in the paper is somewhat different from the scenario in the webpage, but they are qualitatively similar).

The instantaneous age change of the home twin (according to the traveling twin), caused by an instantaneous velocity change by the traveling twin, is qualitatively quite similar to the very rapid age change of the home twin (according to the traveling twin), caused by a short finite acceleration by the traveling twin. So the instantaneous velocity change scenarios are quite valuable as good approximations to what happens when the accelerations are finite.
What you do is using the distance and the speed already traveled to make the calculation backwards, what I suggest is using the first acceleration to consider that it is this twin that will be traveling. One way or another, it is the acceleration that is determinant, otherwise we couldn't tell which twin is traveling, so why not take the first one? Can you apply your equation to the first one?

I repeat to anyone who wants to listen that acceleration is absolute, and that we thus shouldn't change reference frames when acceleration is involved, but @David Cooper does the contrary in his Relativity page (http://www.magicschoolbook.com/science/relativity.html), which probably means that many readers here think the same, so I thought it might be useful to discuss it.
I agree that you shouldn't change frame during your analysis of a set of events if you're working with an absolute frame in mind. What you can reasonably do though is change frame to analyse the same set of events again, and that's what I did in the paragraph you quoted  that is very different from changing frame during a single analysis of that set of events (although there are ways of doing so which successfully produce the same key answers, and people who don't believe in an absolute frame are happy to use those methods).
I think that changing reference frames in this case simply adds a useless complexity to the problem.
It adds unnecessary complexity, but it works. You aren't forced to use that approach, but you ought to recognise that I don't use it either. I only change frame to reconsider the same set of events from the perspective of different frames  you can't know whether the planet's moving or not, so you're making a mistake if you assume that it's stationary in the absolute frame and that a rocket that accelerates away from it must be contracting in length and have its clocks run slow, because if the planet's actually moving in the absolute frame, that acceleration of the rocket could actually be a deceleration which leads to it moving more slowly through space rather than faster, with the result that it lengthextends rather than contracting (i.e. it loses some existing contraction) and its clocks would run faster. If you look at the simulation with the two planets and two rockets, it combines two versions of the twins paradox together into one in such a way that from one frame you can see that one of the rockets accelerates away from its planet while the other rocket decelerates away from its planet. Change frame from A to B and you get the opposite story. (You have to look carefully though, because I'm referring to the point where the planets pass each other and the rockets immediately change which planet they're travelling with at that instant  one of them clearly has to accelerate to move with the other planet, while the rocket that was travelling with that planet has to decelerate to stop next to the stationary planet.)
When we feel an acceleration, we know we are accelerating, and we know the direction, so changing reference frame is like refusing to admit that we are accelerating even if we can feel it.
You can't tell whether you're accelerating or decelerating  they both feel the same. Select frame A and look at the behaviour of the two rockets. Both of them think they're accelerating, but for this frame, one of the rockets is accelerating and the other is decelerating. How do you know whether your own rocket is in the same situation as the rocket that's accelerating in the simulation or the rocket that's decelerating? There's no way to tell. The simulation itself knows that frame A is the absolute frame, but no one in that simulated universe can tell which frame is the absolute frame  it is knowable only to the universe itself.
In my simulations on motion...
I don't think you should draw attention to your simulations in the physics forum until you have some that remove length contraction when you slow your particles back down instead of adding more contraction  they need to be modified until they match up to the real universe. They also need to produce the right amount of contraction, but I think they're currently just producing an unrelated compression that's never released.

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.
Double the length of his trip and see what happens. When he turns round, his twin ages not 27 years in an instant, but 54 years. How can an identical acceleration cause double the ageing?
Imagine that you and I are at different locations in space, perhaps a lightyear apart. We have agreed that at a certain moment in time, you will swallow a haddock. I have a rocket which can perform extreme accelerations, so what happens if I wait until my clock tells me you've just eaten the fish? I can accelerate one way and say, "now he hasn't eaten it yet", then I can turn round and accelerate the opposite way for twice as long and say "now he's eaten it", then I can turn round and accelerate the opposite way and say "now he hasn't eaten it yet", and I can carry on doing that for a long time. I don't even need to bother with the rocket, because all I have to do is set my clock for one frame of reference and say "he's eaten the fish", then set it for a different frame and say "now he hasn't eaten it yet", and so on. In reality, none of the things I do change whether you've eaten the fish or not. In the same way, the travelling twin can't make their stayathome twin age 27 years in an instant just by accelerating, or make them get younger by 27 years by accelerating the other way a moment after that  you are not describing realistic physics.
Einstein's original version of SR did logically accommodate such weird events, but Minkowski eliminated them by creating a 4D framework in which running time is removed from the model. In that version of SR, nothing changes when you change frame because nothing ever moves or ages at all  you simply cut the cake in a different way, but the whole cake is already in existence from past to future and it is therefore not altered by frame changes.

you can't know whether the planet's moving or not, so you're making a mistake if you assume that it's stationary in the absolute frame and that a rocket that accelerates away from it must be contracting in length and have its clocks run slow, because if the planet's actually moving in the absolute frame, that acceleration of the rocket could actually be a deceleration which leads to it moving more slowly through space rather than faster, with the result that it lengthextends rather than contracting (i.e. it loses some existing contraction) and its clocks would run faster.
Two features need to be present for a difference in the elapsed time to be measurable: acceleration and roundtrip. All the other features are useless so they only serve to defend the reference frame principle against the idea that rotation is absolute. If the twin accelerates and doesn't make a rountrip, the feature is useless, and if he does make a roundtrip, then he necessarily accelerates. It's also because light makes a roundtrip in the device we are using that we can measure our rotational motion. There is no other way than rotation to measure our own motion through space. Relativity tells us why we can't measure our motion with a two arms interferometer, but it can't explain the twins paradox or the Sagnac interferometer as easily as with LET. The problem is the reference frame principle, it is superfluous in a roundtrip and the relativists keep using it.
Even if I didn't succeed to simulate the right relativistic contraction yet, it is evident that any contraction happens during acceleration, because it is there that bodies get speed. To me, considering that the earth might be moving away only serves to discuss with relativists, and it is not because it is too massive to accelerate since two spaceships would face the same logic: if one of them doesn't accelerate, then it cannot be moving away, and if we do move it away on the paper, then the accelerating one won't be making a roundtrip anymore since half the trip will be executed by the other one. It's like rotating a sagnac interferometer to the left until the light gets halfway, and then rotating it faster to the right so that we get the right reading. Its a cheat and its useless. Let's use acceleration as a data, because that's what it is.
It adds unnecessary complexity, but it works. You aren't forced to use that approach, but you ought to recognize that I don't use it either. I only change frame to reconsider the same set of events from the perspective of different frames  you can't know whether the planet's moving or not, so you're making a mistake if you assume that it's stationary in the absolute frame and that a rocket that accelerates away from it must be contracting in length and have its clocks run slow, because if the planet's actually moving in the absolute frame, that acceleration of the rocket could actually be a deceleration which leads to it moving more slowly through space rather than faster, with the result that it lengthextends rather than contracting (i.e. it loses some existing contraction) and its clocks would run faster.
We can't know which direction through space the system is moving, but we certainly know which observer is accelerating, so it might lead to future mistakes if we don't take it as a data. We're only at our first steps through that relativistic stuff, so we will probably make huge leaps in the future. Keeping using useless complexities in this case is like stubbornly drawing epicycles while we already know better.
You can't tell whether you're accelerating or decelerating  they both feel the same.
We don't have to know if we are decelerating or accelerating with regard to the universe to know we are accelerating away from somebody else. We know because we can feel our own acceleration, so we also know that the whole redshift is ours, and if we want to discover how relativity works at the particles' scale, I think we have to stick to that principle.
I don't think you should draw attention to your simulations in the physics forum until you have some that remove length contraction when you slow your particles back down instead of adding more contraction  they need to be modified until they match up to the real universe. They also need to produce the right amount of contraction, but I think they're currently just producing an unrelated compression that's never released.
You may be right on that one, but you are still neglecting the way my particles move. They move with regard to light, which is an absolute reference. There is nothing more precise than light for two particles to move with regard to one another. We can't know if we are decelerating or accelerating anyway, so how could the particles know? And if they knew, how could they change the way light travels between them during that time? Even if my simulation would produce the right amount of contraction, for instance while accounting for resistance to acceleration so that the contraction rate would be dampened a bit, reversing the acceleration wouldn't reverse the contraction. Notice that reversing the direction of the traveling twin does not reverse the way his clock records time either. On the other hand, my simulation with four accelerated particles (http://motionsimulations.com/Acceleration%20with%20four%20particles) shows that they can stay synchronized if they all move with regard to light to do so. This way, the arms of the MM interferometer would both contract, and we would still get a null result. It wouldn't change the recorded time of a roundtrip clock either if its horizontal contraction rate would be the same as the relativistic one. So what would it change exactly except permitting us to study how the limited speed of the information may affect motion at the particles' scale, a step that the relativists are not ready to make since it seems to contradict the reference frame principle?

Introducing the Three Twins Paradox:
There is already at least one Triplets Paradox, so I've had to choose a distinctive name for this, using twins instead of triplets, but here we have three twins instead of the usual two. (This may sound unlikely, but there were only two twins to begin with. When they were very young there was an unfortunate incident involving a 3D printer when the girl pressed a button and accidentally produced a living replica of the boy, but none of them can remember which is the copy. So, there are now three twins, and we can consider them all to be the same age, even though one of them is technically younger.)
When the three twins are 5, one of the boys goes off for a trip in a rocket at 0.866c, but he left his teddy behind, so his brother decides to chase after him with it in a second rocket. Unfortunately, this rocket travels at the same speed, so he doesn't catch up until nearly two years later, just after his brother's rocket has turned back. The teddy is accidentally vaporised during the transfer from ship to ship because they pass each other at what they perceive to be a relative speed of 0.99c, but we need not trouble ourselves with these sad details. What matters to us is that at the moment the ships pass each other, the boys disagree about the age of their twin sister. The one who is still travelling away from her thinks she's moving at 0.866c away from him while he is stationary, so she has only reached 6 years old, whereas he is now 7. His twin brother has a different opinion, because he think's he's stationary and that his sister is moving towards him at 0.866c, and he has worked out that when they are reunited, she will be 13 and he will be 9, which means that she must currently be 12.
So, here we have the twin boys, both apx. 7 years old and right together for a moment at the same Spacetime location, but one of them asserts that their twin sister is 6 while the other asserts that she is 12. They can't both be right.

What matters to us is that at the moment the ships pass each other, the boys disagree about the age of their twin sister. The one who is still travelling away from her thinks she's moving at 0.866c away from him while he is stationary, so she has only reached 6 years old, whereas he is now 7. His twin brother has a different opinion, because he think's he's stationary and that his sister is moving towards him at 0.866c, and he has worked out that when they are reunited, she will be 13 and he will be 9, which means that she must currently be 12.
That's a good example of the mess using only the reference principle can do. If I was one of the traveling twin, I would know I was the one to accelerate, so if I would cross one of my twins at the moment I would be turning around, I would know we got the same age. Moreover, if we would both get back to earth at the same speed we got away, I would also know we both got twice as young as our earthbound twin.

Two features need to be present for a difference in the elapsed time to be measurable: acceleration and roundtrip.
This just isn't true. Two clocks (or twins if you like) can go from events A to B simply via different routes/schedules, with no round trip involved, and the time discrepancy between them when they meet up again should be computable in any frame of reference. The answer is frame independent.
Yes, acceleration must be involved for at least one of the two clocks, since if there wasn't, they'd have taken the same route/schedule. But roundtrip is a framespecific concept, irrelevant because the reading on their two clocks is a frame independent fact.
So two factors needed are acceleration (to make the paths different) and that the two are both present at each of the events where clock comparisons take place.

Two features need to be present for a difference in the elapsed time to be measurable: acceleration and roundtrip.
You can do it without any acceleration. Imagine spaceship 1 sitting in space. Spaceship 2 passes it in one direction, then some time later spaceship 3 passes it the other way having passed spaceship 2 on the way there. Suppose spaceships 1 and 2 start stopwatches when they pass each other. At the moment when spaceships 2 and 3 pass each other later on, spaceship 3 sets its stopwatch going too, but instead of starting it from zero, it starts it from the same time that spaceship 2's stopwatch is reading at that moment when they pass each other. When spaceship 3 passes spaceship 1, they compare times and find that spaceship 1 has recorded more time passing than spaceships 2 and 3 have collectively done. Acceleration clearly has no role in these events  the differences in timing are entirely caused by the speed of travel through space making some clocks run slower than others.
All the other features are useless so they only serve to defend the reference frame principle against the idea that rotation is absolute.
I don't know what you mean by "the reference frame principle", and I have no idea why you think rotation is involved in this. All the action takes place on a straight line (and a spaceship with rockets at both ends doesn't need to turn round to travel out and back, so there can be zero rotation involved).
It's also because light makes a roundtrip in the device we are using that we can measure our rotational motion. There is no other way than rotation to measure our own motion through space.
I have no idea what you're picturing that involves rotation.
Relativity tells us why we can't measure our motion with a two arms interferometer, but it can't explain the twins paradox or the Sagnac interferometer as easily as with LET. The problem is the reference frame principle, it is superfluous in a roundtrip and the relativists keep using it.
SR, GR and LET are all theories of relativity, all attempting to explain the actual phenomenon of relativity which we measure in the universe. They all have to use frames of reference, and they are not required to use an absolute frame because they can't detect one.
To me, considering that the earth might be moving away only serves to discuss with relativists,
Not to consider that it might be moving puts you in an awkward position where you just assume it's stationary while aliens on a planet moving relative to the Earth also make the mistake of assuming that their planet is stationary. If you want to consider everything as stationary, you should feel more comfortable with SR where you are allowed to assert that you are stationary, then you can accelerate to join the aliens on their planet, and then when you stop accelerating there you can again assert that you are stationary.
We can't know which direction through space the system is moving, but we certainly know which observer is accelerating, so it might lead to future mistakes if we don't take it as a data. We're only at our first steps through that relativistic stuff, so we will probably make huge leaps in the future. Keeping using useless complexities in this case is like stubbornly drawing epicycles while we already know better.
There has been no advance with this in a hundred years. The accelerations are also a red herring. The person who accelerates most ages less, but there's a variant of the twins paradox where we can change the ratio of the amount of acceleration for the two players. In the standard version, one twin accelerates away (one measure of acceleration), then accelerates to a halt and continues accelerating the same amount again to start the return trip (that's two more measures of acceleration), and then accelerates again to stop by the other twin, so we have a total of four measures of acceleration for one twin and none for the other. But consider a case where the twins are already moving. The stayathome twin accelerates to halt, so that's one measure of acceleration for him. The travelling twin doesn't accelerate until later, but when he does so, he gets two measures of acceleration to turn round and head back to his twin. When he reaches him, he gets a third measure of acceleration. In one case, the acceleration dose is 4:0. In the other case, it's 3:1. In both cases, we get the exact same ageing difference.
We don't have to know if we are decelerating or accelerating with regard to the universe to know we are accelerating away from somebody else. We know because we can feel our own acceleration, so we also know that the whole redshift is ours, and if we want to discover how relativity works at the particles' scale, I think we have to stick to that principle.
What principle? That acceleration and deceleration are the same? That length contraction occurs under both such that something that accelerates and decelerates back to the original speed ends up more contracted than when it started?
You may be right on that one, but you are still neglecting the way my particles move.
It doesn't matter how they move  they're either conforming with the way the universe works or they aren't, and it looks to me like the latter.
They move with regard to light, which is an absolute reference.
Unless you can record the relative speed at which they're encountering the light, all they ever get is a perceived frequency, so it's only a reference for the gods.
There is nothing more precise than light for two particles to move with regard to one another. We can't know if we are decelerating or accelerating anyway, so how could the particles know?
They don't know  they either contract or uncontract, and their functionality either slows down or speeds up, but they can never tell which is happening. If you're going to simulate things though and you want an absolute frame mechanism, your simulation has to know the absolutes and must impose them on the content, but the content of the simulation can't access that information.
And if they knew, how could they change the way light travels between them during that time? Even if my simulation would produce the right amount of contraction, for instance while accounting for resistance to acceleration so that the contraction rate would be dampened a bit, reversing the acceleration wouldn't reverse the contraction.
Then you need to design a better simulation that can reverse the contraction. A broken simulation sheds no light on the workings of the universe.
Notice that reversing the direction of the traveling twin does not reverse the way his clock records time either.
It can do for one leg of the trip.
On the other hand, my simulation with four accelerated particles (http://motionsimulations.com/Acceleration%20with%20four%20particles) shows that they can stay synchronized if they all move with regard to light to do so. This way, the arms of the MM interferometer would both contract, and we would still get a null result.
If the arm perpendicular to the direction of travel is also contracting, your moving clocks will tick at the wrong rate, so again you're discussing a broken simulation that does not match the actual universe. I have a theory of gravity which allows ordinary matter to extend out away from the visible part in a way that looks remarkably similar to the distribution of dark matter and which neatly explains how gravity pulls towards a black hole without curving space in any way, but it doesn't match the pull of dark matter because all it does there is affect the local speed of light, so even though the distribution is right, it sheds no light on dark matter and I don't make the mistake of thinking that it does. It's only when everything matches up that you should get excited about your simulations  a single similarity is most likely nothing more than a coincidence.
It wouldn't change the recorded time of a roundtrip either if the horizontal contraction rate would be the same as the relativistic one. So what would it change exactly except permitting us to study how the limited speed of the information may affect motion at the particles' scale, a step that the relativists are not ready to make since it seems to contradict the reference frame principle?
A roundtrip of what? Light between the particles or the particles going somewhere and back? You effectively have a lightclock, so if you have the wrong amount of contraction, the time that it records will be wrong. You have to get this to match up to the real universe before it has any relevance to any useful theory.

This just isn't true. Two clocks (or twins if you like) can go from events A to B simply via different routes/schedules, with no round trip involved, and the time discrepancy between them when they meet up again should be computable in any frame of reference. The answer is frame independent.
Right, thus contrary to what I said, a roundtrip is only one of the cases where acceleration is involved, but we still can use that information to decide which one of the clocks runs faster.

> ROUND < ! !!! Trip being the prime phrase david.
If the universe was empty, with an unknown force where accelerating the planet, then I believe you could be right, but round trip is not only undertaking the voyage and back, it is the resistance of the pulls of the entire mass of the universe. The planet does not resist the pull of universal gravity but the rocket does.
1) if the rocket escapes the gravitational pull of the influence of the body affecting the planet and then dwells restfully, the rocket has undergone massive acceleration, but presumably that is finished, yet the planet is still undergoing acceleration ?
2) if you are installing enough acceleration into a body to be vertically hovering ie helicopter, are you under acceleration, do the two cancel ?
3) if the planet is orbiting something big enough (massful enough) and the rocket journey is interior to the orbit of the planet, the planet orbiting the gravitational centre quickly enough to rendezvous with the planet (ie rocket ~0.3C), which body has undergone the most acceleration, given that on the interior of the planets orbit gravitational power is higher.

The 'twin scenario', like an annoying fly, it just won't go away.
Free thinking caps for those who want them.
A little history for those who don't know it.
Special Relativity is (ideally) limited to inertial motion, i.e. constant speed with no acceleration, that being the reason it's 'special'.
The coordinate transformations involve one math expression, gamma aka Lorentz factor.
Gamma contains 1 (a constant) and v/c (speed). There is no term for acceleration!
Neither Lorentz nor Einstein used acceleration in developing the coordinate transformations.

The popular triangular path, as seen in Wiki articles and other pop expositions is a greatly simplified representation of the twin scenario. Ann remains at rest at location A, and Bob departs at a constant speed v, reverses direction after an interval of time, and returns to Ann, with instantaneous changes in directions.
The Hoover moment occurs when the viewer notices the B line has a bend in it (actually 3). Bob accelerated and that makes the scenario asymmetrical. Bob will sense accelerations and Ann will not. That would be correct if the accelerations lasted for a finite interval of time. The time for all direction changes is zero, a dimensionless point!
With that, the acceleration is irrelevant and time dilation can be applied to the outbound
and inbound profiles.

Now we confront the issue of 'time jump', where the fictitious mathematical 'axis of simultaneity' (aos) rotates through an angle centered on the point of instantaneous reversal. The aos is a correspondence of signals used to synchronize clocks primarily in a local frame of ref. It represents the perception of the inertial observer. He thinks they are synched but to any outside observers, they aren't.
The graphical spacetime diagram displays a history of positions or speed plots thus the aos does not point in a spatial direction. The physical x axes of two frames with relative motion are parallel by definition. The discontinuous profile used in the twin scenario is an unreal example of motion and leads to unreal interpretations. A moving object cannot influence distant clocks. If the graphic is more accurate with a curve representing the transition from outbound to inbound, B can assume a pseudo rest frame, but with a temporary gfield for the arcing return of Ann's trajectory.

While an object is moving inertially, its length remains constant. The only time it can change is therefore during acceleration. Examining the light clock, some of its energy is used to compensate for the motion of the clock. The remainder becomes the active component of the clock, thus the clock process runs slower than the clock at rest.
The exchange of photons between particles results in the same time dilation effect. The extended times are equivalent to greater distances resulting in a net weaker field strength and a compression of particles.

Excuse me while I look for a swatter.

Unless you can record the relative speed at which they're encountering the light, all they ever get is a perceived frequency, so it's only a reference for the gods.
My particles move with regard to one another, and they only use the light emitted by the other particle to do so. That light tells them to resist to acceleration, to get speed, to get a direction, and to move at constant speed when acceleration has stopped. Isn't that enough to call it an absolute reference?
You effectively have a lightclock, so if you have the wrong amount of contraction, the time that it records will be wrong. You have to get this to match up to the real universe before it has any relevance to any useful theory.
If I reduce the contraction by adding a resistance to acceleration factor, I can probably get the right rate of contraction, so if I then let the clock move at constant speed, it will record the right elapsed time. It won't if I reverse the acceleration though since it will go on contracting while it should stretch, and you may be right about the null result being a coincidence, so I admit that this discrepancy with relativity might still be wrong.
Acceleration clearly has no role in these events  the differences in timing are entirely caused by the speed of travel through space making some clocks run slower than others.
Acceleration certainly has a role in the speed and the direction of the speed though, so it is normal to look for a way it could produce contraction, and visibly, relativists resist to do that. I'm looking for a way to convince them to try it, but in the same time, it helps me improve my knowledge. There is still two important features that using light to move bonded particles seems to get right, constant motion and mass, both being due to the same limited speed of the information exchanged between the particles, so it is really surprising that it doesn't seem to work in the case of acceleration.
Another feature that those simulations would account for if their contraction rate was right is relativistic mass: while the speed would increase, light would take more time to make a roundtrip, and the accelerated particle would have to wait longer to increase its speed, so it would accelerate less and less often, which is the same as resisting more and more to its acceleration if the force stays the same, and it would stay the same since its source would travel at the same speed the particle is traveling. Let's now get down into the particles and apply the same reasoning to their components. Here is my reasoning, but I invite you to develop yours since you know relativity better than me. While the speed would increase, light would also take more and more time to make a roundtrip between the components even if the distance it has to travel contracts, and since the steps between the particles are composed of the steps between their components, the accelerated particle would take more time to produce its own steps, what should slow down the contraction rate of the system. If I'm right, such a simulation might automatically account for resistance to acceleration and it may automatically produce the right contraction rate.
Instead of simulating the steps between the components though, which would be difficult since it takes millions of steps between the components to produce only one of the particles' steps, I could increase progressively the speed of the photon. This way, the photon would take less and less time to accelerate the other particle, so the distance the accelerated particle would travel during that time would get down, and so would the contraction rate. To input the right speed for the photon in order to get the right contraction rate, I only have to compute the added time dilation the accelerated particle would suffer each time it would increase its speed, and increase the speed of the leaving photon by the same proportional amount. If I would add that feature to my four particles' simulation, the vertical arm should not contract anymore, but would the horizontal one keep on contracting when the acceleration would reverse? Well, since the speed of the particles would reverse, the respective time dilation would also reverse, and the time the photon takes to make a roundtrip too, so the contraction rate would effectively reverse since it depends on that time.... Bingo!.... At last, I think I found the right way to simulate the whole process. Do you think it will convince the relativists that I'm right about acceleration being determinant if it works? :0)
Excuse me while I look for a swatter.
Hey @phyti , here's the swatter you've been looking for!

My particles move with regard to one another, and they only use the light emitted by the other particle to do so. That light tells them to resist to acceleration, to get speed, to get a direction, and to move at constant speed when acceleration has stopped. Isn't that enough to call it an absolute reference?
...
I've replied to the above post on the simulation thread https://www.thenakedscientists.com/forum/index.php?topic=71122.150 instead of here because your particlemovement simulations are not yet sufficiently close to describing real physics. They need a lot more work done on them before they're ready to display to the public.

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.
Double the length of his trip and see what happens. When he turns round, his twin ages not 27 years in an instant, but 54 years. How can an identical acceleration cause double the ageing?
Because the effect of the instantaneous velocity change is directly proportional to the separation of the twins.

Instantaneous velocity change is not an observable fact whereas force due to resistance to acceleration is, so since all velocities are due to accelerations, why not take the departing velocity as a fact, and the returning one as a fact also? Does relativity prevent us from admitting the facts?

Because the effect of the instantaneous velocity change is directly proportional to the separation of the twins.
The reason it's proportional to the separation is that it's the distance covered at a particular speed that determines how much the clock runs slow. The accelerations don't impact on the rate that the clocks tick at other than by changing their speed of travel through space, which then leads to them running at a particular rate until the next acceleration. We see this from the experiment which eliminates the accelerations by having ships pass each other and exchange the time.

Because the effect of the instantaneous velocity change is directly proportional to the separation of the twins.
[...]
A few years ago, a wellrespected physicist named Brian Greene (best known as a string theorist) did a TV show for NOVA, and gave an example that gets the same results that I've given in this thread. The link below is a short YouTube clip of his example. Scan to the 6:00 point:
https://www.youtube.com/watch?v=VYZQxMowBsw (https://www.youtube.com/watch?v=VYZQxMowBsw)

A few years ago, a wellrespected physicist named Brian Greene (best known as a string theorist) did a TV show for NOVA, and gave an example that gets the same results that I've given in this thread. The link below is a short YouTube clip of his example. Scan to the 6:00 point:
https://www.youtube.com/watch?v=VYZQxMowBsw (https://www.youtube.com/watch?v=VYZQxMowBsw)
Video doesn't get on well with my computer. Have you studied reply #12 to this thread? It reveals that your way of doing things generates contradictions. In the example I give there, it shows that 6=12.

[...]
So, here we have the twin boys, both apx. 7 years old and right together for a moment at the same Spacetime location, but one of them asserts that their twin sister is 6 while the other asserts that she is 12. They can't both be right.
They ARE both right! And your example can be generalized: at any instant t in the traveler's trip, it is possible that an arbitrarily large number of inertial observers happen at that instant to be momentarily colocated with the traveler, with each of these observers moving at different velocities relative to the traveler. They will each come to a different conclusion about the home twin's age at that instant of colocation. And they are all correct! This is the wellknown "relativity of simultaneity". Each observer has a different "view" about what "now" is at a distance, and each observer's perspective is equally valid. The home twin also has her own answer to the question "How old am I when the traveler's age is t?", and she will disagree with the traveler. And they are each correct.
A similar wellknown thing happens in the famous timedilation result: any two inertial observers moving relative to each other at a constant velocity will each conclude that the other is ageing more slowly. And they are both correct! It sounds inconsistent, but it's not. That's just how special relativity is.

Each observer has a different "view" about what "now" is at a distance, and each observer's perspective is equally valid.
That's a contradiction. Even if the two twins see the other twin as the one who ages less, once reunited, only one of them will be right, and the easiest way to analyze the problem is to consider that acceleration determines the one who is really traveling. That's what your equation does but in a disguised way. At the turn around point, it uses the speed given by the first acceleration and the distance that speed lasts to compute time dilation, and it attributes it to the right twin. How would it know it is the right twin if each perspective would be equally valid?

Each observer has a different "view" about what "now" is at a distance, and each observer's perspective is equally valid.
That's a contradiction. Even if the two twins see the other twin as the one who ages less, once reunited, only one of them will be right, [...]
There IS NO contradiction or inconsistency.
Take the case where gamma = 2.0, and where the traveler spends 20 years of his life on the outbound segment of the trip, and 20 years of his life on the inbound segment.
On the outbound (constant velocity) segment, the traveler says that the home twin is ageing at half his own rate, and therefore that she is only 10 years old right before his turnaround. During his instantaneous turnaround, he says that she instantaneously gets 60 years older. Finally, during his inbound segment, he says that she is ageing at half his own rate, and so she ages 10 years during that inbound segment. So he says she is 80 at their reunion.
SHE says that HE is the one who is ageing slowly, during the entire trip. So she says she is 40 at his turnaround, and is 80 at their reunion.
If you look at their two statements, you will see that they disagree during the entire trip, EXCEPT for the instant of the departure, and the instant of the reunion. I.e., they agree during the two instants when they are colocated, but they disagree all of the time when they are separated (except halfway through the turnaround, at the instant when their relative velocity is momentarily zero ... they both say she is 40 then). When they are separated, their disagreements do NOT produce any inconsistency, just like the famous timedilation produces no inconsistency when it says that both inertial observers moving relative to each other will each say the other is ageing more slowly.

just like the famous timedilation produces no inconsistency when it says that both inertial observers moving relative to each other will each say the other is ageing more slowly.
What is not inconsistent is to consider that motion is so relative that we can't tell which one of us is moving, thus considering that I am at rest and you are moving, or any other configuration, is de facto inconsistent. If motion is relative, then there is no way to tell which twin is actually moving with regard to the other, except if we know which one has accelerated.

If motion is relative, then there is no way to tell which twin is actually moving with regard to the other, except if we know which one has accelerated.
Pretty easy to find counterexamples for this claim.
A pair of twins take a trip. Alice leaves first, accelerating by X amount. Bob leaves years later, also accelerating by X amount, matching Alice's speed. The next day Bod accelerates by X amount again, so he starts to gain on Alice. Years later, they meet and Alice accelerates by X, matching speed with Bob.
They're now in each other's presence again, having both accelerated the same amount each, yet Alice is much older than Bob now.
Another scenario is Alice having an economy model ship that accelerates at 1G, while Bob has the sports model that pulls 2G. Alice goes to Arcturus and back, while Bob spends the time zipping this way and that around the Solar system, always at 2G, but exploring many local places instead of one distant one. Alice comes back and is far older again, despite having accelerated half as much.

Pretty easy to find counterexamples for this claim.
I was talking about the usual mind experiment where only one of the twins accelerates. If both accelerate, then we have to account for the speed and the distance traveled between the accelerations, and it is precisely what Mike's equation does. There is no way to tell which twin is traveling more or less with regard to the other than to account for all the accelerations.

[...]
So, here we have the twin boys, both apx. 7 years old and right together for a moment at the same Spacetime location, but one of them asserts that their twin sister is 6 while the other asserts that she is 12. They can't both be right.
They ARE both right!
Fine, but it's important to make sure everyone understands that that only "works" in an eternal static block universe version of SR. It "works" there because the 6=12 bit becomes 6y=12y while y=0 (which is possible because actual time is completely absent from that model). However, for any model with real, running time, y has to be greater than zero and you then run into contradictions if you try to claim that both twins are right. By using y=0 you're restricting yourself to an eternal static block universe model, but so long as you understand that you're doing so (and don't care that all causality then becomes a mere illusion of causation), and so long as you don't mix this with any incompatible models where time runs, then that's fine.

[...]
So, here we have the twin boys, both apx. 7 years old and right together for a moment at the same Spacetime location, but one of them asserts that their twin sister is 6 while the other asserts that she is 12. They can't both be right.
They ARE both right!
Fine, but it's important to make sure everyone understands that that only "works" in an eternal static block universe version of SR. It "works" there because the 6=12 bit becomes 6y=12y while y=0 (which is possible because actual time is completely absent from that model). However, for any model with real, running time, y has to be greater than zero and you then run into contradictions if you try to claim that both twins are right. By using y=0 you're restricting yourself to an eternal static block universe model, but so long as you understand that you're doing so (and don't care that all causality then becomes a mere illusion of causation), and so long as you don't mix this with any incompatible models where time runs, then that's fine.
I don't understand your comments at all. Time is certainly not absent from my CADO reference frame, or from my CADO equation. I'd like to see the contradictions you refer to above.

I don't understand your comments at all. Time is certainly not absent from my CADO reference frame, or from my CADO equation. I'd like to see the contradictions you refer to above.
I would hope that you agree that 6=12 is a contradiction. 6y=12y is also a contradiction if y>0. In a model with running time, y>0, and that means that in such a model it is not possible for both the twins to be right about the age of their twin sister. The only way you can get away with 6y=12y is if y=0, but that's a model with no time in it  all it has is a static "time dimension". A "time dimension" is not time, but just a special kind of space dimension in which all objects have infinite length. "Past" and "future" in such a model are mere directions like up and down, or left and right. A model only has real time in it if there is change, but in a static block model there is never any change: the entire future is preexisting and was never generated out of the past.
If you're using a model with real time, you can then run events and see if the girl can be 6 and 12 years old at the same time. I can tell you for free that she can't. You can change the way you run the simulation by slowing clocks in different ways, but you'll find that there's always one age that she has at the point when her twins are arguing about her age. If you go for a model where no clocks run slow, you'll find that the boys get back to the reunion point where they meet her again before she's arrived, so you run into eventmeshing failures, but even if you go for a model that erases those failures over Newtonian time, then you find that the girl is actually 7 when her brothers (both 7) are arguing about her age. These models are not compatible with each other and should not be mixed. If you want the girl to be 6 and 12 at the same time, you have to use a static block model where that's possible because it's 6x0 = 12x0 and there is no time in the model. You can take your pick, but please don't mix incompatible models and pretend that the girl can be 6 and 12 at the same time in any model with running time. Mathematics does not allow that.

I think you're correct Le. a observation of a weight is a sign of gravity. There can be no confusion about who's experiencing it.
=
Spelling

I would think that changing reference frames would be akin to creating support for a hypothesis by using a probability math function to bolster another probability math function! It's done all the time but it's questionable science! lol

I don't understand your comments at all. Time is certainly not absent from my CADO reference frame, or from my CADO equation. I'd like to see the contradictions you refer to above.
I would hope that you agree that 6=12 is a contradiction. 6y=12y is also a contradiction if y>0. In a model with running time, y>0, and that means that in such a model it is not possible for both the twins to be right about the age of their twin sister. The only way you can get away with 6y=12y is if y=0, but that's a model with no time in it  all it has is a static "time dimension". A "time dimension" is not time, but just a special kind of space dimension in which all objects have infinite length. "Past" and "future" in such a model are mere directions like up and down, or left and right. A model only has real time in it if there is change, but in a static block model there is never any change: the entire future is preexisting and was never generated out of the past.
If you're using a model with real time, you can then run events and see if the girl can be 6 and 12 years old at the same time. I can tell you for free that she can't. You can change the way you run the simulation by slowing clocks in different ways, but you'll find that there's always one age that she has at the point when her twins are arguing about her age. If you go for a model where no clocks run slow, you'll find that the boys get back to the reunion point where they meet her again before she's arrived, so you run into eventmeshing failures, but even if you go for a model that erases those failures over Newtonian time, then you find that the girl is actually 7 when her brothers (both 7) are arguing about her age. These models are not compatible with each other and should not be mixed. If you want the girl to be 6 and 12 at the same time, you have to use a static block model where that's possible because it's 6x0 = 12x0 and there is no time in the model. You can take your pick, but please don't mix incompatible models and pretend that the girl can be 6 and 12 at the same time in any model with running time. Mathematics does not allow that.
The above still just sounds like gibberish to me. I think you and I will just have to agree to disagree, to keep from wasting any more time and keystrokes.

The above still just sounds like gibberish to me. I think you and I will just have to agree to disagree, to keep from wasting any more time and keystrokes.
The reason it sounds like gibberish to you is that you haven't thought it through carefully. Like most people in this field, you don't apply reason rigorously and keep incompatible models apart. You pretend that you understand time, but you're actually combining a model with no time in it with an incompatible model with running time, and the result is that you end up with a composite model built upon a contradiction. Your solution when confronted with reality is to run away from the truth. With running time, mathematics dictates that there is no possibility of the girl being 6y and 12y at the same time. The only models where she can be 6y and 12y are the models with time removed from them such that y=0. But if you think applying mathematics correctly in physics is a waste of time, then that's up to you.

I got news for you guys! I found a way to produce the right contraction rate on my simulation of acceleration (http://motionsimulations.com/Relativistic%20acceleration), and since it is due to a first particle accelerating before the other one has, it supports my OP idea that we can use acceleration to tell which twin is traveling. If I can succeed to apply it to my simulation on opposite acceleration, if contraction becomes stretching when acceleration reverses, there will be no more event meshing failure like David is pointing to, no more instantaneous accelerations like Mike is suggesting, and no more interminable discussions about that. My simulation will be able to solve any problem where any amount of light clocks start from the same point and get to the same other point, providing it has the parameters of their respective accelerations, direction and speed. They will slow down and contract (or speed up and stretch) at the right rates and only because any information takes time to go from one point to the other. That's precisely what relativity is about, nothing else.

I got news for you guys! I found a way to produce the right contraction rate on my simulation of acceleration (http://motionsimulations.com/Relativistic%20acceleration), and since it is due to a first particle accelerating before the other one has, it supports my OP idea that we can use acceleration to tell which twin is traveling.
All you've done is program in length contraction  it isn't going to overturn relativity. If you get your simulation working fully, you'll eventually find that out, but I'm surprised that you can't already see that an acceleration can be a deceleration to a halt, rather than an acceleration from stationary, and because the difference between the two can't be measured, you can't use acceleration to tell anything about who's travelling on any leg of a trip.
If I can succeed to apply it to my simulation on opposite acceleration, if contraction becomes stretching when acceleration reverses, there will be no more event meshing failure like David is pointing to,
Eventmeshing failures relate to one specific feature of some models. Your simulation of length contraction and its reversal has nothing to do with that.
...no more instantaneous accelerations like Mike is suggesting,
Instantaneous accelerations are real.
My simulation will be able to solve any problem where any amount of light clocks start from the same point and get to the same other point, providing it has the parameters of their respective accelerations, direction and speed. They will slow down and contract (or speed up and stretch) at the right rates and only because any information takes time to go from one point to the other. That's precisely what relativity is about, nothing else.
All you will achieve by that is illustrate a mechanism that is already well understood. If you get your length contraction right, your simulation will effectively be showing a light clock with particles serving as the mirrors of that clock and where the light clock contracts according to its speed of movement.

but I'm surprised that you can't already see that an acceleration can be a deceleration to a halt, rather than an acceleration from stationary, and because the difference between the two can't be measured, you can't use acceleration to tell anything about who's traveling on any leg of a trip.
I know that an acceleration can be a deceleration, I just have to imagine the accelerating twin decelerating to a rest on the screen while the other twin is moving away at constant speed. This way, the twin at rest has to move at twice the speed of the constant moving one to get back home, so he is still the one that ages less, but he is again the one that had to accelerate. There is no way for the constant moving twin to age less if he doesn't accelerate. There is a problem with the speed of the returning twin though if the constant moving one already goes at close to c on the screen: he might have to accelerate at more than c to get back home, and if I try that with my particles, I'm afraid they will never reach c. With LET, things cannot be moving at more than c with regard to light.
Instantaneous accelerations are real.
What do you mean exactly? That changes in speed or direction are always instantaneous?
All you will achieve by that is illustrate a mechanism that is already well understood.
Maybe, but applying relativity to my small steps is new, and they might explain contraction if it works, a phenomenon that is still an ad hoc assumption.

This mind experiment discussed in this thread is only using singular time and associated 3d spatial relativity physics. Are you ok with that?

Hi Opportunity,
The simulations that I present here account for anything that the limited speed of light can account for, so no math can surpass them as far as the logical part of relativity is concerned. Give me a relativity problem and my simulation will give the right answer. What I'm discussing here is the way SR treats acceleration. My simulation on acceleration (http://motionsimulations.com/Relativistic%20acceleration) shows that accelerating a particle before the other one knows about it contracts the distance between two bonded particles, and if I account for the contraction of the particles themselves, the contraction rate is the same as SR's one. I prefer simulations because we can see what's happening, but math should give us the same answer providing we try to solve the same problem.

Tell me you don't see Einstein laughing hysterically playing with the Pythagorean theorem! lol

KISS! lol

I repeat to anyone who wants to listen that acceleration is absolute, and that we thus shouldn't change reference frames when acceleration is involved, but @David Cooper does the contrary in his Relativity page (http://www.magicschoolbook.com/science/relativity.html), which probably means that many readers here think the same, so I thought it might be useful to discuss it.
Here is the exert I'd like to discuss from David's page:
For example, if a rocket leaves the Earth and flies away into space for a year at 0.866 of the speed of light, then turns round and comes back at 0.866 of the speed of light, that trip will take two years from the point of view of the people in the rocket, but four years will have run through on the Earth before the rocket comes back. If we do our analysis from the "frame of reference" in which the Earth is considered to be stationary, then the rocket was moving and its clocks were ticking at half the normal rate throughout both legs of its voyage. However, if we use a different frame of reference instead, we could then imagine that it's the rocket that is stationary during the first leg of its voyage while the Earth is moving away from it at 0.866 of the speed of light, and that would mean that the clocks on the rocket can now be thought to be ticking twice as fast as the clocks on the Earth throughout this half of its trip. During the second half of the rocket's journey though, the rocket will be calculated to be chasing the Earth at 0.99 of the speed of light to catch up with it, and its clocks will be reckoned to be ticking about three and a half times as slowly as clocks on the Earth. The end result will still be that the whole journey will take two years for the rocket (as recorded by its clocks) while four years will still have gone by on the Earth (as recorded by clocks there). So, while we have accounts of events that contradict each other as to when the different clocks were running faster or slower than each other, the most important numbers about how long the whole trip takes will always agree at the end of the process when the two parties are reunited  all accounts determine that the rocket records two years while the Earth records four.
I think that changing reference frames in this case simply adds a useless complexity to the problem. When we feel an acceleration, we know we are accelerating, and we know the direction, so changing reference frame is like refusing to admit that we are accelerating even if we can feel it. To me, the only use of denying it is to extend the reference frame principle to acceleration, and I think it's not a good way to improve our knowledge of relativistic phenomenon. The earthbound observer that starts moving away knows it is not accelerating, and the one that knows he is accelerating is not moving away: where does this happen in real observations? In my simulations on motion, I show the way light could travel between two accelerated particles (http://motionsimulations.com/Acceleration%20with%20two%20particles). There might be other ways, but it's one of them. It links acceleration to relativity instead of sweeping it under the rug like this switching of reference frames does. It's based on the idea that a particle that belongs to a system of two bonded particles necessarily accelerates before the other one knows about it, because that information cannot travel at more than the speed of light.
It is a very simple idea but it has many interesting issues. One of them is that the system contracts during acceleration, one of the features of relativity. The other is that it goes on moving at constant speed once acceleration has stopped, and that this motion is still due to the direction and the speed of light. And the third one is that the first particle resists to accelerate since it is already informed that the second one is not actually moving, a resistance that we can probably attribute to its mass, an hypothesis that looks more promising than the Higgs' one. As I said, there may be other ways to apply acceleration to particles, but why not start with this one? Even if it is not the right way, discussing it might raise up better ones, and at least, we will have something else to do than denying the observations.
I am not sure whether your idea is 100% Einsteinian, & whether u only want Einsteinian input  but i think that it is not 100% Einsteinian, & i think that u do not rule out other ideas.
I dont understand SR & GR, but my memory is that re the twins Alby explained that acceleration affected their clocks  & that a clock's ticking was affected by the history of its acceleration. Yes this is weird, but that is what he said. Whereas supposed scientists around here dont even admit that acceleration has any effect of itself  & completely ignore that that effect might have a memory.
I am an aetherist & am antiEinstein (SR & GR are krapp). Aether theory doesnt offer any obvious reason for why acceleration might affect ticking, other than of course by affecting speed (as for SR). But i suspect that acceleration does affect ticking, ie apart from the obvious change due to change in speed. I think that Alby was correct, albeit for the wrong reasons (ie GR reasons), acceleration does affect ticking  but i dont agree with Alby that the history of acceleration has an enduring effect on the rate of ticking (it willmight of course have an enduring effect on the where the hands of the clock are pointing).
I see that your postings include references to MMXs  u say that your model must achieve a null result re the two legs. No, u are wrong  the MMXs never gave a null result  hencely if your model gives a null MMX result then your model is nonreal.
I see that your postings include reference to LET  do u believe in aether?
I see that your question is open ended  ie a brief overview of the aetherian view is not off topic. A proper analysis of a twins kind of ticking question needs the following considerations.
There is no such thing as time, or at least there is only one time, it is now, this instant, & it is universal.
There is no such thing as time dilation, what we have is ticking dilation.
TD & LC happen in accordance with Lorentz's gamma. The V in gamma is the absolute speed of the clock relative to the aether rest frame (the absolute frame)(the preferred reference frame)  ie V is the apparent aetherwind.
One must apply gamma to each clock to establish the two tickings seen by an observer in the rest frame. These are the true tickings for the two clocks. These are the tickings that age the two twins.
As the twins accelerate the true tickings will change  & these histories of tickings must be summed to give the final true age difference.
The two twins will (when they meet) both be aware of an apparent age difference which will be evident by a comparison of their two clockswatches. This difference will not be the same as the true difference seen by the observer in the rest frame  it will always be less than the true difference (except when zero)(see below).
It is possible that the two clockswatches show the same timeaging  in SR that would be impossible.
But as i said aether theory does not recognize any TD effect due to acceleration  i suspect that there is an effect.

I know that an acceleration can be a deceleration, I just have to imagine the accelerating twin decelerating to a rest on the screen while the other twin is moving away at constant speed. This way, the twin at rest has to move at twice the speed of the constant moving one to get back home, so he is still the one that ages less, but he is again the one that had to accelerate. There is no way for the constant moving twin to age less if he doesn't accelerate.
It's no surprise that the travelling twin has to accelerate because he has to change speed in order to get back to the stayathome twin who moves at a constant speed. What matters is not to put the focus on the acceleration part of that rather than the speed aspect, because that gives people misleading ideas that the acceleration has a special role beyond merely being a change in speed, as is shown by the version of the experiment in which clocks pass each other and make collective timings without any of them changing speed at all.
There is a problem with the speed of the returning twin though if the constant moving one already goes at close to c on the screen: he might have to accelerate at more than c to get back home, and if I try that with my particles, I'm afraid they will never reach c.
There is no such problem  look up relativistic velocity addition and apply it. If you think you are at rest while moving at 0.866c with your twin and then try to accelerate to 0.866c in the direction in which you're already moving, you will then move at 0.99c. If you make a return trip at what you measure as that same speed relative to your twin, your speed for the second leg will be zero. When you're reunited with your twin, you will have aged half as much as him during your trip, just as you would expect (meaning that if you think your twin's stationary and that both legs of your trip are done at 0.866c, those numbers predict that you'll age half as much as your twin too).
Instantaneous accelerations are real.
What do you mean exactly? That changes in speed or direction are always instantaneous?
If you hit a particle with a photon, it will instantly accelerate to a new speed in a single jump. In thought experiments we can simplify them mathematically by allowing accelerations of composite objects to have all their particles accelerated in the same manner simultaneously, taking them directly from one speed to another without any gradual increase in speed. It is not helpful to insist on doing gradual accelerations instead as it makes it much harder for people to follow the maths and check that what's being said is correct.
All you will achieve by that is illustrate a mechanism that is already well understood.
Maybe, but applying relativity to my small steps is new, and they might explain contraction if it works, a phenomenon that is still an ad hoc assumption.
They won't explain contraction. At the moment, all you've done is write code to calculate length contraction which you're then applying to the particle separation. If you want to show the actual cause of length contraction you have to simulate the actual cause of length contraction, and that means you need to apply relativistic velocity addition to the components of particles just as you would to moons orbiting planets. An orbit contracts in length because the moon's increase in speed as it's moving round one side of its planet is slowed relative to the planet while it's speed increases relative to the planet as it goes round the other side  it takes longer to travel round one half of the orbit than the other, even though a comoving observer with the system would see the moon as following a circular orbit and moving at a constant speed. That is length contraction in action, all controlled by relativistic velocity addition and it is a necessary outcome  length contraction is not ad hoc. The same thing will happen in atoms and particles, contracting them in length by affecting the way electrons move around them, although we're not dealing with simple orbits there, so you'd need to find an alternative way to model that, and that means understanding how electrons move. LaFrenière treats particles as waves and produces correct length contraction automatically by doing so, as well as showing how relativistic mass is stored. You need to simulate one or other of these mechanisms if you want the length contraction to come out of a rational process and not just a formula.

LaFrenière treats particles as waves and produces correct length contraction automatically by doing so, as well as showing how relativistic mass is stored. You need to simulate one or other of these mechanisms if you want the length contraction to come out of a rational process and not just a formula.
Lafrenière took Ivanhov's result from his sound standing wave building up between his two speakers, and applied it to its own light standing wave with only one emitter. My two particles' system works like Ivanhov's two emitters. If we could see the light the particles exchange, we would see the standing wave contract while the speed increases, and since the particles need to stand at the nodes of the standing wave to stay synchronized, they would follow the nodes, and the distance between them would contract. To increase their speed though, the particles need to accelerate, and as my simulations show, they can't do that instantly. With two inline particles, one of them has to accelerate before the other if the force is aligned with the particles, and my simulations show that the distance between the particles necessarily contracts before the second particle is informed that it has accelerated.
If we could see the standing wave during the time the first particle accelerates, we would see that it is no more on its node, and we would have to stop the acceleration and wait for the two particles to move at the same speed on the screen for them to get back on sync again and to stay on their nodes. In other words, the standing wave would take place only after the acceleration would have happened, thus after contraction would have happened, because the emitters are not synchronized during acceleration and they have to for a standing wave to take place between them. My simulations don't show that, but the wavelengths are also contracted by doppler effect during acceleration, in such a way that there is always the same number of wavelengths between the particles before and after acceleration. I consider that as a memory of all the accelerations such a system may have, and in my simulations, it is that memory that produces the constant speed (and constant direction if aberration is accounted for) it has when it is not suffering any acceleration. In this sense, constant motion would not be as inert as we actually think.
It's no surprise that the travelling twin has to accelerate because he has to change speed in order to get back to the stayathome twin who moves at a constant speed. What matters is not to put the focus on the acceleration part of that rather than the speed aspect, because that gives people misleading ideas that the acceleration has a special role beyond merely being a change in speed, as is shown by the version of the experiment in which clocks pass each other and make collective timings without any of them changing speed at all.
In the simulations, acceleration produces contraction, not time dilation. Time dilation is due to light taking more time to make a round trip after acceleration has taken place, and contraction is due to the first particle being forced to move towards the second one before it knows about it. The two phenomenon are linked since they are both due to light, but they are distinct.
There is no such problem  look up relativistic velocity addition and apply it. If you think you are at rest while moving at 0.866c with your twin and then try to accelerate to 0.866c in the direction in which you're already moving, you will then move at 0.99c.
I can't see how I could simulate that relativistic velocity addition. If I accelerate my two particles at c, the light sent by the trailing one will not be able to reach the leading one anymore, and since it is light that tells it to accelerate, it won't be able to increase its speed either. Is it possible that this relativistic addition is only meant for relativists to pretend that c can be the same both ways in a light clock? With LET, it is clearly not the same, and more importantly, it doesn't have to for the relativistic effects to take place.
If you hit a particle with a photon, it will instantly accelerate to a new speed in a single jump. In thought experiments we can simplify them mathematically by allowing accelerations of composite objects to have all their particles accelerated in the same manner simultaneously, taking them directly from one speed to another without any gradual increase in speed. It is not helpful to insist on doing gradual accelerations instead as it makes it much harder for people to follow the math and check that what's being said is correct.
In my theory, a single step between the particles is executed progressively by the steps between their components, which execute billions of them during that single step. Maybe the math for such a behavior is too complicated, but the behavior itself is not. I could even make a simplified simulation of it where we could see the components execute many steps while the particles would execute only one. If all those steps were instantaneous, the particles would go from 0 to c in no time, and there would be nothing to see on the screen.

scientists around here dont even admit that acceleration has any effect of itself  & completely ignore that that effect might have a memory.
Hi villain aetherist! :0)
In my previous message to David, I justly explain how that kind of memory would work. Here is my simulations' page. (http://motionsimulations.com/) Take a look at them and tell me if you understand them. They are all based on the idea that the screen can be at rest in aether. When the particles move on the screen, they move with regard to aether. When they get speed, that speed is absolute. Of course, I could also move the screen with regard to aether, but it would have no incidence on the relativistic effets that are happening due to light taking time to move the particles with regard to one another.

With two inline particles, one of them has to accelerate before the other if the force is aligned with the particles, and my simulations show that the distance between the particles necessarily contracts before the second particle is informed that it has accelerated.
Indeed, but whether you accelerate the front or rear particle, there need to be continual adjustments made to the particle separation as they try to stay on the nodes. If you accelerate them too quickly, you will simply break them apart and leave one behind, so you need to accelerate them slowly to keep them close enough together to have time to adjust after each input of force. Because it might take years to simulate such gentle acceleration and to get to a sufficiently high speed for length contraction to show up, you'll need to cheat by using much bigger accelerations and artificially keeping the two particles close together by accelerating both of them equally each time you apply a big acceleration, but you will still be able to apply small accelerations to either particle and see them adjust back to the correct separation.
I can't see how I could simulate that relativistic velocity addition. If I accelerate my two particles at c, the light sent by the trailing one will not be able to reach the leading one anymore, and since it is light that tells it to accelerate, it won't be able to increase its speed either.
You could apply it within the atoms with a simplified version of the atom using electron orbits  those orbits will necessarily be contracted in length by applying relativistic velocity addition to them, and that necessarily gives you the right atom shape for sending out waves of force at the right intensity in all directions (so long as you also take aberration into account) to reproduce the same length contraction between two atoms.
Is it possible that this relativistic addition is only meant for relativists to pretend that c can be the same both ways in a light clock? With LET, it is clearly not the same, and more importantly, it doesn't have to for the relativistic effects to take place.
Relativistic velocity addition applies to LET  it applies to any theory which prevents objects from going faster than c.
In my theory, a single step between the particles is executed progressively by the steps between their components, which execute billions of them during that single step. Maybe the math for such a behavior is too complicated, but the behavior itself is not.
The point I was making is that we don't ordinarily use gradual accelerations in the twins paradox thought experiment because that would complicate the calculations without providing any gain in return. Clearly though, you want to be able to handle gradual accelerations, but the cost of that is that you can't get to relativistic speeds in a reasonable length of time without tearing your objects apart, so you need to compromise. You can accelerate one particle if the acceleration is gentle and then watch the two adjust to share out the acceleration between them, but you should accelerate both equally if you want to get them up to high speed without tearing them apart (from each other). The length contraction that you end up with will then be dictated by the particles adjusting to a comfortable separation rather than by compression or stretch, and you'd be able to use a proper mechanism to provide the length contraction rather than artificially applying a formula to adjust the compression/stretch (which is what you're currently doing instead of providing a mechanism for the particles to adjust to a comfortable separation through interactions with each other).

scientists around here dont even admit that acceleration has any effect of itself  & completely ignore that that effect might have a memory.
Hi villain aetherist! :0)
In my previous message to David, I justly explain how that kind of memory would work. Here is my simulations' page. (http://motionsimulations.com/) Take a look at them and tell me if you understand them. They are all based on the idea that the screen can be at rest in aether. When the particles move on the screen, they move with regard to aether. When they get speed, that speed is absolute. Of course, I could also move the screen with regard to aether, but it would have no incidence on the relativistic effets that are happening due to light taking time to move the particles with regard to one another.
I dont understand your theory etc (i am not a scientist). Is it an Einsteinian sort of theory  koz i dont really understand SR & GR either.
I see that u mention aether  however i reckon that any sort of aether micro theory or macro theory would not result in a twins paradox.
Does your theory result in a similar gamma to Lorentz & to Einstein?
I daresay that there are lots of ways of deriving a similar or identical equationgamma.

Does your theory result in a similar gamma to Lorentz & to Einstein?
I daresay that there are lots of ways of deriving a similar or identical equationgamma.
I don't work with equations, but with simulations. I'm trying to discover what would happen to two bonded particles if, while we accelerate them, thus when they get a new speed or a new direction, whatever bonds them together would only be able to travel at c. That's relativity, but applied to the microscopic world. The first assumption I make is that one of the particles would accelerate before the other knows about it, and then I move the particles by steps on the screen and I observe what's happening. During acceleration for instance, the first particle to accelerate goes on moving towards the other particle before it starts accelerating away from it, so the distance between them contracts, but it contracts so much that I get time contraction instead of time dilation. Also during acceleration, that first particle faces the information from the other particle that it is not moving away, so it resists moving towards it since their bonding distance is getting wrong, a resistance that we can attribute to its mass, which would then be due to the energy information taking time to bond the particles. When acceleration stops, the particles go on moving on the screen only because the information about their bonding is still exchanged between them, otherwise they would stop.
What is happening then is that the redshift produced by the leading particle on the information it sends back towards the trailing one is pulling that trailing one forward, while the blueshift produced by the trailing one on the information it sends forward towards the leading one is pushing that leading one forward. This way, it is the information contained between the particles that maintains the constancy of what we call their inertial motion, not the particles themselves. If we consider that it is light that supports the information, then it is light that produces the bodies' mass, thus their resistance to acceleration, and it is also light that maintains their constant motion once they have accelerated. If I can demonstrate that my simulations are right, they might open a whole new way to study the relativity of motion.

Does your theory result in a similar gamma to Lorentz & to Einstein?
I daresay that there are lots of ways of deriving a similar or identical equationgamma.
I don't work with equations, but with simulations. I'm trying to discover what would happen to two bonded particles if, while we accelerate them, thus when they get a new speed or a new direction, whatever bonds them together would only be able to travel at c. That's relativity, but applied to the microscopic world. The first assumption I make is that one of the particles would accelerate before the other knows about it, and then I move the particles by steps on the screen and I observe what's happening. During acceleration for instance, the first particle to accelerate goes on moving towards the other particle before it starts accelerating away from it, so the distance between them contracts, but it contracts so much that I get time contraction instead of time dilation. Also during acceleration, that first particle faces the information from the other particle that it is not moving away, so it resists moving towards it since their bonding distance is getting wrong, a resistance that we can attribute to its mass, which would then be due to the energy information taking time to bond the particles. When acceleration stops, the particles go on moving on the screen only because the information about their bonding is still exchanged between them, otherwise they would stop.
What is happening then is that the redshift produced by the leading particle on the information it sends back towards the trailing one is pulling that trailing one forward, while the blueshift produced by the trailing one on the information it sends forward towards the leading one is pushing that leading one forward. This way, it is the information contained between the particles that maintains the constancy of what we call their inertial motion, not the particles themselves. If we consider that it is light that supports the information, then it is light that produces the bodies' mass, thus their resistance to acceleration, and it is also light that maintains their constant motion once they have accelerated. If I can demonstrate that my simulations are right, they might open a whole new way to study the relativity of motion.
An aetherist or Einsteinian would be ok with info moving at c tween particles, c being the speed of em fields (photinos) & the speed of light (photons)  but gravity attraction (& retarding inertial forces) move at say more than 20 billion c (but these are weak).
I agree that light produces mass  free photons have mass  & when confined a photon gives us a particle & the mass is millions of times greater  the mass being due to aether being annihilated in photons & aether flowing in to replace the lost aether, the acceleration of the aether giving us g.
But light doesnt support the information that travels at c  the em fields (charge electro magneto) are due to photinos emanating from photons  & photinos are a part of photons. That is a topic ignored by Einsteinians.

If you consider that information may travel at more than the speed of light, then I'm afraid that my simulations won't please you. :0)

If you consider that information may travel at more than the speed of light, then I'm afraid that my simulations won't please you. :0)
Gravity attraction forces atom to nearby atom are probly very weak & ok to ignore compared to charge etc (dunno)  & praps inertia of atom can be ignored (dunno)(i aint a scientist).

Congratulations on getting your thread moved to new theories.
This way, it is the information contained between the particles that maintains the constancy of what we call their inertial motion, not the particles themselves.
How does that work if there's only one particle?
If we consider that it is light that supports the information, then it is light that produces the bodies' mass, thus their resistance to acceleration, and it is also light that maintains their constant motion once they have accelerated. If I can demonstrate that my simulations are right, they might open a whole new way to study the relativity of motion.
The only resistance to acceleration is the amount of energy tied up in the material, and that resistance shows up by affecting the new speed, this depending on how much energy has been added relative to the amount of energy that needs to be moved by it. This applies to single particles. If you have multiple bound particles and don't accelerate them all, there will be a transfer of movement energy between them to share it out evenly, but that should not be mistaken for resistance to acceleration. Your whole way of looking at it is wrong.

It's not so hard, entanglement is the result of an electron decaying into two photons. The two entangled photon share the same angular proclivity of the electron. After they separate they share the same S/T perspective of the parent electron, however, this persprective now has two distinctly different S/T locational bearings. The photon that accelerates away first at the SOL is time dilated. The second photon that remains orients to time contration. Both entangled photon are sharing the other's orientation's perspective. The first photon attempts to adjust by reconciling back to the second photon original perspective of time contraction. This reconcilation of bearings between the two creates a paradox, "a situation that combines contradictory features or qualities." The second photon has reconciled to the time dilation of the first photon prior to the first photon reconciling itself to the second photon. Once the entangled photons adopt the only alternative, time dilation, the paradox resolves itself and both particles separate at the speed of light. lol
THe first photon has conserved more energy then the second. When the 1st photon through time dilation remaining as 6, attempts to reconcile with it's twin by returning in a SOL time contraction, it finds the second photon as being 12. The second photon being 12, stagnant and w/o time dilated acceleration cannot time contract. Time contraction is only available to photon 6 as an alternative. With only time dilation as an alternative, for both accelerate, one 12 one 6. lol

The second photon has reconciled to the time dilation of the first photon prior to the first photon reconciling itself to the second photon reconciling itself to time contraction. The information of a time contraction cannot be greater than the information from a time dilation from a future source deaccelerating from the SOL. lol

Has mistakes but will leave as is! lol

Congratulations on getting your thread moved to new theories.
My goal wasn't to stay in the science forum, but to say what I think, and I did, and not all the forums let us do that, thank's to the flexibility of the administrators here..
How does that work if there's only one particle?
Then it is the information contained between the components that maintains the constancy of what we call their inertial motion, not the components themselves. If information is able to move the particles, not just inform the other particles that they move, then it is always located between the particles.
If we consider that it is light that supports the information, then it is light that produces the bodies' mass, thus their resistance to acceleration, and it is also light that maintains their constant motion once they have accelerated. If I can demonstrate that my simulations are right, they might open a whole new way to study the relativity of motion.
The only resistance to acceleration is the amount of energy tied up in the material, and that resistance shows up by affecting the new speed, this depending on how much energy has been added relative to the amount of energy that needs to be moved by it. This applies to single particles. If you have multiple bound particles and don't accelerate them all, there will be a transfer of movement energy between them to share it out evenly, but that should not be mistaken for resistance to acceleration. Your whole way of looking at it is wrong.
The bonding between two molecules is a lot weaker than the one between two atoms, and if I had to simulate an acceleration on them, the distance between the molecules would contract a lot before transferring the acceleration to the other molecule, while the distance between the atoms would almost not change. A nudge on a first molecule would create a vibration between the molecules, because it would be accelerated backwards before having the time to completely accelerate the other molecule.
Such a vibration could also happen between my two particles if the force on the first particle would stop before it is informed that the second particle has moved away: it would immediately be forced to get back where it was, and it would then be forced to accelerate again forward as soon as that information would come in, what would create a vibration between them, a vibration that would be due to the limited speed of the information that bonds them together. When we hit a balloon, it wobbles while getting away from us because it deforms while being hit. It also happens when we hit a solid crystalline structure, and then we can hear the vibration because it is fast enough to create a sound wave. My particles don't vibrate simply because I consider the acceleration to be progressive at the beginning and constant after. Notice that if they would, they would resist to vibrate, and that resistance would also be due to the limited speed of the information that bonds their components together. I'm surprised that you resist that much to change your mind about that possibility, but on the other hand, I'm happy you keep feeding me back. I need to take care not to entertain an endless vibration though. :0)
Talking of endless vibrations, I think that your simulation on tides already accounts for the outward force rmolnav is talking about. That force is due to inertial motion, and you already move your two bodies inertially while they are being moved gravitationally, so you already account for that force. He simply considers that inertial motion produces an outwards force, while it is also possible to consider that it creates a pulling one. I told him so, but he didn't answer me yet. Since your simulation already accounts for inertial motion, then he can certainly not provide the way to add it. That composite motion brings back the hen and egg feed on the table: which one of the two motions is executed first, the gravitational one or the inertial one? If it's the gravitational one, then the force is outward, and if it's the inertial one, then it is inward. No need to bother with the direction of the forces in a simulation though, only with the direction of the resulting motions.

I'm surprised that you resist that much to change your mind about that possibility, but on the other hand, I'm happy you keep feeding me back. I need to take care not to entertain an endless vibration though. :0)
Have you worked out how mass relates to the mass of particles? If it's actually in the light moving between the particles, how does that light know how much mass it should hold for different kinds of particles?
He simply considers that inertial motion produces an outwards force, while it is also possible to consider that it creates a pulling one.
As soon as he counts a nonforce as a force, he has to counter it with another false force, or apply the centripetal force from the wrong place. I'm still not convinced he can produce an elliptical orbit, but I don't have time to experiment with it, so I'll wait until he makes it absolutely clear how he wants the forces to be applied.

Have you worked out how mass relates to the mass of particles? If it's actually in the light moving between the particles, how does that light know how much mass it should hold for different kinds of particles?
The strength of the light exchanged between the particles is equivalent to the loss of mass due to their bonding, so if we accelerate a particle towards another one, the resistance it offers to move with regard to this light is weak. The main part of its resistance comes from its components' one, which exchange a lot stronger light since they are a lot closer and that the frequency of their exchange is a lot higher. This way, the more there are components, the stronger the light between the particles, and the stronger their resistance to accelerate towards the other one when it has not already accelerated. The same phenomenon happens to the bonding between atoms: the more there are nucleons, the stronger the bonding between the atoms, but it also depends on the way the electrons make their bonding, and in my small steps, there is no electrons, so the strength of the bond must depend on the way the nucleons interact with each other. Whatever the number of components though, the information they exchange in order to move properly with regard to one another is still contained in the light they exchange, so it is all the time located between them. Naturally, I suspect our own memory to work like that too, I suspect the information to be located between the neurons, but that's another story.

The point I was making is that we don't ordinarily use gradual accelerations in the twins paradox thought experiment because that would complicate the calculations without providing any gain in return. Clearly though, you want to be able to handle gradual accelerations, but the cost of that is that you can't get to relativistic speeds in a reasonable length of time without tearing your objects apart, so you need to compromise. You can accelerate one particle if the acceleration is gentle and then watch the two adjust to share out the acceleration between them, but you should accelerate both equally if you want to get them up to high speed without tearing them apart (from each other).
Groups of fundamental particles are pushed to high relativistic speeds very quickly in accelerators everyday..

Groups of fundamental particles are pushed to high relativistic speeds very quickly in accelerators everyday.
That's quite different from a bound pair/group of them with all the acceleration being applied to only one of them and the others reacting to that as the force is shared out between them from the directlyaccelerated one. Also, if you want to simulate things using a JavaScript timer at a maximum of a thousand moves per second with each move representing a trillionth of a second (or quadrillionth  I can't remember what Le Repteux is using), it would take a very long time to simulate an acceleration to relativistic speed, so he needs to compromise.

The strength of the light exchanged between the particles is equivalent to the loss of mass due to their bonding, so if we accelerate a particle towards another one, the resistance it offers to move with regard to this light is weak. The main part of its resistance comes from its components' one, which exchange a lot stronger light since they are a lot closer and that the frequency of their exchange is a lot higher. This way, the more there are components, the stronger the light between the particles, and the stronger their resistance to accelerate towards the other one when it has not already accelerated.
Perhaps you could to display numbers for the mass then, showing where it is for two unbonded particles, then showing how it's distributed when the bond is formed, and then how it changes when the particles are accelerating.

Programming forces looks as difficult as programming feelings: we can feel things but we seem unable to program those feelings. In your simulation on tides, you probably use the gravitation equation because you have to account for the mass concept, otherwise you would have to program an exchange of information between the two bodies like I do, program it to loose intensity with distance, and move the different parts of the bodies with regard to the incoming information. That's what I would have to do to rotate my particles, but in this case, the frequency of the information would have more importance than the intensity. No need to use force then, just motion and information about motion. If we knew what mass is about, maybe we could program force, but we don't. In my simulation on acceleration, mass is the result of a particle producing doppler effect on the incoming information while it is being accelerated towards the other particle, in such a way that it is forced to brake all the time it is being accelerated. It may be a good explanation for mass, but it doesn't help us to program the resistance the particle is feeling with regard to the information.
In my theory, it is the light that escapes from the components' steps that bonds the particles together, because it is during acceleration that light escapes, because the steps are justly made of accelerations followed by decelerations, and because the particles get out of sync with the incoming light during acceleration, thus being unable to absorb it all. If light would not have escaped from the particles, thus if the particles would not be bound, the bonds between their components would benefit from all the light and they would be stronger, and so would be their resistance to acceleration, thus their mass. I could show the mechanism with a simplified simulation, but I can't see how I could use it to measure the loss of mass. All I could measure is the loss of intensity due to distance, and this way, the light exchanged between the particles would be millions of times weaker than the one exchanged between the components. Mass is indeed inversely proportional to the particles' dimension, the smaller they are, the more they are massive, so I guess that the numbers the simulation would display this way wouldn't be very far from those we get from comparing their mass to the loss of mass due to their bonding.
I had another idea about the way my simulation could account for the relativistic effects at the components' scale. I could simply use the time contraction I get at the particles' scale, apply it to the components' scale, thus increase the frequency of the photon produced by the accelerated particle, and observe how it affects the timing and the distance between the particles. In principle, a photon with more energy produces a longer step, so the second particle would make a longer step away from the first particle than with doppler effect alone, which would effectively reduce the contraction due to the first particle accelerating before the second one. That step away from the first particle would then produce more redshift than expected on the photon it is producing, but that photon would also suffer some blueshift from its components, what would reduce the increase in redshift due to the step being longer than expected. More simply, the contraction happening at the components' scale would blueshift the photons produced by both particles, what would push them away from one another a bit during acceleration, thus reducing the contraction at the particles' scale. I'll try that instead of using the relativistic formula.
In fact, from the components viewpoint, the distance between the particles should not look contracted during acceleration since the components themselves would be contracting at the same rate, so it is possible that adding their contraction to my simulation would undo any contraction at the particles' scale. If it was so, reversing the acceleration would not produce any contraction either. When a photon from the accelerated particle would strike the other particle, it would be contracted, but since it would actually be producing the contraction of that particle's components while accelerating it, from their viewpoint, it wouldn't look so. The same thing would be happening to the doppler effect produced by the acceleration of the first particle: since it would be producing the acceleration of the second particle, from its viewpoint, there would be no doppler effect.*
That's a possibility SR doesn't account for. It's one thing to consider that light informs us on motion, but it's another one to consider that it is producing it. This way, the particles would be using light to move with regard to others exactly like we do, a less anthropocentric paradigm similar to putting the sun at the center of the world. That's precisely why I can consider that we shouldn't change reference frames in the twins paradox experiment: maybe we can neglect the way the particles can move, but if they do move with regard to light, then they can certainly not neglect it. If I move two systems of two bonded particles on the screen before accelerating one to rest with regard to the screen, I can certainly not pretend afterwards that it is not necessarily the one that has moved away from the other. That would be both absurd and abusive, and that's precisely what the relativists pretend. If I would be a relativist, that thinking would prevent me from using light to move my particles, because they would be moving relatively to light, not relatively to one another.
* PS. I must comment the idea that there would be no doppler effect since the particles would be moving at the same time the light is coming in. If I was a particle, I would certainly need to see that the other particle is beginning to move towards me before beginning to move away, so I would only move after I would have seen a bit of doppler effect, but since I would be accelerating away, it wouldn't increase as if I would have stayed at rest. If the acceleration was constant for instance, the doppler effect would be constant, and if I would be very sensible to it, I wouldn't let it increase much before beginning to move. That effect seems to dovetail my explanation of the cosmological redshift: I already attributed the redshift to the gravitational acceleration, and the effect is justly produced during acceleration.