...space, Page 2, Dark mass/energy, electron mass in terms of natural constants (gravitation)

This correspondence of Newtonian gravity at large scales and the Hubble expansion yields

-m(x) / (r(x))^2 = H / G (1)

where net mass-energy should be negative as the equation indicates -- otherwise the space being considered in this calibration would contract, rather than expand as observed. Positive mass is distinct from and adjacent to negative mass-energy as indicated in the initial mathematical expression above. The seat and composition of negative mass-energy is to be discussed.

3. Dark mass-energy

An alternative view of non-baryonic dark mass-energy (comprising dark matter and dark energy as characterized above): since no distinction was made between visible and dark mass-energy in calibrating Equation (1) (total mass in a given heterogeneous volume of space is employed), this relation should account for dark as well as visible matter. Assuming -m/r^2 (or H/G) constant in (1) (see Section 5 for the general case or case where systems considerably larger -- the observable universe and beyond -- than galactic superclusters) consider,

-m(s) / (r(s))^2 = -m(v) / (r(v))^2 (2)

where s is a large-scale cosmic spherical void plus shell of galactic supercluster systems, and v is the same void (less shell). Since such shells are thin in relation to the adjacent large-scale voids as referenced, virtually all volume, and therefore mass according to (2), would be in the large-scale void, regardless of void size, and be dark.

Since the sum of visible and dark mass-energy is negative (see Eq. (1) and calibration means), and visible matter is positive by convention, dark mass-energy in this view would be negative. Thus this hypothesized dark mass-energy could be responsible for accelerated expansion in Eq. (1). With no upper limit for r (or given the local supercluster typical), dark mass-energy in this view could be responsible for said observed accelerated universal expansion, as well as the stability of visible groups (Sect. 6.4.4; again, conventionally, dark matter is generally assumed positive and seated among the visible matter, and dark energy on the larger scale has an accelerated repulsive effect therefore having negative mass-energy, where the two are conventionally assumed different in kind; however, it will be shown that negative mass-energy seated in the large-scale voids and positive mass-energy apparently seated among visible matter has the same physical effect below the galactic supercluster scale, and that the two are identical in kind, the difference being only one of viewpoint or scale). The composition of this dark mass-energy is discussed in Sect. 6.1.

4. Electron mass

Examining Equation (1) at the sub-atomic scale, let m be that of the electron, and r be the classical electron radius, ke^2/mc^2 (derived by noting the coulomb energy necessary to hold two point charges, each equivalent to electron charge, e, a distance apart equivalent to the classical electron radius), so that

m^3 = -k^2(H/G)(e/c)^4 (3)

the order of electron mass magnitude.

5. Relationship between space and time

Whereas classical Newtonian space is independent of time, the accelerated expansion of space may be represented by the Hubble parameter in acceleration units (Sect. 2); therefore H = d^2 r/dt^2, and substituting in Equation (1),

d^2 r/dt^2 + Gm/r^2 = 0 (4)

6. Inferences, experimental confirmation and predictions

6.1 The nature of non-baryonic dark mass-energy

Since dark mass-energy is seen as synonymous with accelerated expanding spacetime (see Sect. 3; space and time are linked in this context in Sect. 5; this is not a strict general relativity format of course), and spacetime is seen as synonymous with the gravitational field (Einstein 1961, p. 153-156), it may be inferred that dark mass-energy in this view is gravitational energy.

Although, it may seem improper to enlist the general relativity concept regarding the likeness of spacetime and field in the context of Newtonian gravity, where masses were said to move relative to an absolute unreactive space; however, presently masses are considered relative to one another, where one of the masses is a sufficiently large region of space of radius r having mass -m, where for instance -m and r bear the subscsript v, as in Equation (2).

This negative gravitational mass-energy is seen as primal -- existent before normal positive matter, as follows. In that positive matter might not seem to be directly associated with a negative gravitational field due to mutual repulsion (or a positive particle would normally seem to be directly associated with a positive gravitational field; however it will be seen that a positive particle may indeed be paired with a negative field), the furthest apart these items may be while substantially effecting one another is for the negative field to dominate the adjacent large-scale voids (see also Sect. 3). Conventionally, a strong repulsive tendency occurred about the big bang; presently an accelerated repulsion is observed, as referenced. By Ockham's razor these two repulsions are taken to be the same continuous phenomenon at different times (Eq. (4)), recalling the inflation scenario but without the discontinuities, i.e. as r approaches zero d^2 r/dt^2 approaches infinity. The two repulsions are seen as gravitational in nature also by Ockham's razor, aside from Sect. 3, in that it is physically uneconomical to introduce an unknown effect when gravitation is available, especially when such gravitation accounts for attractive as well as repulsive effects, to be discussed further.

6.2. Gravity or cosmological constant?

In that the energy of Section 6.1 is negative, gravitation per se may account for said observed accelerated expansion of the universe, according to Equation (1) with mass taken to be the mass-energy of the known universe.

The ad hoc cosmological constant is unnecessary to a context where accelerated cosmic repulsion is implied.

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.

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