Changes

I'm writing this essay to explain to people interested in gravitation how it works according to Einsteinian physics.  

I'm writing this essay to explain to people interested in gravitation how it works according to Einsteinian physics.  

Between 1905 and 1915 the theory of gravitation switched from Newtonian math to Einsteinian physics and many Newton's problems got solved, mostly due to the fact that the space is not flat ("flat space" means the same as "Euclidean space"

Between 1905 and 1915 the theory of gravitation switched from Newtonian math to Einsteinian physics and many Newton's problems got solved, mostly due to the fact that the space is not flat ("flat space" is our "Euclidean space"

<ref>

<ref>

"Flat" or "Euclidean" means our regular (x,y,z) space called also "3-space" in which any 3D sphere (called also "2-sphere" since its surface has only 2 dimensions) of surface area <math>4\pi r^2</math> contains volume of space <math>(4/3)\pi r^3</math>.

"Flat" or "Euclidean" means "3-space" (x, y, z space) in which any "2-sphere" (since its surface has only 2 dimensions) of surface area <math>4\pi r^2</math> contains volume of space <math>(4/3)\pi r^3</math>.

</ref>) but is curved having certain [[curvature of space]] and the time reflects faithfully this [[curvature of space]] through the gravitational [[time dilation]] in such way that the whole ''spacetime'' is flat.  

</ref>) but is curved having certain [[curvature of space]] and the time reflects faithfully this [[curvature of space]] through the gravitational [[time dilation]] in such way that the whole ''spacetime is flat''.  

This global flatness of spacetime is an important feature. Without it the movement of certain geometrical structures (tensors) that describe things in space and time (therefore in 4 dimensions: 3 in space and 1 in time) wouldn't have the property of keeping the strict conservation of energy and momentum between the ''now'' and the ''past'' or the ''future''. There wouldn't be any [[conservation law]]s valid in the universe. The things would be spontaneously created from nothing and disappearing without trace from one moment to another just by the virtue of mathematical manipulation (as it happens in the [[Big Bang]] hypothesis in which spacetime is "curved") (luckily not in this universe of ours since then we would be forced to believe in "ghosts" while they would be created and disappear without no reason whatsoever). The creationist might be happy but the [[science]] wouldn't be as we know it today. Now in [[science]] neither energy nor momentum can be created from nothing as it is assumed in the [[Big Bang]] hypothesis with its [[curvature of spacetime]]. [[Conservation law]]s assure that energy and momentum are conserved separately (not as some [[relativists]] think, "together" as Wheeler's hypothetic "momenergy" in which energy is assumed to be able to be converted into momentum and v.v).

This global flatness of spacetime is an important feature. Without it the movement of certain geometrical structures (tensors) that describe things in space and time (therefore in 4 dimensions: 3 in space and 1 in time) wouldn't have the property of keeping the strict conservation of energy and momentum between ''the now'' and ''the past'' or ''the future''. There wouldn't be any [[conservation law]]s valid in the universe. The things would be spontaneously created from nothing and disappearing without trace from one moment to another just by the virtue of mathematical manipulation (as it happens in the [[Big Bang]] hypothesis in which ''spacetime is "curved"'') (luckily not in this universe of ours since then we would be forced to believe in "ghosts" while they would be created and disappear without no reason whatsoever). The creationist might be happy but the [[science]] wouldn't be as we know it today. Now in [[science]] neither energy nor momentum can be created from nothing as it is assumed in the [[Big Bang]] hypothesis with its ''[[curvature of spacetime]]''. [[Conservation law]]s assure that energy and momentum are conserved separately (not as some [[relativists]] think, "together" as Wheeler's hypothetic "momenergy" in which energy is assumed to be able to be converted into momentum and v.v).

This essay is meant to explain this strange physics of [[gravitation]], with which we deal every day but generally don't understand it, don't know how it operates and where the "gravitational force" is coming from, except for some physicists

This essay is meant to explain this strange physics of [[gravitation]], with which we deal every day but generally don't understand it, don't know how it operates and where the "gravitational force" is coming from, except for 3 physicists

<ref>

<ref>

:<math>F=-dE/dx=2mcdc/dx=-2mca/c/2=ma</math> ...... (5).

:<math>F=-dE/dx=2mcdc/dx=-2mca/c/2=ma</math> ...... (5).

And so the ''"gravitational force"'' comes out as <math>F=ma</math>, more accurately than the Newtonian force given by the Newtonian equation  

And so the ''"gravitational force"'' comes out as <math>F=ma</math>, more accurately than the Newtonian force given by the Newtonian approximate equation  

:<math>F_N=GMm/r^2</math> ...... (6),  

:<math>F_N=GMm/r^2</math> ...... (6),  

where G is Newtonian gravitational constant. The small difference between those two forces (Newtonian <math>F_N</math> and Einsteinian <math>F</math>) comes from the difference between flat space of Newtonian math and the [[curvature of space|curved space]] of Einsteinian physics that is responsible for equation (4).  

where G is Newtonian gravitational constant. The small difference between those two forces (Newtonian <math>F_N</math> and Einsteinian <math>F</math>) comes from the difference between flat space of Newtonian math and the [[curvature of space|curved space]] of Einsteinian physics that is responsible for equation (4).  

It is the whole mystery of ''gravitational force'' demystified by Einsteinian ''[[time dilation]]'' and the ''[[curvature of space]]''. Turning out to be the '''inertial force''', ''pushing'' the particle towards mass <math>M</math>, that allegedly ''attracts'' it but in fact only changes the rate of time around itself (slowing it down).  

It is the whole mystery of ''gravitational force'' demystified by Einsteinian ''[[time dilation]]'' and the ''[[curvature of space]]''. Turning out to be the '''inertial force''', ''pushing'' the particle towards mass <math>M</math>, that allegedly ''attracts'' it but in fact, its action only changes the rate of time around itself (slowing it down).  

In the end, the apparent gravitational force of equation (2) is caused by the [[curvature of space]] and the [[time dilation]] that combined, cause the effects of diminishing energy of objects immobilized in curved space. When they aren't immobilized (they are left in [[free fall]]), they follow their natural positions of the greatest probability of being there in the spacetime without producing any forces. As e.g. the Moon following its natural path around the Earth moving at each point of its travel with appropriate acceleration <math>a</math> compensating changes of its total energy  as given by (1). In this way no additional energy can be created or destroyed and the law of conservation of energy is satisfied automatically for all the moving objects of the universe.

In the end, the apparent gravitational force of equation (2) is caused by the [[curvature of space]] and the [[time dilation]] that combined, cause the effects of diminishing energy of objects immobilized in curved space. When they aren't immobilized (they are left in [[free fall]]), they follow their natural positions of the greatest probability of being there in the spacetime without producing any forces. As e.g. the Moon following its natural path around the Earth moving at each point of its travel with appropriate acceleration <math>a</math> compensating changes of its total energy  as given by (1). In this way no additional energy can be created or destroyed and the law of conservation of energy is satisfied automatically for all the moving objects of the universe.

===Introduction to Einsteinian universe===

===Introduction to Einsteinian universe===

The Einsteinian universe (EU), is a theory of universe from which the "expansion of univrese" was eliminated through the calculation of [[intrinsic redshift]], that showed that the alleged expansion is a relativistic illusion due to the curvature of space.  

The Einsteinian universe theory (EUT), is a theory of universe from which the "expansion of univrese" was eliminated through the calculation of [[intrinsic redshift]], that showed that the alleged expansion is a relativistic illusion due to the curvature of space.  

The EU is almost the same as Einstein's stationary model universe of 1917 that was Einstein's guess, very close to the present EU model of universe. It has common with the present model the proved only in 1985, and therefore unknown to Einstein, the lack of expansion, that in original Einstein's model has been acheived via [[cosmological constant]].

The EUT is almost the same as Einstein's stationary model universe of 1917 that was Einstein's guess, very close to the present EUT model of universe. It has common with the present EUT model the proved only in 1985, and therefore unknown to Einstein, the lack of expansion, that in original Einstein's model has been acheived via introduction of [[cosmological constant]], and therefore with purely mathematical means <ref>

 

 

</ref>.

To keep Einstein's field equation of this stationary model stable, and not knowing yet about the ''"[[Hubble time dilation]]"'', discovered by Edwin Hubble over a decade later, and suggesting to some astronomers that the universe might be expanding, Einstein added his ''"cosmological constant"'' to his field equation that stopped the alleged expansion. Later he called this cosmological constant ''"the biggest blunder of his life"''.  

To keep Einstein's field equation of this stationary model stable, and not knowing yet about the ''"[[Hubble time dilation]]"'', discovered by Edwin Hubble over a decade later, and suggesting to some astronomers that the universe might be expanding, Einstein added his ''"cosmological constant"'' to his field equation that stopped the alleged expansion. Later he called this cosmological constant ''"the biggest blunder of his life"''.  

When the ''"cosmological constant"'' turned out to be unnecessary, since it turned out that the Hubble redshift is not caused by expansion of the universe but by the time runing slower at the deep space galaxies in curved space, which in EU simulates accelerating expansion of space with acceleration  

When the ''"cosmological constant"'' turned out to be unnecessary, in 1985, since it turned out that the Hubble redshift is not caused by expansion of the universe but by the time runing slower at the deep space galaxies in curved space, which in EUT simulates accelerating expansion of space with acceleration  

:<math>dH/dt=-H_o^2/2</math>  

:<math>dH/dt=-H_o^2/2</math>  

as observed in 1998 by the Supernova Cosmology Project team of astronomers and therefore predicted by EU over 80 years earlier.

as observed in 1998 by the Supernova Cosmology Project team of astronomers and therefore predicted by EUT over 80 years earlier.

The agreement of value of alleged acceleration of space with the results of observations of Supernova Cosmology Project within one standard deviation showed that the expansion of universe is really an illusion but the news has been never published yet and is not likely to be published soon (except in conservapedia).  

The agreement of value of alleged acceleration of space with the results of observations of Supernova Cosmology Project within one standard deviation showed that the expansion of universe is really an illusion but the news has been never published yet and is not likely to be published soon (except in conservapedia).  

Publishing of such a news would destroy the credibility of estblishment cosmologists and their openly false hypothesis of creation and evolution of universe called the [[Big Bang]] hypothesis.

Publishing of such a news would destroy the credibility of estblishment cosmologists and their hypothesis of creation and evolution of universe called the [[Big Bang]] hypothesis, which assumes creation of energy in the [[Big Bang]] event.

Around 1929 Edwin Hubble discovered cosmological redshift that [[relativists]] started to consider a sign that the universe is expanding. Then Einstein gave up working on his stationary universe, and left his [[cosmological constant]] as it was. He also told his secretary not to let in anyone who wants to talk to him about the universe.

Around 1929 Edwin Hubble discovered cosmological redshift that [[relativists]] started to consider a sign that the universe is expanding. Then Einstein gave up working on his stationary universe, and left his [[cosmological constant]] as it was. He also told his secretary not to let in anyone who wants to talk to him about the universe.

</ref>

</ref>

The [[relativists]] were not able to remove cosmological constant since it might have ruined their [[Big Bang]] hypothesis and named it "[[dark energy]]" creating this way new mystery for themselves to solve (at the taxpayers expense) and so the "[[dark energy]]" remains a mystery for them ever since.  

The [[relativists]] were not able to remove cosmological constant since it might have ruined their [[Big Bang]] hypothesis and named it "[[dark energy]]" creating this way new mystery for themselves to solve (at the taxpayers expense) and so the "[[dark energy]]" remains ever since a mystery for them to solve.  

The establishment scientific journals still resist the publication of the truth about the universe (that it operates according to Einstein's plan and that the Einsteinian gravitation, does not allow the expansion of universe, does not allow the [[Big Bang]] as a way of creation of the universe).  

The establishment scientific journals still resist the publication of the truth about the universe (that it operates according to Einstein's plan and that the Einsteinian gravitation, does not allow the expansion of universe, does not allow the [[Big Bang]] as a way of creation of the universe).  

Einteinian gravitation sugests that the universe is stationary with Newtonian arguments based on relativity of time, which any intelligent high school student should easily comprehend and repeat the Newtonian physics contained in the following sections.

EUT sugests that the universe is stationary with Newtonian arguments based on relativity of time, which any intelligent high school student should easily comprehend and repeat the Newtonian physics contained in the following sections.

First easy to notice feature of EU is that the universe has been always approximately the same. It has been never changing, beyond trivial movements of celestial bodies. The EU is therefore described by the [[Perfect cosmological principle]].  

First easy to notice feature of EUT is that the universe has been always approximately the same. It has been never changing, beyond trivial movements of celestial bodies. The EUT is therefore described by the [[Perfect cosmological principle]].  

The theory is called ''"Einsteinian"'' since it's Einsteinian type theory, except a bit deeper since it includes elements that Einstein didn't know about or didn't care. For this reason there are also a few flaws which had to be dealt with and removed (as e.g. the mentioned [[cosmological constant]]). The new elements and recognition of flaws showed up after 1985 when it turned out that the universe is not expanding since its [[intrinsic redshift]] turned to be represented by [[Hubble constant]] equal  

The theory is called ''"Einsteinian"'' since it's Einsteinian type theory, except a bit deeper since it includes elements that Einstein didn't know about or didn't care. For this reason there are also a few flaws which had to be dealt with and removed (as e.g. the mentioned "[[cosmological constant]]"). The new elements and recognition of flaws showed up after 1985 when it turned out that the universe is not expanding since its [[intrinsic redshift]] turned to be represented by [[Hubble constant]] equal  

:<math>H_o=c/R_E</math>,

:<math>H_o=c/R_E</math>,

where <math>c</math> is speed of light in vacuum and <math>R_E</math> is [[Einstein's radius of universe]], which means that derivation may be right if the Newtonian calculations come out with [[Einstein's radius of universe]]!

where <math>c</math> is speed of light in vacuum and <math>R_E</math> is [[Einstein's radius of universe]], which means that Einstein must have been doing something right assuming the [[perfect cosmological principle]] already in 1917. And so the EUT may be also "right" as far as we know

 

It also means that Einstein must have been doing something right assuming the [[perfect cosmological principle]] already in 1917. And so the EU may be also "right" as far as we know

<ref>

<ref>

Theories are never "right" unless they pass all the possible tests of their validity, which the [[Big Bang]] hypohtesis was not able to pass and that's why it has to be replaced with EU (also unsure but at least better theory than the Big Bang that contains errors, which we don't see in EU, hoping that there are none).

Theories are never "right" unless they pass all the possible tests of their validity, which the [[Big Bang]] hypohtesis was not able to pass and that's why it has to be replaced with EUT (also unsure but at least better theory than the [[Big Bang]] that contains errors, which we don't see in EUT, hoping that in EUT there are none).

</ref>.

</ref>.

   

   

The EU is explaning how the relativity of time and space (notions of non existence of absolute time and absolute space) are working in stationary, neither expanding nor contracting, eternal universe that has neither the beginning nor the end.  

The EUT is explaning how the relativity of time and space (notions of non existence of absolute time and absolute space) are working in stationary, neither expanding nor contracting, eternal universe that has neither the beginning nor the end.  

 

 

:<math>Z=exp(r/R_E)-1</math>,

The EUT which except explaining the mechanism of gravitational force as ''inertial force'' pushing masses towards their most probable positions of minimum energy in which it reveals its quantum nature, explains also why due to relativity of time in curved space the universe ''looks as if it were expanding'', and expansion were accelerating with acceleration confirmed to one standard deviation by Supernova cosmology Project.

where <math>R_E</math> is "[[Einstein's radius]]" of universe, and the [[Hubble constant]] equal approximately

The EUT explains why the value of [[Hubble constant|Hubble "constant"]] <math>H(t)</math>, which in reality is an exponential function, since the redshift is in reality an exponential function of distance (or time, since <math>r=ct</math>, distance <math>r</math> is the same as time <math>t</math> multiplied by speed of light), so the redshift

:<math>H_o=Z/r=v/c/r=70km/s/Mpc</math>  

:<math>H_o=Z/r=v/c/r=70km/s/Mpc</math>  

implies density of space of universe as  

implies the density of space of universe as about

:<math>6\times 10^{-27}kg/m^3</math>.

:<math>6\times 10^{-27}kg/m^3</math>.

The EU explains also why the above [[Hubble constant|Hubble "constant"]] in which <math>v</math> is '''apparent''' recession speed of a galaxy, is really  

The EUT explains also why the above [[Hubble constant|Hubble "constant"]], in which <math>v</math> is '''apparent''' recession speed of a galaxy, is really  

:<math>H_o=c/R_E</math>.

:<math>H_o=c/R_E</math>.

''"[[Einstein's radius of universe]]"'' <math>R_E</math> in the above equation equals roughly 13 billion light years is implied by the above value of [[Hubble constant|Hubble "constant"]] and why it should be consistent with minimum of angular diameters of galaxies between redshifts Z=1 and Z=2 which is additional test of EU.

''"[[Einstein's radius of universe]]"'' <math>R_E</math> in the above equation equals roughly 13 billion light years is implied by the above value of [[Hubble constant|Hubble "constant"]] and why it should be consistent with minimum of angular diameters of galaxies between redshifts Z=1 and Z=2 which is additional test of EUT.

Therefore the EU explains most of numerical results that the [[Big Bang]] cosmology is unable to explain. EU is in fact an extension of Einstein's general realativity but it may not be used by this name because the [[relativists]] highjacked this name for their pseudo scientific hypothesis of the [[Big Bang]] which, when used, might have caused a confusion.

Therefore the EUT explains most of numerical results that the [[Big Bang]] cosmology is unable to explain. the EUT is in fact an extension of Einstein's general realativity but it may not be called by this name because the [[relativists]] highjacked this name for their pseudo scientific hypothesis of the [[Big Bang]] which, when used, might have caused a confusion.

===Step by step derivation of cosmological redshift===

===Step by step derivation of cosmological redshift===

:So the "accelerating expansion of our universe" blamed on mysterious "dark energy" for which cosmologists look since 1998 is just the Taylor term of expansion series of Hubble constant which is no constant but exponential function as shown in steps 6 or 7 (first as Newtonian result and  second as Einsteinian interpretation of this Newtonian result). Cosmologists also call it "cosmological constant" (the ''"biggest blunder of Einstein's life"'') which can be shown not to exist at all. It might be eliminated from Einstein's field equation in rather straight forward manner.

:So the "accelerating expansion of our universe" blamed on mysterious "dark energy" for which cosmologists look since 1998 is just the Taylor term of expansion series of Hubble constant which is no constant but exponential function as shown in steps 6 or 7 (first as Newtonian result and  second as Einsteinian interpretation of this Newtonian result). Cosmologists also call it "cosmological constant" (the ''"biggest blunder of Einstein's life"'') which can be shown not to exist at all. It might be eliminated from Einstein's field equation in rather straight forward manner.

===Metric of universe===

===Metric of Einsteinian universe===

Here is the metric of universe with radial coordinate only (angular coordinates dropped for isotropy of the model):

Here is the metric of universe with radial coordinate only (angular coordinates dropped for isotropy of the model):

:<math>d\tau^2=exp(-2r/R_E)dt^2+2sinh(2r/R_E)dtdr/c-exp(2r/R_E)dr^2/c^2</math>,  

:<math>d\tau^2=exp(-2r/R_E)dt^2+2sinh(2r/R_E)dtdr/c-exp(2r/R_E)dr^2/c^2</math>,  

where <math>\tau</math> is proper time, <math>r</math> is radial coordinate, <math>t</math> is coordinate time, <math>R_E</math> is radius of curvature of space of Einstein's universe (Einstein's radius of universe). This metric approximates to Minkowski metric <math>d\tau^2=dt^2-dr^2/c^2</math> for <math>r</math><<<math>R_E</math>.  

where <math>\tau</math> is proper time, <math>r</math> is radial coordinate, <math>t</math> is coordinate time, <math>R_E</math> is radius of curvature of space of Einstein's universe (Einstein's radius of universe). This metric approximates to Minkowski metric  

 

:<math>d\tau^2=dt^2-dr^2/c^2</math> for <math>r</math><<<math>R_E</math>.  

The Einstein's universe metric seems to be the simplest metric with required by Einstein's property of non symmetry of metric <ref>Einstein's 1950 paper ''"On the Generalized Theory of Gravitation"'', published in April 1950 issue of ''"Scientific American"''. This paper was not placed for some reason in detailed bibliography of Einstein's papers of 1973 ''"Gravitation"'', by Misner, Thorne, and Wheeler. The reason might be that this book assumes at the onset the symmetric metric of spacetime while Einstein excluded such possibility possibly for it potential of creation of energy from nothing utilized indeed later in ''"Gravitation"'' in the form of Big Bang hypothesis. For this reason ''"Gravitation"'' might be considered advocating a creationist cosmology, as contrasted by stationary cosmology of '''Einsteinian gravitation'''.</ref>.

The Einstein's universe metric seems to be the simplest metric with required by Einstein's property of non symmetry of metric <ref>Einstein's 1950 paper ''"On the Generalized Theory of Gravitation"'', published in April 1950 issue of ''"Scientific American"''. This paper was not placed for some reason in detailed bibliography of Einstein's papers of 1973 ''"Gravitation"'', by Misner, Thorne, and Wheeler. The reason might be that this book assumes at the onset the symmetric metric of spacetime while Einstein excluded such possibility possibly for it potential of creation of energy from nothing utilized indeed later in ''"Gravitation"'' in the form of Big Bang hypothesis. For this reason ''"Gravitation"'' might be considered advocating a creationist cosmology, as contrasted by stationary cosmology of '''Einsteinian gravitation'''.</ref>.

Furthermore to make the spacetime flat to comply with the principle of conservation of energy and momentum (that followed from Noether theorem) I needed the missing antisymmetric part of Ricci tensor that would represent the "curvature of time" (the term coined by [[Richard Feynman]]) that would compensate the [[curvature of space]] represented by Ricci tensor to make the spacetime flat ([[Minkowski]]). [[Hubble tensor]] seemed an ideal candidate to fill up this place.

Furthermore to make the spacetime flat to comply with the principle of conservation of energy and momentum (that followed from Noether theorem) I needed the missing antisymmetric part of Ricci tensor that would represent the "curvature of time" (the term coined by [[Richard Feynman]]) that would compensate the [[curvature of space]] represented by Ricci tensor to make the spacetime flat ([[Minkowski]]). [[Hubble tensor]] seemed an ideal candidate to fill up this place.

The metric that I assumed for Einsteinian universe is non symetric and degenerate (with vanishing determinant) and yet is approximates to very neet flat [[Minkowski]] metric <math>d\tau^2=dt^2-dr^2/c^2</math>. I sent this proposal of new Einstein field equation in January 1986 to ''"Rapid communications of Physical Review Letters"''. They received it on January 27, 1986, and rejected on March 14, 1986 by the same referee who rejected my previous stuff about Newtonian calculation of [[Hubble constant]] in [[Einstein's universe]].

The metric that I assumed for Einsteinian universe is non symetric and degenerate (with vanishing determinant) and yet is approximates to very neet flat [[Minkowski]] metric  

 

:<math>d\tau^2=dt^2-dr^2/c^2</math>.  

 

I sent this proposal of new Einstein field equation in January 1986 to ''"Rapid communications of Physical Review Letters"''. They received it on January 27, 1986, and rejected on March 14, 1986 by the same referee who rejected my previous stuff about Newtonian calculation of [[Hubble constant]] in [[Einstein's universe]].

====Future of Hubble tensor====

====Future of Hubble tensor====

The assumption of existence of [[Hubble tensor]] leads to very neat Einsteinian equation <math>R_{\mu\nu}-g_{\mu\nu}R/2=8\pi T_{\mu\nu}+g_{\mu\nu}H/2</math> that is the same as the present Einstein field equation but without his [[cosmological constant]] replaced by <math>\Lambda=-H/2</math>, where <math>H</math> is contraction of [[Hubble tensor]].  

The assumption of existence of [[Hubble tensor]] leads to very neat Einsteinian equation  

 

:<math>R_{\mu\nu}-g_{\mu\nu}R/2=8\pi T_{\mu\nu}+g_{\mu\nu}H/2</math>  

 

that is the same as the present Einstein field equation but without his [[cosmological constant]] replaced by  

 

:<math>\Lambda=-H/2</math>, where <math>H</math> is contraction of [[Hubble tensor]].