Gravity – the Force of
the Fourth Dimension
.
Stefan von Weber, May 2008
.
This paper is giving a short description of the
Cosmic Membrane Theory of
Gravitation worked out by the author from 1969 to 2006. In the beginning
was the Special Relativity of a resting medium, perhaps the quantum vacuum.
Then, in 1994, the author has succeeded in the computing of the curvature of a
three-dimensional membrane in a four-dimensional hyper- space in a simple and
geometrical manner which can be understood by each twelfth-grade scholar. The paper „Kosmische
Membran – ein einfaches didaktisches
Modell zur Allgemeinen Relativitätstheorie„ describes this geometrical way.
In the further years until 2006 the classical and
newer proofs of a theory of gravitation were worked up with regard to the
Cosmic Membrane Theory.
.
Isaac Newton
.
The gravitation is seen as the most
mysterious natural force at all times. The reason is that the gravitation has
two strange features which make the difference to the electrical and magnetic
force. The first strange feature of gravitation is its vast reach. It is acting
not only over a radius of some miles as the electrical force does during a
lightning discharge. Also the reach of the magnetic field of the Earth in the
Earth’s near-space with a value of some ten thousand miles is nothing compared
to the vast distances gravitation can overcome. Its action is holding the
planets of our solar system on their orbits, also the stars of our galaxy
orbiting the center at a distance of many thousand light years. Also the
agglomeration of many galaxies to clusters with diameters of millions of
light-years follows from the gravitation.
The
second strange feature of the gravitation is that it is always attracting.
There is no antigravity.
Isaac
Newton (1643-1727) was the discoverer of the famous gravitational law named
after him. It says that masses attract one another pairwisely, and that this
force is proportional to the product of the masses, and reversely proportional
to the square of the distance between the masses. The constant making an
equation from this relation is the Gravitational
Constant G or g (Gamma), one of the universal constants of nature.
.
(Newton’s
Law of Gravitation)
.
But as usual in science, Newton hasn’t started
at zero. He could refer to the planet laws of Johannes
Kepler (1571-1630). But at first Newton’s Law was showing the deeper
relations between the three planet laws of Kepler.
.
Newton’s Law looks simply, but it isn’t simple. Till now nobody can say
for sure what a mass is. Newton didn’t know the value of the gravitational
constant G or g. This constant we can’t derive theoretically from other, already known
constants. First Henry
Cavendish (1731-1810) could deliver the first numerical value in 1798 by
expensive experiments. He used a torsion balance. The value of the constant is
today known to some digits after the decimal point ( 6.674 28 ´ 10 -11 [m3
kg-1 s-2] ). Also inserting the
distance between masses in Newton’s Law is not a simple act. Newton has needed
twenty years to show that one can simply use the distance of the centers of two
spherical masses. In this time he founded also the infinitesimal calculus, a
second proof of his genius. If we are standing on the surface of our Earth then
each pound mass of the Earth is attracting us differently strong accordingly to
its distance. But we hadn’t to consider this fact, since according to Newton’s
result we can imagine the whole mass of the Earth concentrated in the center,
and the computing is simplified strongly. (We neglect here the oblateness of
the Earth, the inhomogeneous construction of the layers of the Earth and other
unimportant details.) Newton’s genius gave us an exact law, and it proved true
for nearly all computations concerning the orbits of planets, the orbits of
space crafts, or concerning terrestrial issues.
But
also Newton’s genius couldn’t explain because two masses, e.g. two celestial
bodies, attract one another. Surely, he has thought over, but the first answer
came much later.
.
Albert Einstein
.
Two hundred years later Albert Einstein
(1879-1955) entered the stage. He was also an universal genius which made
pioneering discoveries in different disciplines of physics. He made popular the
abstract notion space-time,
a four-dimensional space with three spatial and one time-dimension, found by
Minkowski. But also Einstein hasn’t started at zero.
Names as Carl
Friedrich Gauss (1777-1855), Nikolai
Lobachevsky (1792-1856), Janos
Bolyai (1802-1860), Bernhard
Riemann (1826-1866), Hermann Minkowski
(1864-1909) and Hendrik
Lorentz (1853-1928) are representative for a whole series of famous
mathematicians and physicists. They all opened the gate into the unknown fourth
dimension. If one inspects the four dimensions of Minkowski – x, y, z, -ct – then
one can see that the fourth dimension isn’t truly the time, but a distance
which the light is traveling with speed
c during time t. The minus sign has besides a formal
meaning but has also a plausible explanation: A point with the spatial coordinates x, y, z
disappears with velocity of light into a past, here a hybrid thing of
space and time. It is the merit of Einstein that he overcame paltry
reservations by his General
Theory of Relativity, and despite of all the accentuation of the time in
the artifical word space-time he has treated the fourth dimension as a fourth
spatial dimension in many cases. Who of us can imagine a space-time? Nobody,
but everybody can imagine a curved surface, perhaps a ball or perhaps a
trampoline with a heavy sphere in the midst. And exactly this was the
breakthrough we are indebted to Einstein – the breakthroug which established
the fourth spatial dimension in the minds first figuratively and then
theoretically.
That meanwhile the authors of science fiction literature take nearly as
reality time travels into the past or into the future that follows to a great
extend the inadequate working up of this fourth dimension. Naturally, it’s
nonsense to belive that one could travel in the time as on a road. The author
refers to Immanuel Kant
(1724-1804), or to Stephen
Hawking (*1942). One thing is the time not – a dimension.
The time is a pure product of the human spirit – an important entity for
computation – but really a difficult to understand notion. The time of an “Our
Father in Heaven”, a moment, a day, an year – all these are courses of events
which repeat themselves, or we can repeat them. We can count them or compare to
other courses of events. Indeed, there are only processes, chemical or physical
processes. There does’nt exist any universal time, also not anywhere in outer
space. This has been proved to be valid by physics since clocks change their
running by the influence of gravitation and with their velocity. The persons
managing the GPS, the Global
Positioning System, know best about this. If there doesn’t exist any
physical entity “time” then that has only a formal meaning what we call “time”
in the notion space-time. Well, we can deal with the time, mostly termed
as t.
One car in each two minutes makes 30 cars per hour which roll off the
assembly line. We can measure the time, but it are oscillations only in an
electrical oscillatory circuit of an atomic clock whose
frequency is stabilized by cesium atoms and counted by a high-speed counter.
The General Relativity Theory of Albert Einstein contains Newton’s Law
of Gravitation as a borderline case. Beyond that, Einstein has given the first
practicable theory of the phenomenon gravitation at all. His theory says: By
the curvature of space-time reaction
forces arise with each movement, so as a train makes a lateral pressure to
the rails if it travels through a curve. These reaction forces are the
gravitational forces. In the context of the General Relativity Theory is always
movement. The reason is the term “-ct”.
One carried out a lot of experiments and evaluated a lot of astronomical
observations subsequently. The effects forecasted by Einstein are very small.
So, to measure them, one needs a high art of experimentation and expensive
instrumentation. But all measurements and all observations have proved to be
valid Einstein’s General Relativity Theory (or at least not ruled out).
Therefore, this theory describes the reality with high precission, in special
situations more precise than the simpler law of Isaac Newton.
.
Cosmic Membrane Theory of Gravitation
.
Despite the success the General Relativity Theory is not fully
satisfactory
in some
points, and has the potential for further approvements. One point under
discussion is the space-time. The time is not entitled to have a dimension for
its own, because it is, as discussed above, only a derived, mental, not really
existent entity. But it looks differently for the construction “ct”. This
construction refers to a real distance in a fourth dimension which is still
only loosely connected with the time. Theodor
Kaluza (1885-1954) made this step and postulated the fourth true spatial
dimension. So he found a unified presentation of electromagnetism and
gravitation. Einstein was fascinated by this idea, and arranged the reprint of
the original paper of Kaluza in the Annals
of Physics. Later the fourth spatial dimension was “compactified”
unfortunately by Oskar Klein
(1894-1977), i.e., it was rolled up to create tiny cylinders of Planck length. Because
one couldn’t imagine a fourth spatial dimension one has hidden it simply.
A
second point of critics is that
Einsteins’s field
equations do not directly lead to a solution. They are constructed too
general, and they can represent any possible curvature of space – the simple
gravitational funnel of a star or of a black hole, but also the
famous wormholes. This is the reason, because Newton’s Law of Gravitation is
embedded as a borderline case in the General
Relativity Theory. It chooses the correct solution from a manifold of possible solutions as a kind of boundary
condition.
.
The Cosmic Membrane Theory of
Gravitation uses the model of a three-dimensional membrane which is
expanding in the four-dimensional hyperspace as a balloon.
This theory is a direct further development of the ideas of Einstein and Kaluza
by the author. About at the same time a whole series of physicists have worked
also on the issue of the noncompactified fourth spatial dimension. The author
wishes to mention here some of them, e.g., Lisa Randall (*1962), Raman Sundrum, Tuomo Suntola (*1943), Farhad Darabi, William N. Sajko, Paul S. Wesson, Matej Pavsic.
.
The membrane, in the graph the blue circle, is
our Cosmos. After the Big Bang
our cosmos started to expand and will expand further and further. Our galaxy,
the Milky Way, is only a tiny point at the 3-dimensional surface of this
4-dimensional sphere. Also the whole visible part surrounding us until a
distance of about 14 billions of light years could bee only a small area of the
surface. How small - that is depending
on the unknown speed of expansion VE . The idea with the balloon
isn’t a new one, and was used already in many papers concerning cosmology by different authors.
The surface of the expanding balloon can explain in a simple way, because the
space is stretching and distant galaxies seem to fly away from each other, and
that without any speed relatively to the background radiation. The kind of
material of the membrane is still unknown, although the author has some
conjectures in this case. It is enormously tough, porouse, elastic, and permits
the propagation of all kinds of waves. Further, it is the medium in which
elementary particles be created, exist and move. The physicists have chosen for
it the notion quantum
vacuum. We name it here “mebrane stuff”.
Another conjecture is that the hyperspace is also filled with some
stuff. This stuff has the properties of a gas, and we name it here “ether”. The
ether is so fine that it penetrates the porous membrane without trouble, i.e.,
it doesn’t disturb essentially the expansion. The ether penetrating the
membrane during expansion we name “ether wind”.
Now gravitation
is coming back to the game. Each kind of matter is a distortion in the
membrane, and the ether wind builds up there. The picture shows a galaxy where
the ether wind builds up. The membrane is stressed at this point, and we get a
funnel, a curved piece of space in direction of the fourth dimension.
.
.
Our common three spatial dimensions x, y, z
are embedded in the membrane. Naturally, the relations in the picture
are enormously exaggerated. The Sun sinks about 1000 km, the whole galaxy
scarcely more. Having a diameter of 100.000 light years this is precious
little. Naturally, one could imagine also that the ether wind is coming from
inside the balloon, i.e., an overpressure of ether inside the balloon causes
the expansion. Then the relations would be reversely, i.e., the funnel would
point outside, but the computations would remain the same.
If
another mass is moving in the funnel, e.g. a planet is moving in the
gravitational funnel of the Sun, then this other mass is stressed also by the
ether wind, and has due to the downhill force from
the decomposition of forces the endeavour to move into the centre of the
funnel. This downhill force is our common gravitational force. Only the centrifugal force is
holding the planet in his orbit.
.
What
is supporting this hypothesis? The most striking argument is that a spherical
mass, e.g. a star, produces exactly that (1/r2)-curvature of the
membrane which is demanded by Newton’s law of gravitation, i.e., Newton’s law
is not put in the theory, but it is given by the theory. But this special
curvature we can find only at a 3-dimensional membrane in a 4-dimensional
hyperspace. The author has made a geometrical derivation in 1994 and an
analytical derivation in 1997, which are leading both to the same equation of
curvature without any use of Newton’s law of gravitation. Also a numerical
computation was performed by the author in 1997. A 3-dimensional elastic grid
structure was simulated in a 4-dimensional space. A fictive central load was
given, and then the flexure of the grid was computed. Also in this case the
(1/r2)-curvature demanded by Newton’s law has been found exactly (or
the 1/r-potential).
A
second argument is that the Cosmic Membrane Theory can also explain the effects
forecasted by Einstein. A last argument shall be at this point the simplicity
and plausibility of the model. It deals with elements familiar to us: Force
produces force, and we can see already from the drawing above that gravity is
always attractive.
.
Special Relativity
.
The assumption of a membrane stuff makes old
questions new, questions, from which many physicists think that they are
solved. The membane stuff itself, the quantum vacuum, is used already a long
time in the theory. As well as in the present Cosmic Membrane Theory the
quantum vacuum works with high amounts of inner energy. But the consequences
for the Special
Theory of Relativity are discussed very seldom. Although all results
obtained by Albert Einstein in this area remain true there do exist, however,
questions concerning the interpretation. The best example is the constancy of speed of light.
This constancy is one of the rocks Albert Einstein has built on the building of
his Special Relativity. With the assumption of a medium resting at least in our
three spatial dimensions x, y, z, through which electromagnetic waves do
propagate, the constancy of speed of light becomes an important question. This
constancy is proved by numerous measurements. But also here the Cosmic Membrane
Theory yields a solution in accordance with Einstein – the speed of light will
be measured constant under all circumstances. Also the transformation formulas
for a change of the inertial system are nearly the same as those of the Lorentz transform.
The time transform is identical, even. The coordinate transform differs a
little by the introduction of an additional
cross contraction which was found also independently by Vladimir
Onoochin. But the ratio of length contraction to cross contraction is
exactly the same as in the Special Relativity of Albert Einstein. In several
paragraphs the author has proved the validity of Maxwell’s equations for the Cosmic Membrane Theory of
Gravitation (James
Clerk Maxwell, 1831-1879), furthermore, the far-reaching identity of the
special relativity of the Cosmic Membrane Theory with that of Albert Einstein.
The author used in the discussion paper the following known and famous
experiments:
.
· The interferometer experiment of Albert Michelson
(1852 bis 1931) and Edward
Morley (1838 bis 1923)
· The rotating capacitor experiment by Frederick
Trouton (1863 bis 1922) and his research student Henry R. Noble
· The interferometer experiment with two oppositely directed light beams
on a rotating platform by Georges
Sagnac (1869 bis 1926) (See figure below)
· The explanation of Fresnel’s drag coefficient from the experiments of
Fizeau and Airy Augustin Jean Fresnel
( 1788 bis 1827), Hippolyte
Fizeau (1819 bis 1896), Sir George Biddell Airy
(1801 bis 1892)
· The clock experiment in 1971 by J. C. Hafele und
Richard E. Keating concerning time dilation due to movement and due to the
gravitational field of Earth
· The explanation of the Thomas factor „˝“.
.
.
The rotating Interferometer by Sagnac
.
Classical Proofs of the
Cosmic Membrane Theory of Gravitation
.
Several paragraphs of
the Cosmic Membrane Theory
of Gravitation are concerned with
classical and newer proofs which a theory of gravitation should give.
One expects here an explanation of effects measured already, or forecasts of
effects of future experiments. Classical effects which are sufficiently exact
measured are the Shapiro effect of signal retardation under Sun near signal
trajectories, light deflection by the Sun or by other masses, perihelion
advance of the planets, especially of the Mercury.
Irwin I. Shapiro (*1929)
has measured together with his team the retardation of radar signals
in the case of Sun near signal trajectories of the radar waves. This time delay
is interpreted in the context of the Cosmic Membrane Theory of Gravitation as a
lowering of the velocity of signals in
the gravitational funnel of Sun, and yields the amount measured by Shapiro,
which is also given by the General Relativity Theory.
Measurements of light
deflection by Sun have been spectacular astronomical observations ninety
years ago. In those days one could measure only during an eclipse. Today,
satellites can do this job. Sir Arthur Eddington
(1882 bis 1944) was the first who had successfully undertaken such a
measurement. The deflection is twice as great as the value computed by the
corpuscular theory of light (Johann Georg von
Soldner , 1776-1833). This double value has been forecasted by Einstein and
has been proved to be true by Eddinton and his succeders. The Cosmic Membrane
Theory of Gravitation yields also this double value. Indeed, one half of the
value goes back to gravitation. The other half of the effect goes back to the
above mentioned descent of the velocity
of signals in the gravitational funnel of Sun. This descent has the same
meaning as a change of the refractive index of
the vacuum, and is so one of the causes of light deflection.
.
.
The perihelion advance
of the orbit of the planet Mercury, the nearest
planet to Sun, has already been found soon, so, e.g., by the astronomers Urbain Jean Joseph
Leverrier (1811-1877) and Simon Newcomb
(1835-1909). After a long time of search for a new unknown planet which could
have been responsible for the disturbances, Paul Gerber
(1854 bis 1912) has published about twenty years before Einstein the correct
formula for the computation of the perihelion advance of planets near the Sun.
Paul Gerber’s formula was founded on the assumption that gravity propagates at
the speed of light. But this assumption is leading to well-known difficulties
in the understanding of stable orbits of planets, and so we have to modify the
assumption. Then, Einstein has gotten by the methods of the General Relativity
Theory the same value as Gerber. But in Einstein’s theory a sun near deviation
of the gravitational potential from Newton’s 1/r-potential is playing the most
important role. With this change the orbits of the planets remain stable. The
Cosmic Membrane Theory of Gravitation is using also a relativistic additional
potential of the form 1/r2. One can derivate this additional
potential from the square of the energy under the supposition that gravitation
influences the speed of light as well as the mass of a body. The relativistic
increase of mass of moving particles is known since hundred years, and
experimentally well proved. But inside the gravitational funnel we find the
threefold amount. Only one third comes from the special relativity. The
additional 1/r2-potential doesn’t explain only the perihelion
advance of the orbit of planets, but it can also explain the unexpected
negative acceleration experienced by the spacecrafts Pioneer 10 and 11on
leaving the planetary belt of our solar system. This deceleration was
discovered by the NASA, and is discussed now controversely by physicists and
astronomers. The answer of the author concerning this issue is that the small
additional 1/r2-potential isn’t taken into account by the NASA in
its computations. Within the planetary belt of our solar system the adjustment
computation of the errors hides the small deviation. But outside the planetary
belt the adjustment computation of the errors fails, and the action of the
small potential is becoming visible.
The author proved by a derivation of the
additional small potential from the Einstein-Gerber formula that the postulated
potential can indeed explain the perihelion advance of the Mercury. Another
proof was the numerical integration of the orbit of Mercury under consideration
of the additional potential.
.
Newer Proofs of the Cosmic
Membrane Theory
.
The number of newer
proofs of a theory of gravitation isn’t fixed. Always again new astronomical
observations are made which need an explanation, or physicists forecast new
effects from theory, and try to find them. But gravitational waves, De
Sitter precession (also geodesic precession named) and the Lense-Thirring
effect have meanwhile a half-classical status. The author adds the phenomenon
of Dark Matter, the unexpected negative acceleration experienced by the
spacecrafts Pioneer 10 and 11, and the presently discussed accelerated
expansion of the Universe, all three as newer effects which should be
explained.
Gravitational waves
weren’t measured in the past. But great wave detectors are under construction,
and still greater ones are planned for the outer space. In the Cosmic Membrane
Theory we can imagine two kinds of waves. The longitudinal waves
(or compression waves) are about comparable the sound waves propagating in a
liquid, a solid body or in a gas. Transversal
waves we can better compare with surface waves on a liquid, e.g., the waves
on the sea, or the vibrations of a loudspeaker membrane. The propagation speed
of both kinds of waves can differ. We know that sound waves in water propagate
much faster than gravity waves at the surface. During the movement of the Earth
on its orbit round the Sun both kinds of waves are produced. On the one side,
the cosmic membrane is stretched if the planet Earth passes a position of the
orbit, after the passing the membrane contracts again. That behaviour produces
longitudinal waves. On the other side, the moving Earth presses down the
membrane in the fourth dimension and is producing so transversal waves. Since
the author was successful only in a rough estimation of the elasticity module of
the membrane, one can only give an about value of the density of the membrane
and should restrict to longitudinal waves. Under the assumption that
longitudinal gravitational waves propagate with velocity of light, and further,
that the density of the membrane is equivalent to the energy of the membrane
tension, the loss of energy of the Sun-Earth system is 195 watt. This is the
same value given also by the General Relativity Theory.
The unexpected negative acceleration
experienced by the spacecrafts
Pioneer 10 and 11on leaving the planetary belt of our solar system was
discussed already above in the paragraph “perihelion advance of the Mercury”.
The explanation based on a small additional potential which falls off as 1/r2
can yield the value Da = (8 ± 1) ´10-10 [m/s2], the value published by the NASA.
The De Sitter precession
(also geodesic precession named) and the Lense-Thirring effect
(or frame-dragging effect) are small changes of the direction of the axis of a
free-falling gyroscope, i.e., a gyroscope moving in an orbit in the spherical
gravitational field of a central mass. The Lense-Thirring effect appears
in theory only if the central mass rotates additionally. The NASA and a team of
the Stanford University performed an experiment in 2007, named Gravity Probe B, which
should measure both effects. Because of some unlucky reasons the measuring
accuracy was only ±0.1 arcseconds. But both, NASA and the team of the Stanford University
are working hard to reduce the error. The geodesic precession is due to theory 6.6 arcseconds per year, a value
where the error doesn’t play any role. So, the value of 6.6 has been confirmed
best. But the Lense-Thirring effect is due to theory only 0.04 arseconds per
year, and hasn’t been really confirmed due to the measuring errors of this
experiment.
.
The
author had tried also to compute the value of the geodetic precession in 2006
before the Gravity Probe B experiment has been started, only by the means of
Special Relativity. He has gotten a value near zero. Meanwhile, this value was
ruled out by the Gravity Probe B experiment. In a second try in 2008 the author
accepted the zero result of the Special Relativity, and has concentrated his
attention on the changing properties of the membrane inside the gravitational
funnel. So, the value of 6.6 arcseconds of the Gravity Probe B experiment has
been computed. This value shows that the Cosmic Membrane Theory and General
Relativity do agree also in this special case.
The figure above shows a spherical gyroscope on
its orbit round the Earth in two different positions. In Newton’s theory a
free-falling gyroscope conserves the direction of its spin axis if no torque is
acting on it. Because of the nearly perfect machined spherical shape of the
four quartz balls used as gyroscopes in the Gravity Probe B experiment such a
torque is excluded. Nevertheless, the spin axis does rotate by the tiny amount
of 6.6 arcseconds per year in the direction given by the small red arrow. As
cause the Membrane Theory considers two effects. The first effect considered is
a deceleration or slowing down of each movement in the gravitational funnel,
and is discussed in the Cosmic Membrane Theory for the case of light waves. The
application to matter waves as here in the case of a gyroscope is a conclusion
by analogy. One had to imagine that that part of the gyroscope which is nearer
to Earth has a minimally smaller speed on its trip round the Earth as that part
which is more distant. This difference in the speeds causes a minimal rotation
of the direction of the spin axis. But the computation of the effect is
delivering a value of the precession which is a little too great.
This
surplus of precession is canceled by a second effect. The cause of the second
effect is the change of mass in the gravitational funnel. This change we can derivate
from the square of energy. By the spin of the gyroscope, e.g. in position 1,
mass of the gyroscope is transported from Earth away on that side which is seen
by the viewer (the little white arrow). Hereby the mass shrinks a little. The
surplus of momentum is given to the membrane. The reaction of the membrane is a
force acting on that half-sphere we can see in this position, and acting in the
opposite direction to the movement of the gyroscope on its orbit (the pink
arrow). Because on the backward side of the gyroscope the reverse process is
going on, we have a pair of forces which wants to turn the upper half of the
gyroscope in direction of the viewer. The direction of this torque does agree
with the direction of the little white arrow. Gyroscopes don’t follow a torque
directly, but move laterally. The Theory of spinning tops says the spin axis of
the gyroscope will make a little movement in the opposite direction to the
little red arrow. This small precession corrects the above value which was a little
too great giving exactly the result seeked for. The value of 6.6 arcseconds
found by the Membrane Theory we can compute also with the formula given by de
Sitter or other researchers of the General Relativity, and it is also the value
of the Gravity Probe B experiment.
In
position 2 of the orbit , mass of the
gyroscope is transported in direction of Earth on that side which is seen by
the viewer (the little white arrow). The mass increases a little by the
membrane effect. The missing momentum is delivered by the membrane and acts in
direction of the movement of the gyroscope on its orbit (the pink arrow). The
torque has the same direction also in this position.
The Lense-Thirring effect doesn’t appear in
the Cosmic Membrane Theory in the same form as in Einstein’s theory, because
the transmission of the gravity from mass point to mass point by gravitons is not assumed. But
a similar effect of frame-dragging is thinkable, i.e., the rotating Earth takes
with it a little the surrounding membrane, similarly to a whirl beater which is
whirling the soup. But the author has no imagination of the value of the
effect. He supposes, if the frame-dragging effect is existing at all, it is
smaller than the 0,04 arcseconds of the Thirring-Lense effect.
The
phenomenon of Dark Matter
is another support of the Cosmic Membrane Theory. Vera Rubin (*1928) and many
others have discovered that the stars of most of the galaxies are moving to
fast around the center. If one plots in a graph the speed of the stars against
their distances r from the galactic center then the most galaxies are showing
nearly flat rotation
curves, i.e., the speed of the stars is about 200 km/s, independently of
wheather they are closer to the center or more distant. In the solar system,
however, the inner planets move much faster than the outer ones, and that is
good so because otherwise they would fly away. The visible matter of a galaxy
is not sufficient by far to hold together the galaxy by its gravitation. The
so-called dark matter is filling now this gap. One supposes that 80 to 90
percent of the matter of a galaxy is dark matter. In clusters of galaxies one
supposes still higher percentages. Physicists and astronomers have made a
series of suppositions what dark matter could be, e.g. brown dwarfs, heavy
neutrinos or exotic particles, the so-called weakly interacting massive particles (WIMPs). Today
one knows from astronomical observations that dark matter does appear always
only together with common matter, i.e., together with stars or clouds of gas.
This phenomenon has induced the author to seek a mechanism of the membrane
which is triggered by the common matter, and which causes an additional
deepening of the gravitational funnel. Base and starting point is the supposed
granular structure of the membrane stuff. It could consist of tiny torus-shaped
(donut-shaped) whirlpools. Besides, these tiny whirlpools could be a thinkable basis of a
quantization of the space, and they could become a connecting member between
Quantum theory and theory of gravitation. If the membrane
is perpendicular to the ether wind then the whirlpools are not influenced. The
ether wind is pervading through the pores without any resistance.
.
.
If the membrane is
sloped as inside of a gravitational
funnel then forces can arise which change the membrane, e.g., its
density is increasing. Such changes can produce an additional resistance, i.e.,
the gravitational funnel will become deeper. But under certain circumstances
the change can also cause a lift, i.e., exactly do the opposite. The author has
established an ordinary
differential equation (ODE) of curvature of space yielding the
typical flat rotation curves for models with radial symmetry, e.g., elliptical or spherical
galaxies. The downward-sloped curve in the figure below is the
expected rotation curve without dark matter. This curve shows the speed stars
should have at distance r from the center if no dark matter is involved.
.
Rotation curves
.
Spiral galaxies and their baby form, the bar galaxies,
are more difficult to handle. But the author has solved numerically the partial
differential equation (PDE) using a spatial grid, and again a nearly flat
rotation curve has been computed. So the Cosmic Membrane Theory is delivering a
model of the nature of dark matter which is worthy to discuss: dark matter is not matter in the really
sense, but an effect of the cosmic membrane induced by ordinary baryonic
matter. Besides, the
effects of the dark matter are so small that they don’t influence the movements
of the planets in our solar system.
The accelerated
expansion of the Universe: Adam Riess and Mario Livio from Space Telescope Science Institute had presented in 2001 a supernova 11
billions light years distant from us, but in the Hubble diagram this supernova is only half
as bright as it should be due to its redshift, and therefore
apparently further away than assumed. Astronomers and astrophysicists are
discussing the thesis whether the expansion of the Universe is accelerating or
not since that time. The author has his own opinion concerning this issue. Our
Universe is expanding with nearly constant speed since the Big Bang. But the properties
of the membrane can change, and therewith physical constants can change too,
for example as the skin of a balloon is becoming thinner if it is blown up. The
most important change is the increase of the velocity of light due to the
increasing tension of the membrane. Indeed, one can find a scenario in which
distant supernovae are only half as bright as one expects due to their
redshift. In the figure “Expansion of the
Universe” we can see that an object with redshift z=10 has emitted
its light about at time T=0.1 after the Big Bang. Assuming an age of the
Universe of about 14 billion years the time T=0.1 corresponds to 1.4 billion
years.
.
.
Expansion
of the Universe
×
The
radius of today’s Universe has been set here to R=1. Time T, the abszissa axis,
is the eigentime (proper
time) of a clock moving with the membrane. Time t is the time of a resting
outer observer with the time flow of today. The blue curve, R(t), shows the
radius of the Universe against
eigentime T. Because the first seconds of the eigentime stretched
endless by reason of the thick and only weakly stretched membrane short after
the Big Bang the Universe grew up this time with nearly infinite speed, but
only arithmetically. The green curve, Rz(t), shows the real expansion how an
outer observer with a clock of the present time would have seen it. But the
figure explains also the Inflation
of the Universe which Alan Guth (*1947) has
proposed to explain the flatness problem of the Cosmic
Background Radiation. In the context of the Cosmic Membrane Theory
this inflation was not an inflation of the radius but an effect of the small
speed of light at that time, and of the slow progress of all physical processes
in the fat viscous soup of the young membrane.
.
Some Conclusions
.
The
most important result of the Cosmic Membrane Theory of Gravitation is the
derivation of the gravitational law which one gets automatically if one uses a
three-dimensional membrane in a four-dimensional hyper space. Furthermore, the
membrane model can give us a base for the understanding of the dark matter. The supposed granular structure
of the membrane stuff could be a
thinkable basis of a quantization of the space, and could become a connecting
member between Quantum theory and theory of gravitation. Albert
Einstein’s results remain unchanged nearly completely. Only some kinds of sight
change.
But
the membrane model can also push other disciplines of physics and technics.
Until now, one has assumed that, e.g., the electrons are moving around the
kernels of the atoms without any loss of energy, and this from olden times
until now. Now
we can calm down. The electrons could refresh also their energy
by the ether wind of the expansion, so as flags flutter in the wind.
Furthermore, new matter could form permanently, because the slow down of the
membrane by the ether wind will set free great amounts of energy. The membrane
has, compared with the existing matter, such a vast mass that this slow down
has nearly no influence on it.
Ether
mills are thinkable which can use the inexhaustible kinetic energy of the
membrane for the production of electrical power at some time or other. Ether
sails are thinkable which will speed up the spacecrafts of mankind nearly to
the speed of light.
One
danger one shouldn’t hide: The steadily growing balloon, our Universe, could
rupture one day, and end not only the mankind but also the whole Universe. If Bruce Willis can’t
prevent this debacle then we, nevertheless, can have the hope that there are
still many parallel Universes.
.
I thank Burkhardt Seifert, Zurich, for his
advice and interest in this matter, and I thank Jeffrey O’Callaghan for his imperturbable adherence to the four spatial dimensions of our
Universe.