Special and General Relativity

The theories of Special Relativity and General Relativity, like all particulars, presupposes as given universe. In the present we are proposing a metaphysics of physical monism stating that the universe is constituted by a unitary Space. In the following then, we are going to analyse the compatibility and differences between physical monism and the main concept behind Special Relativity and General Relativity.
Special and General Relativity are two of the most successful theories in physics. If the world is a monist universe, what do they tell us about physical Space?
. First, they are both mathematical constructions, which reflects the spatial nature of the universe. Mathematics is a human construction. Nature, on the other hand, is a universal order independent from our thought. The universe then has a spatial nature and not a mathematical one. And the success of Special and General Relativity reflects how mathematical models can describe the behaviour of physical Space.
. The main contribution of Special Relativity, is to leave aside the idea of space as an absolute reference frame. This reflects an important aspect of physical monism. In a monist universe, Space is not a container of objects, but it is what constitutes them. Although, unlike in Special Relativity, in a monist universe relativistic effects are not the consequence of mathematical corrections, but they are the consequence of events occurring in a unitary Space.
. And General Relativity, by modelling vacuum in Space with (a non-Euclidean) space-time, leaves aside the idea that Space is a fixed element and that actions can occur at a distance. Gravity for example, are the effect of the geometry of space-time on matter; a manifestation of how the laws of physics comes from the behaviour of Space itself.

Special Relativity
The dominant conception of space until the 19th century was given by Newtonian mechanics where space was considered an absolute, fixed and homogeneous reference frame. Another conception of space was of space as an ether, or physical medium where objects and light can travel. In 1887 Michelson and Morley devised an interferometer to study light diffraction with the intention of proving the existence of this ether; but they came up with negative results. The experiments showed that there wasn’t any ether in space.
From Michelson and Morley results, Lorentz came with the idea that the theory of an ether could be partially right. There could be indeed an ether, but it could be suffering contractions on the line of displacement, which would accounts for Michelson’s negative results.
But then came Einstein with an explanation that still holds valid to the present day. Space is not absolute and there is no ether. Einstein proposed that Lorentz’s interpretation was partially right. There are indeed contractions, but these contractions are not on an ether. The contractions are on space and as the result of -Lorentz- transformations from one reference frame to another.

We propose that in a monist universe all the above is partially right. Space is not an ether and Space is not absolute. But in a monist universe, relativistic effects are not mathematical but physical.
In the past, absolute space was conceived as a universal container where all the bodies existed, either in the form of an Euclidean space or a medium like ether. Now we know that this is not true. And in physical monism this cannot be true since Space is unitary, non-homogeneous, dynamic and it can not be taken as a fixed reference.
We know by experience that space is not absolute, but we currently interpret the relativity of space as a mathematical phenomena. In the absence of a privileged reference, all the relativistic effects like space contraction, time dilation, etc. are interpreted as a problem of choice of reference frames. But relativistic phenomena are not just a differences on measurements from one coordinate systems to another, they are physical phenomena. Time dilation, or any other relativistic effect, can be described mathematically, but it is a physical occurrence.
We propose then, that the origin of relativistic effects is not mathematical, but physical. It lies in the nature of physical space. If observers on moving frames can find differences on their measurements, it is because physical asymmetries are not absolute qualities at the point in space, but they are always relative from one point to another. Bearing in mind that in physical monism, motion is not a translation of objects from one place to another, but it is a displacements of asymmetries in space, what mathematical transformations between reference frames (like Lorentz transformations) reflect, are asymmetries form one region of space to another.

For example, given a system that starts travelling at a high speed relative to an observer, the system becomes more energetic, with higher inertia and with higher associated frequencies. Higher speed on the displacement of the system means that the space in the system becomes more asymmetric, more dense and less extent (space contraction). The relative variations in the system are associated with slower displacements, therefore inside the system, time passes slower (time dilation).
Another example would be systems at high altitude where differences in gravity means that there is a difference in the tension or energy in space. The lower the gravitational field is on a system, the less asymmetric space becomes, the lower its associated frequencies and the faster the displacements in the system occur. The physical effects of all these differences in space, is that time passes faster.
Special Relativity then, adequately describes relativistic effects because it uses mathematical models that approximates the behaviour of physical Space. But relativistic effects are physical, originating from the behaviour of Space, and not mathematical.

Space in the end, could be thought as absolute, but in a completely different sense than absolute space was originally conceived. Space would be absolute, not as a fixed reference or as an ether, but as a unitary element. In Space, there is no duality of bodies and space as it was originally (and currently) thought. If Space is all that there is in the world, then everything is constituted by Space, and all the phenomena that we experience are manifestations of its behaviour.

General Relativity
General Relativity is a theory of gravity as the effects of the geometry of space-time on matter. The main differences between General Relativity and physical monism are that it still holds a duality space-matter, and it still describes physical phenomena as if they would be mathematical in nature. Nevertheless, General Relativity manifest important aspects of physical monism. First, it introduces the concept that space is not a static background but it has a central role in defining the laws of physics. And then, as we shall see in the following, many of the physical effects that General Relativity describes reflects the properties of physical Space.

In the following we are going to compare three central concepts of General Relativity with physical monism: the definition of distance, the geodesic equations and the field equations.

General Relativity is constructed on a Riemennian space, where its geometry is defined by the distance between two neighbouring points, given by  ds2=ga b. dxa .dxb forming the ‘fundamental metric form’; and where ga b is the ‘metric tensor’ defining the curvatures of space-time, which depends on the point and on the arc of its immediate vicinity.

Physical Space is not metric. So points in space wouldn’t be separated by a distance. But physical Space does have an extension. And the extension of Space is not an independent variable, but it depends on its geometry, tension and density. If we think of the distance as representing the extension of space, and the metric as representing its geometry, eventually we shall see how general relativity approximates the relations between these variables.

Meanwhile, we can say that Riemannian space approximates physical space, by introducing a geometric structure on space on which the motion of elements depends.
Another resemblance, is that space-time is not Euclidean and the geometry of vacuum is never flat. ‘Straight lines’ of Euclidean geometry are generalised in Riemannian space to ‘geodesic lines’ (lines of extreme distances between their terminal points), where flat space is only a particular case; which is actually never realised. And this is because physical space is totally asymmetric.
On the other hand, Riemannian space differs from physical space, in that its constructed on the assumption that space, at infinitesimal scales, can be approximated to an Euclidean space with Pithagorian relations. If physical space is totally asymmetric, then it is so, just at large, as at infinitesimal distances. So physical space would be nowhere symmetric or Euclidean. Nevertheless, the approximations that Riemannian space makes to the geometry of vacuum at large scales, proves to be extraordinary accurate, useful and practical.

Geodesic equations
For a mass point in space-time, its motion is given by the geodesic equation
d2xa /dt2= -Gab g dxb.dxg /dt.dt     , where the Gab g are constructed from the metric and its first derivatives.
The geodesic equations, are the basic equations of motion for a test particle in a curved space-time. They are derived from the action principle, which tells us that a particle would go from one point to another following the shortest curve between them.
As we mention in the laws of physics, the action principle can be interpreted differently from the point of view of a unitary space. First, points are not physical, so there wouldn’t be any point particles in space. And then, particles wouldn’t go from one place to another, but they would suffer a displacement in space; where, in consistency with the action principle, they would follow paths where the differences on the geometries and their variations are minimum; that is, where there is less tension in space.

The geodesic equations describes the motion of particles in terms of the geometry of space. Which is a step closer to the concept of a unitary space determining the motion of things. In physical monism, just as general relativity says, there are no forces acting at a distance, but Space itself determines the motion and variation of things. Here motion is given by the effects of gravity. But the same concept can be extended to all forces of Nature (electromagnetic, weak or strong). The variation and motion of things, is the variation and motion of Space itself.

With the geodesics equations, the Christoffel symbols (Gab g ) are introduced; which are constructed from the metric and its first derivatives. The condition that makes the Christoffel symbols physical significant is their non-triviality. If they would be equal to zero, space would be flat. And this never happens. So, just as with the non-commutability of symmetry groups in particle physics, we can think of the non-triviality of the Christoffel symbols as a reflection of the asymmetric nature of physical Space. The Christoffel symbols are non-trivial because Space is totally asymmetric.

Field equations
The geometry of space-time is given by the field equations
Rm n -1/2gm n R=-kTm n
which establishes a relation between the geodesics of space-time and the distribution of mass-energy in the universe. The integration of the field equations leads to the determination of ga b as functions of the mass-energy distribution.

The field equations, reflect the dependence of the extension of space with its energy and tension. The distance (ds) and the metric (gm n   ) defines the curvatures of space-time. And as we mentioned before, on physical space, points are not separated by a distance, but by the extension of Space. The extension of space in turn, is not an independent quality, but depends on the tension produced by Space’s asymmetries. And the field equations, reflects this relation. They show that there is a compatibility with the extension of vacuum (curvatures) with its tension (mass-energy distribution). Of course, they don’t express the relation in the way we suggest, since the mass-energy, is not the energy of Space, but of the distribution of energy in the universe. Nevertheless, to have the equivalence of both concepts implicit in the equations, shows their consistency with the notion we are presenting of a unitary Space.

One of the most revealing concepts that we can take from the field equations, is the idea matter could indeed be formed by Space itself. The field equations tells us about the geometry of vacuum due to the distribution of matter in the universe. But if we look at the problem the other way round, and we wonder what constitutes mattes, then the answer is right there: geometries on Space. And this is exactly what we sustain from the point of view of a unitary Space. If Space is all that there is in the world, then both vacuum and matter are constituted by this unitary physical Space.


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