Newton and Einstein, in concert

v. 6 n. 50

NOTICE

1. REGARDING NEGATIVE SIGNS IN EQUATIONS, NONE REFER TO CONDENSED MATTER.
2. Caption for cover image: With conventional active attractive gravity, the relationship is between matter. With active repulsive gravity, the relationship is between accelerated expanding space and matter. Effects are similar at small enough scales, however.
3. The complete archive of these Letters is not available in the "newsletter" category but can be accessed in "posts." Presently, the complete archive can be directly accessed by clicking on the "Fundamental Physics Letters" title next to the logo.

On further consideration, it does not appear necessary to alter the mathematics of general relativity at all, only the interpretation, to possibly resolve the issues mentioned recently. Recalling the conventional expression,

G_uv + Λg_uv = 8πGT_uv, ............................. (1)

the second term on the left conventionally represents the constant slightly curved background of space. But the recent preliminary results of the dark energy survey, DESI, indicates that this term is likely not a constant background, rather an active driver of accelerated expansion, because dark energy (cosmological constant, Λ) appears to be more prevalent in the early universe; therefore, it could properly be placed on the right side of the equation. The right side represents active drivers, and the left side, the responding curvatures of space to these inputs of mass/energy; then,

G_uv = 8πGT_uv - Λg_uv. ........................... (1a)

Yet, the first term on the right in Equation (1a), the energy density term that is said to curve space positively (positive sign) is still conventionally considered to be an active participant; gravity is considered to be fundamentally attractive conventionally due to the presence of visible matter plus radiation; this is the meaning of the implied positive sign for the conventional interpretation here.

The proposed reinterpretation of general relativity at large is that gravity could be fundamentally repulsive and only phenomenologically attractive at smaller scales -- below galactic superclusters, as discussed with regard to the reinterpretation of Newton's gravity (to scale-invariance). [1] The intent is to express this repulsive gravity proposal in terms of general relativity as well.

The cosmological constant term -Λg_uv is reinterpreted as the driver of accelerated expansion of the universe and as gravitational in nature (unlike the conventional interpretation) and as fundamentally repulsive. Note the role reversal of the cosmological constant term -- from static background added to general relativity subsequently for the theory to conform to observation, to essentially as gravity itself representing some 95% of the mass of the universe (popularly referred to as dark energy and dark matter). In the proposed context, dark energy is gravity-driven accelerated expansion, and dark matter is this field on a smaller scale that is tending to push closely-spaced particles together, as about the visible matter represented by 8πGT_uv, the "cosmic web." This small-scale pushing of particles together from large-scale space was described in terms of a sponge analogy, where expanding gas bubbles account for the apparent attractive effects of material among the bubbles.

In comparison, the mass/energy term in Equation (1a), 8πGT_uv, is reinterpreted as visible matter or energy that does not gravitate of its own accord, rather is actively driven together by the -Λg_uv term of large-scale space, principally represented by the accelerated expanding large-scale voids about this visible matter, as in the sponge analogy. The positive sign remains, but is no longer representative of active attraction among visible matter. The term 8πGT_uv can represent the cosmic web among the large-scale voids, and is some 5% of the mass of the universe, where the cosmological term now represents the remaining 95% (again, conventionally dark matter and dark energy).

The reason this 8πGT_uv term was made negative earlier was to emphasize that even at the smaller scales, this term represents space among this matter at this level as also expanding; all space is said to expand (or trying to expand and restrained by the large-scale space, as discussed), but smaller scale space was said to expand less than large-scale space -- the large-scale voids are observed to expand faster than the space among the cosmic web consisting of galactic superclusters, which also expands; only the space below galactic superclusters does not expand perhaps because of the incoming effect from large-scale space, interpreted conventionally as dark matter when adjacent to matter. [2]-[4]

Ultimately, all that exists is space and the energy it contains; elementary particles are zero-dimensional and take up no space.

As long as this is kept in mind, the 8πGT_uv term may remain positive, but understood as not actively positive or attractive. All gravitation is said to be activated ultimately by the reinterpreted -Λg_uv term now on the right, the driver side of Equation (1a). Again, Equation (1a) is the conventional mathematics of general relativity, but may be interpreted that gravity is fundamentally repulsive rather than attractive so that certain benefits may be obtained as mentioned recently.

Note the role reversals of the two terms on the right of Equation (1a). The mathematics of general relativity is unchanged, but the interpretation changes from fundamentally attractive gravity to fundamentally repulsive gravity.

Which term on the right in Equation (1a) has the greater effect?

This depends on the scale being considered. When viewed on the large scale, the cosmological constant term dominates,

-Λg_uv.

This might be unexpected because the cosmological constant Λ is so small (about 10^-52 m^-2). But accelerated expansion is occurring universe wide, and the ratio of mass to size was shown to be

m/r^2 = A/G ................................................... (2)

where A ≈ 10^-14 m/s^2 is the calculated acceleration of the universe. [1] [Note 1] This implies that a large-scale void adjacent to the cosmic web of matter vastly overwhelms the matter, because such a void is 10 to 100 times the size of this web thickness. Such expanding masses have inertia and press on the web from all sides. For instance, when the size of the universe is substituted into Equation (2), the mass value is comparable to the conventional estimate of some 10^50 kilograms. As mentioned above, virtually all the mass/energy of the universe is from space, because fundamental particles are zero-dimensional and take up no space. This is why the cosmological constant term is said to dominate at the larger scales. You would think it also dominates the smaller scales as well under this consideration, but not so.

This is because the large-scale voids on each side of a sheet or string of matter have gravity vectors that oppose one another and practically cancel on engaging matter at smaller scales (see Figure 1).

The vectors in Figure 1 indicate the accelerated expansion of the voids; these voids have mass in proportion to the square of their radii from Equation (2). Where vectors point toward one another, this large-scale force effect tends to cancel; this is why the large-scale -Λg_uv term diminishes in effect at smaller scales within the cosmic web, and the more local term on the right in Equation (1a), 8πGT_uv, dominates at smaller scales. It has an implied positive sign, but is proposed to not be actively attractive; all active driving is due to the -Λg_uv term which represents the accelerated expansion of the universe due to gravity itself, and not an ad hoc structural cosmological constant as conventionally interpreted.

In Figure 2,

Gmn/r^2 and 8πGT_uv have similar roles, as do

G(-m)(n)/r^2 and -Λg_uv.

Note the positive passive (empirical) nature of the first pair, and the negative active (fundamental) nature of the second pair.

[1] (2) An explanation of dark matter and dark energy from unmodified Newtonian gravity* | LinkedIn

[2] Does space ever stop expanding, or trying to, regardless of scale? | LinkedIn

[3] Why does matter clump together? | LinkedIn

[4] (Dark matter as space restrained from expanding | LinkedIn

[Note 1] Equation (2) was developed from the Newton form on the right in Figure 2. [1]