Quantized Cosmic Entropy and its Relation to Space, Time, and Unitons
The Solutions to the Problem of Increasing Entropy and 'the Arrow of Time'
by cand.scient. Louis Nielsen

In the following, I show a connection between the total absolute entropy of the Universe

the cosmic entropy
its total mass, extension and age, and the actual number of the smallest energy/matter-quanta in the Universe. These smallest energy/matter quanta I have given the name unitons. In my holistic quantum theory of the Universe, I have derived equations from which we can calculate the actual extension of the Universe, its actual age and its total mass. I also show that these quantities can be calculated from measured atomic quantities. (Note: The word holistic came from Greek: holos: whole).

If I define that the quantized cosmic entropy is proportional to the actual total number of unitons in the Universe, it can give a solution to the problem of the direction of time - the arrow of time. What we call 'matter' is Bose-Einstein condensations of unitons in the cosmic uniton field.


My discovery - more than thirty years ago - is the following discrete connection between the actual extension R of the Universe and the physically smallest distance in the Universe -the elementary length - r0:


where r0 has connection to Plancks constant h, the velocity of light c0 and the total energy/matter mass M0 of the Universe. kC is coulombs constant, e the electric charge of an electron, me the gravitational mass of an electron and G is the gravitational 'constant', which is a discrete decreasing quantity in my quantum cosmology. (Please see my treatise). Equation (1) connects the most important physical quantities from microcosmos and macrocosmos.
It is a holistic formula. It is 'Die Weltformel'!

The Universe - with its matter/energy and space - is evolving in quantum 'jumps'. The evolution of the Universe is 'controlled' by a COSMIC EVOLUTION QUANTUM NUMBER N3 'ticking' up through the NATURAL numbers.
The Universe was 'born' when N3 took the value 1. In our epoch N3 is equal to 7.2·10127. N is equal to the actual ratio between the magnitude of the electrostatic forces and the gravitostatic forces between two electrons. The value of N in our epoch is: N = 4.17·1042.

From equation (1) we get:


where mu is the physically smallest mass in the Universe. This mass represents the smallest energy/matter quantum in the Universe - the true atom! This smallest energy quantum I have called a UNITON.
We see from equation (2) that the actual Universe - in every of its quantum states - consists of N3 unitons. In our epoch the number of unitons are 7.2× 10127. The existence of unitons in the cosmic space - also in so called vacuum - gives the possibility for a mechanical explanation of gravitational forces which is in accordance with Newtons gravitational law. (Equivalent to the theory proposed by George-Louis Le Sage (1724-1803)).

I calculate the total mass M0 in the Universe to 1.6·1060 kg.

With this value of the mass of the Universe, the value of the elementary length r0 is equal to 1.4·10-102 meter and the actual mass of a uniton is 2.2·10-68 kg. From equation (1) we see that R is proportional to the actual total number of unitons. The actual extension of the Universe is about 1026 meter. From the elementary length r0 we can define a quantum of time - the elementary time - t0:


where c0 is the velocity of light, measured in the laboratory in relation to a 'locally defined time measure'.
When r0 and t0 are cosmic invariant quantities, this implies a cosmic invariant c0. All physical distances (also R), time intervals and masses are equal to a NATURAL quantum number multiplied by the respective elementary quantity (r0, t0 and mu). The Universe was 'born' when it took the first cosmic quantum 'jump' and where it consisted of ONLY ONE QUANTUM, with an extension equal to the elementary length r0 and a mass equal to the total mass M0 of the Universe. This quantum I call THE COSMIC EMBRYOTON.
Gradually, as the cosmic evolution quantum number increased, the original cosmic embryoton divided into more and more unitons. This increasing number of unitons, with smaller and smaller masses, is spreading out in a quantum growing Universe.

Every cosmic quantum 'jump' gives ONE MORE UNITON IN THE UNIVERSE and this quantum change in the universe is equivalent to one cosmic elementary time interval. The cosmic time is equivalent to the the number of unitons in the Universe. ( Time motto: TEMPUS MUTATIO EST ,'Time is change'). We can define the value T of THE INVARIANT, ABSOLUTE, AND DISCRETE COSMIC TIME to be proportional to the actual numbers N3 of unitons in the Universe:


where we have chosen the elementary time t0 to be the proportional constant. T also defines the age of the actual Universe. Equation (4) gives T = 10.7·109 years.

The direction of time - the arrow of time - is in that direction where the number of unitons in the Universe is increasing!
We can write equation (4) as follows:


We see that T is a discrete function of the actual mass of the uniton.
T is inversely proportional to the mass mu of a uniton. The factor ((M0·r0)/c0) acts as a proportional constant.



We can define an invariant and DISCRETE ABSOLUTE COSMIC ENTROPY quantity S by the following equation:


where k =1.38× 10-23 joule/kelvin is Boltzmann's constant, and N3 is the actual total number of unitons in the Universe. In our epoch N3 = 7.2·10127, and this gives approximately: S = 1·10105 joule/kelvin. We see that the law of increasing entropy of the Universe is a consequence of the increasing number of unitons in the Universe. Equation (6) gives a quantization of the entropy quantity.
We can define an ABSOLUTE DISCRETE COSMIC UNITON-temperature, t (in kelvin), according to:


where M0 = 1.6·1060 kg is the total mass of the Universe, c0 = 3·108 m/s is the velocity of light, and mu the actual mass of one uniton. With these values we have for the cosmic uniton-temperature in our epoch t = 1.4·10-28 kelvin, an extreme low cosmic uniton-field temperature! Notice: A consequence of the extreme low cosmic uniton-field temperature is: What we call 'matter' is Bose-Einstein condensations of unitons in the cosmic uniton-field!


The cosmic entropy has connections to the actual extension of the Universe, its actual age and the actual mass of a uniton. The connections are:


We see that S is proportional to R and proportional to T and inversely proportionate to mu . In quantum cosmological units with one entropon defined as:
1 entropon = k = 1.38·10-23 joule/kelvin
we have: The actual total cosmic entropy S is: S = 7.2·10127 entropons.
My discoveries gives a solution to the problem called 'the arrow of time', the experiences that all processes go only in one direction.
The direction of time is in that direction in which the total number og unitons in the Universe is increasing!

The elementary quantum quantities r0, t0 and mu represent an absolute and cosmological system of units.
I call these units: 1 spaton, 1 tempon and 1 masson.

In quantum cosmological units the actual quantum state of the Universe is given by:
The actual number of unitons is:7.2·10127
The actual mass of the Universe is:7.2·10127 massons
The actual extension of the Universe is:7.2·10127 spatons
The actual age of the Universe is:7.2·10127 tempons
The actual total entropy of the Universe:7.2·10127 entropons
Notice, that all the values are equal to the actual cosmic evolution quantum number!

E-mail: louis44nielsen@gmail.com

© Louis Nielsen, May 1999


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