On Dirac's dimensionless constants, large number hypothesis and variable G
v. 6 n. 28
NOTICE
A reader comment in the previous issue led to this Letter. [1]
When the electric and gravitational forces are compared, scale is not normally accounted for. For instance, the gravitational force is commonly given by
F_g = Gmm/r^2
where m can be the mass of the electron, and the electric force by
F_e = kee/r^2,
where e is the charge of the electron, and r in each case commonly cancels when a ratio is taken,
F_e / F_g ≈ 10^39.
However, when r is sufficiently large in the F_g case Newton's gravity no longer holds without the assumption of dark matter and dark energy, which are not accounted for in conventional physics. A conventional contention is that this dark matter is either some unknown particle or that gravitation (Newton's or Einstein's) does not fully account for the situation; dark energy is even less certain conventionally. The assumption of the cancellation of parameter r is questionable. At what distance r does the ratio actually hold? It is not physically correct to cancel parameter r.
Another common term for the "unreasonable difference" in these forces is the "hierarchy problem." [2][3]
Dirac contended that the gravitational constant, G, declines with the age, or size, of the Universe. It is not clear whether he also contends that the number of particles of visible matter increase with the age of the Universe, or the total mass of the Universe is increasing; dark matter and dark energy were not prominent at the time. [4][4a]
If Dirac's contention is that the total mass of the Universe increasing, this would contradict the Law of conservation of (mass-)energy: energy cannot be created or destroyed but only converted from one form to another. It is more conservative in this regard to suggest that total energy remains constant since the instant of creation and that dark mass-energy is being converted to particulate or visible matter plus the kinetic energy of the Universe. [Note 1]
But, still, what is the origin of the total mass energy after creation of our Universe, since the "Law" states that energy cannot be created. This is discussed in terms of speculations prior to the beginning. [5]
Variable G is contentious because principal theories assume constant G. However, this constant said to have cosmic significance is measured in a very primitive manner in the laboratory on the surface of the Earth with two close-together masses and various means of measuring any supposed gravitational attraction between them to only a few decimal places. It is not practical to assume a constant G with these experiments. A possibly more accurate means has been suggested with cosmic distances. [6]
Variable G is also supported by the dark energy survey, DESI, where preliminary evidence indicates that dark energy was more prevalent in the early Universe. This suggests that the potential energy in space is being converted to the kinetic energy of the accelerated expanding Universe, a speeding up and a likely increase in the Hubble constant (velocity per distance) -- and complementary reduction of the gravitational constant. [7][8]
The Hubble constant, H_o, is observed to vary from about 67 to 73 km/s per Mpc from early to later Universe respectively, which may be interpreted as the acceleration of the Universe, rather than any "crisis in cosmology." [9]
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All told, then, it is not unreasonable to consider more closely a variable G, and to refine theories accordingly, refocusing experiments so that one does not, so to speak, look for a dropped coin in the dark only under a lamp post.
[2] (4) RESHUFFLING THE HIERARCHY PROBLEM: Why is gravity so weak regarding the other forces? | LinkedIn
[4] An original timeworn video of Dirac's blackboard lecture on this topic. Regardless of the poor quality of the recording it is to be preferred to any other oral or written presentation because of the detailed treatment of the concept (other than any formal paper by him, i.e., see [4a]. Note that an actual value for the decline of G is predicted, too small for any Earth-based laboratory experiments and not commonly mentioned by others: https://www.youtube.com/watch?v=FTeD2cmoj78
[4a] P.A.M. Dirac, A new basis for cosmology, St. John's College, Cambridge (Revised 29 December 1937). This reference is mentioned but not elaborated in https://www.youtube.com/watch?v=_6F1dvP50Yk
[NOTE 1] The total mass of the Universe from a composite of various specialties is conventionally estimated to be some 10^53 kilograms, which is not far from the theoretical calculation of these Letters from the scale invariant, m/r^2 = A/G, where r is the conventional estimated radius of some 93/2 billion light years and proposed acceleration of the Universe A≈10^-14 m/s^2. [9]
Related material:
A brief video in "Unzicker's Real Physics": https://www.youtube.com/watch?v=_6F1dvP50Yk
Quantitative written overview but omitting Dirac's prediction for the amount G could decline and other details: https://en.wikipedia.org/wiki/Dirac_large_numbers_hypothesis
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