torsdag 8 augusti 2019

Special Theory of Relativity Incompatible with Gravitation

 Sorry to say, but I had to abandon my most beautiful special theory of relativity SR because it could not be combined with laws of gravitation. The demand of Lorentz invariance of course was not compatible with the presence of matter in space. I thus turned to the general theory of relativity giving up Lorentz invariance for covariance, and never returned to SR.

From its start in the 1905 article On the Electrodynamics of Moving Bodies, Einstein connected his special theory of relativity SR to Maxwell's equations for electromagnetic waves. From the two Postulates of SR (1. Relativity Postulate and 2. Constancy of speed of light). Einstein derived the Lorentz transformation connecting coordinates in different inertial systems moving with constant velocity with respect to each other. The catch was that Maxwell's equations in vacuum showed to take the same form in all coordinate systems connected by the Lorentz transformation and thus showed to be Lorentz invariant as required by the Relativity Postulate.

Einstein then tried to extend SR with its requirement of Lorentz invariance to gravitation, but failed and so Einstein abandoned SR for his general theory of relativity. The situation is the same today:
• SR cannot be extended to include gravitation.
• Laws of gravitation are not Lorentz invariant.
This is shown in e.g. Relativistic Theories of Gravitation by Withrow and Murdoch giving a survey of attempts to extend SR to gravitation,  all failing because of incompatibility with observations. The trauma of modern physics can thus be captured as follows:
• Newton's mechanics is Galilean invariant but not Lorentz invariant.
• Maxwell's equations are not Galilean invariant, but Lorentz invariant (in a restricted sense).
• SR is incompatible with mechanics including quantum mechanics.
The trauma is a result of insisting on the Relativity Postulate asking a "law of physics" to have the same formal expression in all inertial systems connected by the Lorentz transformation, that is to require Lorentz invariance.

What then to do?
1. Allow the trauma to continue to paralyse modern physics?
2. Give up Lorentz invariance as a necessity to impose on laws of physics?
I suggest 2. This means that SR is given up because it is incompatible with in particular laws of gravitation. Laws of gravitation cannot be Lorentz invariant if they are going to match observations. This was what Einstein understood when turning to his general theory of relativity. If a theory does not fit with experiments, like SR with gravitation, then it has to be given up.

What then would be the effect of giving up SR? Nothing! It is illustrated by the fact that GPS system works because SR is not included, not because SR is included.

What then about the null result of Michelson-Morley experiment, as the main motivation for asking for Lorentz invariance? Is it possible to explain the null-result without invoking Lorentz invariance? Of course, as will be shown in an upcoming post.

The reason Maxwell's equations in vacuum can be viewed to be formally Lorentz invariant, that is take the same in all inertial frames, is that the vacuum has no material presence in space. As soon as you introduce material presence in space in the form of charges or matter, the idea of Lorentz invariance collapses because necessarily the spatial motion of the inertial system vs the charges/matter must come in. Since SR is incompatible with any form of material/spatial presence, it has to be given up, as Einstein did. Galilean invariance is meaningful, but not Lorentzian.

I have argued that the two postulates of SR themselves are empty of physics. It is possible to give SR a restricted physical meaning by combining the postulates with Maxwell's equations in vacuum showing some compatibility with experiments.  But adding physics in the form of gravitation has shown to not be compatible with experiments. It is now time also for us to give up SR, following Einstein.

Or restrict SR to the domain of its postulates without combination with any physics, in which case SR is empty of physics and carries no incompatibility with observation of physics.

PS In the debate with Ulf Danielson in a previous post, it was not made clear what physics was appended to the two postulates of SR themselves empty of physics, which led to a lot of confusion. Let's see if UD will take up the challenge and comment this post...