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Not calculated without math, explained only. Einstein's SR predicts that the Earth ages abruptly at the moment the traveler turns back, but this does not happen when we study what happens. During the outward journey, the traveler receives Doppler signals that are supposed to show that the Earth is aging less, and then on the return journey he still receives Doppler signals that are supposed to show that the Earth is aging less. These signals do not contain the abrupt aging of the Earth at the time of the turn-around. So there is no abrupt aging of the earth. This simply means that these signals are falsely interpreted as a lesser aging of the Earth by the traveler, i.e. that his estimates are made with false measuring standards, as Lorentz's theory says, and that in reality, the traveler ages less during the entire journey.

What is not really symmetrical is the reality behind Lorentz transformations, not the ether. I can provide you with a non-symmetrical writing of the Lorentz transformation as an Euclidean rotation in space-time and not a hyperbolic one.

No, the paradox can be explained without math within the framework of Lorentz theory, because there is no paradox in this theory. The problem with Lorentz transformations is that they are misleading. As they are symmetrical, we have the impression that inertial reference frames are equivalent. For Lorentz, there are immobile objects in the ether which measure things correctly and moving objects which measure them falsely. The Earth being almost immobile in relation to the ether, we can say that it correctly measures the aging of the traveler, but the traveler being at high speed uses false measurement standards and is mistaken when he measures that the time on Earth passes more slowly than his own. Einstein interprets the equations literally, Lorentz seeks a hidden reality behind these equations. I claim that the postulate of invariance of the speed of light of SR is not consistent with physical reality, therefore that the only possible interpretation of the equations is that of Lorentz.

Yes, we are not at rest. Lorentz explained the null result of the MM experiment by Lorentz's transformations, like Einstein, but while for Lorentz matter contracts and slows down physically as it moves through the ether, Einstein attributes these transformations to changes in physical simultaneities. It is this assumption that implies that the speed of light in one direction is always c. In aether theory the speed of light is measured at c on a round trip due to time dilation and length contraction, but on a one way trip the measurement should give a different result. It is nevertheless impossible to make this measurement because nothing moves faster than light and one must first synchronize two distant clocks using light signals before making the measurement and this synchronization implies in itself that the measurement will give an isotropic result. . ----------------------- Lorentz transformations were established by Lorentz as part of his theory. Minkowski space-time was first described by Poincaré within the framework of this same theory in 1905.

They are THE SAME : https://en.wikipedia.org/wiki/Lorentz_ether_theory

All mathematical solutions are those of Lorentz theory by default. Einstein only gave a new interpretation, he did not produce any new mathematics. The theory of relativity is the work of Lorentz and Poincaré, Einstein only gave a new physical interpretation of Lorentz transformations.

The mathematics of relativity are those of Lorentz theory. Lorentz uses Galilean kinematics so he has nothing to prove. What matters is whether Einstein's explanations are consistent with the physical world. Einstein only gave an explanation for inertial frames with a non-standard kinematic.

Lorentz's explanation is that if we assume the Earth is stationary in the ether, the traveling twin ages less than the Earth during the journey there and back. There is no paradox. Time dilation depends on the twin's speed relative to the ether and not relative to Earth. The observational symmetry of time dilation comes from the observational symmetry of the relativistic Doppler effect. The classic Dopple effect is not symmetrical. If the transmitter is at rest and the receiver is moving it will receive a different Doppler effect than if it is the transmitter which is moving and the receiver which is at rest. But when we add the dilation of time it is impossible to make the distinction, we cannot know if it is the transmitter which is moving or the receiver. Einstein's theory amounts to assuming that the observer is always at rest and moving objects are therefore always at the origin of the observed Doppler effect. But this is a completely arbitrary hypothesis and contrary to physics. It is invalidated during acceleration periods : When we accelerate we perceive the Doppler effect immediately, so the twin who turns around will notice a Doppler effect in the signal coming from the Earth immediately upon turning around, and that means that it is him that causes this effect and therefore changes its speed relative to the ether. The Earth, for its part, must wait for the Doppler effect produced by the traveler to propagate towards it at the speed of light. The situation is therefore not symmetrical and we can distinguish who is at the origin of the motion. We deduce that during the entire period of the twin's return to Earth the situation is never symmetrical since the Doppler effect was generated during the acceleration period. So, observationally, in inertials periods, each can say that it is the other who is experiencing time dilation, but physically this is not the case."

Lorentz always offered a physical explanation for his equations. Objects undergo Lorentz transformations as they move through the ether. What are Einstein's explanations? If his explanations are not physically valid, how do you expect them to replace Lorentz's?

Explain the physics behind the equations. What happens to make the twin come back younger. Lorentz offers a physical explanation for this phenomenon, what explanation does Einstein offer? Equations ? That's no physical explanation.

The ether is detectable during acceleration, it is our speed in relation to it that is not detectable for dynamic reasons: matter being composed of ether waves it undergoes the Doppler effect when moving and prevents any speed-sensing capability in the ether. Einstein's SR is not capable of processing accelerations, otherwise explain to me what happens during an acceleration according to Einstein. The speed of light remains constant and time changes its simultaneity, is that the explanation? This formalism is different from that of Minkowski. In my opinion, this is the formalism of physical reality. Hamilton created quaternions in 1843 and assumed that the scalar part represented time. Maxwell had begun to write his equations using quaternions, but Heaviside and Glibbs dismantled the quaternions to produce the vector calculus, in doing so they separated the scalar part and the vector part, therefore time from space. This article also explains some problems with SR: https://arxiv.org/pdf/gr-qc/0604118.pdf --------------------- You give mathematical equations, but what do these equations say? They say that the traveling twin has traveled the greatest spatial distance and the shortest temporal distance. But Einstein's theory does not say that the twin has traveled the greatest spatial distance because space is relative, it claims that from the twin's point of view it is the Earth which has traveled the greatest distance and in this case it is the Earth which should be younger. Einstein is not able with his postulates to explain what is happening from the traveler's point of view. We are forced to place ourselves in one inertial frame of reference and study the situation in order to be able to account for it, and this inertial frame of reference plays the role of the ether frame of reference. It is thus Lorentz's theory which explains the paradox and not Einstein's. It is also written here: https://en.wikipedia.org/wiki/Twin_paradox#No_twin_paradox_in_an_absolute_frame_of_reference Now, instead of doing mathematical calculations, I suggest you try to explain what happens physically from the traveler's point of view so that he comes back younger. When exactly does he get younger in relation to Earth?

Ether is actually 3D space, it is not a superimposed substance. Ether is not only luminiferous, all particles are waves in the ether. Spin is a rotation of 3D space, it is an exchange of energy between the particle and external space. All fields of physics are states of the ether. Vacuum energy is made up of waves that travel in the ether and exchange energy with matter. Ether is probably a kind of elastic crystal. It can be represented by balls mounted on springs, in the same way that current quantum physics models vacuum energy. The fundamental problem with mainstream physics is that it does not recognize a privileged frame of reference in its equations. However, we know that the CMB constitutes the universe's frame of immobility and it is also the frame of reference of the ether or space. As it does not recognize this privileged frame of reference it cannot recognize that space has a substance In Lorentz aether theory the one-way speed of light is not invariant, only the speed of light over a round trip is invariant. It's explained here: https://en.wikipedia.org/wiki/One-way_speed_of_light#Theories_equivalent_to_special_relativity This is sufficient to verify Lorentz invariance. ---------------------- It is not ad hoc, Lorentz justified in 1904 the reason for contraction by the electromagnetic nature of matter. But above all, we know today that Lorentz transformations are the transformations undergone by moving stationary waves, which is proof of the existence of the ether. These transformations simply indicate that matter in motion is made up of networks of moving standing waves of aether. The immobile frame of reference in relation to the ether is that of the CMB, it is the frame of reference of the universe. Search on Google: “CMB absolute frame”

in electrodynamics the speed of light was invariant with respect to the ether. The success of special relativity is the success of Lorentz, not of Einstein, the constancy of the one-way speed of light is a useless hypothesis. A change in velocity produces a change in the Doppler effect. My conclusion is absolutely logical. You have no arguments. If you were a little bit impartial, you would pose the problem and study the question of whether Lorentz or Einstein is consistent with physical reality. Einstein's interpretation has been proven false by many scientific papers. I have already cited this one : https://www.researchgate.net/publication/228609140_The_twin_paradox_in_special_relativity_and_in_Lorentz_ether_theory Why do you find it exciting to think that the speed of light is the same for all inertial observers when there is no proof of this phenomenon? Lorentz theory passes the tests as well without this postulate. I don't think that's the point. Lorentz's theory is an Lorentz invariant theory as well as Einstein's. As for general relativity, the difference between the interpretation of Einstein and Lorentz is that the ether is deformed by the effect of gravitation but remains a privileged reference frame, like a material deformed under tension.

Einstein's postulate on the invariance of the one-way speed of light is untestable as well. The speed of light is invariant only over a round trip to all observers, making it impossible to decide between Einstein's and Lorentz's theories experimentally on this point.

Walking droplets are mainstream physics. Lorentz transformations are classical wave mechanics and it's mainstream physics.

This is impossible, the one-way speed of light cannot be measured: https://en.wikipedia.org/wiki/One-way_speed_of_light Lorentz's theory is based on a speed of light varying in one direction but = c on the average of the round trip.

What is a acceleration ? it's a change in velocity, so if time dilation is not relative during a change in velocity it cannot be relative after this change, it's the same level of understanding as 1+1 = 2 If time dilation is relative during inertial journeys, how does the twin come back younger knowing that the total journey is only the sum of two inertial journeys? We must add a sudden aging of the Earth during the U-turn, but nothing of the sort occurs in the signals received by the traveler, the Earth does not age suddenly, so there is no physical symetrical time dilation during inertial journeys. The traveler ages less throughout the journeys.

Here there are wave simulators for lorentz transformations : https://ondes--relativite-info.translate.goog/AlainCabala/telechar/download.html?_x_tr_sch=http&_x_tr_sl=fr&_x_tr_tl=en&_x_tr_hl=fr&_x_tr_pto=wapp

You cannot prove that it remains invariant, on the other hand I proved in my first message that it cannot remain invariant. When an object accelerates it necessarily changes speed relative to light, which invalidates Einstein.

Time dilation occurs in a propagating medium when confined standing waves are set in motion. Lorentz transformations are classical wave physics. Here are references: https://arxiv.org/pdf/1401.4356.pdf https://arxiv.org/abs/1401.4534 https://web.archive.org/web/20120228112717/http://glafreniere.com/sa_Lorentz.htm So the Lorentz transformations tell us that matter is made up of standing waves of ether. Electron is probably a standing wave according to Milo Wolff's model.

In a light clock the speed of light is invariant with respect to space but certainly not with respect to the light clock. You are confusing the invariance of the speed of light with respect to space or ether which is Lorentz's postulate and the invariance of the speed of light with respect to all inertial frames which is Einstein's.

If time dilation was a relative effect, it would not be absolute and the twin would not return younger. If the speed of light does not change relative to a moving object, how does a light clock work? It is the measurement of the speed of light that does not vary, not the speed itself. Meters and measuring standards are transformed in such a way that they always measure the same round-trip speed.

How do you know that the speed of light is invariant? This is a eisteinian postulat, not a physical reality. https://en.wikipedia.org/wiki/One-way_speed_of_light So this convention has nothing to do with experimentally verifiable predictions. I have demonstrated that this convention leads to a physical contradiction. This has been proven, for example, walking droplets in oil baths obey Lorentz transformations while moving. Lorentz transformations are proof that matter consists of moving standing waves of ether. C is invariant, but the speed of light relative to moving objects is not. In the absence of gravitation the speed of light is invariant with respect to ether or space The Doppler effect comes from relative speed and is generated during the acceleration period. If you don't accelerate you can't move. So you say yourself that the space twin change is velocity and produces a Doppler effect, so if it is the one moving it is not the Earth that is moving and there is no physical symmetry. Matter waves, gravitaional waves, any ether waves. What you say there is Einstein's interpretation. In this interpretation the lengths contract because the simultaneity physically changes. If simultaneity does not change physically there is no possible length contraction of. But an object which accelerates has no influence on outer space, it therefore cannot change the simultaneity of outer space, it can only change its own simultaneity, that is to say it physically transforms itself because the speed of light changes relative to him and he has to adapt. So the outer space has not changed in simultaneity so there is a simultaneity of the outer space and it is a privileged frame of reference. No, so there is no spacetime in the Minkowski sense. But there is quaternionic spacetime where time is the scalar dimension of space as Hamilton thought when creating quaternions. https://en.wikipedia.org/wiki/Algebra_of_physical_space Einstein's interpretation is based on a literal interpretation of the equations and on the physical existence of Minkowski space-time or block universe. But time is not a vector dimension.

You are confusing time dilation and simultaneity. The change in simultaneity is the origin of length contraction and is a perspective effect. Time dilation is an absolute effect and comes from the decrease in the average speed of light relative to an objet in motion.

I fixed everything before your message.