Essay:Gravitation demystified

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Essay.svg This essay is an original work by W. Jim Jastrzebski a.k.a. JimJast 21 March 2011.
It does not necessarily reflect the views expressed in RationalWiki's Mission Statement, but we welcome discussion of a broad range of ideas.
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I dedicate this essay to Jacek Jezierski, my algebra teacher at Warsaw University Astronomy, who opened my eyes to the magic of tensor calculus. Being born much earlier than the mandatory 19 years before taking this course to comprehend it (the fact faithfully reflected in my first year exam score) hopefully didn't hurt the overall results though.

About this essay[edit]

This is rev 2.2 of this essay.

About rev 2.0[edit]

Starting from rev 2.0 in June 2011, I've realised that relativity might have been discovered also by Mileva Marić (1875-1948) Albert Einstein's (1879-1955) first wife and so the refs to many things in this rev have been changed from singular to plural as in "Einsteins' theory" and "Einsteins' universe" though his blunders were kept in singular, as Einstein's "cosmological constant"[1].

Some stuff without math worth reading instead of this essay[edit]

Before reading this essay, in which I'm trying to explain the physics, math, and history of gravitation and cosmology, you may want to read my earlier prose translated from my English to the official English (so s/he says) by Crum375 The Einsteininan gravitation for poets and science teachers[2] that presents its important physical and political features with skipping its math (to which some people are allergic) altogether, except for brief calculation of apparent "gravitational force", generaly misinterpreted, for misunderstanding of its quantum nature, though not completely explained neither, as it still misses unknown precise designation of carriers of this force (neutrinos?) tentatively called, after Richard P. Feynman, "shmutrinos", since he didn't particularly care about its concrete, physical, representation. It might be enough to know that they can't be shielded with presently known methods of shielding any interactions.

Reading for professional physicists and/or astronomers[edit]

If you are a profesional astronomer or physicist, just this one page paper[3] may be enough to understand why our universe is stationary and eternal, contrary to what was assumed up to February 1985, when the long overdue calculation of dynamical friction of photons in our universe revealed the lack of its expansion and has been confirmed observationally in 1998 with accuracy better then one standard deviation by the "Supernova Comology Project" team of astronomers[4].

About rev 2.1 and Feynman's rant of 1962[edit]

Starting from rev 2.1 I realized that many readers of this essay may be interested in the scientific aspects of gravitation and cosmology but might not know physics well enough to be aware of the developments in cosmology at the turn of 20th and 21st centurries, and therefore, not understand Feynman rant that I quote from time to time in my correspondence with creationists on the talk page of this essay, in a form of a link to it. Therefore I should explain this historical fact of Feynman rant first.

Richard P. Feynman addresses in this rant various kinds of Relativists, under which name they are known to other physicists, who not necessarily work in general relativity and often have no idea what general relativity is abbout. Prof. Roy J. Glauber said about relativists (to me, while I was his student, and asked him to direct me to a relativist I could talk to) that they are the only kind of physicists he knows who unlike other physicists, who can talk for hours about their subject, don't like to talk about their work, and when asked about it become agressive and refuse to answer questions. Prof. Glauber recommended one from New Jersey (while we were in Massachusetts) as the only one approchable enough I could try to talk to. I wrote to him but he didn't answer.

Here is an article on relativists presenting Feynman rant[5].

Details of Feynman's rant[edit]

Richard P. Feynman, who treated science [6] very seriously and so he was pissed off by lack of understanding of seriousness of gravitational issues by mathematicians, who in his opinion didn't care at all about scientific aspects of their ideas (the truth) and were proposing stuff contradicting basic science.

It might be that the way how those mathematicians treated science were already preliminary moves trying to prepare the scientific comunity to the planned takeover of cosmology by creationists. It happened though only in 1973 with the publication of creationists "bible" titled "Gravitation" by Misner, Thorne, and Wheeler, three mathematical physics professors, who pushed creationism, propagating it under the cover of "expansion of space", and the "Big Bang", events deduced from the observed cosmological redshift interpreted as Doppler shift caused by the galaxies receding from the observer, talked about it by scientists as if they were really receding from the observer implying the relatively uniform expansion of space [7], which turned out to be relativistic coupling of Hubble time dilation to the curvature of space, it turned out that the illusion of expansion should be the illusion of accelerating expansion, and it was observed as such with accuracy better than one standard deviation in 1998 with acceleration as predicted by Einsteinian gravitation.

Scientist, who in most cases didn't realise that the observed expansion wasn't real, since at these times of begining of cosmology, even some physicist fell victims to creationist point of view and thought that the universe was created ("somehow") and is expanding, due to observed cosmological redshift (and their lack of imagination preventing them from coming up with a better solution).

At this point it is good to explain to the readers that in science the cosmology is not considered a part of it but something stuffed with "lame superstitions", which might be different from what the readers might think. For a physicist the cosmology, is "science" based on fantasy rather than real testable and repeatable results.

Feynman in his rant addressed those folks who were holding jobs in cosmology, those 126 dopes (in his words), including his professor John Archibald Wheeler, later the principal author of infamous, "Gravitation", a creationist version of cosmology, all attending the Gravity Conference in Warsaw, Poland, apparently without Feynman's knowledge of the already going on trend in cosmology, since Feynman's rant happened in 1962 while the textbook titled "Gravitation", the illustration of this trend was published in 1973. So the possible planned takover of cosmology by creationists might have been new to Feynman. One that he didn't expect from scientists and therefore he didn't do anything to stop it (beyond, writing his letter and pleading never again come to a gravity conference).

Some folks of future generations try to explain Feynman's rant as prompted by Feynman's lack of understanding of new developments in cosmology while those folks don't understand even elementary physics themselves.

Today already after many years of existence of textbook "Gravitation" the cosmologists know very well about those creationist trends in cosmology and knowing what is politcaly correct are biased towards creationism themselves as well, together with the creation of energy from nothing, rather then towards regular physics which is useless as far as their "scientific careers" are concerned.

In science the possibilty of creation of energy from nothing was eliminated sometime in previous centuries (the perpetual motion machine problem). It was still when Einstein was a Patent Office clerk there. The perpetual motion machine was kept outside the patent office considerations for patents. Now the possibility of creation of energy from nothing is even taught at the university level, which may be considered an illusration of the level of deterioration of science since there still are the same rules of application of math to physics held as in old times of relegating the fairy tails out of science. Though apparently not in institutions of "higher education".

Part of Feynman's rant about "scientist" of type (4) might be refering to this neglecting past achievements of science. That remain unchalenged in the eyes of legitimate scientists who tested them at many occasions before but it remains unknown to idiots.

It is particularly difficult to tell a legitimate scientist from a mentally challenged person in times when creationism isn't very popular between scientists, and then those people keep rather low profile and don't advertise themself excessively so the reader should be at least aware that such a problem exists and is a commonplace in academic environment.

Possibly, more than half of all physicists seriously believe in God, which is still less than in general population (ca. 85% worldwide) and therefore they believe in creation of energy from nothing (since how could God mange without such ability?) though it is not as often among mathematicians who create the major myths themselves (e.g. like travel against "arrow of time") and so they are more familiar with their creation (similarly as priests are more familiar with the habits of gods, than the rest of citizens).

I may notice here that science is mostly dispersing the old prejudice rather then discovering new truth, though new truth, especially in technology is created lately in large amounts, creating a push-pull mechanism advancing science and technology at the same time.

It turns out that todays scientists have to use the expertise of engineers to eliminate foolishnes and fairy tales from science. Since engineers are more sceptical of fairy tales in which scientists tend to believe. First of all in cosmology because of its specificity and application of propaganda of the Big Bang "theory". Possibly that's why the discovery that the universe is not expanding was made by an engineer interested in how much of redshift is coming from the "expansion of universe" and how much from dynamical friction of photons. And he found that "expansion" adds exactly zero to the picture. And this is how one more "scientific myth" went down the drain.

In this essay, since I'm trying stick to the real science and since we already know the physical nature of "expansion of universe" (does not exist) and the truth about the "Big Bang" (didn't happen), those things are refered to only as apparent and in quotes. The creationists who are not interested in physics don't need to read this essay since it presents cosmology only from the non creationist point of view (as it really happenes in the real world rather than world of the "expanding universe" of Feynman's "cargo cult science" or at the beginning of 21st century which for the shortage of suitable work places for them needs to employ also inteectually challenged folks as scientists). Recall Feynman's rant as an illustration and warning about our times or if blocking my accsess to physics server is still blocked read story about relativists from CP server: here[8].


Wtat's wrong with expansion of space?[edit]

Basically one thing: it is an illusion.

In February 1985 an astronomy student and a sculptor, though also an electronic engineer (MS in electronics) interested in astronomy, calculated that in the universe of density of our universe (ca. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle 6\times 10^{-27}kg/m^3} there must be a redshift caused by the dynamical friction of photons such that the Hubble constant has to be equal ca. 70km/s/Mpc. Since it was the Hubble constant of our universe with a very good approximation a suspicion arose that there is no expansion of the universe but all the visible redshift is due to dynamical friction of photons. Later it was realized that it is a "relativistic friction" (apparent friction due to relativity of time) and it was generalized to Hubble constant equal Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle H_o=c/R_E} , where c is speed do light, and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle R_E} is radius of curvature of space (known as "Einstein's radius").

At this moment the expansion of universe disapeared from science and the universe became well behaved stationary Einsteins universe with its curvature of space of radius of ca. 13 billion (American billion = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle 10^9} ) light years.

To the astronomers such curvature of space appeared rather as no curvature at all but since the number is important for other applications (like calculation of minimum of angular diameters of galaxies confirming this number) we better keep this number in mind. Some time later the "Einstein's cosmological constant was eliminated from Einstein's equation making it again "elegant" (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle R_{\mu\nu}=8\pi T_{\mu\nu}} , actually it was only returning it to its old form proposed already in 1915 by Einsteins, which became legitimate again by the discovery of existence of Hubble tensor of "curvature of time" as Feynman called it).

This absorption of Einstein's cosmological constant into Einsteins field equation was a nice thing by itself since it closed certain period in cosmology allowing scientists now to leave the foolishness of "cargo cult cosmology" alone and start a new period of scientific cosmology.

This event didn't happen yet since editors of scientific journals don't allow peer review of the offensive paper for already over quarter century, and the eliminated Einstein's cosmological constant is dwelling on the blackboard in room 139, of The Institute of Theoretical Physics, Warsaw, Poland for no mathematician trained in general relativity having yet time to come and verify the removal of Einstein's cosmological constant from Einstein's field equation. And finally closing the "sad period of fools cosmology" when it finally is going to occur to everybody that there was no Big Bang as the universe was never officially created. Just continued to exist for rarher long time as the offensive paper maintains.

The calculations proving lack of expansion of universe were conducted because of the old prejudice dated form 1930-ties when an astronomer and Catholic priest George LeMaitre proposed that observed then in the universe redshift might be caused by recession speed of galaxies, and lack of better explanations at that time the scientists accepted his idea and so, for the next 80 years scientific journals didn't dare to publish anything different. That's the whole mystery of expanding space and the cosmology ("creationist science" going one way and regular science separating itself from cosmology). The split between cosmology and science is reflected by 1962 rant by the mentioned earlier Richard Feynman.

Einsteins came with a different model than the Big Bang. In Einsteins model the spacetime is stationary but Einsteins didn't provide necessary calculations supporting this idea of stationary universe losing the interest in it. The first critical check ever of creationists idea was done by the above mentioned sculptor in February 1985 while attending astronomy course at Harvard-Smithsonian Center for Astrophysics and it ended the period of belief in expanding universe at least in minds of guys like Mike Guillen, at the time the prof. Roy Glauber's assistent teacher of the student group to which the student belonged.

The creationists kept on believing that the universe were created miraculously in the Big Bang and has been still expending.

What is wrong with the Big Bang hypothesis?[edit]

Mostly that the Big Bang never happened.

The Big Bang aficionados, to suport viability of the Big Bang were forced to add to Einsteins' theory an axiom of expansion of space, and neglect the Hubble Time Dilation (HTD), and Hubble tensor (HT), as the reason for illusion of expanding space. That it is an illusion has been proven in this paper. HTD is a curved space phenomenon of proper time running slower at a distance from any observer in the curved space than at the observer itself due to the relativity of time in curved space, because of coupling between time and space discovered by Einsteins already in 1905 but not examined deeply anough to offhand reject the Big Bang hypothesis. In particular the redshift in Einsteins' universe was not calculated due to the assumption of creationist cosmologists that it is "negligible". Though HTD slows the proper time rate at events in spacetime proportionally to integral of curvature of space accumulated between the observer and the observed event. HTD, is consistent with observations even if it seems inconsistent with "natural logic" (as also the whole relativity seemed to be some time ago be but it has been confirmed in so many cases that it may be assumed to be "scientifically proven"). That's why we seem to be forced to acept HTD as solution in all places where BBH authors overlooked it causing artifacts as:

  1. symmetric metric tensor of spacetime (added to EGR as an axiom), rejected by Einstein in 1950, only 2 years after the death of Mileva Marić, whom this author considers the principal discoverer of general relativity who most likely proposed the equation Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle R_{\mu\nu}=8\pi T_{\mu\nu}} considering mathematical skills of her husband,
  2. expansion of space (added to EGR as an axiom to justify the first axiom),
  3. acceleration of this expansion observed as predicted by properly updated Einsteins' theory,
  4. "dark energy" a.k.a. cosmological constant Λ a.k.a. "repulsive gravitation",
  5. the "anomalous" acceleration of cosmic probes Pioneer 10 and 11,
  6. quasars,
  7. creation of energy from nothing, added to justify BBH since without it the BBH fails immediately.

The last item proves that BBH is not a scientific theory but only a lame creationist hypothesis.

Short history of cosmology from 1543 to 1998[edit]

From publication of "De rovolutionibus orbium coelestium" to the recent discovery by the Supernova Cosmology Project team of astronomers who proved the predicted theoretically, by Einsteins' general relativity, illusion of accelerating expansion with, which subsequently I dismissed (only privately, since it was not yet published in any scientific journal AFAIK) the contemporary creationist version of cosmology in which energy was assumed to be created from nothing to justify the lack of assumed dynamical friction of photons or more properly the lack of Hubble time dilation (HTD) and its mathematical representation, the Hubble tensor (HT, the antisymmetric temporal part of Ricci tensor, as its mathematical representation).

HTD in Newtonian physics is interpreted as simply the dynamical friction of photons. In Einsteins' physics though it is an effect of the time running slower in deep space than at any observer roughly proportionay to the exponent of ratio of the distance to this place in deep space to Einsteins' radius. Physically HTD, and mathematically HT, are responsible for all the observed Hubble redshift nulifying the assumed expansion of space that was the creationist explanation through the Doppler shift of observed HTD.

Today all the observations can be explained by natural causes and the universe does not need to be "created". It may exist without any creation and expansion as stationary object forever, which simplifies the cosmology to the great relief to atheists. One mystery down the drain (OMDTD) and that's why creationists call the resistance to the Big Bang cosmology an atheists' plot (at least in Kansas where creationism is still science).

From astronomer Copernicus to inventor Newton[edit]

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 and having no telescope invented yet he couldn't know that the stars were even thousands times farther. Which points to the necessity of existence of engineers for the progress of science.

Today burning scientists at stake to teach them something is not legal, which doesn't mean of course that it won't became legal again, but so far the opponents are just denied publications by establishment editors and in most 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. Though it might be how the evolution solves the problem of progress in science it takes a lot of time. E.g. the discovery that the universe is not expanding, the consequence of Einsteins' general relativity, waits already over a quarter of century 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.

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" which even some ancient Greeks didn't believe in.

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". JimJast (talk) 22:57, 22 March 2011 (UTC)

From inventor Newton to discoverers Einsteins, Mileva Marić and Albert[edit]

In 1687 Isaac Newton (1643-1727) except inventing the telescope with which it bacame easy to show that Copernicus was right and Tycho Brache wrong about the God's wisdom of placing the stars close enough for people to observe their paralaxes, invented also a mathematical a.k.a. "phenomenological" theory of gravitation. He didn't know the physical reason for gravitation, nor cared about them, and so his theory was an invention, a piece of engineering. A phenomenological prescription for what to do to achieve required results of calculations. It was such a good prescription that many people were fooled into believing it as a true, physical theory. It worked almost perfectly till the and of 20th century with putting things into space and on the Moon. Yet it was only a tool for calculating the results of physical phenomena for which the reasons remained unknown.

Newton refused to believe that his theory works due to somme magical gravitational attraction as some less brainy people tried to rationalize the physical reasons for gravitation with. Similarly as nawadays creationists rationalize the reasons for evolution with magical creator of the universe, since they don't want to accept the discovery of Darvin's. Newton didn't believe in magic and action at a distance as creationists do. Neither did Mileva and Albert Einsteins who called it spooky. Newton and the physicists considered it an illusion.

Basically this is the difference between a mathematicians and engineers as Newton an inventor on one hand, who was not curious enough about the reasons for gravitational force to dwell on it for the rest of his life but just dismissed its silly mystical origin and invented also the telescope to observe the sky directly instead to fantasize only about it, as philosophers do, and on the other hand, the physicists as Einsteins. The discoverers whose curiosity was big enough not to stop their research with just looking at the sky as astronomers and philosophers do but also trying to understand what's going on. Where this strange "gravitational force" is coming from. And that's why they finally provided a physical theory with which a high school students like any Jill, Eira, or Jimmy J. could deduce it with simple high school calculus from simple Einstein's equation Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle E=mc^2} . While mystics, who neither invent nor discover, still don't get it.

From discoverers Einsteins back to creationist Wheeler (running in circles)[edit]

In 1905 Einsteins discovered relativity that made possible to discover also the physical theory of gravitation. They partly developed it between 1911 and 1915 but its field equation turned out to be unstable and Einstein stabilized them in 1917 with his "cosmological constant". It destroyed the elegance of Einsteins' equation making the theory a phenomenological one as being valid for only one particular value of density of universe. Albert worried a lot about it, even called it the "biggest blunder of my life " but eventually he gave up fixing the field equation and he said "if you are out to discribe the truth, leave elagance to the tailor ". There was left undetected also another flaw of the theory: the symmetric metric tensor of spacetime.

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 might be expanding on the average. It was their best guess since the notion of curved space was not known yet. Einsteins discovered it only three years later so it was not possible to guess that galactic redshifts are the relativistic effects of curved space.

In 1931 consensus 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 a form of LeMaitre's "cosmic egg", or even a "singularity", 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", the 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 unfortunately not with the principle of conservation of energy (which astronmers tend to ignore). The violation of principle of conservation of energy has been impossible from the point of view of regular physics though. So it clearly couldn't be a right solution.

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: the symmetric metric tensor of spacetime.

In 1950 Einstein, now without Mileva's help, or just remembering her opinions, noticed or recalled that the metric tensor must be non symmetric. He published it in the April issue of "Scientific American ". 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. Unfortunately it was too late for fixing flaws.

Einstein was already over 70, and Mileva dead, and despite he opposed the LeMaitre's idea he was apparently not interested in fixing all the mathematical details of their theory that he stopped to understand. Albert 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 here) they messed the things even further.

From creationist Wheeler to present[edit]

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. MTW assumed symmetric metric tensor of spacetime, and zero value of cosmological constant in apparent attempt to make Einstein's 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's 1279 page "Bible" titld "Gravitation" is adorned with a picture of an angel blowing a horn and a quote from Leibniz states: "One suffices to create Everything of nothing! " on page 1218. The book declares spacetime metric as symmetric and despite tons of quotes doesn't even mentions Einstein's 1950 "Scientific American" article saying that the spacetime metric must be non symmetric.

The necessity of calculating the amount of redshift in (stationary) "Einstein's universe " that would falsify the story of creation was avoided by convincing astrophysicists that it is negligible and then never calculated which takes less than one page and just a four steps between the first and the last equation and derived at much less than a high school level of difficulty. The legend of negligible redshift lives till today among astronomers, so they don't even try to calculate it rigorously, just maintain that they don't understand gravitation. Which is true. The cosmology with never calculated amount of redshift in "Einstein's universe ", 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 Einstein's 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 creation and 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 Einstein's 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 Einstein's universe was supposed to be negligible one W. Jim Jastrzebski, a sculptor from The Boston Museum Scool, a student of Vincent Ricci, and a science buff sharing with his teacher interest in astronomy, calculated this redshift using simple Newtonian math and even simpler Einsteinian physics. The Hubble constant of Einstein's universe turned out to be where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle c} is speed of light and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle R_E} turned out to be (as Jim learned later while taking a general relativity course at Harvard) Einstein's radius of universe. So he proposed that the expansion of space was an illusionillusion caused by "Hubble time dilation", as Jim named it since Hubble discovered it, and Jim proposed that this time dilation should be observed as accelerating expansion with since this turned out to be the second term of Taylor series into which the Hubble redshif could be split. Jim being also an electronic engineer, since sculptors can't survive on sculpture only, were trained well enough to make such simple calculations.

The derivation of Hubble "constant" for stationary Einsteins' universe for all those who want to find whether Jim didn't goof in his derivation is shown in this essay, is in chapter Hubble "constant" of (stationary) "Einsteins' universe".

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 them elegant again.

The plot thickens...

Introduction to contemporary cosmology and gravitation[edit]

Cosmology at the beginning of 21st century[edit]

Situation in cosmology (and gravitation) at the beginning of 21st century can be described as rather messy. 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 are confirmed by observations of real universe by real astronomers, the theorists still maintain that the universe has been created (in a hot Big Bang) and that it is expanding.

The theorists 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 theorist refering the results at "Physical Review Letters " 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. It is inversly proportional to the square of distance from the source of light and not inversly proportional to the distance from source as the hubble reshift is in which it resembles "tired light effect " (TLE). But the TLE it can't be neither since it doesn't work in Einstein's gravitation where the cosmological redshift is coupled to time dilation, which is observed in the sky. The Hubble tensor that explains the math of cosmological redshift became for the astronomers a tabu that can't be even mentioned neither in scientific journal nor in any moderated Internet fora.

For Einstein's 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 "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 part of and mirror image in certain sense (sum of their curvatures adds to zero) doesn't disappear in physical space.

Physical sense of Hubble tensor is that the time at a distant event (in deep space) runs slower than at the observer's event, proportionally to the curvature of space accumulated between the observer and the event at a distance from observer, similarly as spheres around the observer have smaller surface than they would have at the same distance in empty (Euclidean) space (since the physical space has positive curvature).

This effect of slowing 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 Arp (1927-) and Jayant Narlikar (1938-) team, which is also necessary for the principle of conservation of energy to hold. Besides, the fact that the sum of contractions of Hubble and Ricci tensors vanish, provides the means of avoiding the necessity of cosmological constant, making Einstein's field equation elegant again.

Einstein's 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. "

Fate of Feynman's prediction[edit]

Feynman could enjoy the success of his prediction if the editors of scientific journals didn't decide to keep the collapse of MTW's mysticism (the leading trend in 20th century cosmology since 1973 Misner, Thorne, and Wheeler's "Gravitation ") 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 Einstein's (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, all of them physics professors. After all "the beauty of astronomy is that unlike in civil engineering one can be 100% wrong and nobody is hurt " (Late 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 Einstein's universe, and to publish the news of the Hubble time dilation being forgotten to be calculated by theorists, the astronomers still don't know that Einstein's general relativity, explains many gravitational phenomena on which explanation they work, which still doesn't hurt anybody except taxpayers.

The necessary in such scenario creation of energy from nothing, the 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 mathematicians) 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, and astronomers still believe in creation of energy from nothing as theorists explain them with help of "Noether's theorem ".

The reader might understand now why the situation in cosmology was messy and why the fate of Feynman's prediction was such that he stopped attending gravitational conferences, after writing explaining letter to his wife that was published on page 91 of his book "What do you care what other people think ".

Collapse of Wheeler's cosmology[edit]

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 the action at a distance, to expand the universe faster and faster.

The editors of scientific journals might have known that cosmology is a pseudo science 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 Einstein's 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. Being 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 the "general relativity", the name by which Einstein's theory has been already known.

If this trend continues we might be in a danger of establishing laws against engaging in science without a license (applied especially to sculptors like me). Even now I'm banned for life from several math and astronmy fora just for trying to discus Einstein's 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.

How is Einstein's real general relativity doing in the meantime[edit]

Many people actually think that MTW's hypothesis of Big Bang is general relativity and because of this they stopped believing that Einstein's theory of gravitation is any good, assuming falsly that it is the same as the Big Bang hypothesis.

Einstein's real general relativity doesn't allow neither "repulsive gravitation" nor "creation of energy" (even in "negligible amounts"). They are empty ideas that differentiate between physics and mysticism. The spacetime requires intrinsically flat geometry (as long as the space is curved and time dilated). It doesn't need "dark energy" (another empty idea) and gravitation is so simple that high school education suffices to understand it. Even a sculptor with a high school education may explain it to anyone who wants to learn why things fall. That's why "few of the best men are doing work in it [...] It is not that the subject is hard; it is that the good men are occupied elsewhere." [ Feynman ].

Since the editors of scientific journals claim that their readers aren't interested in the results that I got (as e.g. editors of "Physics Review Letters " wrote to me) I show below, for those few who are interested, how the Einsteinian 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's phony "general relativity" and Einsteinian real 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 (which Newton himself already denied) nor that the BBH is. That it is just "cargo cult science".

To mention the quantum nature of Einstein's gravitation it suffices to mention that quanta of gravitational energy are any elementary particles that carry mass from one atom to another (e.g. electrons, photons, but havt to be exremaly resistant to attenuation by regular matter (like e.g.neutrinos or shutrinos or whatever finally turns out to be a graviton so unifying gravitation and electromagnetism is already contained in Einsteins' theory just not stated clearly enough. As Hertz said: "Some physical theories are often wiser 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 electrons, 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 Einstein's gravitation with quantum mechanics. Some others, with religion. 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 in reality 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 therefore 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 (though the problem might have been deeper as e.g. the metric tensor not only non symmetric but also degenerate).

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's. 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. "

Illusion of "expansion of space"[edit]


If one assumes that the redshift of galaxies is due to their velocity (effect called "Doppler effect") then the universe looks as if it were expanding. This is so since the light coming from distant galaxies has on average a smaller frequency (is "redder") than the light generated by the same light sources close to observer. All colors in such light are shifted in the direction of red end of their spectrum. It is consistent with galaxies moving away from the observer and therefore consistent with an assumption that the universe is expanding.

Aditionally, if the relation between redshift and distance from observer is exponential with redshift exponentially growing with distance, then the expansion looks as if it were accelerating. The "acceleration" comes from the exponential character of redshift curve in function of distance which is visible after splitting the curve into Taylor series. If it is an illusion then the second term of this series produces the "illuson of acceleration of expansion of space".

The Big Bang hypothesis (BBH) theorists assumed though that it is not an illusion and declared the reason for smaller frequency of light coming from galaxies is being the recessional velocity of galaxies, causing redshift through Doppler effect.

The overall picture seemed to them as consistent with the "accererating expansion of space".

Yet after analyzing intrinsic redshift due to Newton's laws of interaction of photons with masses of the universe expressed by so called dynamical friction of photons (negative "slingshot effect "), together with Einsteins' general relativity, causing slowing of time due to curvature of space (explained in my one page paper) suggested that those Newtonian effects together with relativistic slowing of time, are responsible for observations, presenting the picture of accelerating expansion of space. And therefore the observations might be caused by the time at galaxies running slower than at observer and then the effect of the expansion of space might be simulated.

However this simulated expansion has to have a certain specific value of acceleration, namely Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle dH/dt=-H_o^2/2} where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle H_o} is Hubble constant at the Earth, which it is just what was observed in 1998 by the Supernova Cosmology Project team of astronomers. It causes a suspicion that the whole "expansion of space" is simulated, and our universe is Einsteins', stationary and eternal.

Furthermore 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 method of Newtonian potential for a planar light wave, with a more detailed explanation of the method of obtaining the result, is here. Obviously both metods of calculation should give the same result (as they do) that Hubble "constant" at r=0 is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle H_o=c/R_E} where c is speed of light and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle R_E} is "Einstein's radius of universe".

Because of the fact that the principle of conservation of energy requires that energy can't be created, the creationists stick to old explanation of cosmological redshift. If you don't know that energy could not be created from nothing you have a tough choice between science that tells that creation is an illusion and the Big Bang theorists who say that according to their best guess the universe is expanding and energy necessarily created from nothing apparently through the divine intervention. Though in the real world it is probable about as much as existence of Santa Claus. But one can't discuss the faith, whether it is about the existence of supernatural or about its absence.

Hubble "constant" of (stationary) "Einsteins' universe"[edit]

Introducing c=speed of light, G=Newtonian gravitational constant, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle \rho} =density of dust of Einstein's universe where one dust particle is roughly one galaxy, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle E_d = E_o - E} , the gravitational energy acquired by the dust due to gravitational interaction between dust and photons (and so "lost" by the light after light of energy Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle E_o} got radiated out from a point in space at radial coordinate Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle r = 0} and reached the radial coordinate r, lost due to the principle of conservation of energy) so the linear density of simulated "Newtonian gravitational force" acting on the dust of Einstein's universe inside the shell of spherical wave is

	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle 4 \pi G \rho( Eo - Ed ) / c^2}

On the other hand this "linear density of gravitational force" is from its definition equal to

	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle d^2 E / dr^2}

Substituting "Einstein's cosmological constant" Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle \Lambda} for Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle 4 \pi G \rho / c^2 = 1 / R_E^2} where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle R_E } is "Einstein's radius" we get a differential equation controlling energy of photons as

	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle d^2E / dr^2 = \Lambda}

Solving this equation, with initial conditions Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle E(r = 0) = E_o} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle (dE/dr)(r = 0) = -E_o/R_E} and selecting solution that has physical sense, one gets

 	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle E/E_o  = exp(- r / R_E)}

It is not a strange coincidence that we get the radius of curvature of space through Newtonian math but a necessary result following from a fact that in universe in which energy is conserved, if the math is right (as the Newtonian math is), the relation between the Hubble redshift and the curvature of space must be as expressed by the above equation.

The Einsteinian interpretation of the above is of course the time running slower at a distance form observer according to relation

	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle d \tau / dt = exp( - r / R_E )}

where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle \tau } is proper time at observed place in deep space and t is coordinate time (the proper time of observer).

This equation presents this "big leap" from Newton's math to Einstein's physics that has to be made to see why Newton's math reflects so faithfully Einstein's 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) Einstein's spacetime. After differentiating eq. (5) at Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle r = 0} we get a relation between the "curvature of time" in deep space in radial direction Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle (d^2 \tau / dt dr)^2} and the curvature of space Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle \Lambda} as

	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle (d^2 \tau / dt dr)^2 - \Lambda = 0}

which shows that the spacetime is intrinsically flat as suggested already by Narlikar and Arp, 1993.

The redshift produced by the effect is

	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle Z = exp( r / R_E ) - 1}

and therefore it simulates the expansion of space with Hubble constant of this apparent expansion at r=0 equal

	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle H_o = c / R_E}

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 Ho = 70 km/s/Mpc implies density of space Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle 6\times10^{-27}kg/m^3} with only twice less relative accuracy as the Hubble constant is determined since Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle H_o^2\propto\rho} . Another application might be calculations of densities and sizes of clouds of dust that quasars are located in from the redshifts of those quasars. JimJast (talk) 15:13, 21 March 2011 (UTC)

Illusion of "accelerating expansion"[edit]

After splitting the Hubble constant into Taylor series the acceleration of this apparent expansion comes out as

	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle dH / dt = - H_o^2 / 2}

and it has been observed within a fraction of standard deviation already in 1998 by Supernova Cosmology Project team and therefore predicted by Einstein's theory of gravitation (a.k.a. Einstein's general relativity) over 80 years earlier.

Since now Einstein's theory can't be falsified by observations as it predicts strict conservation of energy (non falsified yet), Einstein's 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

	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle d \tau^2 = exp(- 2r / R_E)dt^2 + 2 sinh(2r / R_E)dtdr / c - exp(2r / R_E)dr^2 / c^2}

shown above for one spatial direction only, since it is isotropic. For Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle r << R_E} it approximates to Minkowski metric

	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle d \tau^2 = dt^2 - dr^2 / c^2}

JimJast (talk) 15:13, 21 March 2011 (UTC)

Correcting Einstein's field equation[edit]

The Einstein's field equation except invisible (in particularl to Misner, Thorne, and Wheeler, who didn't see it in 1973 while writing their 1279 page "Gravitation", or just forgot it) the 1950 Einstein's abandonment of symmetric metric tensor, contains a well visible cosmological constant of 1917 that makes the field equation stable. As mentioned in the preamble, it makes Einstein's theory (to Einstein's great discomfort: "the biggest blunder of my life") a phenomenological theory. But Einstein's GR is in fact a "physical" theory therefore also a quantum theory as all physical theories must be. The cosmological constant makes no sense in it.

Luckily, due to the value of Einstein's cosmological constant Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle \Lambda _E = 4 \pi G \rho / c^2} it may be replaced by Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle R / 2} where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle R} is contraction of Ricci tensor, and therefore it reduces Einstein's field equation to

	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle R_{\mu \nu} = 8 \pi T_{\mu \nu} }

(in units in which c=G=1) which makes Einstein's GR again an "elegant" physical theory and restores Einstein's universe as the legitimate model of our universe, unfortunately creating the same problem that Einstein had at the beginning when he thought that this might be the field equation. Apparently it might well be. The solution of this problem will be presented in one of next revs of this essay so please be patient :)

JimJast (talk) 13:18, 24 March 2011 (UTC)

Usual arguments "against Einsteins GR from 1917"[edit]

The Big Bang theoretists were bringing against Einstein's GR several objections that are specified below. JimJast (talk) 22:27, 22 March 2011 (UTC)

Einstein's cosmological constant of 1917 and "Einstein's universe"[edit]

Einstein used this constant with value of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle 4 \pi G \rho /c^2} to stabilize his Field Equation and to keep the universe stationary. Later he called it "the biggest blunder of my life". It changed his pretty physical theory into ugly, mathematical (phenomenological) theory. The cosmological constant shouldn't be put there in the first place, however Einstein didn't know how to get rid of this constant. It's not needed any more, but despite that the theorists who don't know how to get rid of it neither, included it in BBH as "Dark Energy". They think that the universe is expanding and it helps now to provide the expansion. The universe is not expanding and there are better ways of getting rid of "cosmological constant" desribed in chapter Correcting Einstein's field equation".

JimJast (talk) 22:27, 22 March 2011 (UTC)

Cosmic Microwave Background Radaition (CMBR)[edit]

This radiation cannot be just the redshifted starlight since then it could not have the black body spectrum that it has. It seems therefore that it has to be the radiation from non-luminous matter that is in thermal equilibrium with the redshifted starlight as it has been already proposed by Fred Hoyle, Thomas Gold, Hermann Bondi in their 1948 "Steady state cosmology" who also, as other astronomers, believed that the universe was expanding.

If it is radiation from non lumineous matter then we can calculate the average size of the pieces of non luminous matter of universe. This is because the probability Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle P} of a photon hitting an obstacle of diameter D on it's way, and transferring to it its energy, which then becomes thermal energy, is approximately proportional to the area of the obstacle Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle P_1 \propto D^2} and to the number of obstacles along the photon's way (inversely proportional to the cube of the distance Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle P_2 \propto L^{-3}} between obstacles). Since for a fixed mass density of the whole space (already determined from Hubble parameter) the distance between obstacles is proportional to their linear size the total probability of a photon hitting an obstacle becomes


and therefore inversely proportional to the linear size of an obstacle. So, knowing the density of matter the obstacles are made of (presumably ice) , the redshifted starlight , presumably re-emitted as a thermal radiation from the non luminous matter of temerature , and assuming the specific density of universe , one may determine the average size of the pieces of non luminous matter of universe as . It is large enough size to make the non luminous matter of universe responsible for the absorption of light in the millimeter wavelength range (see Appendix 3 of orignal "Gravitation Demystified" for details of calculation of the approximate size of an average obstacle). JimJast (talk) 15:13, 21 March 2011 (UTC)

Element abundancies in eternal universe[edit]

For the universe to be stationary while constantly changing one has to figure out the way of stabilizing the element abundancies. And this is one thing that is not yet known, nor any theory about it is worked out similarly as a theory of creation of galaxies for a different reason though.

The theory of creation of galaxies suffer 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) and so there was not enough time to create galaxies. The "theory of element abundancies" has all the time that it needs to get created. Now we just have to figure out 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 -> D -> 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 by future generations of homo sapiens and so the speculations about the cycle might be premature. Also we may not have as much time as we need to discover this theory since homo sapiens are better in inventions than discoveries (85% still didn't discover the origin of God discovered already by George Hammond) but they invented already H-bomb which may end the civilization and then the cycle has to start again (hopefully with a different end).

JimJast (talk) 15:13, 21 March 2011 (UTC)

Second law of thermodynamics[edit]

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, 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 Einstein's universe is.

JimJast (talk) 15:13, 21 March 2011 (UTC)

Arguments against the Big Bang hypothesis[edit]

In the abstract we promissed the explanation of differences of Einsteins GR in relation to the Big Bang Hypothesis. They are explained below. JimJast (talk) 15:13, 21 March 2011 (UTC)

Symmetric metric tensor of spacetime[edit]

It was rejected by Einstein already in 1950 in his paper "On the generalized theory of gravitation" in April issue of "Scientific American" yet still present in BBH in 1973. The symmetry means that movement of any physical object along a closed loop does not change the gravitational energy of that object. It corresponds to Newtonian approximation saying that Newtonian gravitational field is a consevative field. It prevents, between other things, the interaction of light with the universe.

According to the critique of BBH if it were so there couldn't be any HTD calculated so one may consider it a lame argument for expansion if not for the fact that it contradicts the argument that Hubble redshift in Einstaein's universe was derived from conservation of energy with (almost) purely Newtonian math in stationary universe and produced the observed redshift. Which means that photon's treated as particles carrying energy don't see Newton's conservative gravitational field and so BBH is wrong in assuming existence of symmetric metric tensor of spacetime (at least for photons).

JimJast (talk) 15:13, 21 March 2011 (UTC)

"Expansion of space"[edit]

... dealt already in Illusion of expanding space. JimJast (talk) 15:13, 21 March 2011 (UTC)

"Acceleration of expansion of space"[edit]

... resulting from the second term or Taylor series of H(t), where H(t) is "Hubble constant" and t is coordinate time. JimJast (talk) 15:13, 21 March 2011 (UTC)

"Dark energy" a.k.a. "cosmological constant Λ" a.k.a. "repulsive gravitation"[edit]

... irrelevant since there there is no "repulsive gravitation" in universe since gravitational force is an inertial force and Λ gets eliminated from Einstein's field equation. JimJast (talk) 15:13, 21 March 2011 (UTC)

"Anomalous" acceleration of cosmic probes Pioneer 10 and 11[edit]

... is explained with the same mechanism as the cosmological redshift since equations determining the cosmological redshift don't depend on velocity of moving objects. See chapter Illusion of expanding space. JimJast (talk) 15:13, 21 March 2011 (UTC)


Quasars are objects that look like stars but the power they radiate seem billions times greater than that of regular stars. The critic of BBH maintains that such enormous power output is just the matter of wrong estimation of distances of quasars, from their redshifts and application of "Hubble law" in expanding universe. In reality quasars may be even regular stars just located in big and/or dense clouds of dust and so their redshifts might be many orders of magnitude greater than redshifts of light leaving a star of the same mass and subject only to gravitational redshift. See calculations in here. JimJast (talk) 15:13, 21 March 2011 (UTC)

"Creation of energy from nothing"[edit]

... never observed in the real world. JimJast (talk) 12:50, 21 March 2011 (UTC)

Non vanishing "curvature of spacetime" (of unknown value)[edit]

To keep consystency with other parts of the Big Bang hypothesis there had to be added also an assumption that the spacetime is curved since how otherwise energy could be created if the spacetime were flat (as assumed by invariance of tensors, and energy momentum being a 4-vector, which means an invariant tensor)? Therefore the BB aficionados had to add to BBH an assumption of non flatnes of spacetime.

It means that the spacetime in BBH must be curved (of unknown value though, but that it is "non vanishing" means that any 4-vector experiencing parallel transport towards the future (or the past) will show some non vanishing difference of its components to previous position producing contradiction with 4-vectors being invariant. In particular the paralel transport of stress-energy 4-vector will change some of its components violating some laws of physic: either the principle of conservation of energy or momentum.

So this assumption of BBH is equivalent to assumption of creation of energy from nothing ... never observed in the real world. Which is not a proof that it can't happen. It might happen e.g. when the hell freezes over. JimJast (talk) 15:13, 21 March 2011 (UTC)

Basics of Einsteinian gravitation[edit]

In this chapter, in order to not confuse high school students, I keep the old convention, from Feynman's textbooks, of writing masses: is invariant "rest mass" (denoted presently by ) and is "relativistic" mass (denoted presently by where


where is velocity of moving particle in observer's coordinate system and is invariant speed of light. At the middle of particle .

Why Einsteins' gravitation is already a quantum theory[edit]

N.B.: because of recent suspicion of mine, prompted by Albert's failure to get rid of (his?) "cosmological constant" which even I knew how to get rid of, that Mileva Marić, Albert Einstein's first wife, was the main discoverer of relativity, the refs to Einstein as a male has been changed into plural "Einsteins", to be just in the relation to her.

Before we start we should show the difference between three basic types of beliefs: from most ancient, religion, starting thousands years ago after the humans descended from trees into caves, to newer, magic, starting from about 100 centuries ago (a.k.a. math, which occured only recently while the dependence of math on assumptions was somehow overlooked by anscient scientists and surfaced only recently with Russel paradox between 19th and 20th centuries), and the newest, starting from about 16th century, with invention of scientific method, physics or just science. The math, despite being only a good magic, is still considered science, however by non mathematicians only. The same as people who do tricks with cards know that those tricks are not "miracles" just look like them. At least Magnificent Randi knows though he also believes that the Big Bang really happened and refused to pay me this promissed million for doing something that he thinks can't be done: proving that the Big Bang never happened. Well, nobody is perfect. And Magnificent Randi is not even an astronomer. He just trusts that the math is science. It might be explained better by this link.

The tough work the contrmporary gravity physicists put out might be lighter had they known or just accepted the following.

Location of gravitational energy in space and why [edit]

The best argument for Einsteins being right about their physics seems considering the locating the "gravitational energy" of a particle within itself (which was not necessarly Einsteins' idea since I didn't see it either in Einsteins' papers, nor in Landau's for whom it seemed so easy that I still don't understand why he didn't differentiate parts of his invariant energy shown in his "Theory of Fields", to see that it gives "gravitational force", instead introducing a complicated pseudo tensor of energy).

The idea of being gravitational energy (the same as "rest energy") came to me while I've been waiting at downtown Boston, MA for a T-train to "Revere" where I lived, trying in the meantime to solve the puzzle of getting factor 2 in my solution to gravitational force acting on a particle, while I took under consideration the time dilation as I thought that Einstein did. So I had a basically right result if not for the factor 2, which made it not working as Einstein's relativity should. And then I recalled: "It is the same problem that Einstein had with the deflection of light ray". So the solution had to be the same. I just "discovered" the curvature of space :). Adding the curvature of space, instantly improved derivation leaving the solution for gravitational force looking exacly as Newton's:


where is acceleration in proper direction (there is no loss of generality since the same reasoning may be repeated for each spatial direction with the same result).

"My" Einsteinian derivation of "gravitational energy" has an adventage of not adding any mythical "potential energy" to energy density in Einstein's field equation since Einsteinian gravitational energy, , replaces completely the Newtonian potential energy. So the Einsteinian gravitational energy is such since according to its definition its negative derivative with respect to displacement is the gravitational force


where is acceleration in direction and so is Newtonian gravitational force) in this direction.

The derivation of gravitational force is in chapter Math of Einsteinian gravitational force and an older and more detaled version of this derivation (since it is for high school students who might need more detailed derivation which physicists don't need, providing they understand the physics, explained in this chapter) is in Appendix of "Einsteinian Gravitation for poets and science teachers". This Appendix is the only part being otherwise strictly for poets, in which there is any math used. It is placed there to aviod dismissing Einsteinian gravitational force by the Big Bang aficionados as sucked off a thumb :). Now, to dismiss Einsteinian force, requires understanding, and is likely to end up with conversion of all who understand it, to Einstein's physics.

In my university only one professor agreed with my derivation and called it "obvious" and told me that I may quote his opinion in discussions (but he was one who wrote a book on Einstein's theory so he already had an understanding of Einstein's physics, unlike others physics professors). The others (regular) physics professors to whom I described this derivation during 15 minute intermissions in their lectures said that "it is too simple to be true since if it were true they surely would have known it by now, learning it in school".

Many of them expressed an opinion that is "constant" which shows the shortages of education of physicists in area of gravitation. Actually, about 99% of physicists maintain that they "don't ynderstand gravitation". In fact is not "constant" but (as everything else) depends on observer and the reason for gravitational force being able to be calculated Einsteinan way is that is dependent on observer. It happens to be "constant" only at the "middle" of particle (assuming the particle has such a place) and outside of this middle it is different as it is shown while getting its derivative with respect to displacement in chapter Math of Einsteinian gravitational force.

Physically, the "gravitational force" comes from (in general tiny) differences between speed of light being different outside the "middle" of particle and so is slightly different over there producing "gravitational force", which is just .

To have a relatively complete picture of Einsteinian physics we have to mention, that this "gravitational force" is just a quantum effect of particle assuming position of its lowest energy (which causes the movement of the observed object with its certain acceleration pushed by this need of assuming the position of lowest energy until it meets an obstacle that stops its movement towards lowest internal energy. Only then we see the "gravitational force" which we don't see while the particle is in "free fall". There is no "gravitational force" in a free fall and therefore all the atempts to determin "fundamental gravitational force" are futile. There is no such thing in Einsteinian gravitation. The "gravitational force" is a figure of speech denoting inertial force whith which any masive particle pushes aginst the obstacle preventing the particle from achieving its position of minmum energy (as its most probable position, which is only a quantum effect).

Falsifying Einstein's gravitation could be done by proving that that most probable position of a particle is not its position of minimim internal energy , which I didn't do and only believe that it is so since everything seems to point to this quantum nature of Einstein's gravitation.

So now, when we already know the physics of gravitation we can derive (apparent) "gravitational force" ourselves and see why it is equal the force that Newton predicted not believing in it at all thinking that it is only a mathematical trick, with some unknown physical mechanism behind it. As it turned to be the case. And why it is visible now that making it a quantum effect as Einstein did and Jim described it, solved the problem, making it possible to understand not only to all physicists but also theirs grandmas. JimJast (talk) 14:34, 21 March 2011 (UTC)

Physics of Einsteinian "gravitational force" and why it didn't work with the Sun[edit]

The math of gravitational force assumed by pre-relativistic physicists assumed (wrongly though) that all masses in the universe "attract" each other through empty space with a force prportional to product of these masses and inversly proportional to the square of distance between centers of gravity of these masses. The gravitational force should be then


where is some constant of proportionality called the "Newtonian gravitational constant", established experimentally, and are masses, and is the distance between center points of the mass and . Newton, who didn't believe in "action at a distance" didn't believe that this force is caused by "attraction through empty space" but he didndn't come with a better ida.

It lasted until Einstein came up with his relativity and the idea that the force of attraction is an illusion, and it is that mass modifies space around itself so that time aound it runs slower (effect called "gravitational time dilation") and therefore there is an inertial force pushing mass into direction of mass since slower runing time means lower energy of all masses around mass so mass would just be reaching lower energy level in this modified space. The gravitational force should be then


where is amount of energy lost due to this slowing down of time and displacement of a particle within the area of slown down time around mass .

So the result supposed to be the same as this of "attraction" but the physical mechanism of achieving this result completely different. And the "attractive gravitational force" calculated with Newton math supposed to be replaced by the inertial force pushing the particle towards the other, , that modified "the rate of time" in the space around itself because there, at this space, supposed to be lower energy of particle . The particle in this way were supposed to seek the most probable position, the position of lowest energy.

Einstein compared the gravitational field of a star to the acceleration in a rocket ship accelerating with the same acceleration as there would be felt while standing on that star and formulated a principle of equivalence meaning that all gravitational phenomena are equivalent to the behavior of things in accelerating systems. Therefore in such a rocket ship any straight light ray would be seen as bent towards the rear end of the ship while the ship is accelerating forward.

Arthur Eddington's expedition to South America was supposed to check the idea of bending of light rays in the gravitational field of Sun during the eclipse of Sun.

Unfortunately the light rays had bent twice as much as they supposed to in the gravitational field assumed by Einstein with his analysis of bending light rays :) as if the gravitational field was twice stronger on the surface of the Sun than in the accelerating rocket ship.

Einstein went back to the drawing board and discovered that the real "gravitational field" is composed not only of "time dilation" as he assumed before but also from "curved space". As Jim "discovered" too while waiting for a T-train to "Revere". And at the same time Jim understood Einstein's way towards discovering the "gravitational phenomena", the unification of inertial and gravitational forces, and failure of Wheeler's curved spacetime, which was already treated in chapter: Non vanishing "curvature of spacetime" (of unknown value).

So the real "gravitational field" at the surface of the Sun should be adjusted to the curvatutre of space by multiplying this "field" by 2 and Einstein's analysis turned out to be only good for slowly moving bodies. Not bodies moving with speed of light, bent according to "real field" (and real here was the acceleration) which turned out to be twice as strong. This way Einstein's theory predicting both, the gravitational time dilation and the curvature of space and showed out to be superior to Newton's theory that predicted different (smaller) bending light rays, which turned good only for slowly moving objects. JimJast (talk) 16:22, 25 March 2011 (UTC)

Math of Einsteinian "gravitational force"[edit]

This math starts with a famous Einstein identity for relation between energy and matter


where represents mass of that matter and c speed of light, both as as seen by any particular observer. Additionally from special relativity we know that


where and (can be found in Landau and Lifshitz's "Theory of fields") p. 285.


where is invariant speed of light, is "proper" time of observed "event" and is its "observer's time" shown by her wrist watch (assuming it runs precisely). Since both and are variables depending on displacement we may deifferentiate them with respect to displacement and we get


substituting and which we get from analyzing geometry of space in a rocket ship accelerating with acceleration and putting it in (4) we get total Einsteinian force that pushes any particle against its constraints at rest as


As we may see from the above equation the force is as it was guessed by Newton except that now its physical nature is known as due to the quantum effect of particle trying to assume the lowest energy in space of known time dilation and curvature of space in which this "gravitational force" is generated. JimJast (talk) 19:29, 27 March 2011 (UTC)


  1. Rindler, Wolfgang, 1977, Essential Relativity, Special, General, and Cosmological, ISBN 0-387-10090-3, p.109-110
  2. Bontekoe, Tj.R. and van Albada, T.S. 1987, M.N.R.A.S. 224, 349.
  3. Chandrasekhar, S. 1943, Ap. J. 97, 255.
  4. Hernquist, L. and Weinberg, M. 1989, M.N.R.A.S. 238 407.
  5. Weinberg, M. 1989, M.N.R.A.S. 239, 549.
  6. White, S.D.M. 1983, Ap. J. 274, 53.
  7. STScI-2009-08, Refined Hubble constant narrows possible explanations for dark energy,
  8. Narlikar, J. & Arp, H., 1993, Flat spacetime cosmology - a unified framework for extragalactic redshifts, Astrophysical Journal, Part 1 (ISSN 0004-637X) vol. 405, no. 1, The American Astronomical Society, p. 51-56, Bibliographic code: 1993 ApJ...405...51N
  9. Kuznetsova N, Barbary K, et al, A New Determination of the High-Redshift Type Ia Supernova Rates with the Hubble Space Telescope Advanced Camera for Surveys, 2008, The Astrophysical Journal, Volume 673, Issue 2, The American Astronomical Society, pp. 981-998, Bibliographic Code: 2008 ApJ...673..981K,
  10. Misner, Charles W., Thorne, Kip S., Wheeler, John Archibald, 1973, "Gravitation", W. H. Freeman and Co, New York, p. 410-411.
  11. Meissner, Krzysztof A., 2002, "Klasyczna Teoria Pola" ("The Classical Theory of Fields"), Wydawnictwo Naukowe PWN, ISBN-83-01-13717-7, p. 120.
  12. Arp, Halton, 1987, "Quasars, redshifts and controversies", Interstellar Media, 2153 Russel Street, Berkeley, CA, ISBN 0-941325-00-8


  1. Einstein called his cosmological constant "the biggest blunder of my life"
  2. Broken link since the University of Warsaw bloked my access to the physics server for the reason that my PhD work is unoficial project of prof. Namysłowski. The link is going to be fixed after I find a more permanent host for the article.
  3. W. Jim Jastrzebski,
  4. The result being , where is Hubble constant as function of coordinate time where is coordinare distance to a deep space galaxy and is speed of light in vacuum, is Hubble constant.
  5. From
  6. Whenever I produce a link to "science" I do it to underline the fact that at this moment I treat science the same way it is treated in Rational Wiki.
  7. Actually, after closer examination of the effect after 1985 discovery of the real reason for the cosmological redshift. From
  8. From