On General Relativity

Both Fluid Dynamics and General Relativity (GR) are theories based on the idea of a continuum. A continuum is continuous and differentiable everywhere which implies that, if it’s state is known at one instant, then it can be predicted at any future time. A continuum is deterministic. Deterministic theories are unable to account for  random behaviour.

The most remarkable physical property of fluids is turbulence which Kolmogorov was able to describe by abandoning the fluid continuum and using statistical methods.

The most remarkable physical properties of space-time are black-hole event horizons, discontinuities which violate the initial assumption that space-time is a continuum. Furthermore, the deterministic formalism of the tensor calculus underlying GR is unable to account for the excitation of the  polar jets of black holes, perhaps the most continuously energetic objects in the Universe.

The new James Webb Space Telescope is now revealing a Universe whose variety and complexity were not predicted by General Relativity.

General Relativity is far more elegant than Special Relativity (SR) which is quite ugly by comparison, involving, as it does, the awkward Lorentz transformations describing the shortening of measuring rods, increases in mass and so on,  in different coordinate systems. Nevertheless many important results, commonly attributed to GR can be derived from SR.

Maxwell’s equations of electromagnetism (in the absence of ferromagnetic materials) can be derived from electrostatics and SR alone without reference to GR. Two static, electrically charged bodies exert an electrostatic force on one another according to Coulomb’s Law. When they are moving relative to the observer, according to SR, an extra force will be observed, the Lorentz force.  It is due to the Lorentz transformation of the electrostatic force.

The Lorentz force of Coulomb’s Law is commonly known as magnetism.

It follows that, because Newton’s Law of Gravitation is formally identical with Coulomb’s Law (apart from a change in sign), then there must exist a set of gravity equations analogous to Maxwell’s equations. This is indeed the case. They are the gravitoelectromagnetic (GEM) equations and they include a gravitomagnetic field analogous to the magnetic field.

The existence of electromagnetic waves and their velocity can, in turn,  be derived from Maxwell’s equations. Likewise, the existence of gravitational waves and their velocity can be derived from the GEM equations. The velocity of gravitational waves in free space was predicted to be the same as the velocity of light. This was recently confirmed experimentally by LIGO. These predictions about gravitational waves are triumphs of Special Relativity.

As Einstein himself once said, “If you are out to describe the truth, elegance is for tailors”.