Confirmation of Mach's Principle, No. 15 in series

"FUNDAMENTAL UNSOLVED PROBLEMS IN PHYSICS AND ASTROPHYSICS: 2.15 Mach’s Principle. The idea that the mass of a particle locally may be dependent on the distribution of matter globally has a long tradition. Formulated by Mach and admired by Einstein, it is a perennial subject of investigation. Machian theories of gravity have been developed by Hoyle and Narlikar, Liu, Mashhoon, Wesson and others. Reviews of the principle and related questions like the nature of mass, may be found in the books by Rindler (1977), Barbour and Pfister (1995), Wesson (1999) and Jammer (2000). It is certainly possible to construct such theories in both N = 4 and N ≥ 5 that are in reasonable agreement with observations. For example, the N = 5 Kaluza-Klein extension of N = 4 Einstein theory is Machian in nature, but agrees with all the classical tests of relativity in the solar system (Kalligas, Wesson and Everitt 1995). The question that awaits an answer is not so much if such theories can be constructed as whether or not they are needed." --  Paul S. Wesson Department of Physics University of Waterloo Waterloo, Ontario N2L 3G1 Canada prepared for California Institute for Physics and Astrophysics 366 Cambridge Avenue Palo Alto, California 94306 U.S.A. https://www.calphysics.org/problems.pdf

The core of "Mach's Principle" is something like this: the inertia of a body is determined in relation to all other bodies in the universe (in short, "matter there governs inertia here") -- https://www1.kcn.ne.jp/~h-uchii/mach.pr.html

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(see "Particles from Gravity" for updated material on this topic)

6.3. Gravity's mechanism; Mach's principle*

The underlying physical mechanism of conventional, apparently attractive Newtonian gravitation is seen to be the accelerated expansion of the universe where the frame of observation is sufficiently small -- i.e. below the scale of galactic superclusters or within the visible matter intersections of expanding large-scale cosmic voids. Acceleration and gravitational effects are commonly taken to be equivalent; in this case they are identical, to be discussed further. 

    In the case of a thin sheet of galactic superclusters, there is more accelerated expanding space in the two large-scale voids on each side of the sheet than within the thin sheet (the space below about the galactic supercluster scale is not observed to expand); thus the sheet is in effect pressed flat from both outsides, in that accelerated expanding space of the large-scale voids is seen as the active physical mechanism. See also the "sponge" illustration in Section 1 and various sections below. 

   In the case of the elementary particle of Section 4, there is a correspondence between the indivisible particle and space at large (by the parameter H/G kg/m^2). Given the convention that the ordinary electron and positron have positive mass and that large-scale space has negative mass-energy (Sect. 3), the result should be mutual repulsion, as with the case immediately above.  

   Unlike conventional Newtonian gravity (and somewhat like general relativity), particles affect as well as are said to be affected by space. Elementary particles affect space in that one mass affects another, albeit immeasurably in the case of the elementary particle, or a ponderable aggregate such as a planet or even a galactic cluster, repelling an adjacent large-scale cosmic void (having certain negative mass-energy, as discussed). Thus Einstein's principal objection to Newtonian space -- that particles are affected by but do not affect Newtonian space -- is addressed as well (Genz 1994, p. 170), by noting that the proposed Newtonian space is in principle affected by the particle, albeit space on the large scale; quantitatively, from Equations (1), (2) and (3), 

                        m(e) / (r(e))^2 = -m(v) / (r(v))^2 = H/G                     (5)

where e is electron and v is large-scale cosmic void. In a system consisting of a thin sheet of galactic superclusters bracketed by two spherical large-scale cosmic voids, this electron and one of these voids are practically adjacent; both may be considered mutually repulsed "particles." Similarly, another electron a few meters from the first has the other large-scale void adjacent to it. The space between these two electrons is small in comparison to these bracketing large-scale voids. Therefore, these electrons appear to be gravitationally attracted to one another, while are actually pushed toward one another by the accelerated expansion of their respective large-scale voids, an inertial or repulsive gravitational effect. As with the calibration means of Section 2, it does not matter where the center of the large-scale negative mass is located, as long as a sufficiently large volume of space is chosen (on sufficiently large scales the ratio -m/r^2 is practically constant for the observable universe as mentioned); this is why any two electrons sufficiently close within a given sheet of galactic superclusters appear to be mutually attracted gravitationally. Similarly, any two electrons (and by inference all normal matter) on opposite sides of a large-scale (expanding) void or beyond are mutually repelled, as observed.  

   More specifically, consider a large-scale cosmic void adjacent to a thin sheet of galactic superclusters so that this void and any electron within the sheet are practically tangent. Then the gravitational affect between these "particles" is essentially 

                       F = Gm(e)(-m(v)) / (r(e)+r(v))^2 ~= m(e)H                 (6)

after employing Equation (5) to obtain the inertial expression on the far right from the gravitational expression on the left. Similarly, hypothetically considering two nearly tangent electrons (according to the classical electron radius and ignoring electrical charge) within said sheet, classically the gravitational effect between these particles is approximately

                      F = Gm(e) m(e) / (r(e)+r(e))^2 ~= m(e)H                 (7)

Thus, the apparent attractive gravitational effect between the two electrons (Eq. (7)) may be physically attributed (Eq. 6)) to the accelerated expansion of adjacent large-scale voids (or any sufficiently large adjacent segment of space with or without visible matter as mentioned), not only reminiscent of Mach's Principle, but also indicating a quantitative mechanism to link the inertia of the local particle to space at large.

* Excerpt, Particles from Gravity, preprint at fundamentalsphysics.com