[Le Repteux (OP)]

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, 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. 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.

[Halc]

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, 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 straight-up 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.

[MikeFontenot]

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, 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 well-known "time-dilation" 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 home-twin'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 "narrowly-focused" as possible.  Much more complete and wide-ranging information about the traveler's perspective in the twin "paradox" is contained in my webpage:


 https://sites.google.com/site/cadoequation/cado-reference-frame

[Le Repteux (OP)]

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 straight-up 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. 

[Halc]

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 straight-up 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.

[Le Repteux (OP)]

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.

[Le Repteux (OP)]

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.

[MikeFontenot]

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/cado-reference-frame

for a sequence of +/- 1g accelerations by the traveler, and an "age-correspondence" 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 back-to-back 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).

[Le Repteux (OP)]

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?

[David Cooper]

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, 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 length-extends 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.

[David Cooper]

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 well-known "time-dilation" 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 stay-at-home 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.

[Le Repteux (OP)]

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 length-extends 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 length-extends 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 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?

[David Cooper]

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.

[Le Repteux (OP)]

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.

[Halc]

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 frame-specific 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.

[David Cooper]

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 stay-at-home 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 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.

[Le Repteux (OP)]

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.

[Petrochemicals]

 > 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.

[guest4091]

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.
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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.
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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 g-field for the arcing return of Ann's trajectory.
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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. 
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Excuse me while I look for a swatter.

[Le Repteux (OP)]

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!