Lorentz transformation cannot establish the geometry (dimensions) of space and time covariant, except in the covariable contents (existential events) within the invariant dimension of space and time, or so called, spacetime. The geometry of frame of reference and its content are not the same.
As for example, at Planck threshold, geometry of Euclidean space vibrates, reasoning limit in our perception.
To falsify relativistic spacetime, if any, why should one has to encounter Lorentz's abstract mathematical presentation than encountering relativistic spacetime directly?
So irrespective of what Lorentz transformation conveys, the author of relativity did not physically established Lorentz, before he robbed of the independence of time and married off space and time after making them illegally "natural" without providing a single experiment to support this.
His paper, specifically relevant to the time dilation and spacetime should have been rejected by the reviewer of the paper then. As the author of relativity cannot simply present an illegal mathematical presentation and get his paper published for others to prove his paper through experiments.
The author of relativity claimed full credit for his paper in Relativity and remained protected by others as he let others to face the questions arising out of his papers, to Lorentz and the experimenters who confirmed time dilation, biased. The author of relativity should not escape in facing the questions relevant and it's consequences.
All of the experiments with time dilation were biased and invalid as they don't follow the mathematical or scientific norms to hold that the wavelength distortions corresponding error in clock oscillation resulting erroneous time being erroneously presented as time dilation by the author concerned,
When it's obvious that none can get whatever time is, if there is erroneous clock oscillation, or no oscillation at all.
We know, as per SI unit of time, it's frequency that represents time. So before considering Relativistic effects on frequency, or it's wavelength, we canot directly jump on to the relativistic effects on time, because a clock time is always as per the order of time, representation of frequency, resulting oscillations, and subjects to various distortions too.
I have my paper invalidating time dilation as referred below.
Lorents transformation or relativistic spacetime cannot establish covariant spacetime, ash they are invariants indeed.
