| Table of Contents |
|
There were attempts to make out of Einstein's General Relativity a purely magical theory with creation of matter from nothing. The result was a variation of Einstein's General Relativity with an expansion of the universe built in into it as an additional assumption. Later in this text this new General Relativity is called a Big Bang General Relativity (Big Bang GR) since later a Big Bang hypothesis has been added to it as well.
The expansion and the Big Bang hypotheses were deduced by theoretists from galctic redshifts observed by an American astronomer Vesto Slipher in the years following his discovery of blueshift of Andromeda in 1912. Most of these shifts turned out to be redshifts, with ratio of red to blue 4:1. These redshift were then interpreted by theorists as Doppler redshifts that in the absence of better explanation at the time were taken for the evidence that the universe is expanding. It turned out that this expansion was only an illusion caused by unknown at the time, and still considered hypotetical, a relativistic effect of general time dilation.
In Big Bang GR it has been assumed (after Einstein, who changed his opinion only in 1950 when he proposed a non symmetric metric tensor) that the geometry of spacetime is pseudo Riemannian and that the metric tensor of spacetime is symmetric. At such conditions it is impossible to have redshift in photons that move along closed loops in stationary space (Hubble type redshift). Therefore it has been considered an established fact that the Hubble redshift is a result of the expansion of the universe and that without this expansion there wouldn't be any Hubble type redshift in the universe.
But it has been overlooked that the principle of conservation of energy implies existence of dynamical friction for photons which would cause Hubble redshift anyway. It was the line of reasoning of Fritz Zwicky in 1929, ignored by the theorists in favor of the expansion of the universe.
Since the Hubble redshift was already included in the Big Bang GR as a result of expansion of space, and the expansion of space became the basis of the Big Bang GR, the conservation of energy had to be dropped to avoid the contradiction within the theory and the dynamical friction of photons had been assumed exactly zero (to the bewilderment of those astronomers who still believed that energy is conserved).
So in the Big Bang GR the contradiction between expansion of the universe and the conservation of energy had been decided by the theorists against the conservation of energy. The dynamical friction has been assumed to be limited only to Newtonian physics. This limitation of dynamical friction to all particles except photons in the Big Bang GR is an equivalent to an assumption that while all other particles are subject to the principle of conservation of energy and so to dynamical friction the photons aren't, and so while they are moving through the universe, carrying energy and therefore modifying the gravitational field, the energy needed to compensate for their dynamical friction is assumed by the theorists to be created from nothing.
It has been tacitly assumed by astrophysicists (in order to understand the theorists) that this energy is so small that assuming that it is created from nothing won't change any observational results [source: Dr. Bohdan Paczynski, the most famous of Polish astrophysicists of the time].
Actually there exist a back-of-envelope Newtonian calcultion that convinces astrophysicists that this is really the case. Consequently the amount of this energy has been never calculated, just assumed on the basis of this back-of-envelope calculations to be negligible. Unfortunately for the Big Bang GR it isn't negligible and consequently it is a fatal flaw of this hypothesis. It seems that one has to retun to Einstein's GR with global conservation of energy and consequently with non symmetric metric tensor and possibly with the Finsler geometry of spacetime.
It has been shown that restoring the principle of conservation of energy as a valid physical principle and with it restoring the dynamical friction for photons allows to drop the assumption that the universe is expanding, however not, as it might have been expected, through restoring the Newtonian idea of tired light. It is done by a demonstration that in a world where energy is conserved the dynamical friction of photons is a relativistic effect of general time dilation. An effect of the rate of time dilation compensating for the curvature of space for the reason of inability of nature to produce energy from nothing.
Restoring the conservation of energy in gravitation invalidates the (pseudo) Riemannian geometry as a description of geometry of spacetime and requires introduction of more general geometry in which a degenerate non symmetric metric tensor is possible. Consequently it requires an introduction of the mentioned effect of general time dilation as a valid physical principle being a necessary consequence of the more general principle of conservation of energy. This way Einstein's theory, by separating itself for good from the magic of expanding universe, becomes a physical theory explaining all the controversial or not understood elements of Einsteinian physics. It shows the location of gravitational energy, and by this the origin of gravitational force (as its derivative with respect to displacement), reasons for the Hubble redshift, and so it explains the illusion of accelerating expansion of space. Possibly it explains also the surprisingly high redshift of quasars that, as Halton Arp has insisted, are associeted with galaxies of much smaller redshifts and so not even located at the distances assumed by the theorists.
Because of all those things there are several differences between Einstein's GR and Big Bang GR. They are in assumptions about the real world and necessarily in conclusions from these assumptions. These assumptions and conclusions are specified separately in the two tables below:
ASSUMPTIONS
| Big Bang GR | Einstein's GR | |
| reason for gravitation | geometry of spacetime | |
| accelerating expansion of space | fact due to dark energy | see conclusions |
| metric tensor of spacetime | expanding, symmetric, Riemannian | |
| speed of light | constant throughout the whole space | |
| conservation of energy | see conclusions | valid |
CONCLUSIONS
| Big Bang GR | Einstein's GR | |||||||||||||||||||||||||||||||||||
| accelerating expansion of space | see assumptions | illusion due to conservation of energy, Hubble parameter: | ||||||||||||||||||||||||||||||||||
| metric tensor of spacetime | stationary, | speed of light
| local is constant,
non local depends on location in space: | conservation of energy
| invalid
| see assumptions
| reason for Hubble redshift
| Doppler shift due to recession of galaxies
| conservation of energy
| reson for CMBR
| redshifted light from Big Bang
| absorpsion of redshifted starlight by non luminous matter of universe and re-emission at temperature of termal | reason for high redshift of quasars
| speed of recession
| conservation of energy in cluds of dust, | [see paper (in PDF format) reason for gravitational force
| "acceleration of space"
| Fi = - (d/dxi)(gravitational energy of particle)
| gravitational energy
| ?
| internal energy of the particle | location of gravitational energy
| ?
| gravitating particle: x
| density of space
| ?
| 6x10-27 kg/m3
| acceleration of expansion in terms of dH/dt and H0
| ?
| acceleration of space probes
| ?
| average size of pieces of non luminous matter
| ?
| order of one meter
| |
The areas that a theory has no answers for are marked with question marks.
All of them are in the Big Bang GR and it suggests that Einstein's original theory is OK while the Big Bang GR is wrong.
Therefore we might assume that gravitational force and energy may be explained accrding to the old Einstein's theory based on conservation of energy and explain them as such.
Therefore we seem to be justified in explaining gravitation as it is explained in the following sections.
Basics of gravitation
| Note: | For brevity, unless absolutely necessary, we don't make in this section a distinction between vectors as e.g. x and scalars, as e.g. c assuming that all the possible movements are along a straight line and all vectors are parallel to this line. There is no loss of generality since the same reasoning may be repeated separately for each spatial axis with the same result. |
In the Newtonian physcs the gravitational field, named g(x), where x symbolizes location in space and g is directed "down", was meant to be field of assumed fundamental attractive gravitational force acting between all material particles in the universe according to Newton's equation (1.4 in Apendix 1). This fundamental attractive gravitational force was supposed to generate that field of force.
In the Einsteinian physics there is no "gravitational attraction" and so the Newtonian fundamental gravitational force does not exist. The gravitational force is not a feature of some field but a result of structure of time dilation at any particular point in space. "Gravitational field" is not a field of force but basically a figure of speech meaning "area of space where gravitational phenomena take place". The gravitational force is not something acting in this field on its own on matter in this field (as a fundamental force would) but it is generated by the matter in this field by itself when this matter is restricted from following its path of free fall (resticted from taking geodesics in spacetime). It varies according to structure of time dilation in space, which in turn varies according to various conditions and so gravitatinal force is so called pseudoforce (inertial force).
The gravitational force will be derived below for Einsteinian gravitation (with no "gravitational attraction") and then it'll be seen why it is exactly the same as in Newtonian gravitation despite having completely different nature.
The whole Einsteinian gravitation, except mentioned above time dilation, contains in it only curvature of space and conservation of energy as basic physical entities. There is nothing more needed to explain all the gravitational phenomena in the universe including its apparent accelerating expansion.
Conservation of energy means simply that in a closed system there is a fixed amount of energy. None can be created or destroyed. We show in this article that (i) conservation of energy is a basic part of Einstein's theory of gravitation without which it isn't working at all and (ii) that with conservation of energy is not necessary to assume that the universe is expanding.
Time dilation means roughly that the time in any particular point in space runs slower than at a point far enough from any material objects. It means that presence of material objects slows down the rate of time in their vicinity.
Structure of time dilation means how its amount changes along any particular direction. We know how much because it is relatively easy to figure out what mass causes what time dilation since we know the relation between gravitational field and gravitational time dilation (see Appendix 1 for the relevant equations) and the relation between gravitational field and mass that generates it we know from Newton's equation. Time dilation reflects exactly the Newtonian gravitational potential except that it does not contain its ambiguity about its absolute value since it has natural zero value at infinity.
Curvature of space means that at those points where the time is slower there is more space. Dilated time implies increase in amount of space. The curvature of space is a more subtle thing than the time dilaton since there may be different amount of space in three directions in space. We show that there is a way of figuring out how much more space there is in particular direction in space while we'll be determining how Einsteinian gravitation generates gravitational force.
Explanation of Einsteinian gravitation may be started at any point since it is a good theory and therefore all parts of it are consistent with each other. We have to be careful though not to overlook any physics because then we may end up with a magical theory that no one will understand (about what happens now in physics, when my first year physics professor, Dr. Zharnecki, volunteered a remark that "no physicist understands gravitation" and since I protested I'm now obliged to prove that at least some of them do understand gravitation).
Let's start with the most interesting part (that "no physicist understands") namely how gravitational force is generated in Einsteinian gravitation.
How gravitational force is generated
In Newtonian theory it was simple.
There was an assumed special kind of fundamental force of nature called force of universal gravitational attraction.
It was supposed to act between all material bodies of the universe.
This force was supposed to create gravitational field (g) and the energy in this field was called potential energy or potential energy of gravitational field.
Potential energy is of course energy that we get by integration of force of the field
It is the same in Einsteinian gravitation. But in Einsteinian gravitation there is no force of universal gravitational attraction so what about its integral, the potential energy? This part is something that causes most of the problems the people have with gravitational force in Einsteinian physics.
If there is no gravitational force then its integral, the potential energy is zero. Right? Wrong. Because when we lift something, we have to do work against gravitational force so the gravitational force is real. And because of conservation of energy the work we do against the gravitational force can't be destroyed and so it has to be converted into something. And when we lower this something that we lifted, the energy is recovered in the same amount (neglecting the energy that we lost somehow in the process of lifting to overcome various frictions). So we have to be able to introduce such energy that in Newtonian physics was potential energy of the gravitational field and which derivative with respect to distance is gravitational force that we feel standing on earth. Now we only have to find this energy in the nature.
One thing that we know already about this energy is that it doesn't change in a free fall (no gravitational forces in a free fall). We can use this test to check if the energy that we suspect to be potential energy passes this test. Let's go to work and do calculations (maintaining prolatarian vigilance as my algebra teacher Kasia Grabowska advises, not to start doing magic instead of science).
In our frame of reference the total energy of any particle is
| (1) |
| (2) |
The derivative of energy (1) along a distance x (a derivative that when with opposite sign is called "force that pushes the particle" since the particle always tries to achieve the lowest energy level)
| (3) |
Since for a particle at rest
| (4) |
Now we have to prove that our working assumption that
|
The proof
We need to find out how the speed of light c is related to gravitational field g. To figure out this relation we need to remember the following facts: The angle of deflection of light ray in vicinity of material objects is twice as large as it would be predicted by existence of Newtonian gravitational field due to time dilation. Einstein's guess was that half of this angle of deflection is due to time dilation that simulates the Newtonian gravitation and the other half due to the curvature of space that has no counterpart in Newtonian gravitation. Next fact is that when the time slows down everything is running more slowly in the same space. When one side of a light ray runs more slowly than the other the light ray bends in direction of smaller c(x) and the angle of deflection is
In a flat space the angle of deflection of light ray would be due only to the change in speed of light across the ray. In a situation when space is curved the curvature of space bends the light ray without any change in the speed of light since then both sides of the light ray move in the (curved) space straight. The light gets bent due to the space curvature without a difference betwee speeds of light across the ray. So to find observationally dc/dx we need to take a half of the observed angle of deflection of light in gravitational field g and apply equation (5) to it. Angle of deflection of light ray may be derived from an example with a rocket in space, sufficiently far from all material objects not to feel any influence of those objects, accelerating let’s say as much as the particles that fall on the earth. If there is a light ray that enters the rocket perpendicularly to the direction of acceleration of the rocket the observer in the rocket will feel the gravitational field but the light ray won't and so it will move along a straight path in relation to fixed points outside the accelerating rocket. The accelerating with the rocket observer however will see the light ray bent towards the rear end of the rocket (assuming that the rocket accelerates forwards). In the relation to the rocket that is accelerating "up" with acceleration g the ray is dropping "down" with the same acceleration g. The height of the drop is (integrating the acceleration g twice with respect to time)
According to Einstein's principle of equivalence of acceleration and gravitational field this case is identical to the case when the light ray moves across a rocket that is standing on the earth, and so the ray bends in the gravitational field g, the same as the ray seen by the observer in the accelerating rocket.
Since half of this angle comes from the curvature of space and the other half from the change in speed of light across the light ray we take
|
So we proved that energy (1) is potential energy
It turns out that in the real world it is not a gravitational "pull" by "attraction" of some external body but gravitational "push" by inrtia of the particle in space where there is a change of internal energy of the particle. So it is not a body attracting other bodies but other bodies are pushed by themselves towards an attractive body with this body not attracing them but just modifying the space around herself just by her presence in such way that those other bodies get themselves pushed to towards the "attracting" body. "Attraction" is a figure of speech here and what is reall is the "push" towards this attractive center.
Now we need to do the test with free fall to see if energy of a particle in free fall does not change.
Since in a free fall in gravitational field with
| (9) |
Diferentiating with respect to x and ignoring small higher order terms
| (10) |
After substituting (8) and (10) to (3) we have a change of total (potential) energy of a free falling particle as
| (11) |
This concluds the explanation of basics of Einsteinian gravitaton.
The rest of this page shows how conservation of energy is responsible for an effect called here the general time dilation that in turn is responsible for the Hubble redshift (illusion of accelerating expansion of space) and possibly also for the high redshift of quasars.
Illusion of accelerating expansion of the universe
The universe looks as if it were expanding and this expansion looks as if it were accelerating.
This is so since the light coming from distant galaxies has on average a smaller frequency than the light generated by the same sources close to the observer.
The reason for this smaller frequency of photons was assumed to be a recessional velocity of galxies but it turned out that that the time at those sources runs slower than at the observer and so the effect simulates the expansion of the space.
Furtheremore the simulated expansion looked as if the space were expanding with acceleating expansion.
This effect of the time running slower at the greater distance turned out to be necessity if energy couldn't be made out of nothing.
The physics of the effect are explained in the article on the general time dilation in which the apparent expansion of the universe comes out qualitatively and
quantitatively as it is observed in the real universe.
Hubble's constant of this
apparent expansion comes out as
Since the theory can't be falsified for the time being by observations since it predicts correctly the observational results within one σ (which in astronomy means a perfect agreement), then we may look at the cosmic background radiation (CBR) to see how it is doing over there.
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.
If it is so then we can calculate the average size of the pieces of non luminous matter of the universe.
This is because the chance of a photon hitting an obstacle on it's way, and transferring to it its energy, which then becomes thermal energy, is approximately proportional to the area of the obstacle
So, knowing the temperature of the redshifted starlight, presumably Observational evidence for Einstein's GR as opposed to Big Bang GR
| Variable | Einstein's GR predictions | Observed values | σ | Units | |
| theoretical | numerical | ||||
| Radius of curvature of space | R | 4.31 | - | - | Gpc |
| Hubble parameter at Earth | Ho = c / R | 69.6* | 69.6 | 2.8 | km/s/Mpc |
| Acceleration of space probes | ao = c2 / R | 7 | 8.7 | 1.3 | |
| Density of space | 6 | 5.5 | 4.5 | ||
| apparent acceleration of expansion of space | ? | - Ho2 | |||
All of the observed values are functions of the radius of curvature of space (R) that is adjusted so that
The acceleration of the apparent expansion of space is made a funcion of
Four of the above values are predicted by Einstein's GR. None of the observed values is predicted by the Big Bang GR.
|
where
therefore for any observer, the spectral distribution of radiation from all the stars is
where
The average distance between the obstacles L may be determined from the relation
Assuming value of Hubble's constant |
Big Bang hypothesis is a hypothesis that the whole matter of the universe has been created some 14 billion years ago as a small dot, smaller than any pixel on this screen, and it has been expanding ever since (which surely would produce a big bang is we could hear it). Since about half of the 20th century this hypothesis was considered by many serious scientists a true one (they believed then that matter can be suddenly created sponaneously from nothing; there were even proposals to create another universe in a lab by creating a proper conditions for such an event).
Cosmic Baground Radiation is radiation that comes from the sky as black body radiation of temperature
Dynamical friction of photons is a relativistic effect of photons reaching the observer with a redshift depending exponentially on the distance that they travel.
The reason for it is slowing of the time rate at the source of light called general time dilation.
It is named dynamical friction through analogy to a Newtonian effect of kinetic energy loss while anything that moves through the universe interacts gravitationally with its matter losing kinetic energy in the process.
Within the Newtonian magic the dynamical friction of photons is represented by the tired light effect in which the photons move against dynamical gravitational field
Hubble constant is the velocity of (apparent) expansion of the universe equal to the ratio of (apparent) recessional velocity of galaxies to the distance to them. The time derivative of this velocity, dH/dt, is an (apparent) acceleration of the expansion of the universe.
Magic is a machanism through which a mathematical (phenomenological) model that uses non existing entities works. The same as the ordinary magic it works through accidental similarity of the model to the physical phenomenon. A good example is Newtonian gravitation with its gravitational forces that act at a disctance. Newton didn't believe in such forces considering them just mathematical entities that are only imagined and therefore a kind of magical things, as unicorns. Yet knowing their magical nature through the Newtonian equations that describe their behavior we may use these magical things in calculations and get almost true results due to the similarities between the equations that control their magical behavior to the real equations that control the behavior of the real gravitation (unknown i times of Newton). The magical things are usefull as long as one doesn't consider them real and does not conclude about the real world as if those magical things were real. A newer example of magical thing is the expansion of the universe that has been considered real by many 20th and 21st century theorists despite that it requires dropping the principle of conservation of energy. Dropping a well tested principle for some highly hypothetical thing changes the phenomenological theory into a magical theory.
Pseudo Riemannian geometry differs from the four dimensional Riemannian geometry by signature which in Riemannian geometry is
σ is standard deviation of the measured value. It is a cartain measure of the accuracy of measurments. Physically it is the effective amplitude of the noise that is added to the measured variable by the measurments regardless of their number. It is also known as the rms (root mean square) value of the noise of measured value.
| Last update: | Rev 1.3 | Author/Webmaster: |
![I_o_(nu) = c_1 nu^3 / [exp(c_2 nu / T_s) - 1]](pic/eq10.jpg){kind=small}
![I(nu, r) = (c_1[nu exp(r/R)]^3)/(exp[c_2 nu exp(r/R) / Ts] - 1)](pic/eq11.jpg)
![I(nu)=c_3 Integ 0..oo ((p(r)[nu exp(r/R)]^3)/(exp[c_2 nu exp(r/R)/T_s]-1))dr](pic/eq12.jpg)
