måndag 2 september 2024

Poincare vs Relativity Theory



A recent post points to the fundamental difference between material objects with positive mass and immaterial objects with zero mass such as light with connection to the concept of luminiferous aether as immaterial medium for propagation of light under intense discussion as a puzzle of the modern physics emerging at the turn to the 20th century with Einstein's Special Theory of Relativity SR as one solution attempt.  

The mathematician Poincare played a key role with main idea described as follows in Einstein 1905-2005 (eds Darrigol et al):
  • Poincare actually never abandoned the ether. But he refused to regard it as an ordinary kind of matter whose motion could affect observed phenomena.
  • In his lectures of 1899 on Lorentz’s theory, he wrote: I consider it very probable that optical phenomena depend only on the relative motion of the material bodies present –light sources and apparatus– and this not only to first or second order but exactly.
This is precisely the idea I have pursued in Many-Minds Relativity describing propagation of light from emitter to receiver by Maxwell's equations in a coordinate system locked to the receiver, keeping full compatibility with Newtonian mechanics. 

It is natural to compare with propagation of elastic waves in an elastic (material) bar oriented along an $x$-axis of a Euclidean $xyz$-coordinate system together with a similar bar oriented along an $x^\prime$-axis moving with velocity $v$ with respect to the $x$-axis with coordinates connected by the Galilean transformation $x^\prime = x-vt$. Each bar acts as a (material) medium for wave propagation or ether with the same wave speed, and we thus have two ethers represented by the $x$-axis and the $x^\prime$-axis moving with constant velocity with respect to each other, and so being connected by a classical Galilean transformation expressing relativity.      

We can turn this into a similar situation for propagation of light by assuming that the two elastic bars now represent two (immaterial) aethers or coordinate axes connecting emitter to receiver, with the same light speed 

We understand that in both cases aethers locked to coordinate systems act like media or "universa" for wave propagation, which thus are "carried along" with the motion, which is compatible with the null result of the Michelson-Morley experiment triggering SR.

The bottom line is that there is no role for the Lorentz transformation of SR to serve to guarantee the same speed of light in different coordinate systems, since this is already the case if the medium for light propagation is carried along with the motion under Galilean transformation. Therefore SR is not needed and so can be dismissed as a curiosity, as acknowledged by Lorentz. It seems to me that this must have been the position of also Poincare, even if not clearly being spoken out under the intense pressure to come up with something spectacular at the birth of modernity. In this regard Poincare could not compete with Einstein.

More by Poincare:
  • Experiment has revealed a multitude of facts which can be summed up in the following statement: It is impossible to detect the absolute motion of matter, or rather the relative motion of ponderable matter with respect to the ether; all that one can exhibit is the motion of ponderable matter with respect to ponderable matter. (1895) Compare this post.
  • Laws of physical phenomena should be the same, whether for an observer fixed, or for an observer carried along in a uniform movement of translation; so that we have not, and could not have any means of discerning whether or not we are carried along in such a motion. Compare this post.
  • Indeed, experience has taken on itself to ruin this interpretation of the principle of relativity; all attempts to measure the velocity of the earth in relation to the ether have led to negative results. This time experimental physics has been more faithful to the principle than mathematical physics; ... but experiment has been stubborn in confirming it And finally Michelson has pushed precision to its limit: nothing has come of it.

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