Demystified gravitation | ||
with the critique of the Big Bang cosmology and so necessarily
with the explanation of illusion of universal expansion and elimination of Λ from Einstein field equation and other improvements to the theory not even mention its quantization by W. Jim Jastrzebski | ||
PhD program supervised by prof. Józef M. Namysłowski
The Institute of Theoretical Physics, room 139, Hoża 69, 00-681 Warsaw, Poland | ||
"Let me also say something that people who worry about mathematical proofs and inconsistencies seem not to know. There is no way of showing mathematically that a physical conclusion is wrong or inconsistent. All that can be shown is that the mathematical assumptions are wrong. If we find that certain mathematical assumptions lead to a logically inconsistent description of Nature, we change the assumptions, not nature." Feynman "Lectures on gravitation" | ||
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"Everything should be made as simple as possible, but not simpler." Einstein | ||
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"Λ [cosmological constant] = the biggest blunder of my life." Einstein |
Abstract
It has been shown that the big bang hypothesis
(BBH) oversimplified the physics of
Einsteins' general relativity (EGR) by neglecting the
Hubble time dilation (HTD) as the reason of cosmological redshift.
Overlooking the coupling between temporal and spatial parts of Ricci
tensor that makes the spacetime intrinsicaly flat produced such
artifacts as
N.B.: Since rev 1.xx of this paper I've come to the
conclusion that most likely the relativity
has been discovered mainly by Mileva Marić (1875-1948), Albert
Einstein's (1879-1955) first wife, during their possible discussions
of the subject (based on inability of Albert to get rid of Einstein's
"cosmological constant" from Einstein Field Equation but done recently
by me, an amateur mathematician).
For this reason I changed in rev 2 many refs to the theory from
singular to plural calling it Einsteins' theory of relativity
(or gravitation where appropriate).
Preamble
In 1543 Nicolaus Copernicus (1473-1543) postulated that
the movement of the Sun around the Earth was an illusion
due to Earth rotation (why would the big Sun circle the small
Earth instead of a simple rotation of Earth and running around
the big Sun as other planets do?)
He figured it out much earlier than 1543 but it was not too safe
to have a difference of opinions with the establishment so he
waited with publishing the news until he was sure that he was dying
so if something went wrong with his publication the establishment
could be able to burn only his book.
The establishment didn't accept Copernicus' common sense idea for
many years.
It was even worse than that since one of the greatest astronomers
of the time, Tycho Brache, member of establishment himself, rulled
out the possibility that the Sun sits at the center of our solar
system, on the basis of lack of observable paralax of nearer
stars against the farther ones.
He maintained that it made no sense for God to place stars so far
that the paralax were invisible (having no telescope invented yet
he couldn't know that the stars were even thousands times farther).
So establishment astronomers didn't want to support Copernicu's
common sense idea and were producing false arguments against it.
Not unlike nowadays when the establishment astronomers suport the
BBH with false arguments, despite that BBH contradicts not only
Newton's math and Einsteins' physics but its proponents claim also the
necessity of invalidity of principle of conservation of 4-momentum.
Richard Feynman says: "a (4) claim based on the stupidity of the author that
some obvious and correct fact, accepted and checked for years, is,
in fact, false (these are the worst: no argument will convince
the idiot)" [fragment of Feynman's letter from the Gravity
Conference in Warsaw, Poland, to his wife].
This whole establishment's effort might be taking place only not to
disappoint creationist foundations that support the establishment's
scientists with money given to them as gifts for which the establishment
just feels obliged to return the favour pushing the creationism (the
"methaphysical boundries of science" as they call it).
Today burning scientists at stake to teach them something is not legal so the
opponents are just denied publications by establishment editors and
in all cases it suffices.
So any new discoveries have to wait with publications until the old
establishment guys die out.
Which eventually happens and the science progresses.
It takes a lot of time though.
E.g. the discovery that the universe is not
expanding, the consequence of Einsteins' general relativity, waits already
over 25 years for publication.
This is not as bad as in times when the Catholic Church rulled the world
(which reminds us better not to let it happen again).
In 1600 Gordano Bruno (1548-1600) was burned at stake by
the Catholic Church for propagating the Copernican idea and
maintaining that the existence of God, the creator of the
universe has been an illusion too.
Galileo Galilei (1564-1642) was warned of the panishment for
propagating ideas contradicting the establishment.
It is like today, when people are scared into complying
with the establishment's opinion since, despite that they can't
be legally burned at stake any more, they may easily lose their
jobs and most of them, especially their families, still need to
eat [1].
Incidentally, Galileo became a founder of scientific method
with which science discovered many more illusions that people
believed in, in denial of their rather obvious fictitious nature.
Example of such things are "creation of something from
nothing" in which even some ancient Greeks
didn't believe.
The existence of "fundamental force of gravity" is another
such illusion since "force of gravity" turned out in
1915 to be only an inertial force that depends on acceleration of
the object experiencing this force.
Another example is the existence of "magnetic force"
while it turned out to be electric force from different point
of view and then the both forces together were called
"electromagnetic".
Already in 1687 Isaac Newton (1643-1727) discovered a
mathematical theory of gravitation.
He didn't know the physical reason for it.
He refused to believe that it is gravitational
attraction since he didn't believe in
action at a distance.
Neither did Albert Einstein (1879-1955) who called it
spooky.
Both considered it an illusion.
In 1905 Einstein discovered
relativity that made possible to
discover physical theory of
gravitation.
He developed it between 1911 and 1915 but its
field equation turned out to be
unstable and Einstein stabilized it in 1917 with his
cosmological
The observations of galactic redshifts by Vesto Slipher, after
he had discovered the blueshift of Andromeda in 1912,
outnumbered the observations of blueshifts by about four to one.
It gave some astronomers an idea that the universe is expanding
on the average.
It was their best guess since the notion of curved space was not
known yet.
Einstein discovered it only three years later so it was not possible
to guess that galactic redshifts are the relativistic effects of
curvature of space.
In 1931 cosensus of astronomers accepted the idea of
astronomer, mathematician, and Catholic Priest George LeMaitre
(1894-1966), that galaxies move away from us on average and
that the observed redshift may be a Doppler shift due to the
recession of galaxies.
It would suggest that the universe began in form of LeMaitre's
"cosmic egg" and it is expanding ever since.
The redshift caused by the alleged expansion of universe has
been named "cosmological" and the alleged moment of "creation
of universe" (appearing of "cosmic egg" out of blue) has been
named in 1949 the "Big Bang" by Fred Hoyle, an astronomer who
didn't take seriously this event and offered his own
hypothesis about the cosmological redshift in agreement with
so called "perfect cosmological principle" but not with the
principle of conservation of energy and so impossible from
the point of view of physics based on strict conservation of
energy.
The thing that has been preventing the discovery of the reason
for the redshift in stationary space was
the other flaw left in the theory (except the cosmological
constant).
It was the symmetric metric tensor of
spacetime.
In 1950 Einstein noticed that the metric tensor
must be non symmetric.
It turned out to be a necessary step in discovering that the
reason for the cosmological redshift is
the inability of nature to create energy from nothing.
Einstein was already 71 and despite he opposed LeMaitre's idea
he was apparently not interested in fixing all the mathematical
details of his theory that he stopped to understand.
He said: "I stopped to understand my theory when
mathematicians started to explain it to me".
He left to young mathehaticians the explanation of Hubble
redshift.
The young mathematicians failed miserably despite Richard P.
Feynman's (1918-1988) warning against treating
mathematics as superior to physics (see Feynman's quote on the
front page).
In 1973 Charles Misner(1932-), Kip Thorne(1940-), and
John Archibald Wheeler(1922-2008) (MTW)
published their own, mathematical theory of
general relativity based on axioms, ignoring
the relativistic interrelation of time and
space well known already from the special relativity and the
principle of conservation of energy following
from Einstein's assertion of 1950 that metric tensor of
spacetime must be non symmetric.
They assumed symmetric metric tensor of spacetime, and
zero value of cosmological constant in attempt to make
Einsteins' equation "elegant" again, which, according to
Friedmann solution created an artifact of decelerating
expansion of space.
They accepted 1931 idea of George LeMaitre that the universe
got created in the Big Bang event some 14 billion years ago and
is expanding ever since.
MTW book has been adorned with a picture of an angel blowing a
horn and a quote from Leibniz "One suffices to create
Everything of nothing!" on
The necessity of calculating the amount of redshift in
"Einsteins' (stationary) universe" that
would falsify the story of creation was avoided by convincing
astrophysicists that it is negligible.
The legend of negligible redshift (despite it being one more
illusion clarified already by me in 1985) lives
till today among astronomers, so they don't even try to
calculate it rigorously, just maintain that they
don't understand gravitation.
The cosmology with never calculated amount of
intrinsic redshift and with the violation of
principle of conservation of energy became a "standard
cosmological model".
The lack of conservation of energy has been more subtle than the
creation of whole universe from nothing.
It was an assumption deduced from assumed symmetric metric tensor
of spacetime that dynamical friction doesn't apply to
photons.
Consequently photons had to move with no loss of energy in stationary
universe despite their gravitational interaction
with the masses of universe.
Equivalently, the time has to run at the same rate in the whole universe,
which has been false even in everyday life as shown already by Einsteins'
special relativity and also by the gravitational redshift.
MTW's hypothesis allowed exceptions from physical laws to save their
belief that the universe was created and the effect
of their efforts was that their gravitation was not Einsteins' but
Newton's mechanics with its conservative gravitational field,
as if there was no other option but to assume that the energy
of photons that necessarily was dispersed in universe, was
miraculously recreated from nothing to keep redshift of photons
in non expanding universe equal exactly zero to keep viable the
idea of expansion of universe.
One of the recent additions to the list of illusions
rectified by science is the "expansion of the universe" falsified
only in 1985 due to the help of Newton's math and Einsteins' physics
but still kept as a secret by the editors of scientific journals.
In February 1985, neither being aware of logical
equilibristics of mathematicians promoting BBH nor knowing
that the redshift in Einsteins' universe was supposed to be negligible
I calculated this redshift using simple
Newtonian math and even simpler Einsteinian physics.
The Hubble constant of Einsteins' universe turned out
to be
In 1998 the Supernova Cosmology Project showed
that observations of universe are consistent with the above proposition
with accuracy better than one sigma, which allowed
also to eliminate the cosmological constant from
Einsteins' field equation making it elegant again.
Then it turned out that there is a progress in treating hretics
who contradict creationism: I was not burned at stake
(so far) for opposing creationism as Gordano Bruno was but only banned for
life from some moderated physics and astronomy internet fora and the papers
describing the reasons for my proposition were just rejected by editors of
scientific journals like "Nature", "Science", "Nuovo Cimento"
(defunct since), "The Astrophysical Journal" (still in the 20th
century) and by "Physical New Journal" and many others already in
the 21st century, usually without any peer review and they still keep
getting rejected when I try to test those journals for the presence of
editors interested in progress in science.
The only exception in not sending my papers to referees was "Physical
Review Letters" which gave a decent review by its second referee
(the first one resigned the reviewing claiming not understandig my way
of describing my derivation).
The second referee, after multiple corrections of his/her point of view
when I kept clarifying mine, agreed that I'm right formally but
recomended rejection of my paper anyway on the grounds of assumed low
interest of readers of "Physical Review Letters" in the subject.
The plot thickens...
Table of Contents
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Introduction
The cosmology seemed to deteriorate to the point that despite that Hubble constant of Einsteins' universe could be calculated from first principles with just the Newtonian math and high school calculus, by a sculptor with no formal education in general relativity, and the results of calculations were confirmed by observations of real universe by real astronomers, the cosmologists still maintained that the universe was created in a hot Big Bang and that it is expanding.
The cosmologists renamed cosmological constant "dark energy" to keep the creation of energy that the expansion of universe implied.
To many of them, as to an astronomer, mathematician, and Catholic priest Michael Heller, who was awarded $1.6 milion by creationists from The Templeton Foundation for his work on attempting to unify science and religion the "dark energy" might have been a direct proof of existence of supernatural and it seemed to be too precious a "scientific discovery" to be given up to common Newtonian math and high school calculus.
The cosmologist refering the results at Phys. Rev. Lett. insisted that those results "must not be published".
For astronomers who this way were cut off from the information on real state of universe it meant choosing what in their opinion was the more probable option.
The atheists, like Carl Sagan (1934-1996), have chosen even earlier, an eternal, stationary universe but the consensus of astronomers still prefers the expanding, "standard model" universe controlled by simplified Newtonian mechanics in which the time runs at the same rate in the whole universe except for the gravitational time dilation which for sure is not a reason for the cosmological redshift since its math is different.
The Hubble tensor that explains the math of cosmological redshift became for the astronomers a tabu that can't be even mentioned neither in a scientific journal nor in the moderated Internet fora.
For Einsteins' general relativity it meant that there exists, a mentioned above, Hubble tensor or tensor of general time dilation (actually the temporal, antisymmetric, part of Ricci tensor) formed by second partial derivatives of proper time with respect to coordinate time and coordinate distance.
I called this type of time dilation I call "general", to distinguish it from "common" gravitational time dilation that being of vectoral character disappears in homogeneous space.
Hubble tensor, similarly as Ricci tensor, of which it is a mirror image in certain sense (their sum add to zero) doesn't disappear in physical space.
Physical sense of Hubble tensor is that the time at the distance from any observer runs slower than at the observer proportionally to the curvature of space accumulated between the observer and the point at the distance from the observer, similarly as spheres around the observer have smaller surface than they would have at the same distance in empty (Euclidean) space.
This effect of slowing the time rate with distance simmulates the accelerating expansion of space.
Adding up of Hubble tensor with Ricci tensor of curvature of space makes the spacetime intrinsically flat as proposed also by Halton
Einsteins' universe gets vindicated as predicted by Feynman, that "Whenever the predictions of Einstein have been found to differ from ideas of Newtonian mechanics Nature has chosen Einstein's."
(continued from preamble)
The results proved to be unpublishable despite their agreement with observations of Hubble constant and its acceleration, both predicted by Einsteins' GR and both observed by astronomers in deep space.
Feynman could enjoy the success of his prediction if the editors of scientific journals didn't decide to keep the collapse of MTW mysticism a secret.
Officially as not interesting enough to their readers.
My guess is that they decided not to publish the news that the universe is stationary not to embarrass the theorists who were making living off the idea of expanding universe and astronomy seemed to be not important enough to justify such an embarrassment of theorists.
After all "the beauty of astronomy is that unlike in civil engineering one can be 100% wrong and nobody is hurt" [Don A. Lautman, my astronomy teacher at Harvard Smithsonian Center for Astrophysics, Cambridge, MA].
Since scientific journals like "Nature", "Physical Review Letters", "Science", "The Astrophysical Journal", even popular ones as "Physics Today", "Scientific American" and others, refused to publish the news that we live in a stationary Einsteins' universe and news of the Hubble time dilation, the astronomers still don't know that Einsteins' general relativity, explains many gravitational phenomena on which explanation they work, which still doesn't hurt anybody except the taxpayers. The necessary in such scenario creation of energy from nothing astronomers might attribute to miracles that are especially good news to creationists. Einstein already said that he stopped understanding his theory when mathematicians began to explain it to him. He knew that mathematics is not science (which, since "Russels' paradox", is known also to matematicians) and only physics is. But the contemporary astronomers tend not to know that science is divided only into two parts: physics and stamp collection. And that's maybe why physicists don't understand gravitation as described by mathematicians. Feynman called some cosmologists idiots for supporting a "claim based on the stupidity of the author that some obvious and correct fact, accepted and checked for years, is, in fact, false (these are the worst: no argument will convince the idiot)" [fragment of Feynman's letter to his wife from 1962 Gravity Conference in Warsaw, Poland]. In the above fragment Feynman might have meant the principle of conservation of components of 4-momentum which is true in regular physics (see Feynman's statement on separate conservation of components of 4-momentum in "Feynman lectures on physics") while it is invalid in the BBH where the BBH theorists maintain that it is possible to convert in the same reference frame the energy into momentum and v.v. and they just work on ways of achieving it. After 1998 disastrous for BBH observation of accelerating expansion of space (while assuming that cosmological redshift is Dopler shift) the opponents of stationary space patched their hypothesis of expanding space with assumed ad hoc "repulsive gravitation" called now "cosmological constant" and with the existence of exotic "dark energy" contained in this "cosmological constant" that allegedly were using this "repulsive gravitation", through action at a distance, to expand the universe faster and faster. The editors of scientific journals might have known that cosmology is a pseudoscience created to employ scientists who couldn't earn living in any legitimate branch of science. But cosmologists aren't even smart enough to keep low profile, to admit cautiously that "they actually don't know", and to limit their activity to picking up their salaries, allowing at least astronomy to develop at its own pace. Instead they insist, against Einsteins' physics, that quasars and black holes exist, space is expanding, spacetime is curved (of unknown yet intrinsic curvature and direction, they still work on finding it out), the metric tensor of spacetime is symmetric, and the energy is constantly created (most likely through divine intervention) an idea supported by creationist businessmen with their millions of dollars in awards to cosmologists who support creation. But the worst of all is, that they consider investigating the nature of "dark energy" the most important problem of physics of 21st century, blocking resources that are needed in real science and being the referees of gravitation papers they control the publication of papers dangerous to the BBH. The cosmology from cheerful and harmless activity of the previous century became a damper on science. The creationism got into science through the back door of cosmology using mimicry, calling their hypothesis of creation "general relativity", the name by which Einsteins' theory has been already known. Support of creationists for the BBH has been documented by the mentioned already The Templeton Foundation's March 2008 award of $1,600,000 to an astronomer, cosmologist, mathematician, and Catholic priest, Michael Heller from the Papal Academy of Krakow, Poland, "in recognition of scholarship and research that has pushed at the metaphysical boundaries of science". If this trend continues we might be in a danger of establishing laws against engaging in science without a license (applied especially to sculptors). Even now people are banned for life from scientific fora, as it happened couple of times to me, just for trying to discus stationary universe which creationists apparently consider dangerous to the idea of creation. With complacency of people responsible for maintaining those fora, not even creationists themselves. So far... |
Since the editors of scientific journals claim that their readers ain't interested in the results that I got (as e.g. editors of "Phys. Rev. Lett." wrote me) I show below, to those few who are interested, how Einsteins' gravitation works. Why things fall, why the curvatures of spacetime cause the illusion of gravitational attraction and the illusion of accelerating expansion of space. Then I compare the Big Bang general relativity and Einsteins' general relativity in an attempt to show to the readers who are interested, why there is no reason for believing in neither that the Newtonian gravitation is physics nor that the Big Bang GR is.
To mention the quantum nature of Einsteins' gravitation it suffices to mention that quanta of gravitational energy are any elementary particles that carry mass from one atom to another (e.g. leptons of spin 1/2, so they don't need to be of spin 2, as Feynman has been guessing, but may be like photons or electrons and so unifying gravitation and electromagnetism is already contained in Einsteins' theory just not stated clearly enough. As Hertz said: "Some physical theories are often smarter than their creators". The reader may deduce the quantum nature of gravitation from the basics of gravitation and find out that role of gravitons may be taken on by any particles that atoms exchange between themselves like photon's, gluons, neutrinos (or shmutrinos if they exist).
Einsteins' gravitation can be really explained to anyone's grandmother especially when the granny attended a high school, liked physics and math, and is not prejudiced against Einstein, which almost never happens to grandmothers but often to physics professors. Some physic professors would like to abolish the conservation of energy under pretext of reconciling Einsteins' gravitation with quantum mechanics. Apparently those professors don't known that Einsteins' gravitation is already a quantum theory.
In the big bang hypothesis we have a collision of physics (the redshift of photons interacting gravitationally with the rest of universe) with assumed math (the symmetric metric tensor that prevents photons from interacting gravitationally with the rest of universe and having redshift in stationary universe). That's most likely why Einstein solved this contradiction in 1950 by assuming non symmetric metric tensor for the spacetime which allows the Hubble redshift in stationary universe.
Simple calculation reveals that the Hubble redshift observed in our universe is equal with accuracy better than one sigma to the redshift resulting from dispersion of kinetic energy of photons in a stationary universe. Yet, the cosmologists (like MTW) assumed the symmetric metric tensor of spacetime and got necessarily an artifact of expanding space. Despite Feynman's warning the view of nature has been changed to accommodate for mathematical assumptions.
Finally, Einstein's 1950 assertion that metric tensor of spacetime must be non symmetric was not even mentioned by MTW. Those gentlemen assumed at the onset of their monograph a symmetric metric tensor, as also Einstein did at the beginning but for Einstein it was in 1911 when no one yet heard about the cosmological redshift. MTW did it in 1973, 23 years after it was known that Einstein maintained in 1950 that symmetrical tensor field must be replaced by a non-symmetrical one. Yet MTW didn't try then to examine the Einstein's assertion allegedly because it wouldn't be as elegant a metric tensor as the symmetric one. To which Einstein had already said: "If you are out to describe the truth, leave elegance to the tailor."
Gravitational force is therefore not a "fundamental" force of nature but only an inertial force resulting from restrictions on the free movement of a paticle along geodesic in spacetime. Einstein has assumed that the consecutive positions of lowest energy of a particle (positions of highest probability of finding the prticle there) are determined by the curvatures of spacetime that depend on position xi and that they form a geodesic in spacetime (and so far it looks like he was right). The above demonstrates that Einsteins' theory of gravitation is a quantum theory automatically: no "force" decides about the movement of a particle but only the probability of finding it at the position of its lowest energy.
The reason for diminishing internal energy of particle in
vicinity of material objects, along direction towards these
objects, is that along this direction the time happens to
run slower (effect known as gravitational
time dilation) and there is also an equal (in
relational units) expansion of space (effect known
as the gravitational curvature of space)
so it takes even more time to cover the expanded space at
any velocity.
Both effects result in the slowing down of all velocities.
Anything that does any movements, rotations, or vibrations is doing them slower in the "vicinity" of material objects and so it contains less energy than before the particle got into the vicinity of a material object.
The energy of each particle diminishes along this particular direction by the amount that the square of gravitational speed of light is diminishing.
If the free movement of the particle is restricted the restriction produces an inertial force pushing the particle along this particular direction of diminishing energy against the restricting object.
This force (being by its nature an inertial force, since it shows up only when the free movement of the particle is restricted) is called traditionally "gravitational force" and internal energy of the particle is its "gravitational energy" since its derivative with respect to displacement is equal the "gravitational force"
The acceleration must be such since the excess internal energy that the particle loses while the gravitational speed of light gets diminished, changes into kinetic energy of the movement of particle and so the energy is conserved automatically.
And of course in a free fall the total change of energy of particle is automatically zero:
Since gravitational force is a derivative of internal energy with respect to distance
it implies that gravitational energy of a particle in Einsteins' physics is just its internal energy
The gravitational force will be derived below and then it might be seen why it must have quantum nature automatically: An atom, exchanging a quantum of energy, e.g. a photon, with another atom, loses by it also a quantum of its gravitational energy
Why gravitational force is
In our frame of reference the total energy of any particle is
(1) |
(2) |
(3) |
The derivative of energy (1) with respect to displacement x (a derivative that when with opposite sign is called "force that pushes the particle" since the particle always tries to achieve a lower energy level), putting
(4) |
Since for a particle at rest in our frame of reference
(5) |
Then our gravitational energy is the internal energy of a particle, given by (1) at
Now we have to prove that our working assumption that
Why |
We need to find out how the gravitational speed of light c(x) is related to gravitational field g (to the curved space). To figure out this relation we need to remember the following facts:
The angle of deflection of light ray in vicinity of material objects is twice as large as it would be predicted by existence of Newtonian gravitational field due to gravitational time dilation. Einstein's guess was that half of this angle of deflection is due to time dilation that simulates the Newtonian gravitation and the other half is due to the curvature of space that has no counterpart in Newtonian gravitation (this was the way he discovered the curvature of space and its role in gravitation) and was an originall discovery of Einsteins'.
The next fact is that when the time slows down everything is running more slowly in the same space. When one side of a light ray runs more slowly than the other the light ray bends in direction of smaller c(x) and the angle of deflection is
(6) |
In a flat space the angle of deflection of light ray would be due only to the change in speed of light across the ray. In a situation when space is curved the curvature of space bends the light ray without any change in the speed of light since then both sides of the light ray move in the (curved) space straight. The light "gets bent" (but actually going straight in a bent space) due to the space curvature without a difference between speeds of light across the ray. So to find observationally (d/dx)c(x) we need to take a half of the observed angle of deflection of light in gravitational field g and apply equation (6) to it.
The angle of deflection of light ray may be derived from an example with a rocket ship in space, sufficiently far from all material objects not to feel any influence of those objects, accelerating let's say as much as the particles that fall on the Earth. If there is a light ray that enters the rocket ship perpendicularly to the direction of acceleration of rocket ship the observer in the rocket ship will feel gravitational field but the light ray won't and so it will move along a straight path in relation to the fixed points outside accelerating rocket ship. The observer accelerating with the rocket ship however will see the light ray bent towards the rear end of rocket ship (assuming that the rocket ship accelerates forwards). In relation to the rocket ship that is accelerating "up" with acceleration g the ray is dropping "down" with the same acceleration g. The height of this drop is (integrating the acceleration g twice with respect to time)
(7) |
(8) |
According to Einsteins' principle of equivalence of acceleration and gravitational field this case is identical to the case when the light ray moves across a rocket ship that is standing on Earth, and so the ray bends in gravitational field g, the same as the ray seen by observer in accelerating rocket ship.
Since half of this angle comes from the curvature of space and the other half from the change in speed of light across light ray we take
(9) |
Vanishing gravitational force in free fall
So we've showed that energy (1), the total energy of a particle, is composed of its (in general huge) gravitational energy
It turns out that in the real world it is not a gravitational "pull" by "attraction" of some external body but inertial "push" by inertia of the particle in space where there is a change of internal energy of the particle as a function of displacement. So it is not a body attracting other bodies but other bodies are pushed by themselves towards an "apparently attracting" body with this body not attracting them but just modifying the spacetime around herself by her presence in such way that those other bodies get themselves pushed towards the "apparently attracting" body. "Attraction" is a figure of speech here and what is reall is the "push" towards this "apparently attracting" center.
Now we need to do the test with free fall to see if total energy of a particle in free fall doesn't change.
Since in a free fall in gravitational field with
(10) |
Differentiating with respect to x and ignoring small higher order terms
(11) |
After substituting (9) and (11) to (4) we have a change of total energy of a free falling particle as
(12) |
The reason for this smaller frequency of photons was assumed by BBH theorists to be a recessional velocity of galaxies causing redshift through Doppler effect but it turned out that the time at those galaxies runs slower than at observer and so the effect of the expansion of space has been simulated. Furthermore the simulated expansion looked as if the space were expanding with accelerating expansion.
This effect of the time running slower in deep space turned out to be necessity if energy couldn't be made out of nothing and the simple derivation of this effect, from the principle of conservation of energy, is presented below for a spherical light wave and a derivation with a different method for a planar light wave, with a more detailed explanation of the method of obtaining the result, is in Appendix 2.
| (13) |
| (14) |
| (15) |
| (16) |
| (17) |
The Einsteinian interpretation of the above is of course the time running slower at a distance form observer according to relation
| (18) |
This equation presents this "big leap" from Newton's math to Einsteins' physics that has to be made to see why Newton's math reflects so faithfully Einsteins' physics and how the curvature of spacetime (which by-the-way turns out to be intrinsically flat) is the reflection of Newtonian force, which Newton in his wisdom refused to accept as being a physical force but only a mathematical model of something.
Now we know the physics that the Newtonian "force" is a model of.
It turns out to be the curvature of flat (as it is shown in
the next equation) Einsteins' spacetime.
After differentiating eq. (18) at
| (19) |
(20)
| |
The redshift produced by the effect of general time dilation is
| (21) |
| (22) |
The obvious application of this effect is the calculation of density of space of our universe from the value of observed Hubble constant.
The value of Hubble constant
After splitting the Hubble constant into Taylor series the acceleration of this apparent expansion comes out as
| (23) |
Since now Einsteins' theory can't be falsified by observations as it predicts strict conservation of energy (non falsified yet), Einsteins' universe (non falsified yet), and other (non falsified yet) observational results within one σ, (which in astronomy means a perfect agreement), then now we may suggest the metric tensor of spacetime not only non symmetric but also degenerate. Despite that, the resulting metric is quite decent
| (24) |
| (25) |
Now let's look at the CBR.
So, knowing the temperature of the redshifted starlight, presumably
One thing that is not yet known, nor any theory about it is worked out (similarly as a theory of creation of galaxies) for the belief of astronomers that the universe has been created and there is not enough time from the alleged time of creation (13.7 billion years ago, according to the BBH), is what is the cycle of conversion of hydrogen into other elements and then back to hydrogen.
It is already known that most of light elements (from He to Fe) are made from hydrogen through gradual burning hydrogen into heavier elements (H -> He -> Li -> ... -> Fe) in stars and elements heavier than iron are produced in supenova explosions when the pressure in them is sufficient to form the heavier elements. Yet, if the universe is to be eternal (as Eistein's universe model is) there is needed a mechanism for converting all those elements back into hydrogen.
It might be something that happens when two so called "black holes" meet and then got torn appart by tidal forces (as it happens to moons that get too close to their planets). It may be a moment in which all the elements accumulated in those black holes get converted into separate protons and electrons that combine then into hydrogen atoms. It might explain the cycle but it might be also that for discovering the cycle we need to know something that will be discovered only in the future and so the speculations about the cycle might be futile for the time being.
This "law" has been "discovered" in 19th century when people thought that energy can move only from the place of higher energy density (high temperature source) to the place of low energy density (low temperature sink) as in thermodynamic engines and doing all the useful work on its way. There was a fear that when all high energy density sources are exploited all energy in the universe will be dispersed in cool environment with no way of getting energy from this cool environment. It would mean the "thermal death" of universe, mathematically expressed by "law of growing entropy" (a.k.a. Second law of thermodynamics). Now we know that all energy in the universe is gravitational, see eq. (1), and there must be a simple way (if not discribed yet in detail) of extracting useful energy from the cycle talked about in the previous section. So the fear of growing entropy is only metaphysical, important only in BBH, which is invalid anyway (because of conservation of energy expressed by the first law of thermodynamics) as it's shown elsewhere. In real universe the amount of energy is constant and constantly floating from the high energy hydrogen back to the high energy hydrogen, which invalidates "second law" and makes the universe eternal, as Einsteins' universe is.
Luckily, due to the value of Einstein's cosmological constant
| (26) |
In the big bang hypothesis it has been assumed (after Einstein, who changed his opinion only in 1950 when he proposed a non symmetric metric tensor) that the geometry of spacetime is pseudo Riemannian and that the metric tensor of spacetime is symmetric. At such conditions it is impossible to have redshift of photons that move along closed loops in stationary space (Hubble type redshift). Therefore it has been considered an established fact that the Hubble redshift is a result of no other phenomenon but the expansion of universe and that in a stationary universe there wouldn't be any Hubble type redshift.
But it has been overlooked that the principle of conservation of energy implies the existence of dynamical friction of photons which would cause Hubble redshift anyway. Therefore the metric tensor of spacetime couldn't be symmetric. Einstein realized this only in 1950 when he proposed a non symmetric metric tensor for the spacetime.
In the meantime it was the 1929 line of reasoning of Fritz Zwicky (1898-1974) who maintained that because of asymmetry of gravitational interaction between photons and the universe there must be a Hubble type redshift in any light. It was called tired light effect but ignored in favor of the expansion of universe by the gravity physicists for whom it was too exotic an effect not fitting in any way the general relativity since they strongly believed, against reason, in Riemannian geometry of spacetime with its symmetric metric tensor.
Zwicky didn't know how to calculate the redshift properly and so he didn't get the results that he could use to convince the opponents of tired light effect. It was the common problem of many astronomers and astrophysicists who apparently tried to do calculations in Newtonian, approximate (and illegal) way to get the tired light effect.
Apparently the first person who calculated the redshift of photons rigorously, not using any approximations and so getting in 1985 a right result was me. I was not a physicists though but a sculptor, therefore my credibility was zero, so no one (except referees) wanted ever to see my result (and there were only a few of them in over 25 years). The referees didn't find any formal problems with this result but all recommended the rejection of the solution for the reason of not proposing any new physics which apparently referees thought was necessary to solve such a profound problem that even they couldn't solve. So the first result of solving the problem of presence of cosmological redshift in stationary space exactly along Einsteins' lines of reasoning were rejected by Nature, Physical Review Letters, Science, The Astronomical Journal, and even Nuovo Cimento (defunct since then), not to mention many popular science journals like Scientific American and Physics Today.
Zwicky's idea was not even mentioned in MTW who being gravity physicists rather than astronomers might have not even known about dynamical friction, and maybe that's why they had never calculated its value for photons assuming zero value as best fitting their purpose. Had they calculated the value of dynamical friction of photos there wouldn't be a need to assume that the universe is expanding and that the energy is created from nothing, not even to mention that the true nature of quasars could be discovered decades earlier to satisfaction of Halton Arp (an astronomer) and Jayant Narlikar (a pure mathematician) who seem to be the most informed opponents of the expanding space hypothesis.
The plot thickened when Arthur Eddington suggested in 1929 that according to the general relativity (as he understood it) Einstein's universe was unstable with respect to the small fluctuations of radius of curvature of space and so the universe has to either expand or contract. It is an analog of suggestion by some gravity physicists that the orbits of planets are unstable with respect to small fluctuations of their radii since centrifugal force increases with radius and therefore leads to even greater increase of the radius (which would be true if other factors, like conservation of angular momentum, didn't take part in this phenomenon).
So Eddington's suggestion may be ignored as long as all the factors taking part in the stability of universe are not taken under consideration. Besides, it is risky to tell how a system of 1011 galaxies is going to behave if we don't know yet how to predict analytically the behavior of three.
However, most gravity physicists lead by
Since the Hubble redshift was already included in the so called Big Bang general relativity as a result of expansion of space, and the expansion of space became the basis of the Big Bang GR, the conservation of energy had to be dropped to avoid the contradiction within the theory and the dynamical friction of photons had been assumed exactly zero to the bewilderment of those astronomers who still believed that energy can't be created.
In the Big Bang GR the contradiction between expansion of universe and the conservation of energy had been decided by the theorists against the conservation of energy. The dynamical friction has been assumed to be limited only to Newtonian physics despite that Einsteinian physics as more general should explain all observed Newtonian effects. This limitation of dynamical friction to all particles except photons in the Big Bang GR is an equivalent to an assumption that while all other particles are subject to the principle of conservation of energy and so to the dynamical friction the photons aren't (they are supposed to have zero redshift in a stationary universe), and so, while photons are moving through the universe, carrying energy and modifying the gravitational field, the energy needed to compensate for the dynamical friction of photons is assumed by theorists like A. J. Wheeler and others to be created from nothing. It is a point where divine intervention into the affairs of universe is to be assumed by the gravity physicists.
It has been tacitly assumed by astronomers (in order to understand the gravity physicists) that this energy is so small that assuming that it is created from nothing won't change any observational results [source: Dr. Bohdan Paczynski, astrophysicists].
Actually there exists even a back-of-envelope Newtonian calculation that convinces astrophysicists that this is really the case. Consequently the amount of this energy has been never calculated, just assumed on the basis of this back-of-envelope calculations to be negligible. Unfortunately for the Big Bang GR it isn't negligible and consequently it is a fatal flaw of this hypothesis. Obviously one has to return to Einsteins' GR with global conservation of energy and consequently with non symmetric metric tensor and possibly also to assume the non Riemannian geometry of spacetime.
I have been explaining many mysterious features of cosmology as simple relativistic effects of Einsteins' gravitation, explaining physics of the illusion of accelerating expansion of space, providing calculation of Hubble constant of apparent expansion of space and its (apparent) acceleration (confirmed by observations after 1998 with data from Super Nova Project), predicting the Density of universe, estimated already by astronomers within a fraction of order of magnitude.
The calculations narrowed the uncertainty of the density of space to 16% standard deviation (twice the uncertainty of the Hubble constant). Even the average size of pieces of non luminous matter of universe has been provided. And all was done from first principles and Einsteins' general relativity.
It has been shown that restoring the principle of conservation of energy as a valid physical principle and with it restoring the dynamical friction for photons allows to drop the assumption that the universe is expanding, however not, as it might have been expected, through restoring the Newtonian idea of tired light proposed by Zwicky. It has been done by demonstrating that in a world where energy is conserved the dynamical friction of photons is a relativistic effect of general time dilation. An effect of the rate of time dilation compensating for the curvature of space for the reason of inability of nature to produce energy from nothing.
Einsteins' theory, by separating itself for good from the magic of expanding space, became again a physical theory explaining all the controversial or not understood elements of Einsteinian physics. It showed the location of gravitational energy, and by this the origin of gravitational force and it explains also the surprisingly high redshifts of quasars that, as Halton Arp has insisted, are associated with galaxies of much smaller redshifts and so not even located at the distances assumed by the theorists.
Because of all those things there are several differences between Einsteins' GR and Big Bang GR. They are in assumptions about the real world and necessarily in conclusions from these assumptions. These assumptions and conclusions are specified separately in the two tables below:
ASSUMPTIONS | Big Bang GR | Einsteins' GR |
reason for gravitation | geometry of spacetime | |
conservation of energy | invalid | valid |
speed of light | constant throughout the whole space | local is constant c, non local (coordinate speed of light) depends on displacement within reference frame: |
accelerating expansion of space | fact due to dark energy | see conclusions |
metric tensor of spacetime | expanding, symmetric, Riemannian |
CONCLUSIONS | Big Bang GR | Einsteins' GR | ||||||||||||||||||||||||||||||||
accelerating expansion of space | see assumptions | illusion due to conservation of energy predicting Hubble parameter as | ||||||||||||||||||||||||||||||||
metric tensor of spacetime | stationary, reason for Hubble redshift
| Doppler shift due to recession of galaxies
| conservation of energy | reason for CMBR
| redshifted light from Big Bang
| absorption of redshifted starlight by non luminous matter of universe and re-emission at temperature of thermal | reason for high redshift of quasars
| speed of recession
| conservation of energy in clouds of dust, | [see paper (in PDF format) reason for gravitational force
| "acceleration of space"
| [see Basics ...] gravitational (potential) energy
| ?
| the internal energy of particle | location of gravitational energy
| ?
| location of gravitating particle: x
| density of space
| ?
| 6x10-27 kg/m3
| acceleration of expansion in terms of dH/dt and H0
| ?
| acceleration of space probes
| ?
| average size of pieces of non luminous matter
| ?
| order of one meter
| angular size of galaxies as function of distance from observer
| ?
| should have minimum at redshift | |
The areas that a theory has no answers for are marked with question marks. All of them are in the Big Bang GR and it suggests that Einsteins' original theory is OK while the Big Bang GR is wrong. Therefore we might assume that gravitational force and energy may be explained according to the old Einsteins' theory based on conservation of energy and explain them as such. Therefore we seem to be justified in explaining gravitation as it is explained in the following section.
Variable | Einsteins' GR predictions | Observed value | its σ(sigma) | Units | |
theoretical | numerical | ||||
Radius of curvature of space | RE | 4.3 | ? | ? | Gpc |
Hubble parameter at Earth | Ho = c / RE | 69.6* | 2.8 | km/s/Mpc | |
Acceleration of space probes | ao = c2 / RE | 7 | 8.7 | 1.3 | |
Density of universe (of "gravitational energy") | 6 | 5.5 | 4.5 | ||
apparent acceleration of expansion of space | ? | - Ho2 | |||
redshift of minimal angular size of galaxies [verify] | ? | 1 |
Glossary of terms pertaining to gravitation (and some added for entertainment).
Einstein's abandonment of symmetric metric tensor has been ignored by authors of MTW's monograph "Gravitation" who apparently didn't mind the violation of the principle of conservation of energy. It made their theory (BBH) a magical theory.
It turns out that to apply Einsteins' field
equation to explain gravitation in a sensible way that
doesn't contradict any other physics (e.g. the principle of
conservation of energy) it is necessary to assume that the
metric tensor of spacetime is non-symmetric and degenerate (to
prevent its diagonalization).
The observational data imply then that the expansion of
universe is an illusion.
A non symmetric tensor has more independent components so they
might be enough to provide for the illusion of expansion.
This non-symmetry of metric tensor provides for an effect not
yet discovered by astrophysicist which I call
general time dilation and Halton
Arp calls intrinsic redshift.
Without it any gravitational interaction with any moving
object could be used to create energy from nothing in a
similar way as energy is created in the tidal power plant,
by the Earth's oceans moving in relation to the Moon.
In case of the Earth-Moon system the part of rotational
kinetic energy of the Earth is converted into electricity
in a tidal power plant, and part is transferred to the Moon
making it flying higher and higher.
So in general the effect puts a small Newtonian drag on any
moving object in the universe that which is a Newtonian
counterpart of the relativistic effect that is observed in
the real world as reddening of light called
Hubble's redshift.
If we apply that drag to particles of light
(photons) it turns out that they really look as
if they encounter such drag.
The astrophysicists interpret this effect as a Doppler shift
caused by recession speed of galaxies and consequently as the
evidence that the universe is expanding while this effect is
caused only by the time running the slower the farther we
look as required by a non-symmetric metric tensor and
relation between time and space as expressed by identity