Introduction
In my holistic quantum cosmology – which can be studied in: part 1 – I show the existence of a physically smallest quantum of energy, corresponding to a smallest physical mass – called elementary mass. This elementary quantum I shall call a uniton (earlier identified as a graviton). This name shall show that it represents the smallest energy quantum in the actual Universe, and furthermore that it is a unity quantum, used to build matter, fields and the condition called 'vacuum'.
In the following I shall show that what is called vacuum is not an empty space in the proper sense of this word, but on the contrary 'filled' with unitons. The existence of this quantum uniton medium is a rediscovery of the universal ether (from Greek:, meaning air), which had already been introduced in archaic time as the fifth element. (The ether was the 'heavenly' element, the four others being earth, water, air and fire). This ether medium, which was supposed to be distributed over the whole Universe, was considered by all physicists to have a real existence, even if nobody knew what it was consisting of.
The ether – also called the light ether – was supposed to be the medium in which a. o. light travelled. Nobody could in a rational and physical way understand how for instance light could move from a star to us, if there were not 'something' to carry it from one point to another. Several outstanding physicists proposed 'mechanistic' models for the ether, especially models which were able to explain the different properties of light. If such a 'mechanical' light ether existed, it was the belief that it should be possible to show its existence by interference tests. As the Earth moves around the Sun, the possibility exists that the ether will cause an 'ether wind'. If the Newtonian laws for addition of velocities are valid for light, an 'ether wind' would produce different velocities of light, depending on whether the light moves in one direction or another, relative to the universal ether, which in itself defines an absolute frame of reference. According to the theoretical considerations, light moving in the same direction as the 'ether wind' should have another velocity than light moving in the opposite direction.
The uniton medium, which I describe, contains so much mass that the problems with the so-called 'dark matter' and 'missing mass' are hereby solved. In the following I shall show that if the uniton medium is described by the ideal gas model, I can, with certain assumptions, calculate that light phenomena are propagations of uniton oscillations, and that these oscillations are propagated with the velocity of light. What we call photons must be identified with 'oscillation quanta' in the uniton medium. By means of this uniton oscillation model it is possible immediately to understand and reply to the following question: What happens to a photon when it is absorbed by a molecule of matter? The answer is: The oscillation energy is transferred to the molecule, corresponding to the extra oscillation energy which a light source has transferred to the unitons.

The ether and Michelson-Morley's experiment
The Lorentz transformation
In 1887 a very famous experiment was conducted by Albert Abraham Michelson (1852-1931) and Edward Morley (1838-1923). (A. Michelson and E. Morley: "On the 'Relative Motion of the Earth and the Luminiferous Ether", The American Journal of Science, vol. 34, (1887)). By this experiment they wanted to demonstrate the possible influence from the ether on the light. They designed a so-called interferometer, which should show the possible interference effect of light rays. In the experiment, a light ray was divided in two, of which the first was forced to move in the same direction as the Earth moves, the other to move perpendicular to the first. Having travelled a certain distance, the two rays met again. If the ether had different effects on the two rays it would be possible to measure an effect of interference where the two rays met again. The result was surprising: No interference effect was measured. There are the following possible explanations to this result:

1. The ether moves along with the Earth, thus no 'ether wind' arises.
2. The velocity of light – as measured in the chosen frame of reference – is independent of the movement of the light source relative to the ether.
3. The 'ether matter' passes unhindered through the matter of which the Earth consists.
4. The geometrical conditions of the used device is dependent on the movement of the device relative to the ether.
5. Light does not act as waves in this experiment.
6. The ether does not exist.

1. All observers, moving relative to each other with constant velocity, will measure the same value of the velocity of light in 'vacuum', and this is independent of the movement of the light source.
2. The Maxwell equations shall be invariant, relative to a transformation from one inertial system to another.

The number of unitons and their distribution in the Universe
The basis for my holistic quantum cosmology are the quantum cosmological equations, uniting microcosmos with macrocosmos. The most important cosmological equation is the following:

(1)

where R is the actual extension of the Universe, N = 4.16 · 10⁴² is the ratio between the electrostatic forces and the gravitostatic forces of an electron and a positron.   r₀ is the elementary length, deciding the ratio between Planck's constant and the total energy/matter mass, M₀ of the Universe, multiplied by the light constant c₀.
Equation (1) can be written:

(2)

where m_u indicates the smallest physical mass in the actual universe, a mass I have called the elementary mass. This mass corresponds to a discrete quantum of energy, and is therefore denoted as a uniton.
We see from (2) that the number of unitons is given by

(3)

thus a very high number.

An important question is: How is this huge number of unitons distributed in the Universe? In order to be able to reply to this question, we must first pose the following extremely fundamental questions: What does 'matter' consist of? What does a 'field' consist of? And what we call 'vacuum', does it consist of anything?
The reply to the three last questions must be: Everything consists of unitons! As the uniton is the physical possibly smallest energy/matter unit in the Universe, all elementary particles must be built up by unitons.
The following points characterize 'matter', 'fields' and what I shall rather call 'physical vacuum':

1. The density of unitons, viz. number of unitons per volume unit.
2. The geometrical distribution of unitons.
3. The relative motions of the unitons.

• 'Matter' particles are characterized by a relatively high density of unitons.
• A 'field' has a relatively lower density.
• And the 'physical vacuum' has the lowest density.

(4)

where m_e is the mass of the electron and m_u the mass of the uniton. We see that the electron is built up by a huge number of unitons.
The number of unitons bound in 'matter' is given by the number in (4) multiplied by N². Even if this is an extremely high number, the difference between the number of 'free' and 'bound' unitons will be around N³. We can thus presume that there are in average N³ unitons distributed in the entire Universe, most of them distributed outside the areas 'occupied' by 'matter particles'. I must thus conclude that what is called 'vacuum' is absolutely not empty space where nothing exists, but on the contrary filled with unitons, which have physical existence and physical effects. I shall therefore name the space between galaxies, stars, atoms and 'elementary particles' as the uniton space. An abstract space in our mind, where no unitons exist with a physical space of disposal (Verfügungsraum), gives no physical meaning.
As evident from the above it seems that I have rediscovered the universal ether. In my theory, the uniton space is equivalent to the ether. It will now be a challenge to study the physical effects of the unitons.

Many questions can be posed:

• Does a uniton have an electric charge?
• Is electric charge a mechanical characteristic of unitons?
• Does a uniton have a spin; in the affirmative, how much?
• What is the geometric extension of a uniton?
• How are the motions of a uniton?
• Are all forces the result of collisions between unitons?
• Do gravitational, electromagnetic and other forces propagate through uniton space?

(5)

V_R is the volume of the Universe with an extension R, and V_r0 is the volume of a sphere with an extension equal to elementary length r₀. The occupied space of a uniton V_u is then given by:

(6)

The average extension r_u of the occupied space of a uniton is given by:

(7)

The calculated value of r_u is apparently of the same order as the extension of an electron!
The average uniton density in the Universe is determined by:

(8)

From equations (1) and (7) we get for the ratio between the extension R of the Universe and the extension of the occupied space of a 'free' uniton, r_u:

(9)

We see that this ratio is equal to the ratio between the electrostatic and the gravitostatic forces between an electron and a positron, or equal to the ratio between the gravitational "constant" at the 'birth' of the Universe and the gravitational "constant" of our epoch.

The mass M_s of the unitons 'bound' in matter I assume given by the following:

(10)

where m_e is the mass of the electron.
This value is changed if you calculate N from the mass of the proton instead of the mass of the positron. My choice is done from the physical philosophical view that I consider the positron to be more fundamental than the proton. Future observations and experiments must decide which is the correct choice. The mass in (10) will be 1836² times smaller, and the average occupied space for a uniton will be 1836 times greater, if N is calculated, based on the proton mass. The number 1836 is the ratio between the mass of a proton and the mass of an electron.

Analogy between propagation of sound and propagation of light in the uniton space
As uniton space with its discrete elementary quanta – the unitons – is the possible medium through which light and other phenomena, such as gravity, may travel, I shall shortly explain the mathematical description of sound waves, i.e. oscillation of particles. The sound effect is an effect of force caused by particle oscillations. These particle forces can be transferred from particle to particle and thereby from one position to another. Necessary for the propagation of a sound wave is that a medium is present, consisting of 'particles' which can 'convey' a certain oscillation condition from particle to particle. The speed by which an oscillation is transferred depends on the special particle medium. Let us consider the propagation of an oscillation through a row of particles, situated along a straight line. If the oscillations of the single particles have the same direction as the direction of the transmission we call it longitudinal waves. If the single particles oscillate perpendicular to the direction of the transmission, we call it transversal waves.
Let us introduce an x-axis along the considered row of particles. At rest or in equilibrium, each particle has an x-coordinate. Let us denote each particle's displacement from equilibrium with u(x,t). As written, the displacement is dependent on the coordinate, x, and the time, t, as measured on a chosen watch. For u(x,t) the following partial differential equation is valid – permitting a continuous mathematical description:

(11)

In equation (11) v is the speed of the wave (phase velocity).

The general solution function to the differential equation (11) is given by:

(12)

where f₁(x-v·t) is indicating a wave travelling in the positive direction of the x-axis, and f₂(x+v·t) a wave travelling in the opposite direction. The solution (12) thus gives a superposition solution. Waves travelling through space satisfy the more general differential equation:

(13)

where y and z are directions perpendicular to the x-axis.

The speed of propagation of a given wave is determined by the physical properties of the wave medium, for example it can be a gas, liquid or solid matter.
For a gas, where the travelling of a wave is adiabatic, viz. where there is no exchange of heat between interactive 'volume elements', the following equation is valid for the velocity, v:

(14)

where is the ratio between the specific heat capacity of the gas at constant pressure and constant volume, P is the gas pressure, and is the mass density of the gas. is approximately equal to 1.

If it concerns an ideal gas, viz. an idealized particle system with no forces between the particles, the following equation of state can be used:

(15)

where P is the gas pressure, the mass density of the gas, m₁ the mass of the single particle, T_a the absolute temperature of the gas, and k = 1.38 · 10^-23 J/K is Boltzmann's constant.
The absolute temperature, T_a, of a gas is defined as being proportional to the average kinetic energy of a single particle. If a particle has three degrees of freedom for motion, the following is defined:

(16)

where <v²> is the quadratic mean value of the velocities of the single particles.
From (15) we get:

(17)

As the uniton is the smallest quantum in the Universe, it is reasonable to postulate that it moves within its occupied space with an average velocity of c₀, which is the highest velocity in the Universe. Assuming that light is oscillation transmitted by the uniton space, and that the equations valid for particle oscillations are also valid for the unitons, we get for the velocity of transmission of the uniton oscillations, v, viz. the effects of light:

(18)

as it is valid that <v_x²> = 1/3 · <v²>, which gives the velocity of transmission along an x-axis. For we get:

(19)

thus a velocity of propagation equal to the speed of light. Travelling of light from position to position can thus be considered to be propagation of uniton oscillations. A further knowledge of the conditions of motion and interaction of unitons will give a better understanding.

From equation (16) we can determine the equivalent absolute temperature T_a of the uniton space, with a mass of the uniton m₁ = 2.2 · 10^-68 kg and <v²> = c₀²:

(20)

We see that the temperature of the uniton space is very near to absolute zero. At such low temperature, the uniton medium must have superfluent properties, a.o. without friction. This freedom of friction means that all "macroscopic" bodies can move freely through uniton space.

Unitons and their velocities
In my holistic quantum cosmology it is shown that the Universe in our epoch contains about 10¹²⁷ matter/energy quanta. They are created by quantum disintegration of the original cosmic embryoton - the archaic quantum of which our Universe is created. I have called these elementary quanta unitons. The present mass m_u of a uniton is in our epoch about 2.2 · 10^-68 kg. The average distribution of the unitons in the Universe corresponds to an average occupation distance between the unitons of about 10^-17 m. See the section about the uniton. An important question is: By which velocities can unitons move? Immediate physical logics tells us that, being the smallest 'matter/energy quantum' in the Universe, it must be able to move at the highest velocity. With our present knowledge this velocity is supposed to be the speed of light in what is called vacuum. It is disputed whether superluminal velocities exist. Several groups of researchers have conducted experiments indicating the possibility of superluminal speeds.

In the following I shall show that the minimum velocity of the uniton is the speed of light c₀.
By equations I shall motivate this postulate as follows:
Let us use an equation, first introduced by Louis Victor de Broglie (1892-1987): Louis de Broglie, Comptes Rendus, vol.177, (1923)):

(21)

where is the associated ’wavelength’ of a particle with the mass m and the velocity v.      h is Planck's constant.

We now pose the question: Which is the minimum velocity v_min of a uniton, corresponding to the greatest physical 'wavelength'? The greatest physical distance is the actual extension of the Universe, R. The greatest physical 'wavelength' must be equal to R, viz. = R. Using equation (21) we get:

(22)

where .

This shows that uniton velocity is equal to the velocity of light.
Lower velocities will correspond to de Broglie 'wavelengths' greater than the extension of the Universe, and this is physically impossible. If the above deduction is correct it is evident that a uniton can not move slower than the velocity of light.

Holism and not separable events
The de Broglie equation and the cosmological basic equation immediately gives possibilities for uniton velocities higher than the velocity of light, corresponding to de Broglie 'wavelengths' smaller than the actual extension of the Universe. Theoretically the smallest physical 'wavelength' is elementary length. If we use elementary length in the de Broglie equation we get a velocity extremely much higher than the velocity of light. A calculation shows that this maximum velocity is given by: v_max = N³ · c₀, where N³ is the cosmic evolution quantum number. If a signal moves with this maximum velocity, an event going on in one end of the Universe will be able to 'contact' the other end of the Universe within elementary time! The possibility of such extreme velocities may give an explanation for e.g. Alan Aspect's experiment in 1982 (Physical Review Letters, vol. 49, (1982)). Aspect's experiment, and other experiments, show that events happening so far from each other that connection by signals travelling by the velocity of light is impossible, apparently have almost immediate 'contact' with each other. Experiments show that all events in the Universe are connected so, that an information about an event happening in one subsystem is almost momentarily 'transmitted' to other subsystems in the Universe. If actions can move at superluminal speed and thereby arrange almost momentary contacts with all other parts of the Universe must be shown by future experiments and considerations. Theoretically the possibility seems to exist.

What David Bohm (1917-1992) calls "the enfolded order" and which quantum physicists in lack of a deeper understanding call "hidden variables" can maybe find a physical explanation by my cosmological uniton theory.

©    Louis Nielsen April 1997 and February 1998

In my 'Holistic Quantum Cosmology with Decreasing Gravity' (see this), it is a natural consequence that a universal 'quantum ether' exists, consisting of extremely small elementary quanta, which I call unitons (see the beginning of this article). The unitons move with at least the velocity of light. As these unitons may be found everywhere in the Universe, thus also in spaces we call vacuum, it may well be these elementary quanta, which by thrusting effects are the physical cause of gravity, maybe even electric forces, other forces and the inertial effects of bodies.

Today most physicists accept Einstein's gravitational theory without any deeper knowledge of it. We have learnt it in school and at the university, so it must be right, one says, and is satisfied without questions.

In the next section I shall shortly mention a mechanical-physical theory for gravity, developed at the end of the 18th century.

George-Louis Le Sage's mechanical gravitational theory.

Late in the 18th century, the Swiss mathematician and physicist George-Louis Le Sage (1724-1803) proposed a mechanical gravitational theory. (George-Louis Le Sage, 'Lucréce Newtonien', Memoires de l'Académie Royale des Science et Belles-Lettres de Berlin. Berlin 1784). The theory has been discussed by a.o. Pierre Prevost (Pierre Prevost, 'Traité de Physique Méchanique de Georges-Louis Le Sage.' Deux Traités de Physique Méchanique. Geneva, 1818). The theory is based on the following hypothesis:

• The whole Universe is 'filled' with very small particles (Le Sage called them 'ultramundane corpuscles'), which at great speed move in all directions.

• When these particles collide with the particles forming matter, they exert a force on the latter.

• If a body is alone in the space, filled with corpuscles, it will be influenced equally from all sides, the resulting force then being zero.

• If two bodies are present in the particle filled space, there will be a lower density of 'ultramundane' particles between the bodies than outside the bodies, because they 'shadow' for these. A result of this inequality in particle density will be that the two bodies are pushed together.

In an appendix to 'Lucréce Newtonien' Le Sage resumed which properties the 'ultramundane corpuscles' should have. The following must be valid:

1. The extension of the corpuscles is very small compared to the distance between them.

2. Their motions must be linear.

3. Collisions between them must be very rare.

4. The random motions of the corpuscles can be considered to be a 'linear flow' of particles, moving in millions of directions at constant speed.

The magnitude of the forces, pushing the bodies together, can be shown to be proportional with the product of the masses of the bodies and inverse proportional to the square of distance between them, which is identical to Newton's gravitational law! That the magnitude of the forces, pushing the bodies together, is proportional to the product of the masses, requires that the particles of matter, of which a body consist, are discretely distributed and that there is much empty space between the particles.

Le Sage's theory had both supporters and opponents. The opposition was due to the fact that Le Sage's theory was founded on more, partly independent hypothesis. The theory was not a logical consequence of a more fundamental physical theory. The kinetic theory for molecules and the thermodynamic theories were for instance not yet developed, and this meant that Le Sage's theory was almost forgotten the next hundred years after its proposal. When the kinetic theory for molecules was developed at the end of the 19th century, Le Sage's theory was taken up to renewed analysis by good physicists as James Clerk Maxwell (1831-1879) (James Clerk Maxwell, 'Atom' Encyclopaedia Britannica, 9th ed., vol. 3,1890) and William Thomson (Lord Kelvin) (1824-1907) (William Thomson, 'On the Ultramundane Corpuscles of Le Sage', The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science, vol. XLV, London 1873). Physical objections to Le Sage's theory were a.o. the following: If the planets move through a space, filled with particles, firstly they will encounter a frictional force, and secondly their temperature will raise. The problem of friction can be removed if the 'ultramundane corpuscles' are extremely small and move at velocities much higher than the speed of the macroscopic bodies. For the heating problem Lord Kelvin proposed a solution. As in the kinetic theory for molecules he suggested to operate with three forms of kinetic energy, viz. translational, rotational and vibrational. When a 'gravitational particle' transfers impulse to a body and thereby gets a reduction in f.i. the kinetic energy, this loss of energy can be compensated for by a possible partial increase of the rotational and/or the vibrational energy.

Georg Howard Darwin (1845-1912), son of Charles Darwin (1809-82) and professor in astronomy at Cambridge University, showed that Le Sage's 'ultramundane corpuscles' have to perform inelastic collisions with the bodies they collided with, if the exerted forces shall be able to fulfil Newton's gravitational law. (George H: Darwin, 'The Analogy between Le Sage's Theory of Gravitation and the Repulsion of Light'., Proceedings of the Royal Society, vol. 76, (1905)).

The Cosmic Uniton Field as Mediator of Force.

One of the problems of Le Sage's gravitational theory was that it was not a consequence of a more fundamental physical theory. When the kinetic molecule theory and the thermadynamic theories were developed, these theories might have formed the mechanical part of the theory. However, the fundamental assumption, that the whole Universe is 'filled' with 'ultramundane corpuscles', was missing.

This assumption was an ad hoc assumption, which was not a consequence of for instance a cosmological theory.

In my 'Holistic Quantum Cosmology with Decreasing Gravity', it is a consequence of the theory that the Universe is filled with the smallest possible matter/energy quanta, — elementary quanta which I call unitons. As evident from my quantum cosmological theory, the Universe started with one quantum, which I call the cosmic embryoton (the cosmic foster particle). The development of the Universe is controlled by a cosmic evolution quantum number (the cosmic quantum clock), which 'ticks' up through all natural numbers! When the Universe was 'born' it took the value 1! In our epoch, this cosmic evolution quantum number has reached the extremely high value of 7·10¹²⁷.

At every 'tick' of the cosmic evolution quantum number, a new matter/energy quantum emerges — a new uniton! The number of unitons is, at every stage of the development of the Universe, equal to the actual value of the cosmic evolution quantum number — N³. In our epoch this number is extremely high. Due to the expansion of the Universe, a decrease in density of unitons takes place, and simultaneously the mass of each uniton decreases — this is because in my theory I assume that the total mass of the Universe remains constant. This dilution of the cosmic uniton field can give a physical-mechanical explanation of why the gravity in our Universe is constantly decreasing!

Unitons have extremely small extensions, equal to the elementary length, and move with the velocity of light (possibly with higher velocity). All 'matter' is assumed to consist of unitons. Thus f.i. an electron can be considered to consist of a dynamical subsystem of about 10³⁷ unitons. That an electron is a uniton dynamical system means that it in a balanced position emits and absorbs the same number of unitons per unit of time.

As the unitons may be the particles which cause gravitational forces — and for that matter possibly also other forces — and as these elementary quanta apparently fulfil the criteria required by Le Sage's theory, there is a good reason to take this mechanical theory up to renewed studies, 200 years after it was proposed by the mechanically intuitive physicist and mathematician George-Louis Le Sage.

Louis Nielsen, 20th October 1997.
E-mail: LNi@Herlufsholm.dk

  Next article