Newton's gravity might come in two forms: non-local and local.
Non-local and local (scale-invariant) Newtonian forms respectively, where -M is not negative condensed matter.

Newton's gravity might come in two forms: non-local and local.

v. 5 n. 39

While not a new topic, the intent is to make the distinction between the two Newtonian forms more explicit by means of "locality," continuing the recent series on locality in physics as relates to gravity. While locality is indicated for general relativity [Note 1], the proposed local Newtonian Form 2 in the cover image could be more comprehensive (scale-invariant) with an implicit "cosmological constant." "Locality" actually has different shades of meaning these days in physics, and this could be confusing.

Addressing these shades of meaning first, traditionally locality refers to direct contact, as one billiard ball strikes another and a certain result unequivocally occurs. Or, a photon of proper frequency strikes an electron on a metallic surface, and the electron is ejected. Non-locality, for example, traditionally refers to classical Newtonian gravity (Form 1 in the cover image) where it is not known why condensed matter M and m move toward one another gravitationally; this is the infamous "action at a distance" as if by magic.

With the more recent experiments in quantum entanglement, the other meaning of non-locality is where the contact, communication, appears to occur faster than light speed, instantaneously, violating special relativity. This shade of meaning is not part of the present discussion.

Yet another shade of meaning is quantum superposition, where the particle is neither here nor there until measured. This shade is also not part of the present discussion.

The only shade of meaning to be emphasized, then, is the direct physical contact aspect of locality as relates to physics, gravity in particular. There is no direct contact, no discernable gravitational connection in the classical Newtonian form,

F_1 = GMm/r^2

even though condensed masses M and m are not far apart, such as two bowling balls suspended from strings touching one another after gravitational attraction. The relationship between the masses is considered non-local because the reason for the attraction was unknown. This is a rule-of-thumb relation, an engineering equation, a utility equation, and not strictly a theoretical physics equation. Physics is as much concerned with future-oriented "why" and possible advancement, and not only with "how much," as with the more contemporary-oriented engineering.

In this proposed Newtonian form,

F_2 = G(-M)m/r^2

masses -M and m are in direct contact. Mass -M does not represent condensed matter, rather the total mass-energy within a volume of accelerated expanding space, the local galactic supercluster, for instance, to include visible matter, dark matter and dark energy. This space is causing any condensed matter within it to accelerate, as clusters of galaxies are observed to accelerate away from one another. These clusters are imbedded in this space, as is each particle within the cluster. Mass m in this equation and in one of these clusters is one of these particles and is being accelerated away from mass -M in this Newtonian form. Masses -M and m are locally connected; they are in direct physical contact. As a blade of grass is imbedded in soil, mass m is imbedded in mass -M, and as the human figure represented in the closing image is imbedded in mass -M.

This was discussed quantitatively, but the review in terms of locality might be more tangible. [Note 2]


[Note 1] General relativity makes local connections between condensed matter by "curves in spacetime", made clearer by "frame-dragging" experiments, where these curves in space are measured directly with displacements of gyroscopes in Earth-orbit to measure how the rotating Earth drags its space surroundings along with it, as a moving boat drags its water surroundings.

[Note 2] It was discussed that the calculated acceleration of the local galactic supercluster was about that of the Universe at large, and that this acceleration was equivalent to (repulsive) gravity from the equivalence principle of general relativity, so that gravity might be fundamentally repulsive and only apparently attractive at smaller scales. This apparently attractive gravity would be due to two particles sufficiently close having less accelerated expanding space between than about them. Then inflation, dark mass-energy and the cosmological constant would be implicit in the proposed Newtonian form.

Cover image caption: Non-local and local (scale-invariant) Newtonian forms respectively, where -M is not negative condensed matter.

Closing image (less representative locality lines from accelerated expanding space): Sorry Michelangelo, Da Vinci Was the True Master of the Human Form in Art ‹ Literary Hub (lithub.com)

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