The inertia of space

v. 5 n. 23

At the risk of belaboring the point in the previous [1] and other articles hypothesizing the identity of gravity and acceleration (of the Universe), the following is an attempt to qualitatively illustrate how this repulsive gravity at the largest scale can seem to be attractive at the smaller scales. Consequences of this hypothesis have been discussed, i.e., [2] through [8].

The Universe is observed to be accelerating, and this acceleration must have been occurring before the condensation of matter well after the beginning. But the question, acceleration of what? Not condensed matter, at least near the beginning. Inertia is the resistance to acceleration. Acceleration and inertia are normally paired in physics. Conventionally, there is inertial mass and gravitational mass. Something, something physical, must have been accelerating before the presence of condensed matter. It might be seen below that inertial and gravitational mass could not only be equivalent -- from the equivalence principle and basis of general relativity -- but also identical in the case of the accelerating Universe. Then inertial mass and gravitational mass would be different terms for the same thing. While "equivalence" is conditional, "identity" is unconditional.

The conventional notion of a fundamentally attractive gravity has the weight of common human experience from before written history by viewing the motion of objects primarily confined to the Earth, then quantitatively within the Solar system in the past few hundred years, and more recently regarding the galactic scale and above where the notion of universal attractive gravity continues without question. At the higher scales, other terminologies, such as dark energy, and other mysteries are added to physics, although there are various attempts at modified gravity theories beyond general relativity.

Viewing gravity as exclusively attractive regardless of scale raises mysteries such as dark energy, dark matter, the cosmological constant problem, inability to derive elementary particle masses, infinities in quantum equations requiring renormalization, the effective absence of gravitation in the standard model of particle physics, and absence of a satisfying physical explanation of gravitation.

If a given volume of space is expanding, is expansion the only characteristic? Is expansion occurring at the same rate in all of this given volume? The answers are not obvious in a space that is not strictly mathematical, a space that has mass-energy, mass. In such a space the variation in mass at various scales becomes paramount, along with resistance to acceleration at different scales, inertia. "Space" here for the time being means the Universe without condensed matter. This is contrary to the conventional assumption where space is considered everywhere the same (homogeneous and isotropic, arbitrary mathematical assumptions to simplify artificial constructs, which by and large excludes time, everywhen, for even greater simplicity and unreality).

While not conventionally taken into account, it has been discussed in these Letters that the space of general relativity has mass, being equivalent to the pure gravitational field. [9] In the case of the Universe, this field at large is changing, accelerating, implying kinetic energy from potential energy, also implying mass-energy, mass. And this mass, has inertia, even if no condensed matter is apparent; this is the equivalence of inertial and gravitational mass at the root; condensed matter is not necessary for there to be inertial effects. This point cannot be overemphasized.

No two volumes of real space are identical. Take a cookie-cutter to rolled out dough. The punched-out material segments appear to be the same, but weighed carefully enough, there will always be a difference. Regardless of the materials and manner of duplication, there will always be a difference, down to the quantum scale and uncertainty principle, where virtual particles have a range of masses or lifetimes. [10] These real volumes are exaggerated in the two-dimensional representation in Figure 1. Within this given volume of space, are an infinite number of smaller volumes of real (non-mathematical) space, each of which is expanding. Assuming a series of finite smaller volumes, what is the effect in a given sub-volume?

It would seem obvious, but is it really? Recall each section has a certain mass, and sub-volumes are not the same in each, beginning with the widely variable virtual particle scene; recall also that

m ∝ r^2

where fundamentally mass is proportional to size. [11] One sub-mass will press against neighbors because each is undergoing accelerated expansion and has inertia; for adjacent sub-volumes the difference in inertia is marginal, but the effect increases with increasing volume. Over time and a large enough scale there could be pronounced gravitational instability because of these inertial differences from one aspect of the scale to the other, without even considering the presence of any condensed matter. Any sufficiently large pure gravitational field is seen as unstable, [12] (just as the quantum vacuum is unstable, active) and an accelerated expanding field would be more so. Differences in inertia throughout the field also increase with the subsequent introduction of condensed matter.

Randomly sprinkle condensed matter, fundamental particles, into the mix of Figure 1, symbolizing the condensing of matter in the real Universe at a certain time after the beginning. As the Universe is accelerating, in which direction will one of these particles (labeled a in Figure 2) move relative to the sub-volume containing it?

It might be said that the particle imbedded in any one sub-volume moves away from the volume's center of mass, as the entire sub-mass undergoes, or attempts to undergo, accelerated expansion. The "attempts" qualification is made because the inertia of neighboring sub-masses might not permit much expansion in the indicated mass housing the particle. [13] There are hints of "dark matter" here surrounding the particle that is not different in kind from the volume under consideration (the sub-volume containing the particle). The space containing the particle might be "compressed" by the expansion and inertia of surrounding sub-volumes, suggesting a greater mass density of the space about the particle than the mass of the particle per se would suggest.

In a massless mathematical (conventional homogenous and isotropic) space, there would be no such internal inertia tending counteract free expansion. For example, if a large volume of space is finite (with nothing or no resistance at the outer regions), the outer regions would be freer to expand than the innermost regions; there is no mass to counteract the mass of the outermost regions and they may more freely expand, while the inner regions would be more constrained, compressed, have greater density.

Now, in Figure 2 consider an adjacent sub-volume also containing a sub-atomic particle (labeled b), undergoing a similar situation. In which direction will the particles move, toward one another, away, or some other direction, as all sub-volumes undergo accelerated expansion?

Note in the total space in this figure that there is less expanding space between than about the particles. The total space about the particles is greater than the space between them, and there will be more relative expansion and inertia than between the particles, so that overall, the particles would appear to be attracted to one another, even though the exclusive physical mechanism is repulsive. An analogous situation occurs in the formation of a chemical that has been catalyzed to form a common sponge; the forming mechanism is exclusively repulsive, but material appears to be attracted among the voids at all scales from any microscopic region to the edges of the finished product. [14]

In real space this effect is not readily apparent when acceleration is low (in the case of the Universe acceleration is seen as only about 10^-14 m/s^2), [15] but in a rapid acceleration condition such as with exploding dynamite in an atmosphere, there will be a (compressive) shock wave in the outer aspect that tends to resist expansion; this resistance might be analogous to said inertia at larger volumes of space tending to affect particles a and b in Figure 2 as the Universe undergoes accelerated expansion. Degree of acceleration is inconsequential, any acceleration suggests a similar outcome; it is just that the marginal acceleration of the Universe is so out of normal human experience that the mechanism is not given due attention; over the scale of the known Universe, however, the so called "cosmological constant problem" is noticeable, enough to require a physical modification to the mathematical theory of general relativity, and possibly account for the other mysteries mentioned in the introductory remarks. The inertial effect of space itself is paramount and should be recognized as such.

The inertia of space is not recognized as such because it is considered by a different name, the cosmological constant, which is a minor correction to general relativity for large scale considerations, a bothersome afterthought. But this inertia could be gravity itself at its root -- the "tail (cosmological constant) wagging the dog (general relativity as originally expressed). This inertia of space could also not be recognized as gravity itself because it is fundamentally repulsive; and "of course, everyone knows from time immemorial that gravity is always attractive." The recognition of the identity of the inertia of space and gravitation also closes on the question of why gravity is such a weak effect in comparison with the other forces; the acceleration of the Universe could only be marginal as mentioned yet hypothesized as identical with gravity at its root.

In the dynamite situation it is more readily seen how the volume of air within the shock wave is compressed in comparison with the air the shock wave has not yet reached. Similarly, the space in the early Universe could be more compressed (more potential energy) than in the later Universe, which could have more kinetic energy.

So, in which direction is the Universe accelerating?

In this scene, acceleration of the Universe with respect to the particles a and b in Figure 2 would be for them to accelerate toward each other, along with condensed matter in general at small enough scales, so that gravity (as hypothetically identical with this acceleration) would appear attractive in this case. And since it is hypothesized that acceleration of the Universe and gravity are identical, gravity might be fundamentally repulsive, but only apparently attractive at the smaller scales or when the particles are sufficiently close to begin with.

On large enough scales -- galactic superclusters and above -- the Universe is observed to accelerate away from condensed matter in the form of clusters of galaxies, i.e., space is observed to be undergoing accelerated expansion among clusters of galaxies. This accelerated expansion can be thought of as simultaneously tending to "compress" or stabilize clusters of galaxies, which do not take part in the Hubble expansion. Such "compression" might be termed "dark matter," while the accelerated expansion is commonly termed "dark energy." The inertia at the larger scales of real space is greater than that at the smaller scales (taking the inertia of 93 billion light years extent of space into account) and could tend to hold clusters of galaxies in place so that individual galaxies in the cluster remain in the cluster.

In this scene, the direction of acceleration of the Universe and gravity -- whether gravity appears attractive or repulsive -- depends on scale. As originally conceived, neither Newtonian gravity nor general relativity accounted for scale and the inertia of space.

[1] Calibrating general relativity | LinkedIn

[2] (1) Including gravity in unification (GUT) and Planck scales | LinkedIn

[3] (1) Is gravity fundamentally attractive or repulsive (a retrospective)? | LinkedIn

[4] (1) An explanation of early galaxy formation | LinkedIn

[5] (1) Are voids in space empty or consist of undetected matter? | LinkedIn

[6] (1) Testing whether normal particles are gravitational sources or sinks | LinkedIn

[7] (1) An approach to the quasar alignment puzzle | LinkedIn

[8] (1) Small to large scale locality | LinkedIn

[9] A. Einstein, Relativity, Crown, New York, 1961, p. 155

[10] (2) Virtual particles as the "fabric of space" | LinkedIn

[11] Universal relationship between mass and size | LinkedIn

[12] Is matter made from space? | LinkedIn

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

[14] (1) Big Bang to Big Sponge | LinkedIn

[15] (1) Importance of a value for acceleration of the Universe | LinkedIn

Cover image: https://stock.adobe.com/search?k=direction