Let us approach the paradox using the basic physics of a clock in the form of a harmonic oscillator as the most basic model of all of physics. Consider two twins A and B at rest in a Euclidean $(x,y,z)$-system both equipped with identical clocks in the form of harmonic oscillators acting along the $y$-axis initiated in exactly the same way.

Let B take off into a journey along the $x$-axis to a distant point and back again.

Let A and B compare the readings of their clocks when B returns home. What will they find?

**1.**Einstein's (special/general) theory of relativity predicts that B will be younger that A. Since ageing is measured by clocks, this means that B's clock lags behind A's clock at reunion. B's clock may show 1 year while A's clock shows 2 years, if B's has aged 1 year and A 2 years during B's roundtrip. That's Einstein's prediction!

**2.**According to basic physics the performance of a harmonic oscillator acting along the $y$-axis cannot be affected by motion along the $x$-axis, not by uniform translation nor by acceleration/retardation. This means that B's clock during B's roundtrip will work exactly the same way as A's clock and therefore will show exactly the same time when B comes home. This means that A and B will have exactly the same age at reunion.

So, basic physics of clocks as harmonic oscillators shows, without any possible doubt, that A and B will have the same age, while Einsteins theory of relativity predicts that B will be younger.

This is a true contradiction or paradox, which shows that Einstein's theory of relativity cannot be correct. A correct theory about physics cannot give a prediction which contradicts the completely basic uncontroversial physics of a harmonic oscillator.

The twin paradox of unequal ageing thus is only an illusion (of Lorentz "time dilation"). This "resolves" the twin paradox, but the consequence is that Einstein's theory of relativity is also only an illusion.

It is a true paradox that this illusion has come to form the basis of modern physics.

**PS1**When I ask a group of physicists to comment on my twin paradox posts, I do not get the reaction that what I am saying is wrong, but instead an excuse that they are too busy with other aspects of physics to comment, while admitting that the question is of fundamental importance to physics of today, and instead kick the ball back by saying that if I myself try a little harder, I will find a resolution.

**PS2**The marine chronometer constructed by John Harrison in the mid 18th century working at a steady rate independent of travel over sea allowed for the first time precise determination of longitude. The key was to keep away from time dilation.