Max Born was Minkowski’s assistant, and had studied the papers of Lorentz and Poincare, but never heard of Einstein until 1907, when Professor Loria from Crackow came to Gottingen for a visit, and was told by Professor Witkowski “A new Copernicus is born! Read Einstein’s paper!”. Loria and Born went to the library, found a copy of vol 17 of the 1905 An der Phy, and read the paper. Born later wrote: “Although I was quite familiar with the relativistic idea and the Lorentz transformations, Einstein’s reasoning was a revelation to me… which had a stronger influence on my thinking than any other scientific experience”.A Copernicus analogy for relativity was first used in Poincare's long 1905 relativity paper:
We cannot be satisfied with simply juxtaposed formulas which would agree only by a lucky stroke; it is necessary that these formulas are so to speak able to be penetrated mutually. Our mind will not be satisfied before it believes to see the reason of this agreement, at the point where it has the illusion that it could have predicted it.What is Poincare saying here?
But the question can still be seen form another point of view, which could be better understood by analogy. Let us suppose an astronomer before Copernicus who reflects on the system of Ptolemy; he will notice that for all planets one of the two circles, epicycle or deferent, is traversed in the same time. This cannot be by chance, there is thus between all planets a mysterious binding.
But Copernicus, by simply changing the axes of coordinates regarded as fixed, destroyed this appearance; each planet does not describe any more than only one circle and the durations of the revolutions become independent (until Kepler restores between them the binding which was believed to be destroyed).
Here it is possible that there is something analogue; if we admit the postulate of relativity, we would find in the law of gravitation and the electromagnetic laws a common number which would be the speed of light; and we would still find it in all the other forces of any origin, which could be explained only in two manners:
Either there would be nothing in the world which is not of electromagnetic origin.
Or this part which would be, so to speak, common to all the physical phenomena, would be only apparent, something which would be due to our methods of measurement. How do we perform our measurements? By transportation, one on the other, of objects regarded as invariable solids, one will answer immediately; but this is not true any more in the current theory, if the Lorentz contraction is admitted. In this theory, two equal lengths are, by definition, two lengths for which light takes the same time to traverse.
Perhaps it would be enough to give up this definition, so that the theory of Lorentz is as completely rejected as it was the system of Ptolemy by the intervention of Copernicus. If that happens one day, it will not prove that the effort made by Lorentz was useless; because Ptolemy, no matter what we think about him, was not useless for Copernicus.
Lorentz invented relativity as an electromagnetic theory. Poincare showed in this paper that the same principles could be applied to gravity and everything else.
There are two obvious explanations for this coincidence: (1) gravity and everything else have an electromagnetic origin; or (2) relativity is really a theory about our methods of measurement.
These two explanations are as different as Ptolemy and Copernicus.
Lorentz tried to explain everything in terms of electromagnetism. Poincare was not saying that Lorentz was wrong or useless, but rather claiming to have a distinctly superior interpretation of relativity.
The latter explanation is what is now accepted. The core of relativity is that it is a spacetime theory, and it redefines what we mean by measuring space and time.
Einstein does not say anything like this until several years later. Poincare was the first to make relativity a spacetime theory, and Minkowski popularized it in 1908.
Update: I further explain the Poincare Copernicus analogy in the comments below.