Archive for the ‘Science’ Category

Monism and Quantum Gravity


How does Monism compare with Quantum Gravity theories?

The most general scientific theories of the universe are theories of Quantum Gravity. Theories of Quantum Gravity are attempts to unify General Relativity with Quantum Mechanics in a single mathematical formalism (where General Relativity is the theory describing gravity and Quantum Mechanics the theory describing the behaviour of sub-atomic particles). There is not a complete theory of Quantum Gravity yet, and there are several approaches to it. The two main approaches are String Theory and Loop Quantum Gravity.

So, how does Monism compare with String Theory and Loop Quantum Gravity?

String Theory has many compatibilities with monism. The theory is based in the idea that there are no point particles in the world. Particles have an extension, and what are now considered to be fundamental particles are constituted by more fundamental extended elements called string. According to Sting Theory, the properties of particles are given by the different modes of vibration of strings. From a monist point of view, the modes of vibration described by String Theory gives an insight into two fundamental aspects of Space: one is the geometric nature of Space and the other its dynamic nature. Although in a monist universe Space is more fundamental than strings, the description of the behaviour of strings can be thought as a model for the behaviour of Space.
Loop Quantum Gravity get even closer to a description of a monist universe. The theory introduces two important concepts. First, it sustains that space, at Planck scales, is not continuous but it has a discrete structure. And second, the theory satisfies a condition that many consider fundamental for a unification theory: background independence. That is, it can describe events without the need of a reference space or fields in space, but through space itself. In other words, events can be thought as processes that don’t occur in space, but they are defined by space itself. From a monist point of view, Loop Quantum Gravity not only reflects the geometric and dynamic nature of Space, but it also reflects the most fundamental aspect of Spatial Monism: elements are not objects in Space but they are constituted by Space itself. Background independence is not only a useful mathematical construction, but it is a reflection of the nature of the universe: a constituted by Space.

Monism and theories of Quantum Gravity are compatible. Quantum Gravity theories describe different aspects of monism. And the more the theories advance towards background independece, the closer they get to a monist description of the universe.




We know from biology that evolution is a process of selection, like natural or sexual selection, by which living organisms tend to improve their capacity to survive and/or reproduce. We also know from biology that this process is a consequence of the successful transmission of genes. Evolution is not about the survival of the individual, but the survival of genes. And the genes that survive are the ones who carry the information that allows them to successfully transmit themselves.

Evolution and complexity

We know evolution mainly from biology, but evolution is in the end a physical process. And like all physical process, it is related with the stability of systems. In the case of evolution, it is related with the stability of genes. Evolution happens because it increases the continuance of genes. And a change that increases the continuance of genes is a change that takes genes into states of higher stability.

Genes are self-duplicating complex systems that increases their stability as a consequence of an evolutionary process.

Complexity is the reason for which evolution is possible. Particles, atoms and minerals don’t evolve because they are simple systems, therefore they have more rigid dynamics (see Complexity). It is only complex systems, like living organisms, that have a flexible dynamics that allows evolution to happen.

Unlike development, evolution might or might not be related with an increase in complexity. For example, species might evolve into different breeds, varieties or types with no increase in complexity.

And just like development, evolution is not an inevitable process. Things don’t tend to evolve ‘naturally’. Things, by nature, tend to remain in the most stable states. Things only evolve when changes in the system increases its stability. That is, when changes in the organism improves the continuance of genes.



Development is a term used to describe many particular processes, like cognitive development, moral development, social development, etc. But so far we have no description of the process itself. We sustain that development is universal natural occurrence. That is, it is a process that is common to all systems. Not all systems develop of course: molecules and atoms don’t develop. But for those that do, like organisms, neural networks or societies, the process is the same.

We define development as the process by which systems increase their complexity. That is, systems develop when they expand their differentiation and integration of their constituting parts (see Complexity).

In other words, development is a gradual and continuous process of growing complexity.

With a growing complexity development bring to systems several characteristics:

When systems develop they tend to become more stable. With an increase in complexity, systems become more flexible, adaptable and autonomous, which are often related with higher stability (see Complexity).

In a developmental process, higher states of complexity grow from previous lower states. And as a consequence, the dynamics of higher states tend to be subordinated to the dynamics of lower states.

The intensity of development also diminishes in time. And this is because in nature everything tends to remain in states of minimal variation.  The higher the development and the more stable the system becomes, the lower the tendency towards further development. As a consequence, higher states of development are more rare than lower states of development.

Development can sometimes be described in terms of stages. Developmental stages are qualitative distinct dynamic states. And given that development is a continuous process, there is no skipping of developmental stages.

Another important characteristic of development is that it is not an inevitable process. Systems don’t develop ‘naturally’. Systems by nature tend to remain in stable states. Systems only develop when given necessary conditions for development are met.

The opposite process to development, regression, is related with a decrease of differentiation and/or integration and a decline into simplicity. Simplicity in turn, is related which dynamic rigidity, dependency and instability.

Examples of developmental processes:

Social development

Moral development



In the following we are going to analyse the compatibility between Spatial monism with certain cosmological phenomena (not finished).

Vacuum’s energy
. Gravitational red-shift
. Cosmological constant
. Spontaneous symmetry breaking
. Energy density of vacuum in particle physics
. Dark matter

Speed of light
Light is normally attributed with two qualities: to have a constant speed in vacuum, and this speed to be a limit on which energy can travel (nothing can travel faster than light). From the point of view of physical monism, there is no reason why this should be so. Speed, in its classical interpretation, is the rate of motion in space over time. From a monist point of view, speed would be a rate of displacement in the continuity of Space. And in a unitary Space there is no reason why the speed of light should be constant. Indeed, in an asymmetric Space it wouldn’t be so. There is also no reason why there should be a limit to the rate of displacement of energy in Space. This would depend entirely on the degree of asymmetry in Space, and there are no restrictions to this. So theoretically, from a monist point of view, the speed of light might not be constant and things might travel faster than light. And there are some empirical evidence showing that the constancy of the speed of light and its value as a limit might actually not be true, suggesting the validity of physical monism.

First of all, the constancy of the speed of light in vacuum is not a physical property, but a definition. It is not by measurement that we know that the speed of light is constant. We can indeed measure the speed of light, but measurement presupposes a metric space. And on a metric space like space-time for example, the metric depends on the speed of light. Space-time is constructed from the premise that light has a constant speed and that the speed of light is independent from any reference frame. So it is by definition that the speed of light is constant. And it is an important definition, for it allows us to construct metric spaces (of physical significance). Without them, we wouldn’t be able to measure or predict anything.
It happens that light might be the best reference we have to construct metric spaces, for it is the fastest carrier of information we have about the physical world. As far as we can perceive, the speed of light could be constant for there is no faster carries of information to show us otherwise.
From formulations on a metric space like space-time, results that the speed of light marks also a limit to the speed that energy can travel in vacuum; that is, nothing can travel faster than light.
And there is an element of truth on this, for it also happens that light is the minimum information that we can receive from the physical world. Any variation of energy lower than the absorption or emission of a photon is totally transparent to us. So physically, it is true that nothing with a higher energy than light can travel faster than it. But there is no reason why information with lower energy could travel faster. The problem is, that if there is any, we wouldn’t know about it.

From the point of view of physical monism, the constancy of the speed of light and its value as a limit to which information can travel in Space are possible but not necessary conditions of the nature of light. In fact, a totally asymmetric Space would suggest that the speed of light would not be constant. And there is empirical evidence that shows that this might be the case.

. The speed of light might not be constant. We know that the speed of light in mediums other than vacuum is not constant. The higher the density of the medium the lower the speed of light. And because of this phenomena we have effects like refraction, chromatic dispersion and, for example, rainbows.
In vacuum there is no chromatic dispersion, but there is similar a phenomena that might be showing a similar effect: gravitational red-shift. It is known that light travelling through a gravitational field changes its frequency. In particular, light originating from massive star shows red-shifts. In General Relativity, these changes on frequency are interpreted as functions on changes in the geometry of space-time. In physical monism, vacuum wouldn’t be emptiness, and asymmetries in the geometry of Space would be associated with tension and energy. And just as in medium with density, changes in the frequency of light could be associated with changes on its speed. Higher gravity, would be associated with higher asymmetry and tension in space, and lower frequency and speed in light.

. No limit to the speed that energy can travel
. Universe’s background radiation
. Twin particle experiment

The universe’s expansion
. Dark energy –     The universe is expanding at an accelerated rate.

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.

Particle Physics


The study of particle physics, like the study of 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 most fundamental concepts in particle physics.
The study of subatomic particles begins with Quantum Mechanics and it follows with Quantum Field Theories. These theories are some of the most robust and successful theories in physics. It is in particle physics that science achieved the most accurate measurements and prediction about the physical world. So, if the universe is a monist universe, what does particle physics tell us about physical Space? Several things:
. First, the behaviour of subatomic particles is totally different from our classical conception of things. The physical world, at its most fundamental level, behaves in a totally different way from our classical ideas about the physical world. So to understand Nature we have to be ready to leave aside our normal interpretation of the world and embrace the idea that the world might be totally different from what we normally think. To understand Nature, we have to be ready to challenge our normal perceptions and conceptions. Our normal interpretation of the world are nothing more than useful simplifications in the most familiar cases, but they don’t reflect Nature’s reality.
. Second, particle physics depends strongly on mathematics; something that reflects the spatial nature of the universe. Unlike what Pythagoras, Newton and many others believed (and still believe), the universe has a spatial Nature and not a mathematical one (see mathematics). Mathematics is a human construction. Nature, on the other hand, is a universal order independent from our thought. Mathematics in physics is useful and successful if it can model and describe the behaviour of physical Space.
. And third, particle physics describes the physical world in terms of probabilities due to the impossibility of knowing physical states with arbitrary accuracy. There is a limit on the information we can get from the physical world, therefore there is a limit of what we can know about it. If we think of physical states as states in the geometric and dynamic nature of Space, then the need to describe Space in terms of probabilities reflects its unicity; where it is impossible to isolate different aspect of Space, and where it is impossible to isolate the observed from the observer.

Quantum Mechanics
Matter, at sub-atomic level, reveals properties which are totally unfamiliar from our daily experience. These properties are the object of study of Quantum Mechanics, of which some of the main ones are: discrete values on physical quantities, uncertainty on physical quantities and a duality wave-matter. If the world is a monist universe, and particles are constituted by a unitary space, then these properties should be compatible with the properties of a unitary space:

. Quantified values of dynamic variable: particles have dynamic states with variables (like energy, charge, angular momentum, spin, etc.) that don’t change in a continuous way, but they are restricted to a discrete set of values. These discrete dynamic states are related to the geometric nature of space. If particles are constituted by space, then the quantified values on the dynamics variables of particles are a manifestation of the geometric nature of space.
Notice that discrete dynamic quantities doesn’t mean discontinuities in space. The discrete dynamic states of particles are associated with a geometric property of a unitary and continuous space.

. Uncertainty principle: it is impossible to simultaneously measure complementary dynamic variables (like position and momentum) with arbitrary accuracy. The more we know about one variable, the more indeterminate the other variable becomes. So there is a limit on the information we can receive from a particle. And this is compatible in many ways with physical monism. First, it reflects the unicity and continuity of space. When we measure something, we invariably interfere with it. And this is because of the unicity and continuity of space where it is impossible to isolate the experimenter from the object of experience. At large scales, this interference might be negligible. But at sub-atomic scales it is not, and it is manifested on the uncertainty principle. Second, it reflects the invariability of space. A variation on some dimensions might allow us to measure a dynamic variable. But because space is invariable, variations on some dimensions would induce variations on other dimensions so the overall variation of space is zero (see conservation laws), making it impossible to simultaneously measure space in all its dimension. The uncertainty principle also reflects the nature of the particle as a physical element that is not in-itself (see metaphysics). Particles are not finite objects that can be isolated from the rest of space. Instead, they exist in the continuity of a unitary space. This is why when we measure them, we interfere with them.

. The duality particle-wave: both light and matter manifest corpuscular and wave properties. This reflects two things: first, it reflects the common nature they share for being both constituted by the same physical space. And second, it reflects the dynamic nature of space. Matter and light, rather than being solid bodies or waves, can be both thought as dynamic systems in space.

Quantum Field Theory
Quantum Field Theory was developed from the principles of Quantum Mechanics, and it is the most general -and successful- theoretical framework describing the behaviour of particles. The most fundamental concepts related to it are: the concept of fields, symmetries and quantization (in particular, path integral). Again, if the world is a monist universe, then these concepts should be compatible with physical monism.

. Fields
The properties of particles can be effectively contemplated as manifestations of fields. So fields in the end, are a more fundamental concept than the concept of particles themselves.
Mathematically, fields are functions of space-time which become physical significant if they also  responding to transformation properties.

The biggest contrast between the mathematical representation of fields and a unitary space, is the multiplicity of spaces that science uses to describe particles: there is a background space-time, we have the fields themselves into which points in space-time are mapped, and there are the group spaces where the transformations of fields take place. So the description of physical phenomena depends on a multiplicity of mathematical spaces. If space is all that there is in the world then all the physical variation occurs on a unitary physical space.

Nevertheless, fields offers a practical and useful approximation to the behaviour of physical space.
First, fields take us closer to abandon the concept of particles as finite elements dissociated from space. Instead, particles are studied as dynamic systems as a whole, with information distributed in the continuity of space.
Fields also take us to abandon the concept of forces acting at a distance. Instead, the universe is made by the interaction of fields. Physically, if there is a unitary space, there is no simultaneity and all interactions occur in the continuity of space.
And although fields are not an explicit representation of the geometric nature of a unitary space, they do have, alongside with symmetry groups, all the necessary information about the asymmetries of space to describe the behaviour of particles.
In other worlds, fields and symmetry groups form a successful model of the physical world,  because they contemplate many properties of a unitary physical space.

. Symmetry Properties
As we mention in the section on subjectivity, a point of view is objective if it is independent from place and time. Similarly, the concept of symmetry would be the equivalent on physics to an objective point of view on the laws of nature. The study of Nature is based on the premise that Nature is everywhere and always the same. From this premise, the laws of physics are a symmetry of nature then, if they are independent from where or when we are looking at them.

Symmetries are mathematically interpreted through transformations, such as rotations or translations on space and time, that leaves invariant the physical properties of particles. So a transformation would represent a symmetry of Nature if the dynamics of a system remains invariable under such transformation.

One of the main differences between monism and science, is that science treats Nature as if it would be an external entity from time and space. Nature is thought to be symmetric, because it acts as an external force affecting elements at every moment and at every place identically, ensuring that the same fundamental laws remain in operation. On the other hand, from a monist point of view, space is all that there is in the world, Nature is not external but immanent to elements, and it is given by the behaviour of space itself.

The invariance of physical laws is the invariance of space itself.
The laws of physics are always and everywhere the same because they are relations on a timeless and unitary space, that itself is everywhere and always the same. And they are independent from where we are looking at them because physical events on a unitary space occurs locally, independently of place and time.

Non-commutative algebra reflects the asymmetric nature of space.
Nature is described in physics through symmetry groups of a non-commutative algebra. Even light, that can be described through an Abelian group, is in the end a particular case of  more general fields  described by non-commutative algebra. So non-commutability and commutations rules are at the heart of Nature’s structure. And if Nature is given by the behaviour of a unitary physical space, then we can interpret the need of non-commutable algebra as a reflection of the asymmetric nature of space. On a space where its geometric structure is everywhere asymmetric, the order of their rotations is not indistinguishable. And the rotation itself is not arbitrary, but it follows an order modelled by commutation rules.

Symmetry groups reflects the relation between the extension and the asymmetries of space.
The more energetic and the shorter the range of the forces, the higher the degrees of freedom on the symmetry groups describing the particle (U1, SU2, SU3, etc.). If particles are constituted by space itself, then highly energetic particles are associated with highly asymmetric space. So we can relate the degrees of freedom of a symmetry group to the degree of asymmetry on physical space. In general, the more asymmetric space is, the lower its extension, the more energetic the particle is and the shorter the range of the associated forces. So high asymmetries on space needs higher degrees of freedom to describe its dynamics.

Laws of Physics


The laws of physics are invariable and universal relations among physical quantities occurring in Nature. One the characteristics of the laws of physics is that they are not isolated or unrelated, but they show coherence and compatibility. The coherence in the laws of physics is compatible with laws coming from a unitary substance. In a monist universe, the laws of physics are laws in the behaviour of a unitary space (and they are universal and invariable because space itself is a unitary and inalterable substance).
One of the ways this coherence is manifested, is on how all the diversity and multiplicity of laws can be reduced to three main principles: conservation laws, minimal variation and maximal dynamic stability.

. Conservation laws, like conservation mass, energy, momentum, charge, etc., are related to the invariability of physical quantities in closed systems.

. Principles of minimal variation are related to the laws of motion. The most important example is the action principle. The action principle is one of the most fundamental principles in physics. Most of the laws of physics, from classical mechanics, optics, wave mechanics, electrodynamics, gravitation to particle physics can be derived from it.
The action principle states that a system evolving from an initial to a final point, does so through paths that minimises the action (where the action is normally a function of position and velocity).
The origin of the action principle can probably be traced to Maupertuis’ principle of least action. Maupertui stated that the quantity of action (a function of mass, velocity and distance) necessary for motion is the least possible. Another early form of the action principle, came in Fermat’s principle of least time, stating that a ray of light travels from one point to another in such a way as to make the time taken a minimum. Eventually it was taken into the mathematical form dòds/v=0  (where the variational condition was represented as an extremum rather than a minimum). For practical solutions on classical physics, the most convenient representation comes in the form of Hamilton’s principle, which states that the path a particle takes from point to point is that one which extremises the action s=òL.dt=extremum ; where the action s is given in terms of the Lagrangian (L). The motion of a particle then, is determined by its Lagrangian; which is a function of its position and velocity. Lagrange defined this functions as generalisation of the laws of mechanics, with the property of being invariant under transformations from one coordinate system to another.
On its most general form, the action principle is given by a four dimensional integral over a Lagrangian density; which is a function of fields and their derivatives.

. Principles of maximal dynamic stability, like the second law of thermodynamics or Pauli exclusion principle, are related to the laws describing the evolution of systems. In Nature, systems tends to evolve towards states of maximal dynamic stability.

These principles are, in a way, telling us how physical space behaves. Given that they describe the behaviour of a single entity, we would expect them not to be independent, but mutually related. And this is exactly what we find:
. One manifestation of this mutual dependence is found for example, in the first laws of thermodynamics (DE = Q – W   , where the energy of a system increases if energy is added as heat, and decreases if energy is lost as work done by the system), which combines the conservation of energy with the evolution of the system towards dynamic stability.
. Another -and more explicit- manifestation is found in Noether‘s theorem. Noether’s theorem is one of the most important theorems in physics; showing the relation between the conservation of physical quantities and the action principle. It states that any symmetry transformation that leaves the action of a system invariant, is related to the conservation of a physical quantity (where the physical quantity is also related to the generators of the transformation). So for example, the conservation of momentum is related with invariance under space translations, conservation of energy is related with invariance under time translations, conservation of angular momentum is related with invariance under rotations, etc. In brief, Noether’s theorem shows how in Nature, the laws governing the motion of systems are linked to the conservation of their physical quantities.

The physical world then, seems to be governed by a set of universal and invariable laws. But the laws of physics remains principles; and a principle, by definition, is something that is valid without explanation of why it is so. And here with science, we find a clear example of the difference between knowledge and understanding. We have a great deal of practical knowledge about the physical world: we know its laws, we can sometimes achieve extraordinary degrees of accuracy on our predictions, and we rule and dominate the physical world with technology with sometimes extraordinary degrees of precision and efficiency. Yet, despite all this knowledge, we have little understanding about the physical world. We might know the laws that governs it, but we have no idea of why the physical world behaves as it does.
Practical knowledge (e.g. science) is a study of particulars with a useful purpose (e.g. measurement, prediction, technological applications, etc.). Understanding on the other hand, involves contemplating particulars as part of a universal. In the present, our particulars are the laws of physics and the universal the world’s metaphysics. So far, the laws of physics remain principles without any explanation of why they are so. To understand were the laws of physics comes from, we would have to understand the world’s metaphysics. In the present we are proposing a metaphysics of a monist universe. And physical monism, not only explains why these laws of physics are universal and invariable, but it also allow us to interpret them from the properties of space. Metaphysics then, might not be necessarily practical, but it allows us to form a better idea of why the world behaves as it does.
To begin with, in a monist universe the principles of interest are not three, as in physics, but two: conservation laws and dynamic stability. Minimal variation can be left aside, since minimal variation is related with the motion things in a classical sense, and in a monist universe the classical concept of motion looses its meaning. In a monist universe, the concept of space as a container of object where object move from one place to another, ceases to be valid. Space and objects are one and the same thing. And motion, is not a translation of objects from one place to another, but it’s a displacement of asymmetries in the continuity of Space. The motion of particles then, is a particular case of the dynamics of Space. That is, principles of minimal variation (like action principle) can be reduced to principles of maximal dynamic stability.
In a monist universe, we can interpret conservation laws as a manifestation of the invariability of space. In a unitary space physical quantities cannot be created nor destroyed. They might change indeed form one state to another. But if they do, their change is not arbitrarily but subject to the invariability of space. So the conservation of physical quantities are related to space‘s unitary and invariable qualities as a substance.
Dynamic stability can be interpreted as the dynamics of space itself. Physical space has a geometric, asymmetric and dynamic nature. So we can think of principles of dynamic stability, as the tendency of space to close upon itself towards the states with the lowest geometric differences and variation; that is, towards states with the lowest asymmetry, tension and energy. As a result, systems in Nature tends to evolve towards the states of minimal variation and maximal dynamic stability.
In the classical conception of things, the motion of particles is related to principles of minimal variation (in particular to the action principle). From a monist point of view, minimal variation is related to the dynamics of space. So in a monist universe, the motion of particles is a consequence of the dynamics of space.
An important concept that the action principle introduces, is the notion that the path of a particle is related to the function that characterises it (i.e. Lagrangian). That is, it is impossible to dissociate the particle from space. With the introduction of fields, this concept is taken even further: particles cease to be finite elements in space; instead, we have to think of them in terms of fields in space. But in any case, classical physics still fells short of contemplating the unicity or non duality of particle-space.
In a monist universe, where particles are constituted by a unitary space, the action principle can be contemplated in the following way: the paths that extremises the action of a system can be thought as the paths of maximal dynamic stability. That is, among all the possible paths that the particle can follow, the particle will follow the ones where the asymmetries in space are minimal, and where there is minimal variation of tension and energy. In other words, the motion of particles is confined to path related with states of maximal dynamic stability.
And this would still remain valid in Quantum Mechanics, where there is uncertainty on the path that a particle follows, and where the probability of its path is calculated through a path integral, given by an integral on all its possible paths and weighted by their respective action.

While science is the study of the invariable and universal laws of Nature governing the physical world, physical monism is a theory on the metaphysics of the universe (which can explain why there is only one Nature and its laws are universal and invariable). The current scientific point of view of the universe is not a monist one. And one of the main difference between science and monism, is that while in science Nature seems to be external to elements, in physical monism Nature is immanent to them. For example, in physics, physical elements are normally modelled as passive objects whose behaviour is governed by laws external to them. In a monist universe, physical elements have a dynamic nature since they are constituted by a dynamic space. Their behaviour then, is not governed an external order, but it is immanent to them and given by the behaviour of space itself.

Physical quantities


Physical objects are known to us through their physical properties. The properties of interest in science in particular, are those which can be quantified and measured (physical quantities). It is through properties like mass, energy, charge, angular momentum, magnetic momentum, etc. that we can explain and predict the physical world around us.

Laws of physics, are universal and invariable relations among physical quantities in Nature.

We propose then, that in a monist universe, physical elements are not isolated elements in-themselves, but they are constituted by a unitary space that is common to everything in the universe (see metaphysics). The physical quantities of elements then, are not isolated properties of elements, but they come from the physical nature of space itself(see physics). That is, properties like mass, charge, spin, energy, magnetic or angular momentum, etc. are related to the geometric, asymmetric and dynamic nature of space. Different geometries and asymmetries in space gives elements different physical properties.

In a monist universe, the laws of physics are laws coming from the physical nature of space, and they are universal and invariable because space itself is a unitary and inalterable substance (see laws of physics).

As a qualitative analysis of how tangible physical properties can be related to the nature of a unitary space, we are going to define three generic variables: frequency, tension and extension. We are going to consider these variables as variables in space itself, which are directly related to its nature, and which can also be  related to normal physical properties.

. We can think of frequency as a variable related to the dynamic nature of space. The dynamics of space in turn, is related to the degree of asymmetry in space. So frequency bears a direct relation with the asymmetries in space: the higher the asymmetries, the higher the dynamism in space, and the higher the associated frequencies.
. Extension, can be thought as a variable related to the geometric nature of space, given by the extension of space on its dimensions. The extension of space bears an inverse relation with its asymmetries: the higher the asymmetry between the dimensions, the lower their extension.
. And we can think of tension in space, as a variable related to its asymmetric nature. Tension bears a direct relation with the degree of asymmetry: the higher the asymmetry, the higher its associated energy or tension.

These generic variables serves to illustrate how the physical nature of space can be related to tangible physical properties. For example:
. Frequency is a physical quantity of all particles. All particles, material or not, have an associated frequency related with their wave nature (showing how the dynamic nature of space underlies the dynamics nature of the universe).
. Extension can be related to geometric properties of elements, like spin, charge, magnetic momentum, etc. The geometry of elements determines their function and the way they interact with the surrounding space. For example, the geometric structure of molecules determines their enzymatic properties. The geometric structure of atoms is related to their place in the periodic table and to their chemical properties. And the geometric structure of particles is related to properties like charge, spin, magnetic or angular momentum, colours, flavours, etc., which determines the way they behave in the presence of fields or the way they interact with each other.
. And tension can be related to properties like energy, force, linear momentum, etc.

These generic variables also serve to illustrate how the laws of physics can be thought as relations in a unitary space. For example:
. The frequency of particles is directly related with their energy; which is compatible with the idea that higher frequencies in space are related with higher tension.
. Charged particles are subjected to forces in the presence of fields; which is compatible with the idea that interacting geometries in space can create variations in the asymmetries and tensions in space.

neural complexity


The following is an example of neural complexity from the book Consciousness by G. Edelman and G. Tononi.

“As an illustration, it is useful to calculate complexity for three extreme examples of the organization of a cerebral cortical area corresponding to an old, diseased brain; a young, immature brain; and a normal adult brain (the simulated examples are actually based on the primary visual cortex of the cat). The simulated cortical area contained 512 neuronal groups, each of which responded preferentially to a given position in the visual field and to a given stimulus orientation.10 The simulated cortical area was based on a detailed model that was used to investigate how the brain can give rise to the so-called Gestalt properties of visual perception—the way stimuli are grouped to form objects and are segregated from the background.” For the present purposes, we required that the simulated cortical area was isolated; it did not receive any visual input, and its neurons were “spontaneously” active.12
The first example in figure 11.3 (top row) represents a cortical area in which the density of intra-areal connections among different groups of neurons had been deliberately reduced (for example, in an old and deteriorated brain). In such a cortical area, individual groups of neurons are still active, but, because of the loss of intra-areal connections, they fire more or less independently. Such a system behaves essentially like a “neural gas” or, if examined on a computer monitor, like a TV set that is not properly tuned. The electroencephalogram of such a cortical area shows the absence of synchronization among its constituent neuronal groups.13 The entropy of the system is high because of the large number of elements and their high individual variance: The system can take a large number of states. From the point of view of an external observer or homunculus who might assign a different meaning to each state of the system, this system would indeed appear to contain a large amount of information. But what about information from the point of view of the system itself—the number of states that make a difference to the system itself? Since there is little interaction between any subset of elements and the rest of the system, whatever the state of that subset might be, there is little or no effect on the rest of the system, or vice versa. The value of the mutual information is correspondingly low, and since this holds true for every possible subset, the complexity of the system is also low. In other words, although there are many differences within the system, they make no difference to it. Such a neural system is certainly noisy, but it is not differentiated. The second example is of an immature, young cortex, in which every neuronal group is connected to all other neuronal groups in a uniform way (see figure 11.3, bottom row). In the simulations, all groups of neurons soon started oscillating together coherently almost without exception. The calculated EEG is hypersynchronous, resembling the high-voltage waves of slow-wave sleep or of generalized epilepsy. The system is highly integrated, but functional specialization is completely lost. Since the system can take up only a limited number of states, its entropy is low. The average mutual information between individual elements and the rest of the system is higher than in the previous case, since there are strong interactions. However, when larger and larger subsets are taken into consideration, the mutual information does not increase significantly because the number of different states that can be discriminated does not increase with the size of the subsets. The complexity of the system is correspondingly low. In other words, because there are few differences within the system, the difference they make to the system is small. The system is integrated but not differentiated.
In the third example, corresponding to a normal, adult cortex (see figure 11.3, middle row), groups of neurons are connected to each other according to the following rules. First, groups of neurons having similar visual orientation preferences tend to be more connected to each other. Second, they are connected so that the strength of the connections decreases with topographic distance. These rules of connectivity closely correspond to those found experimentally in the primary visual cortex.14 In this example, the dynamic behaviour of the system is far more complex than in the previous two: Groups of neurons show both an overall coherent behaviour yet group and regroup themselves dynamically according to their specific functional interactions. For example, neighbouring groups of similar orientation preference tend to fire synchronously more often than functionally unrelated groups, but at times, almost the entire cortical area may show short periods of coherent oscillations, as reflected by a calculated EEG that resembles that of waking or REM sleep. The entropy of the system is high, but not as high as in the first example (although the system can have a large number of states, some are more likely than others). The mutual information between individual elements and the rest of the system is, on average, high, reflecting significant interactions, just as in the second example. In contrast to the second example, however, the average mutual information increases considerably when we take into account subsets composed of a larger number of elements. Thus, the overall complexity is high because, in such a system, the larger the subset, the larger the number of different states that the subset can bring about in the rest of the system, and vice versa. In other words, there are many differences, and they make a lot of difference to the system. The system is both integrated and highly differentiated.”


FIGURE 1 1.3 HOW COMPLEXITY VARIES, DEPENDING ON NEUROANATOMICAL ORGANIZATION. Complexity values were obtained from simulations of a primary visual cortical area. The figure shows three cases. In the first case (upper row), the simulated cortical area has sparse connectivity (first column: Anatomy). Neuronal groups fire almost independently (second column: Activity): the 30 small squares within the rectangle indicate the pattern of firing every 2 milliseconds (from left to right and from top to bottom) of 512 neuronal groups that are spontaneously active. The third column represents the EEG, which is essentially flat, indicating that the neuronal groups are not synchronized. Complexity (the area under the curve in the fourth column) is low. In the third case (lower row), the simulated cortical area has random connectivity. Neuronal groups are completely synchronized and oscillate together. The EEG shows hyper-synchronous activity reminiscent of slow-wave sleep, epileptic seizures, or anesthesia. Complexity is low. In the second case (middle row), the simulated cortical area has a patchy connectivity that corresponds to the one found in the cortex. Neuronal groups display continually changing integrated activity patterns. The EEG shows that synchronization waxes and wanes and that different groups of neurons synchronize at different times. Complexity is high.