We can now understand what mathematical condition will have to be satisfied for Lorentz’s principle of correlation to hold. The principle asserts that all things are so adjusted in nature that absolute velocity through the ether must ever elude us. In other words, all electrodynamic experiments will yield negative results. But this obviously makes it necessary that the laws of electrodynamics which govern all electrodynamic phenomena, hence all electrodynamic and all optical experiments, should remain unchanged in form when we pass from [Pg 136] one Galilean system to another. In mathematical language, the laws of electrodynamics will remain invariant when we submit them to the space and time transformations. Now we have said that when submitted to the classical space and time transformations, the invariance of the equations of electrodynamics does, not hold. It appeared then that, contrary to the negative results of experiment and contrary to Lorentz’s principle of correlation, velocity through the ether should be detectible by electromagnetic experiments. Science was thus placed in an exceedingly difficult position; the equations of electrodynamics had been so strongly confirmed by extremely accurate experiment that we could scarcely question their accuracy. There remained, but one alternative, namely, to suspect the accuracy of the classical transformations. This was indeed the course followed by Lorentz. He succeeded in establishing the transformations which would be in harmony with the invariance of the electrodynamic equations, and he found these to differ perceptibly from the classical ones; although reducing to the latter in the case of low velocities. The new transformations constitute the celebrated Lorentz transformations.[44] [Pg 137]