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.

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