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The Quantum-Universe before the Planck-time.
The first Cosmic Quantum-process.
Derivation of E = Mc^2.

By Louis Nielsen     Denmark

Treatise:  http://www.rostra.dk/louis

THE BEGINNING OF THE UNIVERSE.
How was the beginning of the Universe? The 'Standard Model' in
cosmology based on the general theory of relativity can not give
acceptable calculations for the evolution of the Universe when it had
an age smaller than the planck-time about 10^(-43) sec.
Most cosmologists, trying to describe the earliest phases of the
Universe by the Big Bang model, use the Planck time bout 10^(-43) sec,
as the nearest possible time which can be used to approach the
'moment' of the Big Bang.
Events before the Planck time cannot be described by the conventional
cosmological theories. Einstein's general theory of relativity, which
is basic for the accepted cosmological models, collapses when we try
to analyse the early Universe. The reason is that the theory of
general relativity is not based on quantum physics. If time-intervals
and distances are smaller than the planck-time and the planck-length
then we must use a quantum-mechanical theory.

In the following I give a quantum-mechanical model of the quantum-
evolution of the Universe before the planck-time. The model is based
on quantization of space, time and mass.

THE SPACE-ATOM AND THE TIME-ATOM.
THE VELOCITY OF LIGHT.
The Universe with all its matter, motions and interactions has been
developed from ONE primordial matter-quantum with a primordial mass M
equal to the total mass of the Universe and a primordial extension d
which define the quantum of length - the cosmic space-atom. The
primordial first 'particle' in the Universe I had given the name 'The
Cosmic Embryoton'.
The Universe came into active existence when the cosmic embryoton had
separate into two scale-invariant matter-/energy-quanta with masses M/
2. These first two active matter-/energy-quanta I call the 'Primordial
Unitons'. Each of the unitons had an extension d equal to the quantum
of length and each of them had been accelerated up to the velocity of
light c.

The first cosmic quantum-process which is the first cosmic change in
the embryonic Universe defines the first cosmic quantum of time-
interval t. The velocity of light c is given by the ratio between the
'space-atom' d and the 'time-atom' t:

(1a)  c = d/t

As d and t are cosmic absolute and invariant quantities we see that c
also is a cosmic invariant quantity.

UNITONS, THE UNIT-QUANTA OF THE UNIVERSE.
The two primordial Unitons disintegrate into more and more scale-
invariant unitons that are spreading out in an active and expanding
Universe.
The quantum-evolution of the Universe can be described by a 'Cosmic
Evolution Quantum Number' which is 'ticking' up through the natural
numbers. (Please study my treatise)
The actual value of the 'Cosmic Evolution Quantum Number' is equal to
the actual total number of created unitons. In our epoch the Universe
consists of about 7*10^127 unitons.

THE PRIMORDIAL COSMIC QUANTUM-WORK.
The total cosmic embryonic physical work W(cosmic) done when the
cosmic embryoton is separated into the two primordial unitons is equal
to the total energy E(cosmic) of the evolving Universe.

A simple calculation, based on Newtonian physics, show that the total
energy E(cosmic) of the Universe is given by E(cosmic) = M*c^2 where c
is the velocity of light.
The calculations are:
Each of the two primordial unitons with masses M/2 is acted by a force
F applied over a distance d. The value of the force F is given by the
second law of Newton:

(2a)  F = (M/2)*a = (M/2)* (c/t)

In equation (2a) a = c/t is the acceleration of the primordial
unitons, the greatest possible acceleration in the Universe.
The force F is the maximum value of a force in the Universe and it can
be regarded as a Quantum-force.

The total cosmic embryonic work W(cosmic) is equal to the released
total kinetic energy E(cosmic) given by:

(3a)  W(cosmic) = 2*(F*d) = 2*(M/2)*(c/t)*d = M*c*c = M*c^2 =
E(cosmic)

The total primordial released kinetic energy E(cosmic) is thus given
by:

(4a)  E(cosmic) = M*c^2

We see that equation (4a) is the same energy-/mass equation that
Albert Einstein derived in 1905, but here it is derived more simple
and the derivation is based on the first primordial cosmic quantum-
jump when the Universe came into active existence!

THE PLANCK QUANTITIES.
The so-called Planck quantities are not based on a physical theory,
and neither they are themselves basis for a physical theory. They are
'constructed' purely by dimensional analysis, based on  Newton's
gravitational constant G, the velocity of light c and Planck's
constant h. The intention of Max Planck (1858-1947) was - in 1899 - to
find a unit of length l(pl), a unit of time t(pl) and a unit of mass
m(pl), independent of specific local systems.
( Reference: Max Planck: ,Über irreversible Strahlungsvorgänge'.
Sitzungsberichte der Preußischen Akademie der Wissenschaften, vol. 5,
p. 479 (1899) )

The Planck quantities are defined, without the geometrical number pi,
by:

(1)  l(pl) = ((h*G)/c^(3))^(1/2) = 4.1*10^(-35) meter

(2)  t(pl) = l(pl)/c = 1.4*10^(-43) sec

(3)  m(pl) = ((h*c)/G)^(1/2) = 5.5*10^(-8) kg


THE QUANTUM-COSMOLOGICAL UNITS.
Let us define the following absolute quantum-cosmological quantities:
The elementary length, the 'quantum of length' d, the elementary time,
the 'quantum of time't, and the actual elementary mass, the 'quantum
of mass' m.
The absolute quantum-cosmological units are defined by:

(4)  d = h/(M*c) = 1.4*10^(-102) meter

(5)  t = d/c = 4.7*10^(-111) sec

(6)  m = h/(R*c) = 2.2*10^(-68) kg

In equation (4) M = 1.6*10^(60) kg is the total and constant mass of
the Universe (See my treatise about a calculation of the value of M),
h is Planck's constant and c is the velocity of light. In equation (6)
R = 1*10^(26) meter is the actual estimated extension of the Universe.
The magnitude of the mass-quantum m in equation (6) is the value in
our epoch.

All lengths, time-intervals and masses are quantized.

THE QUANTUM-EVOLUTION OF THE UNIVERSE.
I postulate that the connection between the actual extension R of the
Universe and the 'quantum of length' d is:

(7)  R = n* d

We can call n the 'cosmic evolution quantum number'. As the Universe
evolves in 'quantum jumps' n is 'ticking' up through the natural
numbers, beginning with the number one when the Universe came into
existence.
A discovery is that n is equal to the third power of the actual and
variable ratio between the magnitude of the electrostatic and the
gravitostatic forces between two electrons. (Please see my treatise)

The connection between the total mass M of the Universe and the actual
'quantum of mass' m is:

(8)  M = n*m

In (8) m is the mass of the actual - and variable - smallest energy-/
matter quantum in the Universe. This energy-/matter quantum I have
given the name Uniton (The cosmic unit particle).
In our epoch n = 7.2*10^127. The actual value of n is equal to the
actual number of possible Unitons in the Universe.
In our epoch the number of possible Unitons in the Universe is thus
equal to 7.2*10^127.

The connection between the actual age T of the Universe and the
'quantum of time' t is:

(9)  T = R/c  = n* t


RELATIONS BETWEEN THE COSMIC QUANTUM-UNITS AND THE PLANCK'S-UNITS.
The quantum-cosmological quantities define a set of cosmic quantum-
units, which are much smaller and much more fundamental than the
Planck units. In my dissertation I show the connection between the
cosmic quantum-units and the Planck units, and furthermore I show
which role the Planck units play in the quantum-evolution of the
Universe.
>From the equations (1) and (7) we can calculate the value n(pl) of the
cosmic evolution quantum number when the Universe had an extension
equal to the Planck-length l(pl) and an age equal to the Planck-time
t(pl). We get:

(10)  n(pl) = l(pl)/r = 2.9*10^(67)

n(pl) - which is a natural number - is also the number of unitons in
the Universe, when its age was equal to the Planck-time.
>From equation (8) we can calculate the mass m(t(pl)) of a single
Uniton when the Universe had an age equal to the Planck-time t(pl). We
get:

(11)  m(t(pl)) = M/n(pl) = 5.5*10^(-8) kg


INTERPRETATION OF THE PLANCK-QUANTITIES.
The result in equation (11) is interesting. Comparing the value in
equation (11) with the value in equation (3) we see the following:
The Planck-mass m(pl) is equal to the mass m(t(pl)) of the Uniton,
when the Universe had an extension equal to the Planck-length and an
age equal to the Planck-time!
The relatively great Planck mass has been an enigma. The above give
the explanation of the great value of the Planck mass.
When the Universe had an extension equal to the Planck-length
4.1*10^(-35) meter, then it had an age equal to the Planck-time
1.4*10^(-43) sec, and it consisted of 2.9*10^(67) Unitons, each with a
mass equal to the Planck mass 5.5*10^(-8) kg.

The Planck quantities can thus be derived from the more fundamental
quantum-cosmological quantities:
The quantum of length r, the quantum of time t and the total mass M of
the Universe.

You can study more in my treatise:
 http://www.rostra.dk/louis

Serious comments are very welcome.

Best regards
Louis Nielsen
Denmark