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5D Space-Time-Energy World-Universe Model is a unified model of the World built around the concept of Medium, composed of massive particles (protons, electrons, photons, neutrinos, and dark matter particles). The Model provides a mathematical framework that enables precise calculation of medium-bound physical parameters: Hubble’s parameter, intergalactic plasma parameters, temperature of microwave background radiation and the rest mass of photons. This paper aligns the World-Universe Model (WUM) with the theoretical framework developed by Prof. P. S. Wesson, albeit assigning a new physical meaning to the fifth coordinate. In the World-Universe Model, 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.

We can’t solve problems by using the same kind of thinking we used when we created them.

Albert Einstein

WUM is proposed as an alternative to the prevailing Big Bang Model of standard physical cosmology. The main difference is the source of the World’s energy. In the present work, we focus on the physical meaning of the fifth coordinate and provide a brief overview of WUM.

World-Universe Model (WUM) utilizes the following principles:

Variable gravitational parameter. This hypothesis was proposed by Paul Dirac in 1937 [

Continuous creation of matter. Hoyle and Narlikar in 1964 offered an explanation for the appearance of new matter by postulating the existence of what they dubbed the “creation field”, or just the “C-field” [

According to WUM, the World is a 3-sphere that is the surface of a 4-ball Nucleus of the World. The 4-ball is expanding in the 4-dimensional Universe, and its surface, the 3-sphere, is likewise expanding. The total surface energy of the 4-ball is increasing as it expands, thus creating new matter in our 3-sphere World.

Supremacy of matter was postulated by Albert Einstein: “When forced to summarize the theory of relativity in one sentence: time and space and gravitation have no separate existence from matter”.

Existence of the Medium of the World was 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 1846. 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 [

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.

Mach’s principle. A very general statement of Mach’s principle is “Local physical laws are determined by the large-scale structure of the universe”.

Fifth dimension. In 1983, Paul S. Wesson suggested that a fifth dimension might be associated with rest mass via

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.

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” [

Fundamental parameters and units. In accordance with ME, there are two measurable physical characteristics for electromagnetism and gravitoelectromagnetism: 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.

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.

In Section 2 we propose a new physical meaning of the fifth coordinate and give a short summary of WUM. In Section 3 we calculate the parameters of Low Density Intergalactic Plasma that is part of the Medium. Based on the plasma parameters, we calculate Temperature of the Microwave Background Radiation and the rest mass of photons. In Section 4 we point out on decisive role of the Medium of the World composed of massive particles in 5D Space-Time-Energy WUM.

Let’s proceed to discuss the origin, evolution, and parameters of the World speculated by the WUM in light of the Space-Time-Matter theory developed by Paul S. Wesson.

The World was started by a fluctuation in the 4-dimensional Universe, and the Nucleus of the World, which is a 4-ball, was born. The Nucleus antipode length (the furthest distance between any two points of the Nucleus 3-sphere) at the Beginning was equal to a.

The Nucleus has since been expanding through the Universe so that the antipode length R is increasing with speed

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

Let’s introduce a dimensionless time-varying quantity

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. The WUM is based on Maxwell’s equations, and McCullagh’s theory [

The (almost) constancy of the universe fundamental constants, including Newtonian constant of gravitation G, is now commonly accepted, although has never been firmly established as a fact. All conclusions on the constancy of G are model-dependent [

A commonly held opinion states that gravity has no established relation to other fundamental forces, so it does not appear possible to calculate it indirectly from other constants that can be measured more accurately, as is done in some other areas of physics. The World-Universe Model holds that there indeed exist relations between all Q-dependent, time varying parameters: G, H (Hubble’s parameter), R (Size of the World),

Recall the well-known Friedmann equation for the critical energy density of the World

Equation (2.2.1) can be rewritten as

where

Let’s introduce a length parameter

In our Model,

which is equivalent to:

where

According to the Equation (2.2.6), G is proportional to

that

the gravitational parameter G equals to:

and from (2.2.2), the critical energy density equals to:

where

Calculating the value of Hubble’s parameter

which is in good agreement with

calculated and measured parameter

Parameter Q defines both the size and the age of the World measured in terms of a and

In frames of WUM the parameter G can be calculated based on the value of the energy density of the Medium of the World

where a dimension-transposing parameter P equals to:

Then the Newton’s law of universal gravitation can be rewritten in the following way:

where we introduced the measurable parameter of the Medium

cient G; and gravitoelectromagnetic charges

and

and the impedance of the Medium

We apply the following transformation to Maxwell’s equations for the gravitoelectromagnetism: multiply “mass” by the parameter P and divide the impedance and gravitomagnetic parameter of the Medium by the same parameter P. As a result of this transformation:

All parameters of the gravitoelectromagnetic field have dimensions of length and time; “mass” dimension has disappeared;

All physical parameters of the World measured in terms of a and

Absolute size and age of the World equal to Q;

The gravitoelectromagnetic charge has a dimension of “area”;

The impedance of the Medium

It follows that measuring the value of Hubble’s parameter anywhere in the World and taking its inverse value allows us to calculate the absolute age of the World. The Hubble’s parameter is then the most important characteristic of the World, as it defines the Worlds’ age.

The second important characteristic of the World is the gravitomagnetic parameter

Taking its inverse value, we can find the absolute size of the World. We emphasize that the above two parameters (

In WUM, time and space are closely connected with the Mediums’ impedance and gravitomagnetic parameter. It follows that neither time nor space could be discussed in absence of the Medium. Matter, then, is primary to time and space. It follows that the gravitational parameter G can be introduced only for the World filled with matter, as Einstein has postulated.

While in our Model Hubble’s parameter H has a clear physical meaning, the gravitational parameter

theory of general relativity.

Amount of additional surface energy of the 4-ball Nucleus provided by the Universe

and the energy density of the Medium

The total amount of the surface energy at cosmological time

The energy density of the World

and equals to

All physical parameters under consideration depend on Nucleus diameter

According to Overduin and Wesson: “a fifth dimension might be associated with rest mass via

In WUM, the Medium of the World has the following parameters:

The gravitomagnetic parameter

The energy density

The 3-dimensional cubic hyperarea of a 3-sphere

In our opinion, the fifth dimension is associated with these parameters via

where

The physical laws we observe appear to be independent of the fifth coordinate due to the very small value of the dimension-transposing parameter

One way to prove the existence of the fifth dimension is direct measurement of truly large-scale parameters of the World: Gravitational, Hubble’s, Temperature of the Microwave Background Radiation. Conducted at various points of time, these measurements would give us varying results, providing insight into the 5D nature of the World. Unfortunately, the accuracy of the measurements is quite poor. Measurement errors far outweigh any possible 5D effects, rendering this technique useless in practice. To be conclusive, the measurements would have to be conducted billions of years apart.

Let’s consider an effect that has indeed been observed for billions of years, albeit indirectly. Take the so- called “Faint young Sun” paradox. One of the consequences of WUM holds that all stars were fainter in the past. As their cores absorb new matter, the size of macroobjects

The proposed approach to the fifth dimension is in agreement with Mach’s principle: “Local physical laws are determined by the large-scale structure of the universe”. Applied to WUM, it follows that all parameters of the World depending on Q are a manifestation of the fifth dimension of the World. The Medium of the World composed of massive particles is the manifestation of the metric depending on

In this Section we prove that the Medium of the World consists of massive particles, including photons. We find parameters of the Low Density Intergalactic Plasma, which allow us to calculate the Temperature of the Microwave Background Radiation and the rest mass of photons.

In our Model, the World consists of stable massive elementary particles with lifetimes longer than the age of the World. Protons with mass m_{p} and energy _{e} and energy

Low density intergalactic plasma consisting of protons and electrons has plasma frequency

where

Let’s assume that

tons and electrons are then proportional to

mula calculating the potential energy of interaction of protons and electrons contains the same parameter

we substitute

The above value is in good agreement with ordinary matter’s share in the World

From Equation (3.1.2) we obtain the value of the lowest radio-wave frequency

Substituting size of the World

A. Mirizzi, G. G. Raffelt, and P. D. Serpico found that the mean diffuse intergalactic plasma density is bounded by

The black body spectrum of Microwave Background Radiation (MBR) is due to thermodynamic equilibrium of photons with low density intergalactic plasma consisting of protons and electrons.

where

Thus calculated value of

At the Beginning of the World, the extrapolated value of

Note that

Photons with energy smaller than

where

The calculated mass of an axion is in agreement with

According to special relativity, energy of an axion

Taking into account the dispersion relation for plasma:

and the value of phase velocity

we calculate moving axion energy

where ν is photon frequency. In our Model, the total energy of a moving particle consists of two components: rest energy and constituent energy. A particles’ constituent energy is the response of the Medium to the particles’ movement.

A photon is then a constituent axion with rest energy

The higher the photons’ energy, the closer its speed approaches c. But the fact that axions possess non-zero rest masses means that photons can never reach that speed. It is worth to note that the speed of light in vacuum, commonly denoted c, is not related to the World in our Model, because there is no vacuum in it. Instead, there is the Medium of the World consisting of elementary particles.

J. M. Overduin and P. S. Wesson postulated that “Metrics which do not depend on

The World-Universe Model supplies the fluid that J. M. Overduin and P. S. Wesson have predicted: it is, in fact, the Medium of the World. According to WUM, empty space does not exist; instead, the World is filled with Medium that consists of massive particles: protons, electrons, photons, neutrinos, and dark matter particles. The inter-galactic voids discussed by astronomers are in fact examples of the Medium in its purest. Consequently, the Medium of the World as described by WUM can serve as further evidence in favor of the fifth-dimensional view of the World.

5D Space-Time-Energy World-Universe Model is the unified model of the World around the concept of Medium that successfully describes all of the primary parameters and their relationships. The Model allows for precise calculation of values that is only measured experimentally earlier: Hubble’s parameter, low density intergalactic plasma parameters, temperature of microwave background radiation and the rest mass of photons. While the Model needs significant further elaboration, it can already serve as a basis for a new physics proposed by Paul Dirac in 1937 and Paul Wesson in 1983.

I am very grateful to Prof. Paul S. Wesson for the development of Space-Time-Matter theory. Many thanks to Pete Carroll, William Straub and Nainan Varghese for our stimulating correspondence; Felix Lev and my son Ilya Netchitailo for valuable discussions.

Vladimir S.Netchitailo, (2015) 5D World-Universe Model Space-Time-Energy. Journal of High Energy Physics, Gravitation and Cosmology,01,25-34. doi: