Espaciotiempo propiedad estructural de la materia en movimiento version 1
ABSTRACT In this essay, the theoretical contradiction between General Relativity and Quantum Gravity about gravity is ended, since spacetime is not structural quality of the gravitational field like Einstein stated. Exactly spacetime is structural quality of the matter and field. This is spacetime is not continent but content, neither the category of the relations between material bodies and their events. The particle-wave, of matter and field, has three special dimensions and one temporal dimension. Thus, spacetime is structural quality of particle-wave. The spacetime is the dimensional geometry of the particle-wave itself and for others. Universe exists inside of the vacuum. Therefore, the matter and its movements are self-contained. Now only Quantum Gravity is possible.
It was accepted during 2010 in four of the five major world events. These are: EGM13, 13th EASTERN GRAVITY MEETING, USA (North Carolina State University), May 21 - 22, (Presented and included in the Report EGM13). GR19 2010; Mexico city, 19th conference on general relativity and gravitation, July 5-9 (Presented and included in the Report GR19). ERE 2010, 6-10, September Spain (Granada), Spanish Relativity Meeting and PETROV 2010 ANNIVERSARY SYMPOSIUM ON GENERAL RELATIVITY AND GRAVITATION, Russian Federation (Kazan) 1-6 November. In Petrov´s Symposium the abstract was published in "Program and Abstracts", page 65, and the paper was published in "Contributed papers", pages 101-109. I attended to Petrov´s Symposium and I lived the best days of my life. Thank you, very much in Colombia to Vera Pak, to the government and the people of Kazan, in special professors Asya Aminova and Sergei Sushkov of the Kazan´s University , Dieter Brill of the Maryland´s University , Mister Roman physic student of the Kazan´s University and all marvelous people that attended.
SPACETIME STRUCTURAL PROPERTY
OF THE MATTER IN MOVEMENT
The theoretical contradiction between General Relativity and Quan-
tum Gravity about gravity was ended, since spacetime is not structural
property of the gravitational field like Einstein said. Exactly spacetime
is the structural geometric property of the matter and energy that it
gives their geometric dimensions. Thus, spacetime is not continent of the
matter (Substantialism), since it is contained. Neither is the category of
the relations between material bodies or between their events (Relation-
alism) since is not relational property; spacetime is structural property.
The particle-wave, of matter and field, has intrinsically three spatial di-
mensions and one temporal dimension. The spacetime is intrinsically the
structural quality of particle-wave. The spacetime is the geometric di-
mensions of the particle-wave itself and for others. Therefore, the matter
and its movements are containing itself. Now only Quantum Gravity is
Key words: classic General Relativity.
Space and time are linked to the shape (geometry) and to the movement (physics)
of the material objects. Updates to the geometry and physics are connected,
also with the evolution of concepts of space and time. Originally the geometry
was united with the material form, but when it become a formal science, space
and time were separated from the material form and they were happened to
be governed by laws of reason. Space and time acquire an independent and
abstract existence for many centuries, disconnected from material existence. At
General Relativity again the space-time were connected with material existence,
where space-time is conditioned by the matter and in turn matter condition it,
but space-time maintaining their own ontological entity like a substance or as a
General Relativity is a geometric dynamic theory (Wheeler, 1963) of space-
time, which maintains that it is not vacuum and is bent due to its content of
matter and energy, whose particles are obligated to move freely within causal
geodesics, timelike to particles with nonzero mass and lightlike to electromag-
netic field particles, which causes gravity; therefore, gravity is not a force but
an aspect of the geometry of spacetime. ”The space-time has no claims for
himself an independent existence, but claims the category of structural quality
of gravitational field” (Einstein, 1954).
It has tried to unify General Relativity with Quantum Physics, which ex-
plains gravity as the effect of the gravitational material field. ”In quantum me-
chanics, the gravitational force is attributed to exchange of gravitons between
the particles of bodies ... ” ”From a mechanical point of view, considering the
quantum-gravitational field, the force between two particles is transmitted by a
particle of spin 2 called the graviton” (Hawking, 1988).
The strategies of unification are: explain the gravitational field as material
since General Relativity or explain all fields as geometric fields since Quantum
Physics. But, unification continues in litigation since according with conclusion
of the group II Society Space-time, space-time is an enigma (Lorente, 2006).
The contradiction between the gravitational field as geometric field and the
gravitational field as material field is examined in this work, since perspective
of General Relativity, for to overcome it.
2.Substantialism and relationalism
The issue of space and time emerged of the questions of the presocratics: What
contain the Universe and its evolution? Is space their continent?. To which
were added questions about the intelligibility of local movement that led: Are
space and time relations?.
Plato and Aristotle argued that space and time are the fixed background
which contains the universe and its evolution while Heraclitus and Democritus
that space and time are relations that register the movement between the objects
which compose the Universe.
In the seventeenth century, the discussion came to Newton and Leibniz: is
real the space or results from the relations between material objects?. This
dilemma led to that space-time relations are seen as relations between points
at which events occur (substancialism) or as the relations between the events
themselves (relationalism). Matter provides the dynamic on a fixed background
(substantialism of Newton). In the intrinsic dynamics (relationalism of Leibniz)
is deleted that background.
Leibniz refuted to Newton, he denied persistence of spatial points in the time,
saying that if the world was somewhere else, inverted or moving it would have
ontological redundancy, while the spatial relationships among its components
not would be altered. But Leibniz cannot explain the inertial structure and,
therefore, the inertial motion. For this reason the substantialism of Newton
endures because of the inertial structure of the movement, which exists and
would be independent of matter, but, stripped of absolute motion with respect
to the absolute space and formulated in the context of the space-time manifold
(General Relativity) in exchange for space.
The space-time has an affine structure that makes possible to establish the
existence of absolute motion with respect to this, which would be independent
of the presence of matter or field. Thus, the existence of this inertial struc-
ture is taken as an inherent structural property of space-time (Sophisticated
In sophisticated substantialism the transformations Galilei’s should be inter-
preted as different representations of one same physical reality. These changes
do not create worlds displaced in space. Although the identity of the points in
space is suppressed is replaced by redundancy of possible representations. So
Leibniz’s ontological redundancy become possible representations of the same
But, as in General Relativity, space-time is identified with the gravitational
field, Rovelli says (1997), the debate continues between substancialism and re-
lationalism, since it has not been resolved which is real or property of another.
Space-time is real or is the gravitational field?.
Relationalism and substantialism are identified in that space-time is a geo-
metric object and differ in that in the relationalism is an geometric ideal object
refereed to the material existence, while for the substantialism is a geometric
real object, its substantial nature is understood as presence, existing by itself,
although, is not material presence.
3.Space and time continents of the matter and
According to Newton space-time is the container of the matter and their move-
ments. Space, time and matter are absolutes and independents.
Matter is defined as aggregations of particles arranged in the elements or
substances. Each particle is capable of acting instantaneously at distance, in
vacuum, and exerts forces (fields) that are transmitted in vacuum, directly, to
other particles. Substance is for all state o form of matter and field is for electro-
magnetic and gravitational forces. Space and time are non-material substances.
Space and time can to exist completely vacuums and are independents of
the system of coordinates that is chosen. With investigations of Faraday and
Maxwell was assumed that the space contains the ether, medium to transport
electromagnetic waves. Due to the lack of interaction between ether and matter,
in the Newtonian neo review, the ether is defined as structural property of space-
time. However, today, the ether remains in dispute, preferring the relationalism
extended object while the substantialism property of the space.
Space y time is defined in Euclid’s geometry, according to the configura-
tion space (R3,t), metric (ηij,t). The configuration space (R3,t) are points
and topology, while the metric (ηij,t), consists of Euclidean geometry, inertial
structure and absolute causality. Euclidean geometry allows infinite speeds.
Space and time in Euclid’s coordinates is an inertial system in which the
objects in movement, free of forces, will maintain their relative state of rest
or rectilinear movement uniform with respect to other systems. This inertial
character of the movement arises directly from Euclidean geometry. Also it
serves for to establish the other structures of the accelerated and gravitational
Between reference systems the coordinates are transformed according to
Galilei’s group which does not apply when the reference system, contains the
electromagnetic field, it is outside the scope of Newtonian mechanics.
4. Spacetime fixed background
The scientific theory of space-time is Einstein’s relativity, which has the Special
Relativity of flat space-time, and General Relativity of curved space-time.
The relativistic space-time is an absolute continuum of four dimensions (in-
terrelated by c speed and interchangeable according to different moving ob-
servers), which exists independently of matter and field to which contains. It
is merely a frame for the physical events without affecting space-time. Space-
time tells matter how to move ’but matter does not affect the space-time. The
event is the true element of the space-time continuum. The physical reality of
space-time is truly material, as resident in the material event. But Einstein did
not end with the existence of abstract point of Newton.
Space-time may be devoid of matter but not of field. Electromagnetic and
gravitational fields have energy. But, the space-time as inertial structure is a not
material field. The space-time empty of matter, electromagnetism and gravity,
in itself constitutes the substratum of the inertial structure, ie, plane geometry
is a field that cannot be made up of events and it returns to Newton’s points.
The physical problems of the movement are treated as geometric problems
in the continuum of Minkowski (R4,ηuvmetric) that, therefore, are determined
geometrically. In the spacetime of Special Relativity applies the principle that
all laws of physics (except gravity) are the same for all inertial observers. Gravity
has no geometric character and it is a force, with no instant action and their
problems have no solution. The relativism of the components of space-time is the
result of Einstein’s interpretation of the Lorentz transformation, which implies
that the length it contracts and time it dilates in proportion to α = (1−v2/c2)
between reference systems in relative movement.
Special Relativity is in contradiction with Leibniz’s relationism because it
is based on universal time, which implies absolute simultaneity of Newtonian
mechanics, while relativism of space and time in Special Relativity, is based in
the relative simultaneity, because the connectivity between the events is con-
strained to the speed c. Minkowski’s space-time like in Newton is a substance
no material, in fact, it is the fixed substrate which serves of continent of matter-
5.Spacetime property of the gravity field
In General Relativity the distribution of mass-energy of the universe determines
the geometry of spacetime (Lorentz’ manifold M4,guvmetric), which is intrin-
sically curved because of the tension that exerts mass and energy (Tuv) on each
Spacetime takes relative character determined by the physical conditions in
it. guvis only the metric of the manifold M (spacetime bare) that describes the
curvature (gravitational field) of the manifold. The author believes that Einstein
erred when he defines spacetime as the structural property of the gravitational
field, since, according to the existing logic in General Relativity, the curvature
is the property and not the entity that supports the manifold, therefore, the
right thing in terms of General Relativity is that the gravitational field is the
structural property of spacetime.
The gravitational force is fictitious, since only is the effect of the curvature of
spacetime in itself, in the trajectory of particles in movement when do not follow
geodesic lines, so force is replaced by the metric of spacetime. Also it twists
due to bodies’ movements, phenomenon called gravitomagnetism. Problems of
gravity are resolved geometrically.
The movement is always relative and the laws of physics are covariant
in all reference systems: inertial, accelerated and gravitational.
Schwarzchild (1916) introduced the assumption that the guvmetric must tend
at infinity to the Minkowski metric ηuv, which restored the property complete
inertial structure of spacetime, beyond the limit at which the matter ceases to
act on it. The same is true on the infinitesimal limit and, in general, all solu-
tions for a vacuum spacetime (Tuv≡ 0). Besides, of the principle of equivalence
between inertial and gravitational mass is apparent that gravity is the inertia
movement in curved spacetime. In addition, the background independence of
General Relativity is not that of relationism, which denies the existence of a
background, but refers to the independence of the geometry of spacetime with
respect of an only geometry, what is certain is that it is not static but dynamic,
since that, due to its interaction with matter, it changes its intrinsic geodesics,
which determines the change in the bodies movement.
The laws of the gravitational field of General Relativity suggest that the
Minkowski space-time is the simplest case of the laws of nature, as in, ds2=
dxudxvthe guvare in function of the coordinates, which are determined by the
transformation chosen arbitrarily, but these are not arbitrary functions of the
new coordinates, since such functions must be recovered by ds2= ηuvdxudxv,
through a continuous transformation of four coordinates, so the guv functions
must satisfy the condition of Riemann. Also suggests that the spacetime of
Einstein is not essentially different from Minkowski space-time, ie that there is
a primitive identity between them.
The best interpretation of General Relativity spacetime is of the substantial-
ism but due to the Leibniz equivalence principle it produces indeterminism in
front of hole argument (Earman,1986 y Norton, 1988,2003) direct consequence
of the general covariance. The solution is to link the metric field with the man-
ifold M (thesis of sophisticated substantialism). However, despite the sophis-
ticated substantialism, persists the dilemma raised by Rovelli each other ’the
gravitational field is nothing but a local distortion of the geometry of spacetime
(substantialism) or the geometry of spacetime is nothing but a manifestation of
the gravitational field (Relationism).
6. Space-time a state of the matter
In the theory ’space-time-mass’ it says that because there is no empty space,
therefore, space and mass (mass-energy) are the same thing, since the mass is
space, but mass and space are different. How can the mass-space, be same and
different thing?. The theory space-time-mass is background-dependent. The
response is based on another contradiction: empty space as topological space,
The geometric curve of spacetime is made of geometric particles that serve as
the continent of the particles of energy, forces and matter. Thus, the geometric
particles are the lowest state of existence of particles with mass or energy and the
mass-energy is transformed into geometric particles and vice versa. Therefore,
the space-time is a phase of matter.
7.Spacetime and quantum gravity
With the goal of unifying General Relativity with Quantum Field theory has
been formulated Quantum Gravity, which seeks to describe everything in the
universe in terms of the quantum field.
The Quantum Gravity is associated with the Planck scale since their explicit
quantum-mechanical effects are confined to it and similar to General Relativ-
ity, has a space-time description but replaces causality (determinism total) by
uncertainty relations. Quantum theory does not deny the principle of real de-
termination, by laws and causes, but whether the deterministic description of
The Quantum Gravity explains the gravitational interaction of matter-energy
from virtual graviton and assumes quantum spacetime. The event as a point on
the manifold M becomes an extended object without structure (field). The char-
acteristics and properties of spacetime at the quantum level are closely linked
to the physics of the quantum vacuum states that are associated to the residual
energy of the overlapping of the fields, in averaged of energy zero, known as
zero-point energy (ZPE), composed of virtual particles without real particles.
In addition, there another vacuum that is of negative energy, generated by
eliminating the electromagnetic waves that appear inside the uniformly accel-
erated reference system. Since, in the quantum vacuum worth the principle of
relativity of motion, but not the equivalence between an inertial system and a
uniformly accelerated system. An observer cannot determine its speed through
the quantum vacuum fluctuations, ie cannot set the absolute motion, but can
determine accelerated system. Therefore the gravity cannot be the curvature of
spacetime, as General Relativity says due to the general covariance of the same.
In consequence, there can be no privileged observers so the total tensor energy-
momentum, Tuv (including the contribution of the gravitational field g) must
be identically zero that ensures to the observers the energetic balance between
the flow associated to matter ϕ(Tuvcontent) and the associated to gravitational
field g (contained in −(c4/8πG) guv) in a way that both flows are canceled.
The two main theories of quantum gravity are: Superstring M (favoring
substancialism) and Loop quantum gravity (LQG) (favoring the relationism).
In M theory, the dynamic spacetime (M4,guv) is the brane, which is a geometric
object continuous. The brane would be incrusted in the bulk in Planck scale,
which is an extra space of 6 or 7 dimensions. In M there may be several branes
and the particles are open and closed strings of the brane. The strings are under
tension and vibrate in a number infinite ways.
Gravitational interaction is caused by the vibration modes of the closed
strings that correspond to the graviton virtual. The Standard Model particles
are excitations of open strings confined to the surface of branes while the gravi-
ton would be the only one that would exist also in the bulk that would be the
cause of the weakness of gravity.
In LQG exists only the manifold (M). Therefore, quantum spacetime is bare,
composed of a network of elements called spin. The connections between vertices
and edges of the spins generate graphs that evolve to new structures. The
particles are entangled braids differently in spacetime. Because the network
changes in every place at every moment, it requires of a structure-mechanism
of quantum superposition that gives persistence to particles. This would be
analogous to the qubit, which at each moment can be in two states. Calculations
show that the resistance of the quantum qubit preserve braids in spacetime, and
explains how the particles can have a very long lifetime in the midst of quantum
8.Geometric structure of the particle-wave
The Universe is field-matter contained in the vacuum that is the background.
Field-matter-vacuum always exists in the wave-particle structure subject to mo-
tion. The vacuum is energy of the point zero subject to quantum fluctuations.
The field-matter-vacuum has the geometric property of volume. Its geo-
metric structure has the three dimensions of latitude, wide and length. These
dimensions are the geometric property associated to the mere condition of static
existence of the field-matter-vacuum that has the potentiality to serve as con-
tinent of other structures. The vacuum is by excellence the continent of all the
other structures of the field-matter. Due to this potentiality of continent that
has the volume, the three dimensions are the geometric spatial property of the
field-matter-vacuum. Space means continent.
The movement of translation and/or rotation of the matter, the variations
of the field and the fluctuations of the vacuum from the geometric point of view
cause that field-matter-vacuum leaves its three-dimensional continuous and one
fourth dimension is generated. This is a mathematical law of dimensional geo-
metric spaces N: if N leaves its continuous N, in a direction k contained in the
(N+1) continuous then the geometric space of (N+1) dimensions is generated.
Thus, the field-matter-vacuum in motion has four dimensions. The fourth di-
mension corresponds to the dynamic reality of the existence of the field-matter.
The fourth dimension is the temporary geometric property of the field-matter-
vacuum. Time means becoming of the existing.
The wave-particle of vacuum is compound of virtual particles. Also the
wave-particle of field although can additionally be compound of real particles.
The particles of vacuum and field are without mass according to four vector
moment subject to superposition principle. The wave-particle of matter is com-
pound of real particles with mass according to four vector moment subject to
exclusion principle. Therefore, the wave-particle exists in four dimensions that
are intrinsic geometric property.
The spacetime is objective, that is, exists independent of consciousness and is in-
trinsically connected to the material existence, which is the necessary condition
of its existence. The separation between spacetime and material existence at the
thought occurs during transit from the philosophical of the ancient to scientist
knowledge. They understood the opposite of what it is, that is, space-time as
the condition of material existence and movement.
Such inversion, in the connection between material existence and spacetime,
was inferred of the geometry of Euclid, constituted as a formal science before of
the physics, and is a fact that the science of the geometry was walking ahead of
the science of physics, up with General Relativity, physics become geometry.
The root of the separation between spacetime and material existence is not
physics but epistemological. Inside of Euclids conceptual framework was un-
derlying the physical science of Galileo and Newton; they established absolute
space and time, acting on the mechanical motion of matter in determining the
inertial structure of the uniform rectilinear motion.
The geometry of Minkowski and the Michelson-Morleys experiments on the
speed of light made conceptually possible, that in Special Relativity, it estab-
lished the link between the mechanical motion of matter and spacetime, putting
the speed limit c.
Einstein looked a physical theory of general covariance, according to the
geometry of Riemann. He, with base in the equivalence between inertial and
gravitational mass, formulated the equivalence between all mechanical move-
ments of material existence, and the mutual dependence between the spacetime
and the material existence. Although, ontologically as separate entities. Also
define spacetime as the structural property of the gravitational field. Question
in dispute because can be it opposites. The consequence is that the rest of the
material existence lacks of spacetime in contradiction with all our experience.
In the theory mass-spacetime it would be a geometric state of the material
existence and equal that Einstein it ignores that all material form has spacetime.
M and LQG are geometric theories about of quantum gravity and all material
existence. Spacetime generates totally the material existence. Therefore, all
material existence originally is geometry. The replace of the material content
by its form is consequence of the General Relativity. Ortega and Gasset had
said, in Einstein’s visit to Spain in 1923: You geometrize physics.
Substantialism and relationism coincide in considering the gravitational field
like being-in-itself. However, substantialism and relationism differ with respect
to the space-time that, while for the substantialism is the structural geometric
property of the gravitational field, for relationism the spacetime is simply a
category of thought, which express the being-in-relation-to (Hegel). The error
of the relationism is to define space in relation to the movement without respond
which is the container of the universe. While the error of substantialism is not
respond what it’s made spacetime.
These problems are resolve with spacetime structural geometric property of
the material existence (thesis of this work). Since the vacuum is the universal
container of material existence and the vacuum it self-contained. But, What is
the gravitational field?. Is the curvature of spacetime? Is a force of interaction
that curves the spacetime?. The spacetime, as the geometric dimensional prop-
erty of the material existence, as the very matter, must exist according to the
characteristic of the wave-particle. Therefore, the spacetime must have various
structures differenced according to: virtual and real particles, massless and with
mass particles, the superposition and exclusion principles, the determinism and
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