The paradox can only be solved if one considers that at least one twin has a non-inertial movement, and thus their respective situation is not equivalent.
In what way does that "solve" it?
In the twin paradox, the twin making all the correct and accurate predictions about who is really older, and by exactly how much, is the one on the earth.
Just because one lives in a non-inertial object (eg in a rocket, or on earth) doesn't mean one cannot make computations using an inertial frame, for instance centered on the sun. A frame of reference is a mental thing, a product of our mind. You still don't get that.
All they need to do is use an inertial (e.g. in this case sun-centered) frame of reference
You don't really want to understand this, Lay. You want to not understand it, and that's what you are doing quite successfully. Keep up the bad work
You don't understand what you are talking about, Lay,
BTW, the reason we humans can treat the sun as inertial is the very very small size of its acceleration as compared to its current velocity. The effects are too small to be detectable. The sun's trajectory barely deviates from a straight line in any detectable manner over the period of a human life.
The International Celestial Reference System (ICRS) is the current standard celestial reference system adopted by the International Astronomical Union (IAU). Its origin is at the barycenter of the solar system, with axes that are intended to be "fixed" with respect to space. ... the ICRF is important because it definitely does not exhibit any measurable angular motion since the extragalactic sources used to define the ICRF are so far away. The ICRF is now the standard reference frame used to define the positions of the planets (including the Earth) and other astronomical objects. It has been adopted by International Astronomical Union since 1 January 1998.
Barycentric Coordinate Time (TCB, from the French Temps-coordonnée barycentrique) is a coordinate time standard intended to be used as the independent variable of time for all calculations pertaining to orbits of planets, asteroids, comets, and interplanetary spacecraft in the Solar system. It is equivalent to the proper time experienced by a clock at rest in a coordinate frame co-moving with the barycenter of the Solar system: that is, a clock that performs exactly the same movements as the Solar system but is outside the system's gravity well. It is therefore not influenced by the gravitational time dilation caused by the Sun and the rest of the system.
I recommend you try and get your head around that the concept of frame of reference
Ether and the Theory of Relativity by Albert Einstein (1920)
Certainly, from the standpoint of the special theory of relativity, the ether hypothesis appears at first to be an empty hypothesis....but the hypothesis of ether in itself is not in conflict with the special theory of relativity....there is a weighty argument to be adduced in favour of the ether hypothesis. To deny the ether is ultimately to assume that empty space has no physical qualities whatever. The fundamental facts of mechanics do not harmonize with this view.
The ether of the general theory of relativity is transmuted conceptually into the ether of Lorentz if we substitute constants for the functions of space which describe the former, disregarding the causes which condition its state. Thus we may also say, I think, that the ether of the general theory of relativity is the outcome of the Lorentzian ether, through relativation.
According to the general theory of relativity space without ether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense. But this ether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts which may be tracked through time.
There is no difference between the two theories in term of what empirical data they predict