Investigation 
This investigation is stimulated by the search for dark
matter. The existence of dark matter
has been proposed to explain the observation of strange gravitational
phenomena in space. This page
investigates the hypothesis that instead of dark matter the universe contains
a significant amount of antigravity matter.
According to this hypothesis it is the antigravity matter that has
caused these strange gravitylike fields.
The reader is advised to read the Behaviour page
for an introductory explanation of some of the concepts discussed here. Hypothesis The hypothetical antigravity matter has the following
characteristics: ·
Antigravity matter is made of particles. ·
Particles of antigravity matter have positive
mass and inertia. ·
Particles of antigravity matter are repelled from
other particles of antigravity matter by a force which is similar in strength
and behaviour to the opposite of gravity. ·
Particles of antigravity matter are repelled from
normal matter objects by a force which is similar in strength and behaviour
to the opposite of gravity. Normal
matter particles and antigravity matter particles rarely interact apart from
via antigravity. ·
Light is deflected away from antigravity matter
in a way that is similar to the opposite of gravity. Light does not otherwise interact with
antigravity matter. ·
Antigravity matter has existed for a large part
of the life of the universe. Initial Deductions The following deductions are made assuming the
hypothesis above is true: ·
Antigravity matter has spread out throughout
interstellar and intergalactic space to form a thin atmosphere. There is little or no antigravity matter
near the sun or any other star because of the repulsion between antigravity
matter and normal matter. ·
The deep space antigravity matter atmosphere
behaves like a conventional theoretical ideal gas and has the bulk properties
of density, temperature and pressure.
These affect its behaviour in addition to the effect of
antigravity. Because of the expansion
of the universe the deep space antigravity matter atmosphere has a low but
nonzero temperature. ·
In a gravity field free normal matter particles
move in the opposite direction to free antigravity matter particles. However in an antigravity field normal
matter particles and antigravity matter particles move in the same
direction. Therefore antigravity is
not exactly the opposite of gravity. Symbols In the calculations and discussion below and referenced
from this page the following symbols are used.


Maths with no AGM Pressure Initially
we carry out a mathematical analysis based on simplifying the assumption that
antigravity matter is cold and AGM Pressure is so low that it can be
ignored. This is developed in Basic Maths. One conclusion from
that page is that if the pressure of antigravity matter is negligible the AGM
Exclusion Density should be independent of the mass of the normal matter
object. An
intellectual exercise to try to help to visualise antigravity matter is
described in AGM
Container. Initial Analysis of the AGM
Exclusion Density According
to the AGM Theory several types of normal matter objects should be at or
close to the AGM Exclusion Density.
This is described in Behaviour.
An initial rough collection of the densities from common sources is plotted
on the right. The density
of these objects is obviously not independent of radius. The densities appear to decrease with
increasing radius. That is what might be expected if AGM Pressure was
involved. However the maths developed in Basic Maths is not valid for cases where
AGM Pressure is nonzero. We therefore take an alternative analysis
approach in the following sections by using a simulation. 

Introduction to an
AGM Pressure Simulation A
simulation of antigravity matter under the influence of AGM Pressure has been
produced. A sample result is shown on the right. The simulation
is described in Introduction to AGM Pressure
Simulation along with some example
results. Some initial
conclusions from the AGM Pressure Simulation are:


The graph
on the right is developed in Analysis
of Bok Globules and also in the draft paper Antigravity Matter and Bok Globules. The black
points represent 11 Bok Globules. The red line is the Dnx Line as predicted by the AGM Pressure
Simulation. That is, it shows the relationship between the AGM
Exclusion Density and the radius of the AGM Boundary as the mass of the
central normal matter object varies while keeping Gnn,
Gna, Gaa, Dab, and Pab constant. The
position of the Dnx Line has been adjusted to fit
the Bok Globule points by choosing suitable values for Gna,
Gaa, Dab and Pab. The position of the line can be varied but
the gradient cannot.
The
gradient of the red Dnx Line from the simulation
appears to fit the gradient of the Bok Globule data. However this
gradient is different from the trend in the Initial Analysis of the AGM
Exclusion Density above. The equation
of the red line is: Radius = 2.1 ×10^{7} × Density^{0.501}^{} Where
radius is in meters and density is in kg/cu m. 

Further Exploration
of the AGM Exclusion Density In the
section above we chose a set of simulation parameters that allowed the AGM
Pressure Simulation to produce a Dnx Line that
matches the data from the 11 Bok Globules. In this section we investigate how
the AGM Exclusion Density varies as the normal matter mass increases
further. This leads to the graph on the right.
It can be
seen that the antigravity matter has two behaviours. At small scale the
antigravity matter particles are pushed apart mostly by AGM Pressure and
antigravity is irrelevant between antigravity matter particles. This
leads to the sloping Dnx Lines. At larger
scale the antigravity matter particles are pushed apart mostly by antigravity
and AGM Pressure is irrelevant. This leads to the vertical Dnx lines and AGM Exclusion Density independent of
radius. The scale at which the two behaviours meet is referred to as
the “G/P limit”. Therefore
at small scale the antigravity between antigravity matter particles can be
ignored and Gaa can be assumed to be zero. This means that a mathematical analysis of
the effects of AGM Pressure becomes much easier. This is set out in Maths with AGM Pressure. This confirms that the gradient of the
lower part of the Dnx line should be 0.5 on a
log/log graph. From the
Bok globule data and the Maths with AGM Pressure in the page linked above we
can estimate that:
If the red Dnx line is extrapolated to smaller scale an estimate can be made of the radius of the Sun’s AGM Boundary if it were not affected by antigravity matter wind. That radius is about 1.1 × 10^{15} m which is about 0.11 lightyears. This gives an AGM Exclusion density for objects of that mass of about 3.9 × 10^{16 }kg m^{3}. 

Globular Clusters An analysis
of the Milky Way’s globular clusters is described in Analysis of Globular Clusters. The conclusion from that analysis is that
the distribution of globular clusters on the graph on the right is consistent
with them orbiting within antigravity matter. Their increased density
is caused by the antigravity matter wind caused by their own movement. Further
results are set out in Analysis of Globular Cluster Colour. This identifies unexplained patterns in the
relationship between globular cluster radius and colour. This may not be caused by antigravity
matter, but is referenced in the analysis of elliptical galaxies. Elliptical Galaxies Elliptical
galaxies have been found to have a ratio of normal matter to apparent dark
matter of approximately 0.8. (source). Therefore
from Basic Maths
8) we estimate that: = 0.8 Further
analysis is described in Analysis
of Elliptical Galaxies. Once a plausible correction is applied to
the data elliptical galaxies can be made to behave as predicted and have approximately the same
density. (This is not presented as evidence for the existence of antigravity
mater but is at least not evidence against antigravity matter) The vertical red dashed line in the graph
on the right shows an estimate of the lowest reasonable value for large scale
AGM Exclusion Density, Dnx. However the actual large scale Dnx could be much higher than that if the AGM Boundary of
a typical elliptical galaxy is deep inside the galaxy. From this and the Basic Maths we estimate that: Large scale AGM Exclusion Density = Dab × Gaa/Gna > 1.4 ×10^{21}
kg/cu m. 

Antigravity Matter in the Milky Way We assume that the local
interstellar cloud is drifting along with the antigravity matter in
interstellar space near the Sun. That
is, it has low velocity relative to the antigravity matter (as explained in Behaviour). The local interstellar
cloud is approaching the Sun from the direction of the galaxy centre Sun (source). Therefore the antigravity matter is orbiting the
Milky Way at approximately the same circumferential speed as the Sun, about
220 ×10^{3} ms^{1} (source), and moving radially outwards at a
speed of about 25 ×10^{3} ms^{1} relative the the Sun (source). This
complies with the description of antigravity matter within a spiral galaxy in
Behaviour. Consider a particle of
antigravity matter on that trajectory in the vicinity of the Sun but away
from the influence of the Sun’s gravity.
Its centripetal acceleration is provided by an antigravity matter mass
reduction of M inside its orbit. The particles’s centripetal
acceleration = . The Sun is moving in a circular orbit around the
Milky Way. Its centripetal
acceleration is mostly provided by the same antigravity matter mass reduction
of mass M. The Sun’s centripetal
acceleration = . But we know that the Sun is
in a circular orbit and the antigravity matter is on a spiral orbit moving
outwards (as explained in Behaviour). Both are
moving circumferentially at the same speed.
Therefore the antigravity matter particle’s centripetal acceleration
must be less than or equal to the Sun’s centripetal aceleration. Therefore And
Gaa
Gna Andtherefore
using the equation from Elliptical Galaxies section above Gna
0.8 Gnn 

The graph
on the right is created in Analysis of Abell
1689. This shows the density of
antigravity matter within and around the cluster against radius. This
shape is consistent with an antigravity matter vortex. That analysis also concludes that: > 1.2 × 10^{20}
kgm^{3} 

The graph
on the right is created in Analysis of the Coma Cluster.
This shows the variation in antigravity matter density around the
cluster. The Coma Cluster has a much
weaker vortex than Abell 1689. 

An Upper Limit Estimate of the Background Density of Antigravity
Matter In the Behaviour page it is explained that a rotating spiral galaxy will
cause the antigravity matter to orbit the galaxy. The antigravity matter flows out of the
galaxy to be replaced by more.
Antigravity matter is being continuously accelerated by the rotating
galaxy disc. If the density of
antigravity were too high this the disc would lose energy very quickly and
spiral galaxies would be rare. However
if the density of antigravity matter were too low there would be no drag and
the effect would not occur. By considering the distance
to the nearest stars we estimate the average density of the local stars to be
about 7.0 × 10^{21} kg m^{3}. We take that as the average
density of the galaxy disc. We then
take that as an upper limit on the density of antigravity matter. Therefore Dab
< 7.0 × 10^{21} kg m^{3} 

Calculation This investigation has
developed the following estimates: 1) = 1.3 ×10^{15} mkg^{1} (from Further Exploration of the
AGM Exclusion Density above) 2) = 0.8 (from Elliptical Galaxies
above) 3) Dnx = Dab × Gaa/Gna > 1.4 ×10^{21}
kgm^{3}. (from Elliptical Galaxies above) 4) Gaa Gna (from Antigravity Matter in the Milky
Way above) 5) Gna 0.8 Gnn (from Antigravity Matter in the
Milky Way above) 6) > 1.2 × 10^{20}
kgm^{3} (from in Analysis of Abell
1689) 7) Dab < 7.0 × 10^{21} kg m^{3 }(from
An Estimate of the Background Density of Antigravity Matter above) 3) and 4)
give Dab > 1.4 ×10^{21} kgm^{3}. 5) and 6)
give Dab > 1.5 ×10^{20} kgm^{3}. This latter
is a surprisingly high value for Dab and conflicts with 7). 7) is only based
on a rough estimate so the conflict is not too serious but it does suggest
that Gna and Gaa are both
close in value to Gnn to at least minimise the
conflict. 

Guesses We now make
the following guesses: ·
The
density reduction in Abell 1689 is only 50% of the
background density. This is because we
consider it would be unlikely that vortices would clear all antigravity
matter out of a volume of space. ·
Gna = Gaa = 0.8 × 6.67 × 10^{11} = 5.3 × 10^{11} kg m^{3} as suggested in the Calculation
section above. Based on
these guesses Dab = 2 × 1.2 × 10^{20} / 0.8 = 3 ×10^{20}
kgm^{3}. Pab = 1.2 × 10^{15} kgm^{1}s^{2}.^{} The large scale AGM Exclusion Density = Dnx = 3 ×10^{20} kgm^{3}. 

Gravitational Effect in the Solar System Antigravity matter should
cause the Sun’s gravity to appear to be increased but this has not been
detected. In this source the error on the known mass of the
Sun is +/ 0.000126 of the mass of the Sun.
This value has been measured though its various gravitational
effects. Therefore the effect of the
antigravity matter must less that this.
Using the
figures above in Guesses at a radius of 130 AU (which is approximately the
distance of Voyager 1 from the Sun) the antigravity matter will increase the
Sun’s apparent gravity by a factor of (1 + 3.7 × 10^{10}). Closer in the effect will be even less. 

Consider the possibility that antigravity matter particles are related
to Neutrinos Neutrinos have previously
been discounted as dark matter candidates because they would clump together
under gravity. If they are antigravity
matter this does not apply. The mass
and tempterature of neutrinos have been estimated through cosmological
arguments. However these arguments
assume that they have gravity. Again
if they are antigravity matter this does not apply. It has been estimated that
the average density of neutrinos in the universe is 336 per cubic centimetre
(source).
Most of these are relics from the beginning of the universe. . If we assume that: ·
Neutrinos are,
or have somehow become antigravity matter particles ·
Antigravity
matter acts as an ideal gas and follows Boltzmann’s law PV = nRT. Then for a unit volume Temperature = Pab/(336 × 10^{6}
× Boltzmann’s constant) And therefore the
temperature of antigravity matter is 0.25 degrees. The mass of
an antigravity matter particles can be estimated as Dab / (336 × 10^{6})
= 8.9 × 10^{29} kg. Based on
the figures in the Guesses section above this is about 5.5 % of the mass of a
neutron. 

The Sun’s AGM Boundary An estimate
is made above of the radius of the Sun’s AGM Boundary if it were not affected
by antigravity matter wind. That
radius is about 1.1 × 10^{15} m which is about 0.11 lightyears. However there is expected to be a local antigravity matter wind (as explained in Behaviour) and this will distort the Sun’s AGM Boundary so that it has a point of closest approach to the Sun facing the antigravity matter wind and a tail stretching out in the opposite direction. One simplistic way to calculate the radius of closest approach is using the conventional escape velocity equation except that V is the velocity of the antigravity matter wind at a distance. V = Where M is the mass
of the Sun and R is the radius of closest approach. This
equation would calculate the closest approach if affected only by repulsion
between an antigravity matter particle and the Sun. However we expect that AGM Pressure will
have an additional effect slowing down the approaching antigravity
matter. We therefore create a computer
algorithm calculating approach velocity, density and pressure during the
approach. We assume that the starting
wind speed is 25 ×10^{3} ms^{1} as estimated in the
Antigravity Matter in the Milky Way section above.
Taking the other figures from Guesses above leads to the result shown
on the right. Using this
algorithm we conclude that a closest approach of antigravity matter would be
3 × 10^{11} m = 2 AU. This is
a problem because it is difficult to see how it fits with other observations
of the solar system. Resolutions of
this could be: ·
Perhaps
the approach velocity is much less. ·
Perhaps
antigravity matter is affected in some way by the solar wind or by the
neutrinos emitted by the Sun. 
© Copyright Tim E Simmons 2008 to
2016. Last updated 24^{th} March
2016. Major changes are logged in AGM Change Log.