Image credits: (top to bottom)

1. Image from:

http://imgsrc.hubblesite.org/hu/db/2002/02/images/a/formats/large_web.jpg

2. Pincushion Protea, Golden Gate Park, San Francisco, Elaston Scientific (c)

Where do physical ideas come from? Here we are just discussing ideas because precisely they underlie any physical theory. The idea commonly emerges in the form of hypothesis that explains a group of new facts. However just this component, the molding of hypothesis, is the most enigmatic link in the whole creative process. The new knowledge – hypothesis – can not be deduced from existing theories, for if this knowledge is already contained there then it is not new.

Newton said: “I feign no hypotheses” but this was not exactly correct. What he meant was his inability to establish physical mechanism of transmission of gravity between planets and the Sun. However the law of universal gravitation was also a hypothesis. What was Newton’s contribution in the law of gravitation? Newton’s law F = G **m**1**m**2/**r**^{2} was released in his 1687 work the *Principia*. The inverse-square law of gravity was proposed by French astronomer Ismail Bullialdus in his Astronomia philolaica, 1645. Robert Hooke proposed the idea in the letter to Newton. Experimental test of the law in the laboratory was done by Cavendish only 111 years later in 1798. Formally, only after Cavendish’s experiment, the gravitation became **universal**. But Cavendish's only goal was to measure the density of the Earth. Gravitational constant G as the fundamental constant was measured 186 years after Newton by Cornue and Baille in 1873. What has Newton done? He advanced hypothesis and tested it with the astronomical measurements of Kepler. The Kepler’s experimental laws were consistent with the hypothesis of gravitational law. This was Newton’s triumph; he proved this law not even knowing G and masses of planets and the Sun. The hypothesis was corroborated and became the law.

“I keep the subject of my inquiry constantly before me, and wait till the first dawning opens gradually, by little and little, into a full and clear light” Newton explained his method. However more important was his definition: “Genius is a patience of thought concentrated in the certain direction.” The first part of this definition was explained by Newton in the previous quote. The creation of a fruitful hypothesis requires continuous intensive reflection on a particular subject. The second part of Newton’s definition is not so simple. What does it mean “in the certain direction?” Why is this direction known to genius but not to others? Here is a main mystery of creativity.

Let us imagine the problem as a forest and the unknown hypothesis settled somewhere in the thick crown of one of the trees. How do we find it? The simple strategy is to follow the branches of all the trees in the hope of reaching a goal: tree by tree, branch by branch. This is a strategy of the ordinary human. Newton’s “in the known direction” means different behavior. For some reason genius makes only very limited number of attempts. If he starts with the wrong tree, he realizes it very soon and goes to the just the right tree and finds the only true way along the branches. How can he do it? No one knows, even the genius himself. The simple explanation is the intuition but nobody knows what it means. Instead of exploring all possible paths, a successful researcher “feels” correct one and follows it persistently.

Thus what makes the search for the correct hypothesis successful are two Newton’s attributes: patience of thought and intuition.

Another good example of creation of fruitful hypothesis is a creation of electromagnetic theory by James Maxwell. When Maxwell started to study electricity and magnetism this area of knowledge represented immense ocean of separate laws. After intensive analysis he picked out Gauss’s law, Faraday’s law of induction and Ampere’s law. There were obvious relations between electricity and magnetism but intuition prompted him that these relations were not complete. Maxwell postulated displacement current that allowed him to derive the electromagnetic wave equation. This hypothesis unified electricity, magnetism and light into one electromagnetic theory. The contemporaries did not accept this hypothesis. Even Thomson and Stokes supposed displacement current as unnecessary extravagance and Poincare wrote that Maxwell’s system resembles clumsy mechanical factory. This was consequence of mechanical model which Maxwell exploited to derive his equations. Later Hertz and Heaviside reduced a number of equations and produced a symmetrical set of four equations. Equations became beautiful in form but physics that was laid down by Maxwell did not change.

So the fruitful hypothesis, by whatever method it is obtained, is of paramount importance since it brings *the new knowledge*. There is not any strategy regarding creation of this hypothesis but its exact mathematical presentation and theoretical justification is not very crucial. A maiden appearance of a hypothesis normally is not aesthetically beautiful and usually the author piles around fairly crude system of props to “warrant” its appearance. Later many researchers will clear definitions, polish mathematical formulation and find numerous analogies with other theories.

New physical paradigm can not be derived strictly mathematically from a narrow circle of abstract conceptions. The extensive study of complete set of the relevant experimental and observational data has to be done before formulation of new hypothesis which can emerge then as a result of intuition. Therefore new physical idea can not be* derived *but rather it can be *guessed *basing upon facts.

Two conceptions lie in the foundation of elastonic hypothesis:

**2. A concentration of the elastic energy of physical space in the form of soliton-****like entities – elastons.**

Under soliton we comprehend here a long living spatial formation protecting its shape against spreading. Where does the concept of elasticity come from? It was inspired by the Clifford’s model: The Space-Theory of Matter (1870). James Beichler wrote:

*“Nearly a half century before Einstein developed his general theory of relativity, the Cambridge Geometer William Kingdon Clifford announced that matter might be nothing more
than small hills of space curvature and matter in motion no more than variations in that curvature.”*

Clifford’s model was not a first application of non-Euclidean geometry to the real physical world. We need to recall the history of these applications. About 2300 years ago Euclid compiled his *Elements *from a number of works of earlier authors. His geometry is a summary of a previous human experience about properties of the surrounding space. It is very important that Euclidean geometry is a not a mental scheme but reflection of a real physical milieu and therefore it was consistent with reality from the beginning. Every step of this geometrical construction was in concert with experience.

Lobachevskiy reported his non-Euclidean hyperbolic geometry in 1826. He believed that only scientific experience can reveal which geometry is realized in the physical space. Lobachevskiy used data of parallax angle for Sirius measured by the Belgian astronomer d’Assad Montardier. He came to a conclusion that a radius of curvature of space is very large and deviation from Euclidean geometry, if it exists, is within the limits of errors. Lobachevskiy also supposed that the geometry of real space may depend of physical forces acting in nature.

There is a long standing discussion of the Gauss’s measurement of the curvature of the real space from three mountaintops in Hannover during geodetic survey in the 1820’s. Gauss introduced a definition of intrinsic curvature and was able to make this estimation. However observation in the optical triangles of this size had extremely low sensitivity.

Riemann, who developed non-Euclidean theory of higher dimensions, stated in *On the Hypotheses Which Underlie Geometry *that we can find out by experience the nature of space:

*“Either therefore the reality which underlies space must form a discrete manifoldness, or we must seek the ground of its metric relations outside it, in binding forces which act upon
it. This leads us into the domain of another science, of physic, into which the object of this work does not allow us to go to-day.”*

Gauss and his student Riemann discussed astronomical observations for the purpose of testing geometry of the physical space. Irish astronomer Ball also made parallax observations in 1881 to distinguish between Euclidean and non-Euclidean spaces. However accuracy was not sufficient to make a decision.

In contrast to Lobachevskiy, Gauss, Riemann and Ball the Clifford’s model advanced in 1870 was an absolutely new idea. Matter is a portion of curved space moving on the average flat background. Clifford equated effective curvature of the physical space to matter. He started to develop mathematical model where the new entities “twists” represented matter and electromagnetism. Clifford assumed four-dimensional elliptic space with fourth dimension to be time. Unfortunately he did not finish his model due to his early death in 1879. Later Einstein used the idea of curved four-dimensional space-time to explain gravitation GR. Alternatively, Hilbert, Einstein’s collaborator, Weyl, Klein and others in the beginning of the 20th century attempted to make synthesis of curved space with Mie’s purely electromagnetic theory of matter. This line of thought originating with Clifford dried up as GR became the prevailing theory in physics.

Sir Arthur Eddington in his *The Expanding Universe *1933 noted:

“*The so-called facts are in any case theoretical interpretations of observations. The only question is, Shall we for this interpretation use the fullest resources of modern theory?
For my own part I can see no more reason for preferring the theories of fifty years ago than for preferring the observational data of fifty years ago."*

The very same approach may be applied to the GR itself which Eddington advanced in his book. Eddington argued further:

*“This does not constitute an objection to the theory, for there is, of course, no reason for supposing space to be flat unless our observations show it to be flat; and there is no
reason why we should be able to picture or describe the system in flat space if it not in flat space.”*

So if we know now that the space we live in is flat, what the reason do we have to treat it as curved? The President of Royal Astronomical Society Arthur Milne said in his Presidential Address in 1944:

*“The point is not whether a spherical universe free from internal self-contradiction, but whether it can exist. The analogy with the experiences of two-dimensional inhabitants on the surface
of sphere is imperfect because it relies for its effect on our own acquaintance with a third dimension. The objects in an Einstein spherical universe cannot be put into correspondence with
objects in nature unless every object at a distance is theoretically visible in two opposite directions, the one showing its front, the other its rear. I decline to accept this fantasy
until it is known that there is no other way out.”*

The GR itself can not predict global curvature of the space. It follows from a Friedman’s solution for homogeneous and isotropic universe that for the case of flat space the density of the matter has to have a specific value. However this critical value is much higher than follows from the observations. A deficit of the matter is more than 90%. This is a cause of introduction of 95% of dark matter and dark energy.

At last we have arrived! Instead of more precise description of Newton’s gravity we received the problem of explaining where 95% of the universe’s stuff is to be found. By the way Eddington explained:

*“Einstein almost inadvertently added a repulsive scattering force to the Newtonian attraction of bodies. We call this force the cosmic repulsion, for it depends on and proportional
to the cosmic constant. It increases proportionately to the distance. We have no direct evidence of an outward acceleration of the nebulae, since it is only **the velocities
that we observe.”*

We do not discuss increase of repulsion with distance that in itself is utterly unphysical but here is another knavish trick. According to Eddington, cosmic repulsion is applied to the matter. Then the matter may be accelerated and dispersed, that represents motion of matter *through space*. But later Eddington (and other admirers of GR) asserted that here is an *expansion of space*. It is not clear how the *expansion of space* follows from the acceleration of matter *in space*. To make this subject absolutely opaque some theorists say that physical space is relational, meaning it does not exist as an entity. If it does not exist, then what is expanding? Some attempted to solve the problem of singularity closely associated with GR in an inflation scenario. But as was shown by Gliner the inflation does not explain formally the nearness of the metric after inflation to flat. The matter and vacuum-like medium do not follow to scale factor. The inflation expansion of the universe without alteration of density of medium contradicts the energy conservation law.

A huge activity during last years is devoted to the so-called “quantum gravity.” Usually theory has to explain experimental facts. There *are not any* observations of quantum effects of gravity at present. And what is worse, there is no any idea how to measure such effects. Some researchers even doubt whether such effects are detectable in principle. So, it is unclear for now what is the object of “quantum gravity” is. Most likely the nature of physical space has to be object of theoretical study. Then we can hope to find the nature of gravity as a consequence of this study. The same thing may be said about gravitation waves. Hard work during years and spending of hundreds of millions dollars did not make any progress.

Besides that, there is no conventional nature of universal expansion of the universe. Some researchers suggest expansion of space between galaxies, others think about motion of galaxies through space, while minority says that “expanding space is a dangerously flawed way of thinking.”

One cosmological scenario is called eternal inflation. In this model the rapidly inflating phase of the early universe gave rise not to one but to the infinite number of universes. This is a very strange reasoning: why should we have to explore infinite number of inaccessible universes if we can not yet explain even our single one?

Some modern theories like string theory exploit idea of higher dimensions for explaining of our World. Here is again not the problem of their internal logical consistency but of their relations to the reality. This kind of reasoning has huge problem from beginning: how to hide unobservable dimensions.

There is a big set of approaches in modern physics that try to explain how classical space-time emerges from underlying structures. These are so-called background-independent theories. However it may turns that underlying structure of these theories is just physical space itself how we understand it.

Another striking discrepancy between the theory and observations is in astrophysics: accretion, infall or condensation as a source of formation of stars and galaxies nowhere to be found. Quite the contrary, everywhere we can see an outflow of matter in the form of jets and clouds. How can ubiquitous outflows support the hypothesis of accretional creation of stars and galaxies is not clear. Of course some week accretion exists but its rate is absolutely insufficient for creation of the stars and galaxies. It may be added more examples but we think it is enough for this introduction.

The elastonic paradigm was initially formulated in 1994. It was very poorly articulated and roamed between the editors of astrophysical journals for a few years. The paper was improved in the process and was sent on 192nd Meeting of American Astronomical Society in San Diego. The paper was sent in December 1997 and was presented on the 10th of June 1998. In this paper the basic principles and some consequences were presented. The different behaviors of our Metagalaxy were discussed; in particular a possibility of both decelerated and accelerated increase of the volume of Metagalaxy depending on creation of the particles. It is amazing but at the very same time the new paradigm of cosmic acceleration sprang out. It was amazing because the fraction of the energy density of the universe in the form of the cosmological constant ΩΛ which during 70 years treated to be ΩΛ = 0 in a moment became ΩΛ ≈ 0.73. That is according to GR about 73% of the universe contain turned into mysterious “dark energy”. The modern science has no any idea where are these “dark” components.

It looks like there is an artificial problem. The human experience before and after Euclid treated the space that we live in as flat. Einstein proposed that it may be curved. After experiments with aircrafts, balloons and satellites and measuring isotropic MBR and spending billions of dollars scientists came to the decision that the space is flat. However Euclid knew it 2300 years ago. What is the difference between Euclidean flat space and Einsteinean flat space? Euclidean one is simply naturally flat but for Einsteinean one to be flat we need unseen dark matter and dark energy.

Here we presented only some simple arguments that show that the picture of the real world so far is not simple. Well, then we need to investigate once more the applicability of the non-Gaussian geometry to the World we live in. And, what is more, we need an impartial reasoning about the nature of the physical space. The readers concerned with subsequent development of these ideas may go to the part Publications. One version of the model was presented on the Tenth Astrophysical Conference, College Park, Maryland, on October 11-13th 1999 and appeared in the AIP Conference Proceedings # 522. The last version is submitted in 2008 on arXiv: astro-ph/9910305 v2.

So what are the essential properties of proposed model? If we do not change existing models of nature we will never obtain new knowledge. However, one should not change models arbitrarily. The only way is to advance new model and adjust it with observations at every step. The ultimate model may turn out far away from initial one, however just this process is a feedback with a real world for we can not thrust it unnatural ideas. As was said, the original elastonic idea sprung out from Clifford’s model of matter. However, in the process of adjustment it was considerably altered in accordance with the real observations of milieu. The idea of representation of matter as a space curvature was rejected from the very outset. The matter was considered as a by-product of evolution of space. This idea of evolution assumed ever greater importance as the original idea matured. As a result, a reality of a physical space as the entity independent from the material bodies became clear. Some new ideas occurred concerning the nature of the local and global cosmic space. These ventured to look from a new standpoint at the famous Newton – Leibniz debate about nature of space. As the original idea was adapted to increasing number of observational facts, mostly from astrophysics, it turned into a new cosmological paradigm. Unexpectedly, more and more observational facts lined up in the frame of a new paradigm. What is especially agreeable is a logical consistence of both big scale cosmic events, like cosmic expansion, and the very local phenomena like jets from the young stars, galaxies and quasars. In the frame of a new paradigm the ubiquitous astrophysical “central engines” and even the foamy structure of the World, otherwise incomprehensible, naturally come into existence.

Thus, the central idea of a new paradigm is an existence of a certain entity – the elaston, which can give rise to the physical Euclidean space, matter and energy all the way along its evolution. There are no spatial singularities.

There is the question in any cosmological model: “Why, after an infinity of nonexistence, was the World generated, at one moment rather than another?” In this model the answer is simple; the existence of our World is only a moment in the perpetual evolution of space. The elaston emerges as a link in the infinite transmutation of space so it is not a peculiar *moment* in cosmic time.

Some consequences of the model are:

1. The naturalness of ubiquitous jets and outflows on the scales from protostars to galaxies.

2. The naturalness of “central engine” that creates flows of space, matter and energy.

3. Expansion of the World is simply a consequence of elaston evolution.

4. The natural origin of “foamy” structure of the World.