**PART TWO**

**Summary**: A
geometrical analysis of the Hubble constant showed that it should not be
constant but data from the most distant supernovas show that it is
constant.. This is only possible if time is expanding. The Hubble constant
is an acceleration constant conforming to the criteria of a fundamental
force of nature. It corresponds to a previously suggested force that arises
from mass. This force is responsible for the expansion of the universe as
well as the acceleration of mass towards a gravitational source. Time is
inversely related to mass. As time slows so mass reverts to energy. This
fuels solar and all stellar radiation as well as gravity. Hydrogen fusion is
endothermic and plays a key role in maintaining the stability of all stars.
Helium is violently exothermic at very high temperatures destroying most of
the mass in supernovas. Time
slowing releases energy at a constant rate and through its effect on the
mass of the moon leads to a reasonably precise prediction of the height of
the tides in mid Pacific Ocean. The time/mass effect causes excess heat for
all the planets. It is responsible for the violent storms in Jupiter’s
equatorial belt. It is probably responsible for Saturn’s ring system through
destroying small icy moons. The time slowing effect on the dust surrounding
the solar system explains of the characteristics of the Background Microwave
Radiation. The universe’s system of time is an exponential oneso resolving a number of paradoxes relating to the universe’s age.
The Big Bang theory does not take into account the role of gravity, and a
replacement is suggested,

**
1.
****
Theoretical considerations**

The physics underlying the Hubble constant is obscure.
Dimensionally the Hubble constant, the ratio of velocity to distance, is
describing a frequency, which is inappropriate. If velocity increases with
distance this describes acceleration. The denominator of the Hubble constant
should therefore be time. The only fixed relationship between distance and
time is c, the velocity of light. It follows that the denominator in the
Hubble constant should be the time for light to travel the distance quoted
in the ratio.

There is disagreement as to the exact value of the
constant. If the age of the universe
is 13.7 billion years, theHubble constant, H_{o},_{
}should be 47.6 km.s^{-1}Mparsec^{-1 }(equations 1 & 2)
giving an acceleration constant of 4.62 x 10^{-10 }m.s^{-2}.
If H_{o }is 51.8 km.s^{-1}Mpc^{-1}
(see later) the acceleration constant is 5.0 x 10^{-10} m.s^{-2}
and the age of the universe is 12.58 billion years.At this acceleration for this length of time the velocity of the
furthermost galaxy should be 0.66 of the velocity of light and the distance
travelled by that galaxy should be 4.16 billion light years or 1273 Mpc.
Yet velocities from Supernovas have
been observed that are much greater than 0.66c and distances have been
deduced that are much
greater than 1273 Mpc (Tables 1 and 2).If 73.5 km.s^{-1}Mpc^{-1} is the Hubble constant
(NASA 2009) the acceleration is 7.14 x 10^{-10} m.s^{-2 }and^{
}the age of the universe is only 9.13 billion years. In this time the
furthermost galaxy should have
travelled only 2.19 billion
light years. Clearly there must
be another factor to be taken into account to correct these anomalies.

There is another problem. A geometrical analysis based
on the Euclidean geometry of similar figures (Figure 1) shows that if the
visible universe is expanding at a constant acceleration then the ratio of
velocity to distance cannot be constant over time. The geometric analysis
(Appendix 1) shows that the equation defining the Hubble value
*should* be

Equation 1.
H_{o} = v/D = 2 x
100 x 3.26 x (Age –D_{T})^{-1}

where v is the velocity in km/sec of the galaxy being
examined, D is its distance in Mega parsecs, Age is the age of the universe
in earth time (that is the system of time used on earth), D_{T }is_{
}the_{ }time for light to travel the distance D, with both Age
and D_{T} being in units of billions of years. 3.26 is the
conversion factor for parsecs to light years.

Thus the only way for H_{o} to be constant
would be to multiply the value by the ratio of ages, (Age-D_{T})/Age.
That is if H_{o} doubled then the ratio of ages would equal 0.5,
i.e. the period of the second is halved and so on.The time corrected equation 1 is therefore

Equation 2
H_{o} = v/D = 2 x
100 x 3.26/Age

The key conclusion is if the Hubble constant is truly
constant, that is it is constant throughout time and space, then time must
be expanding and has been expanding since the beginning of time. Moreover
the rate of time expansion is 1/Age where Age is the age of the universe incosmological seconds.
Equation 2 is testable.

**
2.
****A
new fundamental constant**

Sandage (1993) found
that the very outer stars of galaxies had accelerations of slightly less
than 50 km.s^{-1}Mpc^{-1}, or slightly less
than 5 x 10^{-10} m.s^{-2}. That is they were
comparable to the Hubble constant. The two Pioneer probes also have
accelerations of the same order of magnitude, Anderson (2002).Three bodies, of vastly different masses, galaxies, the outerstars, and the Pioneer probes, having more or less than same
acceleration points to a system of acceleration which is independent of
mass. In this it is akin to
gravity and suggests that the Hubble constant is describing a fundamental
constant of nature. This independence of mass suggests that, like gravity,
the force causing the acceleration must arise from the components that make
up mass. The theoretical nuclear
physicist, the late Burkhard Heim (Leitz
2006, Hauser 2009) postulated that in addition to the four fundamental
forces of nature, the weak and strong intra nuclear forces, the
electromagnetic force and gravity there must exist two other forces. That is
there is a family of three fundamental forces with gravity-like properties
in that they affect the movement of mass. A Hubble constant fulfils Heim’s
suggestion as being one of these three forces (he called them interactions,
Hauser, 2009). The others are standard gravity as described by Newton, and a
gravito-electro-magnetic force. A force with a constant value of between
4.62 and 7.14 x 10^{-10 }
m.s^{-2 }that is independent of mass would be such a fundamental
force if it can be shown to be constant in all time frames. This may be
compared with the Gravitational constant G (6.67 x 10^{-11}).

If the radius of
a proton is 10^{-15 }m and the mass of a proton is 1.6 x 10^{-27
}kg then the gravitational force at the surface of the proton is ~250
times that of the acceleration force also acting on that surface. It follows
that if the radius of a spiral galaxy is proportional to its mass then, at
the outer 1/15^{th} of the radius (250^{-0.5}), the
gravitational force acting on any star will equal the acceleration force
resulting in a velocity that is twice that predicted from the gravitational
strength of that galaxy. Any star in this outer 1/15^{th} fraction
of the radius will have velocity even greater. All the observations that
have been attributed to “dark matter” can be explained by this Heim force.
The consequential distribution of velocities also explains the hitherto
inexplicable shape of the spiral arms of our Galaxy with the edges of the
spiral arms moving faster than expected.

Proof of the existence of this fundamental force, one
that is constant in all time frames, and its rider, that time is expanding,
will be by showing that even at the furthest limit of our observations the
Hubble value is constant and not rising according to the prediction of the
geometric analysis given in equation 1. Furthermore, proof that time is
expanding, will be the demonstration of the existence of the consequences of
that time expansion (see later).

**
3.
****
The observational data**

The data of 60 supernovas were taken (Tables 1 and 2).
This data consists of two populations of Type 1A supernovas, Hamuy et al,
(1996). Perlmutter et al, (1999). The first
population, the Calan/Tolelo set, consists of 18 supernovas that had
estimated distances ranging from 64 to 654 Mpc. The second set, the
Supernova Cosmology Project, (SCP), consisted of 42 Type 1A supernovas whose
distances ranged from 750 to 4500
Mpc.

The assumption behind Type 1A supernovas is that they
emit a set amount of light that decays in a particular fashion and so can
act as standard candles. It
follows that with uniform expansion of the universe all such supernovas with
the same velocity should have the same magnitude as they will be at the same
distance from their origin. But supernovas can occur anywhere in a galaxy
including behind dust clouds which can obscure some of the light.The results, tables 1 and 2, show that this is the case and
variations up to 0.5 of Magnitude have occurred between galaxies of similar
velocities.

The equation used to derive the distances is a
refinement of that developed by Kayser et al (1997).It includes subtracting the values for Galactic extinction in the
observed B band, given in the
original data, and for relativistic
time dilatation (Appendix 2)

Equation 3
Log Distance (Mpc) =
(Mag-(-19.7) – 25)5^{-1}

Mag is the B-band effective peak magnitude, the -19.7
refers to the magnitude of a reference supernova type 1a at a distance of 10
parsecs, whilst the 25 refers to the ratio of Mega parsecs to ten parsecs
adjusted for the conversion to log base 2.5 from log base 10.The 5 refers to converting back from log base 2.5 to log base 10 and
for the inverse square law.

For the faster supernovas there is a second time frame
superimposed on that due to universal time expansion. This is relativity
induced time dilatation. The effective B band magnitude is similar to that
described (Perlmutter et al. 1999) but must include an allowance for the
relativistic effects.

Equation 4.
Effective Mag = observed Mag - A_{x} – K-
a(s-1)

The red shift is also contaminated by the relativistic
time dilatation so that the velocity will appear to be slower than it should
be. The equation for calculating the Hubble constant (see appendix then
becomes

Equation 5
H_{o }= v x(1/(1-*v*_{c}^{2}))^{1.5}
x ((antilog(Effective Mag + 5.3)/5)^{-1}

The relativity factor is the standard time dilatation
derived from special relativity theory. The velocity
*v*_{c
}is the velocity expressed as a
fraction of the velocity of light.

In the Calan
Toledo data the velocities of the supernovas were sufficiently low that the
relativity effect was insignificant. This was not the case for the the SCP
data. Equally the brightness, or rate of photon emission and so magnitude,
was affected from the same cause. The supernovas were dimmer than they
should have been for their distances.

The results (tables 1 and 2) gave a mean Hubble value
of 51.8 +/- 1.35 km.s^{-1}Mpc^{-1} for the Calan/Tolelo
data. For the SCP data the mean for the uncorrected Hubble value was 32.2
+/- 1.0 km.s^{-1}Mpc^{-1}. When the relativity time
dilatation factor shown in Equation 5 was applied it was found that the mean
Hubble value for the SCP data was 47.9 +/- 1.2 km.s^{-1}Mpc^{-1}.
Such a value predicts that the age of the universe is 13.61 +/- 0.35 billion
years compared with the generally acceptedvalue of 13.7 billion years. Allowing for the various uncertainties
in the calculation of each of equation’s components it was concluded that
the Hubble constant was indeed constantover the whole range of distances covered by the data with a value
around 48-52 km.s^{-1}Mpc^{-1}.

Gribbin .(1999)
in his book describes an analysis of
1388 galaxies at distances of up to 100 M.parsec and reported Ho at 52+/-6
km.s^{-1}Mpc^{-1}, but there is a plethora of reports to be
found in both in print (Gribbin, 1999) and on the Internet giving different
values. The more recent reports
show two populations of values. One population, based on the brightness from
supernovas or Cepheid stars centres around 51-5 km.s^{-1}Mpc^{-1}.
The other based on a variety of physics concepts, but relying on the
anisometry of the microwave radiation, centres on a Hubble value of 73.5
km.s^{-1}Mpc^{-1} (NASA.2009)

4.
**
Reconciling the different Hubble values**.

If the Hubble value really is 73.5 km.s^{-1}Mpc^{-1}
then the lower Hubble values (derived
from the SCP optical data) implies that some of the light is being
intercepted, falsely increasing the magnitude by a factor of 1.44.From the inverse square
law increasing the distance by x 1.44 reduces the brightness by 58%.More than half the light has apparently been intercepted by dust.
This interception would apply to all astronomical light sources
outside our Galaxy and possibly outside the Solar system.That is their distances should be 2/3rds of their current calculated
values.

For the M31 or Andromeda Galaxy this means that its
distance is only 1.6 x 10^{6 }light years away from the Solar
system. That galaxy has a diameter of 0.228 x 10^{6 }light years. It
follows that M31 is only about 6 galaxy diameters from the edge of our
Galaxy. Photographs of colliding
spiral galaxies show that at a separation distance of two galaxy diameters
there is massive distortion of the structure of the galaxies due to mutual
gravitational attraction. At six
galaxy diameters distance there should be some signs of this distortion but
M31 show no sign of this. The inference then is that light is not being
intercepted to anything like the extent suggested. But this loss of more
than half the light from light absorption rests on the assumption that the
Ho is 73.5 km.s^{-1}.Mpc^{-1}.This was derived from measurements of the strength of the incoming
microwaves. The hidden assumption is that the microwaves originated solely
from some kind of Big Bang. One particular anomaly is that this Hubble value
predicts that the age of the universe is 8.87 billion years (Equation 2) but
the 73.5 km.s^{-1}Mpc^{-1} calculation
relied on the age of the universe as being 13.7 billion years. Another
assumption is if there is a dust cloud surrounding the solar system it does
not absorb microwaves. But if there is a dust cloud intercepting more than
50% of the incoming light then it would be generating low energy microwaves
as a direct consequence of the effects of time slowing on mass (see later).
Time slowing must occur if the Hubble value if truly constant.It follows that the NASA’s WMap data may have been contaminated by
locally produced microwaves with the anisometry (on which NASA’s calculation
is based) caused by irregular clouds of dust.

For comparison
if 5% of the incoming light was absorbed by dust the effect would be a
change in the magnitude of 0.055, which is well within the error of
measurement. A measure of uncertainty
still exists as to the precise value of the Hubble constant.

**
5.
****
Theoretical conclusion**

What is very clear is that the Hubble value does not
increase with distance as it should according to the geometrical analysis,
summarised in Equation 1. The
conclusion must be that the Hubble constant is constant throughout the
universe and this only possible if time was and is expanding.That is the Hubble constant is indeed constant in all time frames and
so fulfils the criteria necessaryto be considered as an expression of a fifth fundamentalforce of nature. The observations which led to the three hypotheses,
dark matter, dark energy and inflation, are fully accounted for by this
fundamental force and the expansion of time.
It also follows that the pace of time initially was very fast, by a
factor of 10^{6} and has slowed to become the present pace of time,
and is continuing to slow .The expansion of the universe is slowing down.

**
6.
****
Time and Mass**

There is a major
additional factor. Time and mass are inversely related.This can be seen in various physics equations. Thus the pendulum
equation shows that the period of the pendulum cycle is inversely related to
the square root of the gravitational force experienced by the pendulum.That force in turn is proportional to the mathematical product of two
masses. It follows that if time expands mass must be reduced.
Equally if time was quicker mass
would be greater.

A similar effect is seen in the energy equation of
quantum mechanics.

Equation 6.
Energy = h x frequency = mc^{2} = h x n/time

where h is
Planck’s constant, and n is the number of cycles of a wave in one second.

Another example
is in special relativity theory. The special relativity equation relating
time to velocity, equation 7, means that at a velocity of 0.8c time would
have expanded by another 0.66. Similarly the special relativity equation
relating mass to velocity, equation 7, shows that at the same velocity mass
would have decreased by a factor 0.6.

The two equations of special relativity are

Equation 7.
T_{expanded }= t_{normal}(1/(1-*v*_{c}^{2}))^{0.5}

Equation 8.
M_{reduced }= m_{normal}(1-*
v*_{c}^{2})^{0.5}

where *v*_{c}**
**is the velocity expressed as a fraction of the velocity of light.
That is one equation is the inverse of the other.The change in mass with velocity in equation 8
is a direct effect of expanding time
and its effect on mass.

**
7.
****
The Age of Universe in cosmological time**

The universe would appear to operate its own system of
time, hereinafter called cosmological time. When time first started its pace
was very fast but it has been slowing exponentially ever since converging to
the pace of earth time, that is the
rate of time expansion has now become so small that within the period of
human existence the pace of time seems to be constant leading to the
assumption that the period of the second has always been unchanging.There is no evidence that justifies that assumption.The calculation of the age of the universe in earth time is based on
that assumption.

Fundamental to
calculating the cosmological age of the universe is the doubling time.This is the time taken for the period of the second to double. Given
the exponential nature of time expansion this period is the same for all
doublings. It can be calculated
from the expression Age/2^{0.5 }where Age is the Age derived from
the Hubble constant, equation 2. The age of the universe is then the product
of the doubling time multiplied by the number of doublings since time
started.

Relativity theory shows that when gravitational
acceleration equals the speed of light, time, the period of the second, is
infinite. Time is at a standstill. That is the start of cosmological time
occurred when a large primeval black hole began to disrupt. This is in
contrast with the Big Bang model which posits that time started when a
singularity burst and time has continued to accumulate at a uniform rate to
reach its present earth time age.

The universe has been calculated as having some 10^{80
}nucleons, (Hawking, 1988) giving a mass of 3.35 x 10^{53} kg.
At the beginning this mass, or its equivalent, would have been concentrated
into a black hole. The equation which defines the radius of a black hole is

Equation
10
c = GMr^{-2}

If the mass was 3.35 x 10^{53 }kg the radius
would have been 28.88 light years.But time was much faster then.Whenever time was twice as fast mass would have doubled.
The radius of the primeval black hole would then have been

Equation 11
r =(GM2^{n}c^{-1})^{0.5}

where n is the number of occasions that time was twice
as fast as its successor period. The value of n can be found from
how often(2^{n}) those 28.88 x
2^{n/2 }years doubled to
become the age of the universe in earth time units.
This can be found from

Equation 12
28.88 x 2^{n/2} x 2^{n} = earth time
age

The cosmological age of the universeis then n times the doubling period.

Table 3 shows the results with three different values
for H_{o}.

**
**

**
**