No Unified Field Theory
Modern physics is supposedly based on Einstein’s general theory of relativity for gravitation, Maxwell’s electromagnetics and quantum mechanics, but there is no unified field theory including both gravitation and electro/quantum mechanics.
Einstein spent the later half of his life in lonely fruitless search of a unified theory, while the physics community came to accept the perceived incompatibility of general relativity and electro/quantum mechanics as an unsolvable problem, and marched on.
But an incompatible theory is like a body with cancer which slowly takes life away and the lack of a unified field theory has led modern physics into strange directions away from rationality, towards multidimensional string theories and multiverses way beyond any human comprehension.
The position is locked with deep trench lines: gravitation is to be described by general relativity and general relativity is incompatible with electro/quantum mechanics. General relativity is a geometric theory describing gravitational forces as effects of “curved space-time”, but there is no geometric theory for electro/quantum mechanics, which is basically a field theory in Euclidean “flat” space-time.
It is thus natural to ask why gravitation has to be described by a geometric theory of relativity instead of Newton’s theory, and there does not seem to be any good answer, but dogmatics.
Of course a physicist would say that the (anomalous precession of the) perihelion of Mercury can be explained by general relativity but not by Newtonian gravitation and so Newtonian gravity has to be abandoned. But claims of impossibility seek support from inability or ignorance, and may easily be incorrect, as indicated below. As concerns the urgent problem of dark matter/energy general relativity offers nothing better than Newtonian theory.
Newtonian Field Theory
Let us then scrutinize Newtonian gravitation before we dismiss it, remembering Einstein’s “Newton, forgive me”, and recalling from the previous post on God’s Equation , that Newton’s theory follows from two basic postulates:
- The gravitational force field (per unit mass) is given as , where is a gravitational potential.
- Matter density satisfies , and thus (with normalization).
1. is the same as saying that the gravitational energy of a body only depends on its location (e.g. altitude) and not on the path to be brought there, that is that the gravitational force field is conservative.
We take 2. as a definition of gravitational mass density, noting that 2. is the same as saying that the flow of the gravitational force field into any volume is equal to the amount of gravitational mass in the volume.
Newton’s 2nd Law for gravitational acceleration takes the form:
- that is ,
We thus find that Newtonian mechanics including
- Newton’s theory of gravitation
- Newton’s 2nd law
- the equivalence principle,
can be viewed to be “created” from
- a given conservative gravitational force
- assuming gravitational acceleration is the same for all bodies.
We thus find that Newtonian mechanics is so general that there is no reason to seek a generalization in the form of Einstein’s general relativity.
Instead of dismissing Newtonian mechanics we are thus led to seek a generalization including dark matter/energy, possibly by allowing to take on negative values, as explored in Newtonian Gravitation of Matter and Antimatter.
Altogether, Newtonian mechanics is compatible with electro/quantum mechanics and it is possible that it may be generalized into a unified field theory combining gravitation with electro/quantum mechanics in some form of selfgravitating MHD.
Generalized Newtonian Field Theory
The mass-potential equation (Poisson’s equation) may be generalized into the wave equation:
with Euclidean time and a finite speed of propagation, corresponding to using a retarded potential, which reduces to the previous case as tends to infinity.
The anomalous precession of Mercury can be explained with such a retarded Newtonian gravitational potential as shown in On the Origin of the Anomalous Precession of Mercury’s Perihelion by J Gine,which gives the same Gerber’s potential as obtained by Einstein by general relativity.
Regularization with instead a parabolic equation (heat equation) of the form
is also thinkable.
Newton was well aware of the fact that gravitation by action at distance may not be the right approach:
- That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it.