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European Journal of Applied Sciences – Vol. 12, No. 4

Publication Date: August 25, 2024

DOI:10.14738/aivp.124.17371.

Eriksson, J.-T. (2024). Dirac’s Variable Gravitational Parameter G Offers a Link Between Gravity and Quantum Mechanics.

European Journal of Applied Sciences, Vol - 12(4). 217-232.

Services for Science and Education – United Kingdom

Dirac’s Variable Gravitational Parameter G Offers a Link Between

Gravity and Quantum Mechanics

Jarl-Thure Eriksson

Åbo Akademi University, Åbo, Finland

ABSTRACT

The Standard model has successfully depicted the universe from a tremendous

number of astronomical observations. However, the model faces several

problems, it does not provide theoretical explanations for the origin of the Big

Bang, dark energy or dark matter. The theory behind this article, CBU for

Continuously Breeding Universe, was developed according to known principles of

physics. The universe is an emerging system, which starts from the single

fluctuation of a positron-electron pair. Expansion is driven by the emersion of new

pairs. The gravitational parameter G is inversely proportional to the Einsteinian

curvature radius r. The Planck length lP and Planck energy WP are dependent of

the curvature and accordingly by the size of the universe. As a measure of the

change of the state between a stationary body (G0) and a moving body (G1) the

ratio G1/G0 unites the Special theory with the General theory of relativity.

Relativity means that the motion of a body always is relative to another body

according to the ratio of their G values. The introduction of different individual Gs

implies symmetry in the twin paradox, leading to the first credible solution to the

problem.

Keywords: Special relativity, general relativity, quantum mechanics, Planck units, twin

paradox

INTRODUCTION

Theories about the origin and evolution of the universe have varied over the years, but the

leading paradigm has remained the same: The Big Bang (BB) theory, first published by the

Catholic priest Georges Lemaitre, also a recognized astronomer, [1]. The idea of a universe

undergoing continuous expansion was based on Edwin Hubble's earlier observations. The

label Big Bang was a sarcastic suggestion made by the well-known British astronomer Fred

Hoyle, who strongly opposed to the theory. Here the Standard model will be used referring to

the Big Bang approach.

The cosmic microwave background radiation (CMB) is the main reason for the success of the

Standard model. The homogeneous distribution of a sudden occurrence of EM radiation in all

directions, about 380,000 years after the Big Bang is considered the best evidence of an

energy relic left over when the rest of the energy was bound to matter at the "last scattering"

moment.

However, there are some serious problems with the Standard model. The origin of the energy

at the Big Bang instant is an open question. To explain the expansion of the universe, one has

had to introduce an extra factor into Einstein's general relativity equations, the cosmological

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European Journal of Applied Sciences (EJAS) Vol. 12, Issue 4, August-2024

constant . The constant represents what is known as dark energy. This is an unscientific way

of doing physics, when you do not understand a phenomenon, you invent a label and start

working as if there is a theory. One should always be able to explain the physics behind and

develop a reasonable understanding. The same goes for the concept of dark matter, which

seemed necessary to explain the strange rotation patterns of the galaxies. But in an

accelerating universe, the Coriolis effect offers a plausible solution to the problem.

Furthermore, there is a physical explanation for the term "dark matter" in the energy density

equation. It has an exact match with the kinetic energy due to the rate of expansion. A brief

analysis is presented in Section 4.2.

In 1937, the renowned British physicist Paul Dirac published an article in Nature entitled The

cosmological constants, [2]. In the article, he developed the hypothesis of large numbers. In

the background there is the coincidence of a large ratio between EM forces and gravitational

forces, typically 1040 and its squared value 1080 which also stands for the Eddington number,

the estimated number of protons in the universe, i.e. the energy content. However, the

response was sceptical, as the theory offered very little to elaborate on. Dirac published a

more detailed paper in 1974, [3], where he presents the general ideas of Multiplicative

Creation and Additive Creation. He saw these as different options not both combined. The

former refers to an inherent production of matter and the latter implies a continuous influx of

new matter. In this article we will show that a combination of both takes place, the universe

grows due to the influx of electron-positron pairs caused by quantum fluctuations. Protons

and antiprotons are "swinged out" from the black holes in the centres of the galaxies, a

process similar to the creation of electron-positron pairs inside the universe. Protons,

electrons and their antiparticles are generally considered the only stable elementary particles

available.

The objective of this study is to show that by admitting G to change we solve many of the

conflicts that burden the present paradigm. This precondition was also stressed by Dirac. The

change rate is very slow, typically dG/dt/G = 2,2·10-18 1/s = 7,0·10-11 yr-1. There are several

recent studies, that come close to the limit, Benvenuto et al. 2,5·10-10 yr-1[4], Biesiada et al.

4,1·10-10 yr-1 [5] and Bing Sun et al. 10-9 yr

-1 [6]. Moreover, using interpretations of an

erroneous theory (the Standard model) weakens the reliability of the results. We cannot even

measure the current G with an accuracy better than 5 decimal places. The benefits of

accepting a variable G are so compelling that we have to accept the uncertainty of studies

performed. We will find that Albert Einstein in his paper on the cosmological constant derived

the radius of curvature RE (his designation). If aware of the expansion of the universe he could

have foreseen that G decreases with increasing RE, Section 2.2.

It is important to realize that G is not a gravitational constant, but a measure of the curvature of

space, curvature radius RE (the interpretation of Einstein).

CREDIT TO EINSTEIN

First Version of W = mc2

In 1905 Albert Einstein published a series of articles with a ground-breaking effect on physics.

The Brownian motion paper rendered him the Noble Prize in 1921. But the most significant

was that “On the electrodynamics of moving bodies”, [7], that is the article on Special

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Eriksson, J.-T. (2024). Dirac’s Variable Gravitational Parameter G Offers a Link Between Gravity and Quantum Mechanics. European Journal of

Applied Sciences, Vol - 12(4). 217-232.

URL: http://dx.doi.org/10.14738/aivp.124.17371

relativity. Einstein uses very sparsely references, but here he refers to Lorentz’s theory of the

electrodynamics of moving bodies, [8]. The substance is almost the same, but Einstein is

clearer and more goal-oriented in his presentation. A most significant contribution is given at

the end of Einstein’s paper, where he in principle defines the mass-energy analogy: E= mc2.

In Einstein’s thought experiment an electron is accelerated from 0 to a velocity v, the force

required for the acceleration is

F = eE = me

dv

dt

d(γv)

dv = meγ

3

dv

dt , (1)

where d(γv)

dv

= γ3 is obtained from Lorentz, [8], e and me are the charge and the mass of the

electron respectively, E is the electric field causing the acceleration and

γ =

1

√1 −

v

2

c

2

. (2)

The conservation of momentum requires that

eEdt = meγ

3dv. (3)

By multiplying with dx/dt we obtain the energy equation

dW = eEdx = meγ

3

dx

dt dv = meγ

3vdv. (4)

Integration of the last term leads to the equation

W = mec

2

(γ − 1). (5)

The equation applies to any mass m and it has been accepted as a universal expression for the

kinetic energy of a body the velocity of which has been changed to v relative to a reference

point. Eq. (5) also indicates that the body contains the energy W = mc2. Einstein only realized

this in an article later the same year, [9].

Eq. (5) forms the core of the Special Relativity theory. A body accelerated to a velocity v gains

extra energy, but in its own coordinate system the energy is the same. The laws of quantum

physics on the atomic and molecular level applies independently of the state of motion. But in

relation to the environment the body has changed its state. This has puzzled scientists over

the years. Obviously, acceleration is not related to the new state, the time period of

acceleration can be arbitrary short compared to the travel period in, say, the Twin Paradox,

see Section 5. The state shift must be something else.

We suggest a hypothesis that the state of motion is connected to the local curvature

parameter G according to the following relation: