3.1.2 Poincaré’s Relativity
In 1900, Henri Poincaré (1854-1912) recognized that local time is actually indicated by moving clocks. He built on Lorentz work and formulated his new conceptions mathematically. He then introduced the Principle of Relativity and tried to harmonize it with Electrodynamics. He declared that simultaneity is only a convenient convention which depends on the speed of light, whereby the constancy of the speed of light would be a useful postulate for making the laws of nature simple and easy.
In June and July of 1905, Poincaré declared that the relativity principle is a general law of nature, including gravitation. He corrected some mistakes of Lorentz and proved the Lorentz covariance of the electromagnetic equations. However, he used the notion of an aether again as a perfectly undetectable medium, and distinguished between apparent and real time, but most historians of science argue that he failed to invent Special Relativity.
At the beginning of 1906, independently of Einstein, Poincaré published a substantially extended work of his 1905 paper, the so-called: “Palermo paper”, in which he spoke literally of “the postulate of relativity” and showed that the transformations are a consequence of the principle of least action. He also developed the properties of the Poincaré stresses, and demonstrated in more detail the group characteristics of the transformations, which he called the Lorentz group, that will be described in section 2.4.
Poincaré also noticed that Lorentz transformation is a rotation in four-dimensional space about the origin, by introducing
as a fourth imaginary coordinate, but he continued to refer to an aether as undetectable medium. He also described coordinates and phenomena as local or apparent for moving observers and real for observers at rest in the aether. By these various conceptions, Poincaré anticipated much of Einstein’s methods and terminology, but he did not invent Special Relativity.
However, Poincaré’s philosophical and physical discussions involved many details beyond Einstein’s theory, both the Special and the General, and he may have been very close to realizing the perpetual re-creation, or the inner levels of time. As we have just mentioned above, he already tried to use imaginary time to express Lorentz transformation, though he does not seem to have ever been close to thinking of space itself as the real time. It is this eccentric property of the Duality of Time that makes the normal time genuinely imaginary, thus hyperbolic and intrinsically granular.