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Dynamics of the Continuum Space-Matter

Eduardo Lpez SandovalCentro Brasileiro de Pesquisas Fsicas,

Rua Dr. Xavier Sigaud, 150CEP 22290-180, Rio de Janeiro, RJ, Brazil.

Tel.: 52 21 21417220E-mail: [email protected]

Abstract This essay reflects on the universe in its deepest essence analyzing the nature ospace, matter, and time, considering them an indissoluble unity evolving. It is

considered that this development, therefore, determines the dynamics of mattein space, or conversely, that determines its dynamic evolution, a universe withobeginning or end, and unlimited. This aims to build a cosmology in its deepes

sense, more metaphysical

Any intelligent fool can make things bigger, more complex, and more violent. It takes a toucof genius - and a lot of courage- to move in the opposite direction.

Albert Einstein

Introduction

The understanding of the universe, studying the Cosmology, in its deepemeaning is the study of the universe as a whole, as the totality of phenomenand depend of our understanding of the basic physical quantities ( space, timmatter,etc.) and fundamental principles that govern it. That is to say, ometaphysics in the sense given by Aristotle as the study of the basic constituenof the world-space, time, matter, etc.. [1]. Whenever there has been a shift tomore correct conception of these, we come to a deeper understanding about threality of the universe. The description that we give of these fundamentaphysical quantities is related to the description of its dynamics.

At present there are two opposing positions regarding the metaphysicadescription of the universe: 1) as an abstract object (Idealism) or 2) as a concrobject (Realism or Materialism). The philosophical difference between these is t
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the abstract object has no existence in space and nor has causal power [1]. Thetwo positions or competing visions of the world are represented by quantummechanics (QM) and General Relativity (GR). In the first case, the universe is t vision offered by the MC, according to the Copenhagen interpretation, where thclassical causality and determinism are replaced by probabilistic wave function ofposition of the particles, obtained from the Schroedinger equation. However therhas been a (albeit small) contrary to this interpretation with Einstein, de BroglSchrodinger, Bohm, etc. They believe in a causalist universe, where particles follopath in physical space, and not abstract mathematical space, as in the abovinterpretation. Einstein summed it up well in his famous phrase: "God does not pldice with the universe." As for the latter position is the General Relativity, bhandles some complex concepts such as the four-dimensional curvature ospacetime, its principles are closer to the direct experience of measurable physiquantities, or indirectly by its effects. Here it is possible to have an image or phys view of the world (according to Berkson expressing the idea in his book [2]). Wthis theory, Einstein gives his vision of a continuous causalist Universe. These twpositions are competing to show which is the most accurate in the description of thUniverse.

Descartes is the first to attempt to explain the universe describing the dynamiof the bodies (though not the mathematization), that it is necessary to discuss thessence of space and matter to the understanding of the interaction between thmatter and its movement through the space. He proposes a universe filled with fluid ethereal. His vacuum was not empty: all space was filled with matter swirether in large and small vortices and produces what we call gravitational effects [3

The Newtonian dynamics, but achieves a mathematical description of thmotion of celestial and terrestrial bodies, does not delve into the essence of gravi when Newton says "Hypothesis non fingo" (I do not invent hypotheses), recognizthat he has not an explanation about the nature of gravity.

Although it does define the space and time as absolute and universal, mutualindependent and matter moving through it without affecting and where the matteinteracts between them, with a force acting at a distance instantaneously, withoany intermediary medium and according to their gravitational force law [4]. Besihe proposed the three laws of the dynamics of the matter with which he gets tdescribe the universe with a very good mathematical approach, but not deeper inthe nature of space and time. Coulomb subsequently obtained a similar equation fthe interaction of electric charges inspired by the Newton's theory. This kind of theory or conception of space is referred to as continent, orcontainer, because it represent only a passive scenario (not interact with matter, bis filled with an ethereal substance) which perform the dynamic events with a tithat elapse in a similar manner, and independent between them, anywhere in thuniverse [5].

Leibniz opposed to the idea of an absolute space and time, arguing that them


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exist only for their relationship between different objects in the universe. Hproposed an abstract idea about the universe, which means that space is discretdiscontinuous. This kind of universe is known as relational [5].

The Weber's law generalized the Newtonian gravitational interaction bincluding in its formula the velocity between the bodies. He proposed his la without explaining why the velocity should influence the interaction between bodHe also applies it to the interaction between charges and get to deduce the equatioof electromagnetism, currently known as Maxwell equations [6]. According Webber, the potential of this force is:

2

20

11

4 2i j ij

ij

q q V U

r c

(1)

where ijr is the relational position of two moving particles and ijijdr

V dt

is theirrelational velocity.

Moreover, Gerber, proposes a similar law, but inferred from the interaction oretarded potential of the bodies. Although it does not explain the reason for thitype of interaction, or the nature of the signal traveling at the speed of light [6Its potential, applying it to explain the precession of the perihelion of Mercury

c

V r

mmU

ijij

ji

1

1 (2)

Where ijr is the relational position of the mercury planet and the sun, andij

ij dr V dt its the relational velocity .Faraday discovered electromagnetic induction law. To explain this phenomeno

implies the existence of a field, in which the interactions between the electrcharges is transmitted through the space adjacent to it is contained. He alsproposed that these fields are generated by forces in the center where are the electcharges, without specifying exactly what are these forces, or to propose anmathematical model.

Maxwell takes the field concept of Faraday, and relies on the idea of a space fil with the ether, which gives physical substance to the field, and here he develop

mathematical model to synthesize the behavior of the electromagnetic phenomenin the equations baptized with his name, and whose success is crowned with thphysical description of light. He continued to maintain the idea of an absolute spaand time [2].

Einstein, in disagreement with the hypothetical ether, and influenced by Macdisagreed with the concept of absolute space and time independent of the matteand suggested, first,an unified space-time system with to the bodies in uniforrelative motion between them, dismissing the idea of the existence of any absolu


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reference (including ether). This theory is known as Special Relativity, but then wgeneralized for the bodies with acceleration, with the Equivalence Priciple that sthat this acelarating movement is equivalent to the effect of the gravity force in tbodies. His General Relativity Theory supposed that a four-dimensional space-tim(with space as a fourth spatial dimension) whose curvature is influenced by tpresence of mass, and that in turn influence the trajectory of bodies. In his ow words [8]:

When forced to summarize the general theory of relativity in one sentence: Time and space and gravitation have no separate existence from matter . ... Physical objects are not in space, but these objects are spatially extended. In this way the concept empty space loses its meaning. ... Since the theory of general relatively implies the representation of physical reality by a continuous fconcept of particles or material points cannot play a fundamental part, ... and can only appearlimited region in space where the field strength/energy density are particularly high.

An alternative approach recently proposed by A. K. T. Assis in his theorbased in the Relational Mechanics by Leibniz's idea of a relational space, along wthe idea of Mach on the inertia of bodies caused by the mass of the entire universIn this work, he attacked the main base of the Special Relativity when it said that dynamics of bodies is caused by the interaction between the bodies and not threferential system where its dynamic is quantified. Here he explains that no matthat the law has different equation or different form in each referential, as long equal quantitatively describe the same phenomenon [9]. Furthermore, Assis used Weber force law to quantify the interaction between the bodies [6].

Dynamics of the continuum Space-Matter

Our first impression of the universe is that it is continuous. The best evidencuntil now could be the existence fields of the matter: electric and gravitation Although the General Relativity Theory (GRT) considers a spacetime (3 +dimensions) continuous, it is assumed that it contains matter and that folded spactime, such as a ball in a bidimensional cloth, where the matter influences the spaand the space in turn influences the movement of the matter.

In our hypothetical model we assume an indivisible unity, a dynamic continuuof space-matter, and borderless. We also assume that space has only thredimensions of space, without time dimension, when time is caused by the dynamof space-matter: we consider that the motion of the matter as a fundamentaphysical quantity, and time as a byproduct of this. Here we are considering thmatter as the same nature than space, but with a fold or greater spatial tension, thdecays in the space from its center to a radial distance by the well-known inversquare law. This last property as a result of the stress distribution in a thre


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dimensional space, as is the case of light [10]. It's another metaphysical conceptof the universe: space-matter, as "elemental substance of which all physical objeare" and moving. Here none is more fundamental, and both are in perpetuadynamic interaction. Although the difference between space and matter could bconsidered as stress level, and consider as Mario Bunge explains that "everythithat is part of the physical world is a piece of space, and all substantial propertyownedof a substantial chunk of space . Therefore, any physical thing could beexplained in terms of space, could be the vortex of Descartes, mounds of the spacfrom Clidford or wormholes from Wheeler "[5]. Here the matter, the electrimagnetic or gravitational fiels are expressions of the same space with differedegree or stress level and dynamic, and in a different scale.

Our model is more like the Faraday model, or the previously mentionedDescartes, Clifford and Wheeler models. Differs from Einstein model because hmade a distinction, although subtle, between space-time and matter; also proposan equation to describe the universe, but we consider that it is not possible and not correct, because it makes no sense to consider the time as another dimension tthe same level of the spatial. Furthermore, the curvature of space is only possibledefine surfaces for volumes not, ie not to dimensional space. For the GRT, it idefined mathematically to the three-dimensional curved surface of a foudimensional volume which we have no way to prove its reality.

Besides, Einstein's equations describe with its tensorials equations as if eapoint in space were a center of tension, as it is the case in application of elasbodies or liquids, and not just in places of space where exist matter or where thereconcentrated. This is not possible as it is describing a transition in a continuousystem in an area with a singularity at the center of each individual or distributionthese. Another point against it is that the tensor equations are very complicateequations to solve, inclusive for only two particles. Although it is possible application for unitary and continuous systems, as in the cases of black holes neutron star, where the tension in this clase of body is for each point of its volumand may be treated similarly to a continuous and/or elastic body.

In conclusion, we believe that it is not possible to describe the universe in all thcomplexity of its structure with this equation, both for its technical difficulty, asdoes not correspond to a model of the real universe, in our opinion.

According to a previous work, we proposed a static universe: infinite, eternand self-sustaining, with centers of rotation in equilibrium with each other [10].homogeneous universe in balance, although to the scale of galaxies there exist bevents like births and deaths of stars and black holes, but that in the global averaremains unchanged. In such universe is not necessary a dynamics equation becauglobally there is not beginning or end: no global evolution. What it is necessaryfind are the fundamental principles that help to explain and give substance to thlocal laws of the universe, and their evolution, and why the universe remaihomogeneous and unchanging. So, for our model of the universe it is not required


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global equations. The closest equation about the Universe could be the Navier-Stokes Equatio

(NSE), as deduced from the principle of continuity, describing the transport anconservative amount of some kind, which in this case equation refers to the masenergy and momentum, the three universal principles of conservation that have tbe respected in the description of the universe at any scale. Although its deductiis made in a net transport on a local system enclosed by surface that bounds it. new cosmology requires universal principles rather than equations of the univer which are plausible local laws. The NSE has like a special case the Newton's secolaw, and also according to Marmanis [12, 13], can be derived the Maxwell's eqtions with a viscosity extra term, taking as analogy of the potential a relation tdepends of the density, and the flow with squared velocity. Then, applyinincompressible fluids as analogy of our model of the universe, it will only descrthe universe as a continuum, with the peculiarities and differences of certain areasthe universe that we studied are singularities representing the charge or mass mattand, as already explained, the stress that produce decays as the inverse square of distance. The tensorial mathematical of the NSE does not describe this behavior, explained before, and therefore we must find another way to model it.

Moreover, in the classical mechanics Newtons the gravitational field was givephysical interpretation as a force acting at a distance instantaneously; but thgravitational potential so far not been given any physical meaning. Ielectromagnetism the electric field itself is considered a physical quantity, but noits potential. The potential in both cases has been used as a useful mathematictechnique for to obtain a simpler and easier solution, under which the equations be solved are of scalar type. Newton did not consider the potential physical realbecause it assumed that interactions were instantaneous, and no need for aintermediary field. However in the electromagnetism, in the Coulomb law or in tPoisson equation, was necessary that the electric interaction travels through spacand also it helped to describe the electromagnetic wave phenomenon.

In electromagnetic theory, the Linard-Wiechert (LW) potential describes theffects of a scalar and vector potential of moving electric charges, whose interactihas a retarded time according to the distance and traveling at the speed of ligh The effect of this potential has been interpreted as transmission of information, bit do not explained what is physically transmitted, and how it is transmitted. Butclear, is that the effects of the charge can not be described as an effect of action atdistance. In the case of potential Gerber [14], which is of the Weber potential type [6] anincludes, besides the retarded time, the velocity of the interacting bodies, accordito a new interpretation developed by Jaume Gine [14], gets explain physically tretarded potential gravitational interaction, but with double effect, going fromsender to receiver and back [15]. The importance of this potential is that is gettithe exact calculations of the perihelion precession of the Mercury planet [15] a


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the deflection of light passing near of the sun [16], similar to the results obtain with the General Relativity, but based entirely on different concepts anmathematical.

These same results can be obtained with the Weber potential but adjusting parameter [16]. In fact, these potentials can be interpreted as a particular case of tLW potential, but with the difference that last is considered the orientation of thposition and velocity vectors of the particles with respect to a reference system, ainstead in the Weber or Gerber potential or particle interaction is relational [5, 8 The physical interpretation we give this kind of potential is that the effect of timdelay by the moving particles is similar to the Doppler effect by the accumulationdepletion of the "signal" of potential between them [18]. This could be explained physically why using the Gerber potential the corre

results are obtained for the deflection of light and the perihelion precession oMercury. This is because when considering this correction to the classiccalculations have to take into account the Doppler effect caused by the relationmotion between the planet and the sun, it is reflected the waves of its potential othe planet in the sun, and this effect slightly affects the sun because its great mabut the reflected wave it is significant to cause precession for the planet.

Similar to the scalar potential, it has been considered that the vector potential alhas physical reality according to the interpretation of the Aharonov-Bohm effect (BE) [19]. For a reinterpretation of the A-BE and that gives mathematical detailsour model, see Appendix A: Quantum Hydrodynamics and the Aharonov-Bohm effect .

Finally, and according to all this arguments and more that will give give lat we propose the hypothesis that the potential that better describe the dynamics othe Continuum Space-Matter are those obtained with the general solutions oMaxwell's equations for scalar and vector potential (LW potentials) for chargparticles with q charge or m mass with relational interaction (here just express with m, but is indifferent):

1( , ) ( )

(1 )r r t q m

vr

c

y( )

( , )(1 )r

q m v A r t

vc r c

(3)

where r is the relational distance between two particles, v r its relational velocity, andv its rotational velocity of the particle that generates its potential with respect to tspace or static universe and / or around its own axis (spin). Although it can bconsidered that the vector potential as a special case of the scalar, and can brewritten as [20]:

( , ) ( , )v

A r t r t c

(4)


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These potential include as condition the Lorentz gauge and that unlike coulomgauge where the interaction is instantaneous, the transmission is contiguously, a wave and with the speed of light; this gauge guaranteeing the continuity of tspace-matter [13, 20]. Also these potentials describe the singularity of the partic with the inverse square law and the transmission of disturbance by the continuospace.

We adopt these two potentials that describe how the relational interaction of thmoving bodies in a space-matter continuous Universe, and with physicasingularities in the charge centers or matter in motion. We interpret physically potential as the tension or pressure of space-matter in analogy to a fluid accordito Marmanis work [12, 13], but using the LW potential that takes into account thesingularities (sources). This potential, therefore, describe the mutual interactibetween two or more particles in motion (thepotential is the pressure caused by the charge or mass of the bodies); the vector potential A described the vortex in thespace caused by the own rotation (spin) or a loop of current of chage (or matterboth generating the magnetic field, according to the hydrodynamic interpretation Maxwell Equations did by Marmanis [12] and Rousseaux [13]. A similar effect exist in the case of rotation of the masses. The two types of interactions betweethe particles will move contiguously, as already explained, by the space as a spher wave at the speed of light, similar to a fluid traveling in the pressure variation wha body is moved on it; each body will receive the pressure variation of the othbodies (similar to the Doppler effect, as already mentioned), besides the own causto another bodies and that it returned, according to LW potential, as we considehere. With the sum of its potential (dependent on its position and velocity) will taits mapping, and with the resulting potential gradient, we will describe the dynamof bodies. As additional hypothesis, here we no longer believe that there is gravitational or electric field contained in the space, but is the same space thsuffers stress (which are manifested in these two physical quantities), and wheremoves.

Therefore, with the LW potential, which includes the fields and potentiaconsidering that the mass and electric charge are similar effects to different scabut not a field that travels through space, but a disturbance or effect on the samspace that is transmitted at the speed of light (in a similar way to mechanical wav That the two effects have the same transmission velocity could to indicate that thassumption is true.For the particular case of electric charges with two types of polarities, wconsider that the negative charge could have a physical representation as compression of space, ie a force towards the center (negative potential). In the caof the positive charge would be a tension or forces out of its center (positivpotential). This model would be similar to the idea of Faraday forces centeralthough in our case would be the stress of the space, analogous to the metaphor o


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massive bodies with roughly the same acceleration as the predominant strain caused by the greatest mass, and not makes much difference to be detected.

In the study of this dynamic, our reference system is only a mathematictool: static, fixed in space, not necessarily fixed in translational bodies rotational motion, and therefore does not influence or determine its dynamics, such for Newtonian mechanics or Special Relativity. Although we do noconsider space as absolute as it changes locally in accordance with the motion the bodies, we can suppose hipotetically a fixed reference system on the univeand that, on average, to large scale, is static, as shown in a previous work [1and that helps us describe the dynamics of space-matter. Although it should nmatter which reference is taken (may be in a body (particle) in motion), bshould not influence the dynamics of bodies, as implemented in the RelationMechanics, and that (unlike special relativity ) is the interaction between bodthat determine its dynamic. The reference system we choose has not to influen

it, and must describe the same phenomenon, as explained Assis in its book abothe relational mechanics [9]. Although the Quantum Mechanics describes the quantization of energy an

displacement at the atomic level, and that is the paradigm of the idea of discontinuous universe, has recently proposed an alternative model that can explathese as caused by the dynamic effect the retarded potential in the orbits whethere are steady states without torca [21]. This could be an indication that it possible to explain the quantum behavior of the particles with such retardepotentials in a continuous space-matter. Furthermore, according to the theorproposed by Madelung, is possible to describe the solution of the Schroedingequation with a wave function as a continuous charge distribution in the space, anthat replacing this function on the Schrodinger equation, we get a system oequations similar to those of the classical hydrodynamics, and which are knownthe quantum hydrodynamic equations [22]. According to an explanation given Feynman to the theory of superconductivity [23], and we consider that theequations are more correct than those obtained with the interpretations given bBohm (according to Madelung) [22], or the same Madelung [22], or more recen Tsekov [24] for an explanation of the nature of quantum mechanics (see Append A, to read our interpretation):

V t

(5)

and22

2 ( )2 2m

V qt m

(6)


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with qAV m

. The first equation is the law of continuity of these potentialsand density, and the second is the equation of quantum hydrodynamics. Thespotentials could be those of LW, but here for the atomic distances the retardedeffect could be very small.

It is physically possible to interpret these equations using the Aharonov-BohEffect (A-BE). That is, its possible to understand what these equations meaninterpreting the physics of these equations according to our model of continuouuniverse because, as Feynman said in his lectures, "getting to explain thphenomenon would help to understand the quantum phenomena". According toour hypothesis the interference in the electronic distribution that occurs in thscreen is due to the wave function of thepotential (which according to ourhypothesis, it is the in the Schrodinger equation) that representing the electrons inthe space when moved in the direction of the windows (with the the speed of light These waves interfere before and after passing the windows, since electrons precethem, and that is what causes that these have this type of distribution, sincinterference from their fields favors this orientation of electrons on the saminterference pattern. This distribution can be described as the square of the sum the waves generated by these physical potential, and we're not considering them aprobability function according to the Copenhagen interpretation. From thiinterpretation we can make an analogy with the hydrodynamics, as any body thmoves in a fluid and generate a wave with other waves of other moving bodiinterfere with each other in the changing fluid pressure and displacement, and boare modifying the motion of the bodies. But also these particles have an owinternal rotation (spin) or rotational translation in a loop that generates a rotationdisturbance of the space and physically interpret as the magnetic field. Accordin with this ( explained with more detail in Appendix A), this will cause that the A-the interference is modified in the presence of a magnetic field by the rotating pof the vector potential; or aout of phse when the magnetic field is isolated, bremains the effect of the scalar field. Therefore, according to this metaphor the function is interpreted as the potential of the internal rotational or own rotation(spin); A would be the potential of the rotational moment.

In the expression on the right of the equation (6) we have the expression witthe density gradient and according to our interpretation representing the gradient the pressure, divided by the density, i. e., the mass enthalpy. This density is the resof the sum or linear interference of all w aves and that, as we said before, physically interpret as the waves generated by the potentialof the relational movement of the particles.

With this equation, we can see that it is possible to describe the quantumbehavior of a set of particles with the Quantum Hydrodynamics, as long as we knoits scalar and vector potential. This undoes the myth that the Quantum Mechanic


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describes a discrete universe, and we see that it is possible to explain it as continuous system, like liquids. It also shows that the basic fields for all the fieldsphysics are the scalar and vectorial fields.

Moreover, paradoxically the quantization for retarded potential not only occur the atomic level but also at the level of the solar system, where in this casaccording to the rule from Titius, the planets (or satellites) orbit the sun (or anplanet) following a geometric progression of its distance from the sun (or plan with respect to the rotational period, which is a function of position (n = 1,2,3, .of the rotational center [21]. Although exist very much controversy as to wheththere is a physical interpretation of this regularity, the most plausible explanationthat this is caused by the rotational resonance of the planets, or satellites. Accordito this, only exist certain areas permitted where its rotation are orbits with cyccan be stationary, which complies with the principle of conservation of angulmomentum (without torca) and that there are not unstable due to resonancealthough paradoxically located near these areas [25, 26]. These stationary orbcould be limit cycles according to the qualitative theory developed by Poincare infamous theorem [27], and demonstrated by Bendixon [28].

In this work we have no needed to propose relational force or an actionreaction law, as these are already involved in the potential of the continuousystem of space-matter and which is obtained by calculating its gradient anapplying Newton's second law. It is still satisfied only for forces which aderived from a retarded potential.

The main objection has been taken to such forces or retarded potentials lik Weber, is that it does not comply with the principle of conservation of energyGerbers law does not have this problem, and neither the LW potential, becausaccording to the demonstration by F. Bunchaft & S. Carneiro [29], this satisfies tenergy conservation principle.

Analysis and Discussion

In our model of the continuous universe we are considering that the space anmatter are indivisible units, without borders, but with particles with a singulcenter. The only difference between this particle and the space would be the hidegree of tension that exists near the center of the particles, and which prevenany disturbance or particle can be moved on it. Outside of the singular zone, thtension decreases proportionally with the inverse of the distance, and is what known as the field of the particle. In addition, this disturbance is the stress othe space itself and not a field disturbance that travels through space.

This conception of space and matter is known as the raw material. Its maiproponents are Descartes with its vortices, Clifford with mounds of space


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Faraday with his strength centers and Wheeler with his wormholes. Thihypothesis contrasts with the idea of absolute space that sees the space as passive scenario, abstract, where matter interacts between them, without interaitself with the space. Here are the theory of Newton and even the SpeciaRelativity. The other conception about the space, is the relational, whicconsiders the existence of space and time by the network of relationshipbetween objects (atoms, fields) and events [5]. The original proponent of thidea was Leitniz, and currently has been revived by Assis [9].

The importance of having clear a metaphysics (in the Aristotle's sense),i. e.a vision or image of the world (and not just an abstract idea or mathematical) [is that it gives the possibility to say what is the space, time and matter, etc. andtry to verify the facts in its physical essence, and the relationship between theFor physical essence we mean it is an entity that we can recognize with osenses, and we can quantify or verify directly with a measuring device,

indirectly with a model. Because only in this way, trying to understand thessence of the universe is as we get a better understanding of physicaphenomena and we can also obtain the best estimate of physical quantities.Wcould have a mathematical model of the world (there are many examples othem actually) that we could describe with good numerical approximationphysical phenomenon. But this does not mean that we understand what is realhappening. Our mathematical model could be as a black box, but the samignorance of the essence of the physical quantities keeps us from to know thelimitations, and improve it. As expressed by Berkson [2]:

A metaphysics allows us to advance in the development of a new theory closest to reality.

A group of equations mean nothing if there is not a model that interprets eac variable with a physical quantity.

Every theory has its metaphysical presuppositions although we are not awaof it, but these are necessary for this to be meaningful. Probably we will nevknow they are in essence the physical quantities of our theories, and perhaps abeyond the limit of what we can understand, but they allow us to explain andescribe facts and consequences of these, in some cases we can model anquantify. For example, will probably never know the true nature of space or timbut conceptually we can imagine and approach using analogies, but never haabsolute certainty of its essence or ontology.

In this paper we start from the idea that the universe is continuous, unlike th worldview of the Classical Mechanics from Newton or the Relational mechani where the matter is supposed to be separate in the space, and as a result thinteraction between the particles is instantaneous. But suppose that thicontinuity has inhomogeneities (without losing continuity) and propose how a


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elastic membrane analogy with center with stresses is distributed throughout tsheet. These centers are singular points whose influence is transmittecontiguously and continuously, and whose potential decays as the inverse distanlaw through the space. We could also make an analogy with a liquid in icontinuity and properties already explained. These analogies are limited to tcreation of a model, if we fails to describe with any degree of accuracy tuniverse, the metaphysical assumptions are validated, then, although we do nknow to what extent is real, or not get their full esence, get us closer to a moaccurate understanding. In this sense, our model gives a clearer picture of thuniverse, and simplify much of the mathematical compared to other models.

Our model, unlike GRT from Einstein, and even Clifford theories or Wheelephysical geometry is more physics than geometric, because described as analogy the accumulation of tension in an elastic membrane instead of thmathematical concept of a curvature in a three dimensional surface of a fou

dimensional space. It also defines and proposes less arbitrary elements than othmodels, making it more acceptable. The GRT considers the space-matter as duality where the Rienmanian structure contains the space matter, and as onchanges the other. In contrast, we consider the space-matter as a unity, indivisible continuity. In addition, the GRT proposes an equation of the univers which we do not consider possible, and instead propose local interaction betweparticles with the LW potential, with the NSE as the equation of conservation othe matter-energy.

We believe that the fundamental in our universe is the above mentioned aunity and indivisibility of space-matter, with none being more fundamental th

the other, in constant tension, and eternal and infinite coexistence. We considethat the particles are singular zones of space with a density (or tensiondepending of the model used) that is going to a very large value, almost infin(physical singularity), and causes no other particle or wave can move through The space would be the outside zone, where out of its boundary the stresdecays proportionally with the inverse of the distance.

The causal effects of interaction of the particles travel in the space similato the electromagnetic wave interactions. The gravitational effects as thprecession of the perihelion of Mercury, or the deflection of light to a massivbody like the sun, can be explained as retarded potential effects of gravity,Doppler effect of the gravitational potential [20]. The deflection of the light cbe explained by the same tension that produces mass of the sun in the space, an which causes the vibrational frequency of the light increases, and the wavelendecreases when approaching these, and deviates. If our distance parameter is t wavelength of light, and the frequency of vibration of the time, we caunderstand why it travel longer than its average life could afford. This same effcould explain the pion decay retarding and contraction in its length.


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The particle does not have a sharp boundary within limit with the space, buthe tension of the space near the center is so great that any particle or wave jugets moved to a limit radius. Its influence decays with the inverse distance lawouter space, because this is distributed through the three dimensional space, with the light transmission [10]. The accumulation of the particles accumulatensions in space in a similar way with a elastic membrane. Thus, the dynamicsthe bodies or the radiation will be determined by the modification of the spacinduced by the tension produced by the particle system, and follow the directioof the gradient with lower potential (tension or pressure). The bodies or thsame light can follow curved trajectories according to these gradients. In a spaof this type there is no difference between these movements (particle or fieldsince it is the space itself, or the same stress of the moving space. Thus, thtension is which determines the curved movement and not a curved space Although this could be interpreted as the same space is curved (or the optim

trajectory is a curved space), but unlike the GRT, this happens in three spatidimensions, and not on a "curved surface" of three dimensions (somethinabstract and difficult to imagine), but on the same three-dimensional spacaround the matter distribution centers or charge.

A traditional or usual position in classical mechanics was thought that thlight was not attracted by gravity, which suffered no deviation from the straigpath, even though there are classical calculations that predict the deviation wsome approximation to the observed. This is a remnant idea of reductivdichotomy of space and matter. But if we think the space as a continuous spacmatter field as we do here, this view change, and with the retarded potenti

correction is obtained accurate results in the perihelion precession of Mercu[16] and the light deflection [17] . The Universe have not a proper geometry: it is a dynamic of particle

modifying the tension of the space, and which in turn modifies its trajectory bthe three-dimensional space. Here we do not talk of geodesic curve nor forcbut gradient of the potential. The concept of force may be used only in the caof two particles, or a particle in an average field of a set of particles, becausemost cases the dynamics of two particles, i. e., the evolution of the spatigradient, is more complex, and its solution requires considering it, which changeach instant time. Therefore, it is more correct to define it as interaction, sincthe force indicates only that a body acts upon the other, while the secondindicates that bodies interact with each other. The concept of force could bapplied only in the case of a distribution of matter or charge with the averagfield acting on a particle, and the field of the particle not affecting the particposition of the distribution. It is applied as ideal or approximate solution, but more realistic situations, it should be considered its global dynamics, i. e. tinteractions between each bodies in the temporal evolution of the potential fo


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the continuous space. That we consider the potential as the space tension is an interpretation, but

it correct? Also that the interactions of the matter is due to forces, or due to thcurvature of four-dimensional space or any other concept is arbitrary, becausthem only are models of the universe. The best model, analogy or metaphor whave to bring better understanding and a better description of the dynamics othe Universe. And this will be the best proof of its truth, the correctmetaphysical, as explained in the beginning.

According to our view, the potential represents a stress level (equipotentiaof the space, and the gradient the pressure that pushes the bodies (tensioncenters or matter) through the space with less tension. Now, according to thPoisson law, the divergence of this tension that represent the compression othe space, would be physically its mass, that for a particle would be, by singularity, infinite in its center and decaying with the inverse-square law out o

Then, it is possible to represent the tension of space with the scalar potenti without using tensors. According to this work, time is not primary physical variable such as spac

matter or motion of bodies, but a parameter that arises from the dynamics ospace-matter continuum, as a byproduct of the processes in nature. Time implithe existence of processes as physical or biological clocks, have cycles, beginnand end, evolution, dynamics and evolution of the universe, locally and globall Although exist a feeling, a sense of time, it is often difficult to quantify direcin the same way as for the length. The most accurate way is to take as parameter the vibrations of electromagnetic radiation, where the time i

measured with the frequency, and the dimension with the wavelength. But thealso suffer modification due to gravity as the mass, and therefore it is not aabsolute unity and universal as discussed in special and general relativity.

It is consider like charge the particles (center of tension) that interact witwo polarities, and as a mass to its dynamic due to the tension of the spaccaused for themself. This is the Equivalence principle from Einstein, and he with will explain an interpretation with our model. The interaction as chargephysically significant only at close range, and the gravity when the mass is hig That's why even when electrical interactions must to use its inertial massm in thesecond Newton law

Then, the difference between charge and mass would be noticed to differenscale as the charge is the interaction that is significant only in the vicinity of singular radius (nuclear force, principally), while out of this, the effect act as Coulombian force. The gravitational force is noticed to a higuer spatial scabecause this rise as an accumulation of the tension caused for the union of thparticles. The tension is caused by the the charges of opposite polarity, whicnullify its charge at the local level, but increasing global tension. This is w


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gravity is an interaction of greater intensity to longer range of distance thaelectric: it is cumulative.

The amount of mass is equivalent to the amount of tension, and the more igrows, it has more inertia. What this means is that for a body would be mordifficult to change its dynamics (trajectory or acceleration) when its mass greater mass than the other mass around it (because the tension produced arounit is greater), or throw out of its apparent static state. So, the particle, or thdistribution of particles with a greater mass dominate the movement of thother with less mass. An example is the solar system where all the planets rotaround the sun.

For charged particles (regardless of its polarity) its displacement is to the arof lower pressure (pressure gradient) because in areas with higher stress (charg with the same polarity) this can become so large that they can not move moand repulsion is exerted (because their tendency is to move to the area of low

pressure). For the mass, on the contrary, its movement is accelerated due to thhighest tension in its surrounding space, since here the interaction betweebodies emerges from its dynamic movement due to the tension of the space (oa scale larger space), and the tension changes its path or acceleration towamore massive bodies, and and it only remains static when collides with anothbody of much greater mass, such that the tension between them is so large thprevents the displacement out of there of the less massive, and is trapped in thpath of the massive body throught the space.

In our model the nuclear force is the same that the electric force, only that aa special case when the two particles with opposite polarities (proton an

electron) are practically together and annul its opposite tensions to any othecharges, which prevents them to disjoin. This could to explain the nuclear fusioand the nuclear formation. As a hypothesis we assume that the neutron could bformed with these two types of particles, and is why it is possible that a protobinds to a neutron, and the negative charge of the electron could bea link, or gluto the two positive charges, avoiding repulsion. And consequently the corstructure for heavier elements would be a structure with two polaritieinteractions in equilibrium.


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References

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19. Aharonov , Y.; Bohm D. (1959).Significance of electromagnetic potentials inquantum theory . Phys. Rev. 115: 485 491.http://prola.aps.org/abstract/PR/v115/i3/p485_1

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21. J. Gin, On the origin of the quantum mechanics,Chaos Solitons Fractals, 30 (2006),no. 3, 532-541. http://arxiv.org/PS_cache/physics/pdf/0505/0505181v4.pdf

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26. Peter Lynch , On the significance of the Titius-Bode Law, Mon. Not. R. AstronSoc.341, 1174 1178 (2003).http://www3.interscience.wiley.com/cgi-bin/fulltext/118873443/PDFSTART

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29. F. Bunchaft & S. Carneiro,Webber-like interactions and energy conservation , Foundationsof Physics Letters, Vol. 10, No. 4, 1997.http://www.springerlink.com/content/624k0j5186h92764/fulltext.pdf
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Annex A

Quantum Hydrodynamics and the Aharonov-Bohm effect

According to quantum mechanics, probabilistic amplitude of a particle that goes from a another place b in the presence of a magnetic field with vector potential A is:

0| | exp

b

A Aa

qb a b a A dl

h

, (1a)

An equivalent manner to write this equation is by the Schroedinger equation,

12

qA qA qi t m i i

(2a)

According to this, we can deduce the current equation that has the following expression:

12

qA qA J m m

, donde

i (3a)

Traditionally, the current is interpreted as the product of the probability density of the partilocation and velocity. The operator in brackets represents the velocity V

qAV

m

therefore we can write

mV qA

where is defined as the dynamic moment.

In this work we interpret the as the waves of the retarded potential generated by theparticles with their movement and * is interpreted as the intensity of the wav e. Now, as thethese waves are linear, the resulting distribution or result overlaping will be the sum of althem, and therefore we can write a general solution to a fluid Similarly, according to tinterpretation of quantum mechanics made by Madelung and Bohm [23]:

( , )

( , ) ( , )i r t

hr t r t e

(4a)

where2

( , ) ( , )ii

r t r t is the total intensity of the waves overlap, and( , )i r t is its

phase. Now, substituting the wave function (4a) in (3a), we obtain the current equationq

J Am

(5a)

By analogy with the classical current equation we know that


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mV qA . (6a)

Now substituting the function (4a) in the Schrodinger equation (2a) we obtain

qAt m

(7a)

o

V t

And we also get

2 22 ( )

2 2m qA

qt m m

(8a)

that can be expressed as

222 21 12 4 2m

V qt m

(8b)

This equation is analogous to hydrodynamics equation, except for some details. For exampthe velocity V is not directly deduced of the gradient from a scalar potential, but the sum othis with the vector potential A (eq. 6a). This gives also it the property of being a rotationalpotential. As is the scalar potential of the phase, its gradient is its rate of change. The velocity V (thedifference of these two potential) is only an analogy with respect to liquids. Regarding expression of the second term of the eq. (8b), it can be expressed analogously to the equatias the mass enthalpy of a hydrodynamic fluid:

22 21 14 2

pm

(9a)

So we can write

22 2 14 2

pm

Equation (9a) also has physical meaning analogous to fluid dynamics, because as we obsepotential gradient is a function of the density, as happens with traditional fluids. Furthermothe expression in parentheses is analogous to the approach used in the density functiontheory to model the electric potential of the molecules.


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We can see that the equation (6a) is an expression much similar to the gaugtransformation, A A , except for the sign and the constants. We could generalize the wave function (1a) and (4a), and to replace by the more general line integral of the equa(6a) in (4a),

( , ) ( , )

iqA dl

hr t r t e

(10a)

Consequently we can to reduce this to

( , ) ( , )iq

i A dlr t r t e

(11a)

which is a generalization of Equation (1a) and (4a). This shows us what could be the physinterpretation of the vector potential and gauge transformation.

With this we can to interpret the Aharonov-Bohm effect. We know that for two windoware passing a flow of electrons, behind of which there is a solenoid with isolated magnfield. Although the electrons are not receiving the influence of the magnetic field, undergoephase shift distribution in the screen where are colliding, with respect to when the solenoidoff.Of the function (11a) is inferred that this effect is due to the rotational vector potential A iszero, but not its scalar part, which is what causes the out phase. Therefore, we conclude that the linear integral of the moments of the scalar and vectpotential around a closed path of the equation (10a) can be interpreted as the rotation of thspin operator and the current loop respectively. These represent physically the vorticity of system, i. e., the effect of the scalar magnetic field (the electron intrinsic rotationor spin).


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Figure 1. Distribution of the electric field and the equipotential between similar charges (aopposite (b) with a negatively charged plate (c) and charge distribution (d).

my article 7

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