Judgement Day (19 page)

Notice that equations
(12) and (13) do not collapse within the Schwarzschild radius, as
radius ‘r’ approaches zero, mass (from the perspective of someone
on earth) becomes infinite and time becomes infinitely slow. This
idea has huge implications for “black holes” because it means that
the laws of physics do not collapse but it is only Einstein’s
equations which collapse. However I will talk more about black
holes in Part 3.

Modified Newtonian
dynamics (MOND) has attempted to explain dark matter by tweaking
Newton’s equations for gravity on the outskirts of galaxies. The
creator of MOND, Mordehai Milgrom, proposes that gravity behaves
differently when gravitational acceleration becomes very small. He
has found that when studying galaxies, if centripetal gravitational
acceleration varied as a function of radius ‘r’ rather than the
square of the radius ‘r
²
’ then the velocities of stars
on the outskirts of galaxies could be explained without the need
for the theoretical dark matter.
⁸
Let’s now examine how
my equations would behave when studying gravitational acceleration
within a galaxy.

Recall

And equation (12)

Now we have

As r becomes
relatively small, as compared to a very large mass, the equation
becomes

Although without the
changes in the gravitational constant balancing the changes in the
speed of light, gravitational acceleration would change with the
change in the speed of light, so really we should rewrite this
as

(14)

As all other terms are
constant as r becomes relatively small centripetal gravitational
acceleration varies as a function of radius ‘r’ rather than radius
squared ‘r
²
’ at a relatively small distance from the
centre of a very large mass, just as explained in the empirically
based MOND theory.

Let’s do a plot of
rotational velocities around a point mass, with
m
_E
/m
_∞
given a value of 10.

The above plot is very
interesting with regards to the search for dark matter
.
We can see that for large mass, by my theory, we have
essentially a linear relationship between distance ‘r’ and the
rotational velocity. M
y theory could be the explanation that
we have been searching for. The position where the lines intersect
is the location where the sot
in my equation
is the same as it is on earth, i.e.
Δt
_r
/Δt
_E
= 1. Although the trends shown on the
above plot are very interesting, further investigation on the
subject of dark matter is required.

My hypothesis, in
addition to the possible explanation for dark matter, would also
logically explain the observed acceleration of the universe as it
expands. According to my theory, as the universe expands the
gravitational field strength within the universe would decrease and
therefore time would become faster. As the universe expands and
time becomes faster within the universe, not only would the
expansion of the universe accelerate, but the wavelength of light
travelling from distant galaxies would shift further towards the
red as the sot increases while this light is in transit. The
mysterious expanding force acting on the universe, which has become
known as “dark energy,” could be easily explained by gravitational
time dilation. I will discuss the expansion of the universe further
in Part 3.

Part 1d: Partial
Derivation Of The Gravitational Deflection Of Light

Since momentum is
inversely proportional to the speed of light (10)