5D WORLD – UNIVERSE MODEL SPACE–TIME–ENERGY

In 1983, Paul S. Wesson developed 5D Space-Time-Mass theory that associates the fifth dimension with rest mass. The gravitational constant serves as the dimension-transposing parameter. This paper puts the World-Universe Model (WUM) onto the theoretical basis developed by Prof. Wesson, with the following modifications: the fifth dimension is associated with the total energy of the Medium of the World, and the gravitomagnetic parameter of the Medium serves as the dimension-transposing parameter. The Medium of the World composed of massive particles (protons, electrons, photons, neutrinos, and dark matter particles) is the manifestation of the 5D Space-Time-Energy WUM.


INTRODUCTION
World -Universe Model (WUM) utilizes the following principles: Variable gravitational parameter. This hypothesis was proposed by Paul Dirac in 1937 [1].
Continuous creation of matter. A similar idea was proposed by Paul Dirac in 1974 [2]. According to WUM, the World is finite and is expanding inside the Universe which serves as an unlimited source of energy that continuously enters into the World.
Existence of the Medium of the World stated by Nikola Tesla: "All attempts to explain the workings of the universe without recognizing the existence of the ether and the indispensable function it plays in the phenomena are futile and destined to oblivion". Unique properties of the Medium were discussed by James McCullagh in 1839. He proposed a theory of a rotationally elastic medium, i.e. a medium in which every particle resists absolute rotation. This theory produces equations analogous to Maxwell's electromagnetic equations [3].
In WUM, the World consists of the Medium (protons, electrons, photons, neutrinos, and dark matter particles) and Macroobjects (Galaxy clusters, Galaxies, Star clusters, Extrasolar systems, planets, etc.) made of these particles. There are no empty space and dark energy in the WUM.
Decisive role of energy postulated by Nikola Tesla: "There is no energy in matter other than that received from the environment". Principal role of Maxwell's Equations (ME) that form the foundation of classical electrodynamics. The value of ME is even greater because J. Swain showed that "linearized general relativity admits a formulation in terms of gravitoelectric and gravitomagnetic fields that closely parallels the description of the electromagnetic field by Maxwell's equations" [4]. Hans Thirring pointed out this analogy in his "On the formal analogy between the basic electromagnetic equations and Einstein's gravity equations in first approximation" paper published in 1918 [5]. It allows us to use formal analogies between the electromagnetism and relativistic gravity. It is worth to note that the equations for Gravitoelectromagnetism were first published in 1893, before general relativity, by Oliver Heaviside as a separate theory expanding Newton's law [Wikipedia, Gravitomagnetism].
In accordance with Maxwell's equations for electromagnetism and gravitoelectromagnetism there are two measurable physical characteristics: energy density and energy flux density. For all particles under consideration we used four-momentum to conduct statistical analysis of particles' ensembles, obtaining the energy density as the final result.
Fifth dimension. In 1983, Paul S. Wesson suggested that a fifth dimension might be associated with rest mass via 4 = / 2 ∝ .
WUM follows this idea, albeit associating the fifth dimension with the parameters of the Medium of the World: the gravitomagnetic parameter and the total energy.
Fundamental parameters. Two Fundamental Parameters in various rational exponents define all macro and micro features of the World: Fine-structure constant α and dimensionless quantity Q . While α is constant, Q increases in time, and is in fact a measure of the Size and the Age of the World [6,7].
WUM is proposed as an alternative to the prevailing Bing Bang Model of standard physical cosmology. The main difference is the source of the World's energy. The Model was developed in [6][7][8][9][10][11][12][13][14]. A number of results obtained there are quoted in the current work without a full justification; an interested reader is encouraged to view the referenced papers in such cases.
In the present work we focus on the physical meaning of the fifth coordinate and provide an overview of WUM in a new light. In Section 2 we present the historical overview of five-dimensional spacetime theories. A paper "Kaluza-Klein Gravity" by J. M. Overduin and P. S. Wesson provides an excellent review of such theories. In Section 3 we propose a new physical meaning of the fifth coordinate and give a short summary of WUM in a new light.

COSMOLOGY
Let's proceed to discuss the origin, evolution, and parameters of the World speculated by the World -Universe Model (WUM) in a new light of the Space-Time-Matter theory developed by Paul S. Wesson.
WUM is built on two major assumptions: the universality of physical laws and the cosmological principle. The cosmological principle states that on large scale the World is homogeneous and isotropic. WUM envisions an expansion of the World.

THE BEGINNING AND EXPANSION
About 14.223 billion years ago the World was started by a fluctuation in the Universe, and the Nucleus of the World, which is a 4-ball, was born. The antipode length (the furthest distance between any two points) of the World's Nucleus at the Beginning was equal to where 0 is the classical electron radius. The Nucleus has since been expanding through the Universe so that the antipode length is increasing with speed equal to the gravitoelectrodynamic constant for cosmological time and has the length: The corresponding diameter of the Nucleus is: The 4-ball is the interior of a 3-sphere which is the World in our Model. The 3-dimensional cubic hyperarea of a 3-sphere is: The extrapolated energy density of the World at the Beginning is much smaller than the nuclear energy density [6,7].

THE CREATION OF MATTER
Recall the well-known Friedmann equation for the critical energy density of the World : where G is the gravitational parameter and is Hubble's parameter:

3.2.3
where is the gravitomagnetic parameter and = 2 3 is the energy density of the Medium.
According to Paul Dirac, the gravitational parameter is proportional to −1 and is decreasing in time as ∝ −1 [1]. It means that and are also proportional to −1 and are decreasing in time as = 2 3 ∝ −1 . In frames of WUM the critical energy density equals to [7]: where 0 is the basic unit of energy density The energy density of the World is inversely proportional to the Nucleus antipode length R: and equals to necessary for the flat World at any cosmological time . It is important to note that:  In our calculations we used the measurable Fundamental unit -energy density;  All physical parameters under consideration depend on Nucleus diameter which is in fact the fifth coordinate in our Model. The quantity Q is the dimensionless value of it. The physical meaning of this coordinate is discussed in the next section.

PHYSICAL MEANING OF THE FIFTH COORDINATE
According to P. S. Wesson: "a fifth dimension might be associated with rest mass via 4 = / 2 ∝ . The chief effect of this new coordinate on four-dimensional physics was that particle rest mass, usually assumed to be constant, varied with time".
In our opinion the fifth dimension is associated with the parameters of the Medium of the World: The physical laws we observe appear to be independent of the fifth coordinate due to the very small value of the dimension-transposing parameter / 2 . Notice that the precision is 7 times higher. We can now go back and calculate the value of G to equal = 6.67420(11) × 10 −11 3 −1 −2 3.4.7

Q-DEPENDENT, TIME VARYING PARAMETERS OF THE WORLD
Higher precision in measuring any of Q-dependent parameters yields higher precision for all of them. For a complete list of parameters dependent on Q , refer to Appendix A. We propose to introduce Q as a new fundamental parameter tracked by CODATA, and use its value in calculation of all Q-dependent, time varying parameters.

EXPERIMENTAL PROOF OF THE FIFTH COORDINATE
WUM gives the following explanation of the "Faint young Sun" paradox: all macroobjects of the World were fainter in the past. As their cores absorb new energy, the size of macroobjects and their luminosity are increasing in time ∝ 1/2 ∝ 1/2 (see equation 3.4.6) and ∝ ∝ correspondingly [6,7]. For example, taking the age of the World ≅ 14.2 Byr and the age of solar system ≅ 4.6 Byr, it is easy to find that the young Sun's output was 67.6% of what it is today. Literature commonly refers to the value of 70% [18].
Interestingly, Nikola Tesla shared the same opinion. In 1934, "Dr. Tesla disclosed that he has lately perfected instruments which flatly disprove the present theory of the high physicists that the sun is destined to burn itself out until it is a cold cinder floating in space. Dr. Tesla stated that he is able to show that all the suns in the universe are constantly growing in mass and heat, so that the ultimate fate of each is explosion" [19]. where is the mass of a proton, is the mass of an electron, is Boltzmann constant, α is the fine-structure constant, ћ is Dirac constant.