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The Doppler effect is an effect due to waves, so what changes is the speed relative to the waves. Lorentz transformations are classical wave mechanics equations, they cannot exist without a propagation medium. Acceleration causes variation in the Doppler effect and therefore variation in the speed of the waves relative to the accelerating one. The study of acceleration shows that the symmetry is observational but not physical. Only at the end of the trip, until the Doppler effect is transmitted at the speed of light, because it is not light which changes speed in relation to the waves. What do you mean by “en route” What works is the mathematical law, not Einstein's interpretation. Here : https://en.wikipedia.org/wiki/Twin_paradox#Relativity_of_simultaneity you can see that there is a "simultaneity jump" Its in Lorentz theory you have to disentangle what you observe from what’s happening with the clocks, in Einstein's theory what’s happening with the clocks is considered physical reality, it's the only way to explain the constancy of the speed of light, or else this constancy itself is not physical reality and then it's no more Einstein interpretation but Lorentz. If time is not physical, neither is Minkowski space-time and Lorentz is right.

You are talking about mathematics, this mathematics was discovered by Lorentz, Poincaré and others, and accounts for observations. I talk about the physical interpretation of these equations, and I show that Einstein's interpretation does not work. You are trapped in the idea that the accuracy of SR's mathematical equations necessarily validate Einstein's interpretation. There is no doubt that Lorentz's interpretation works because it uses classical kinematics, but Einstein's interpretation uses a anomalous kinematics that must be proven consistent with the physical world. Look at this: https://en.wikipedia.org/wiki/Talk:Twin_paradox/Archive_5#GR_section_removal The GR section of the twin paradox has been removed from Wikipedia because it is invalid. On the other hand, at the end of the article you have a section which explains that the paradox disappears if we assume a privileged frame of reference as in Lorentz theory : https://en.wikipedia.org/wiki/Twin_paradox#No_twin_paradox_in_an_absolute_frame_of_reference

The first relativity theory is the Lorentz Ether Theory : https://en.wikipedia.org/wiki/Lorentz_ether_theory Only this theory correctly uses Lorentz transformations in accelerated frames of reference, Einstein's relativity only works in inertial frames of reference. Explain to me what happens according to Einstein's theory of relativity in accelerated frames of reference. If you observe an object that is accelerating, you see that the Doppler effect it perceives is due to its change in speed relative to light. If we place ourselves in the reference frame of the accelerating object, what explanation do you find for the Doppler effect other than the same thing, a change in the speed of light? During inertial phases, it is impossible to know who is moving and who is stationary relative to the ether, but during acceleration it becomes visible, because the one who accelerates is the one who changes speed relative to the ether and who produces the Doppler effect. In the twin paradox, the traveling twin ages less from the Earth's point of view during the outward and return journeys, and from the traveling twin's point of view it is the Earth that ages less during the outward and return journeys. This is because each assumes that it is the other who is moving and undergoing time dilation. But this assumption is arbitrary, it could very well be the observer who is moving and the observed who is at rest, the observed Doppler effect would be the same because the relativistic Doppler effect is symmetric. In fact, once the traveling twin accelerates to leave Earth he undergoes time dilation, but due to the symmetry of the relativistic Doppler effect, he can assume that it is Earth that is moving and undergoing the Doppler effect. As I have already explained, the fact that he perceives the effect instantaneously shows that he is the one who is moving and undergoing time dilation. All that I am saying here is nothing more than Lorentz's theory, which claims that the symmetry of Lorentz transformations is only observational and not physical. In fact, Einstein's theory does not work in accelerations, it predicts physical changes in simultaneity that do not exist experimentally. It predicts that the Earth ages suddenly at the time of the U-turn, but this is false because the light signals emanating from the Earth do not undergo a jump into the future, they are entirely predicted by kinematic Doppler effects. The Earth's jump into the future comes only from resetting the clocks. After the U-turn, the clocks are resynchronized because the speed of light has changed and they need to be recalibrated. The estimated time of the Earth is then projected into the future, but the light signals from the Earth are not projected into the future, it is only the hands of the clocks that change. There is no physical jump. ------------------------ Look at this paper : https://www.researchgate.net/publication/228609140_The_twin_paradox_in_special_relativity_and_in_Lorentz_ether_theory

I didn't assume anything. This is the Doppler effect solution of the paradox : https://en.wikipedia.org/wiki/Twin_paradox#What_it_looks_like:_the_relativistic_Doppler_shift The traveling twin notices an acceleration of the Doppler effect as soon as he turns around, the sedentary twin only towards the end of the trip. This asymmetry cannot be explained by Einstein's SR. Where does the Doppler effect come from if it does not come from the one accelerating? It is the speed of light that is changing relative to the one accelerating.

Einstein's relativity is based on the idea that it is always the observed object that moves relative to the ether and not the observer. If we prove that it is the observer who is moving relative to the ether we invalidate Einstein. Lorentz says that the observed and the observer can both move relative to the ether The relativistic Doppler effect contains time dilation so if the Doppler effect comes from the one accelerating, time dilation can only come from him too. You cannot resolve the paradox with Einstein's SR, if you believe you do it it is because you are using Lorentz theory, as the mathematics is the same you cannot decide with them. To decide, we must study what happens during an acceleration, and we then see that Einstein's SR is experimentally invalidated. Einstein's SR does not know how to deal with accelerations. You can't solve the paradox with GR, this was invalidated by the scientific community a long time ago, anyway there is no gravitational field during an acceleration. By the way, I'm not talking about GR but about LET You cannot solve the paradox with SR, but only with LET.

Is Einstein's theory of relativity able of solving the twin paradox? When the traveling twin turns around to reach Earth, it observes a blueshift of the light emitted by Earth instantaneously, not after some time. This seems to suggest that the blueshift arises from the twin's own acceleration and therefore its own motion through ether, not from the apparent movement of Earth relative to it. The Earth, on the other hand, must wait for the blueshifted light from the traveling twin to reach it at the speed of light. This seems to indicate that the observational symmetry of special relativity is not physical, but that there might be an underlying asymmetry as proposed by Lorentz's ether theory. Here is another line of reasoning that leads to the same conclusion: Consider two bodies, A and B, in relative inertial motion. A accelerates and immediately observes a change in the relativistic Doppler effect of the signal emitted by B. It then stops accelerating. This change in the relativistic Doppler effect is composed of a kinematic and a transverse Doppler effect component. According to Einstein's relativity, from the point of view of A, the change in the Doppler effect arises from the change in B's motion. It includes the transverse kinematic Doppler effect component, therefore B undergoes a change in time dilation. However, this change in the transverse Doppler effect does not originate from a change in B's motion but from A's acceleration. We are certain of this because it appears as soon as A accelerates. If it came from B, A would have to wait for it to propagate from B to A at the speed of light before perceiving it. Since the change in the relativistic Doppler effect does not originate from B, B cannot experience the change in time dilation. On the other hand, since A causes the change in the Doppler effect, he undergoes the change in time dilation but observationally perceives it as happening to B due to the perfect symmetry of the relativistic Doppler effect. Indeed, A can always imagine that the signals it receives are distorted by the change in B's motion since the observed deformation is the same as if B had changed its motion. However, since A knows that the change in the Doppler effect arises from its own acceleration, he knows that he is the one experiencing the change in time dilation. Here a citation by Langevin : https://fr.wikisource.org/wiki/L’Évolution_de_l’espace_et_du_temps