Please be aware that Einstein’s relativity theory has already been disproved both logically and experimentally (see “Challenge to the special theory of relativity”, March 1, 2016 on Physics Essays and a press release “Special Theory of Relativity Has Been Disproved Theoretically” on Eurekalert website: https://www.eurekalert.org/pub_releases/2016-03/ngpi-tst030116.php ). Einstein’s relativity has redefined time and space through Lorentz Transformation. The newly defined time is no longer the physical time measured with physical clocks, which can be easily demonstrated by the thought experiment of candle clocks:

There are a series of vertically standing candles with the same burning rate and moving at different constant horizontal velocities in the inertial reference frame of (x, y, z, t). At any moment t, all candles have the same height H in the frame of (x, y, z, t) and the height has been calibrated to physical time. Therefore, we have the simultaneous events of the observation measured in both relativistic times and physical times in the frame of (x, y, z, t): (Candle1, x1, y1, H, t), (candle2, x2, y2, H, t), …, (CandleN, xN, yN, H, t) in the frame of (x, y, z, t). When these events are observed on anther horizontally moving inertial reference frame (x’, y’, z’, t’), according to special relativity, these events can be transformed to the frame of (x’, y’, z’, t’) through Lorentz Transformation: (Candle1, x1′, y1′, H, t1′), (Candle2, x2′, y2′, H, t2′), … , (CandleN, xN’, yN’, H, tN’) where t1′, t2′, …, and tN’ are relativistic times of the events in the frame of (x’, y’, z’, t’). It is seen that these events have different relativistic times after Lorentz Transformation in the frame of (x’, y’, z’, t’), i.e., they are no longer simultaneous measured with relativistic time in the frame of (x’, y’, z’, t’), but the heights of the candles remain the same because the vertical heights here do not experience any Lorentz contraction. Since the heights of the candles are the measures of the physical time, we can see these events still have the same physical time, i.e., they are still simultaneous measured with the physical time. Therefore, the physical time is invariant of inertial reference frames, which is different from relativistic time. As relativistic time is no longer the physical time we measure with physical devices, the description of special relativity is irrelevant to the physical world.

Now let’s have a look at the symmetric twin paradox. Two twins made separate space travels in the same velocity and acceleration relative to the earth all the time during their entire trips but in opposite directions. According to special relativity, each twin should find the other twin’s clock ticking more slowly than his own clock during the entire trip due to the relative velocity between them because acceleration did not have any effect on kinematic time dilation in special relativity. But when they came back to the earth, they found their clocks had exact the same time because of symmetry. Thus, there is a contradiction which has disproved special relativity. This thought experiment demonstrates that relativistic time is not our physical time and can never be materialized on physical clocks.

Now let’s look at clocks on the GPS satellites which is thought as one of the evidences of Einstein’s relativity.
Many physicists claim that clocks on the GPS satellites are corrected according to both special relativity and general relativity. This is not true. The corrections of the atomic clocks on the GPS satellites are absolute changes of the clocks, none of which is relative as claimed by special relativity. After all corrections, the clocks are synchronized not only relative to the ground clocks but also relative to each other, i.e., time is absolute and special relativity is wrong.

This is a fact as shown on Wikipedia. But some people argue that the clocks on the GPS satellites are only synchronized in the earth centered inertial reference frame, and are not synchronized in the reference frames of the GPS satellites. If it were true, then the time difference between a clock on a GPS satellite and a clock on the ground observed in the satellite reference frame would monotonically grow because of their relative velocity while the same clocks observed on the earth centered reference frame were still synchronized. If you corrected the clock on the satellite when the difference became significant, the correction would break the synchronization of the clocks observed in the earth centered frame. That is, there is no way to make a correction without breaking the synchronization of the clocks observed in the earth centered frame. Therefore, it is wrong to think that the clocks are not synchronized in the satellite frame.

Hefele-Keating experiment is also considered as another evidence of relativistic effects. It is clear that all the differences of the clocks after flights in Hefele-Keating experiment were absolute (i.e., they were the same no matter whether you observe them on the earth, on the moon or on the space station). But according to relativity, if the clocks were observed on the earth, the two clocks after flights had experienced the equivalent paths of same velocity and same distance in same elevation, and thus should generate the same kinematic time dilation and the same gravitational time dilation, directly contradicting the experimental result. Therefore, the differences of the clocks were nothing to do with the velocities relative to each other or relative to the earth as claimed by special relativity, but were the result of the velocities relative to one medium which seems fully dragged by the earth on its surface but partially dragged on the altitude of the airplanes. It is wrong to interpret the differences of the displayed times of the clocks as the results of relativistic effects.

The increase of the lives of muons in a circular accelerator or going through the atmosphere are also absolute changes which are the same observed in all reference frames.

All so-called relativity proofs are just misinterpretations of experiments and observations without exception, and all what relativity describes is irrelevant to physical phenomena, including the speed of light which in special relativity is constant in all inertial reference frames, but which in real physical world still follows Newton’s velocity addition formula (see the paper).

That is, time is absolute and space is 3D Euclidean. There is nothing called spacetime continuum in nature.

There’s no counter-evidence to General Relativity so far, not even the cited paper. Just think of how big headlines in news outlets would be if any actual counter-evidence was found. (No, there is no censorship out there regarding that, otherwise the article linked would long be gone, wouldn’t it be?) General Relativity is one of the most successful theories so far regarding the number of prerequisites (rather short formulas, just 2 arbitary constants: velocity of light and gravity constant) and the precision to which its predictions were validated. Still, there are theoretical issues, so it is widely believed that GR is just a special case of a more advanced theory, just as Newton’s theory of gravity was a special case of GR. But we are far away from being able to tell what such a more advanced theory would look like, there are just no experiments so far that would tell deviations from GR and thus give us any evidence (or would actually hint at what a more complete theory would look like).

Claims that the numbers measured in the experiment mentioned would fit better to an aether-style theory are pointless because of the limited precision of measurement; these numbers including error margin already fit so well to predictions made using General Relativity that there’s just no point in using this as evidence against General Relativity. Also, if there was such a big effect on such an old experiment, newer, far more precise experiments would have seen much bigger effects. But they didn’t.

Also “because acceleration did not have any effect on kinematic time dilation in special relativity” is just wrong. When you accelerate, your frame of reference as definied in Special Relativity is changed. Predictions made by Special Relativity are only valid for non-accelerated observers. For twins meeting twice you could e.g. define an observer moving linearly between first and second meeting point in spacetime and there’s just a single such reference frame. If one twin does not accelerate they will stay at the observer’s location, aging exactly along with the observer, while only the accelerating twin will have time dilation effects (aging less), easily calculated through integrating their time dilation based on velocity over time. Problem solved.