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The Mysteries of the Fundamental Physical Dimensions
Jan 1, 2013

“The most beautiful system [the universe] could only proceed from the dominion of an intelligent and powerful Being.” (Isaac Newton)

The Newtonian physics, quantum mechanics, and the theory of relativity took the modern community to the boundary of the two realms of physical and metaphysical existence. Nevertheless, the nature of the fundamental physical dimensions still remains an open question resting on the related areas of science

The fundamental concepts of Newtonian physics are Time, Length, Mass, and Electric Charge by means of which all the other classical physical quantities such as velocity, force, momentum, energy, current, electric field, magnetic flux, etc. can be derived and expressed as their combinations. Classical physics stands on the assumption that material, having two basic intrinsic properties of mass and charge, and immaterial phenomena are all contained in an absolute space and an ever-flowing absolute time. These four physical dimensions, without asking the nature of them, provide a practical framework for a description of the gravitational and electromagnetic forces and thus a description of the physical world and an interpretation of the events occurring in it up to a certain degree. However, the Newtonian picture of the universe is neither adequate for a deeper understanding of the corporeal reality nor appropriate for linking that reality to the ones possessing higher degrees of the Universal Existence.

Starting from late 19th and early 20th centuries, the Newtonian picture of the world has been changed due to two revolutionary theories, which have been proved both experimentally and theoretically that they are superior to and not compatible with the classical descriptions and assumptions. They are the relativity theory and the quantum mechanics. In physics, a field is a physical quantity associated with each point of Space-Time. For example, the Newtonian gravitational field is a vector field specifying its value at a point in Space-Time, which requires three numbers, the components of the gravitational field vector at that point. Quantum field theory constructing quantum mechanical models of systems classically parameterized by an indefinitely big number of degrees of freedom, namely fields, is the natural and quantitative language of particle physics. The current set of fundamental fields and their dynamics are summarized in a theory called the Standard Model. All particles and their interactions observed to date can be described almost entirely by the Standard Model although most particle physicists believe that it is an incomplete description of nature, and that a more fundamental theory, the Theory of Everything, awaits discovery. Figure 1 represents an overview of the various families of elementary and composite particles, and the theories describing their interactions.

The relativistic quantum field theory of the subatomic world does not only include the strong and weak nuclear forces in addition to the electromagnetic and gravitational interactions of the classical picture, but also provokes some ideas about the nature of the fundamental concepts of the classical physics. Symmetry of a physical system is a physical or mathematical feature of the system that is preserved under some change. The Standard Model says, for instance, that the electric charge is the generator of the U(1) symmetry of electromagnetism. U(1), the unitary group of rank 1, is the simplest internal symmetry group of the Standard Model. It can be visualized as the rotational symmetry of a circle about a perpendicular axis passing through the center of the circle. It represents a continuous symmetry because a circle can be rotated by an angle and remains unchanged. It is an internal symmetry since this circle does not lie in the physical space but in the complex plane of mathematics. More abstractly and more generally, a charge is any generator of a continuous symmetry of the physical system under study. When a physical system has a symmetry of some sort, Noether’s theorem implies the existence of a conserved current. The thing that flows in the current is the charge; the charge is the generator of the symmetry group. This converts our classical concrete idea of electric charge into a mathematical abstraction. Conservation of energy and conservations of linear and angular momenta are nothing but the applications of Noether’s theorem to the translational symmetry in time and translational and rotational symmetries in space, respectively.

Classically, which is equivalent to macroscopically, mass is associated with matter and can be defined as a quantitative measure of an object’s resistance to the change of its speed. But in the Standard Model of the subatomic scale, the mass of the elementary particles are explained by the Higgs mechanism which refers specifically to the generation of masses for the W and Z bosons through electroweak symmetry breaking. The Large Hadron Collider at CERN is currently searching for Higgs bosons, and attempting to understand the electroweak Higgs mechanism. The Higgs mechanism is the process that gives mass to elementary particles. In 1905, Einstein proposed mass-energy equivalence (E=mc2) in his paper entitled “Does the inertia of a body depend upon its energy-content?” In relativity, all of the energy that moves with an object (that is, all the energy which is present in the object’s rest frame) contributes to the total mass of the body, which measures how much it resists acceleration.

When we come to the remaining two fundamental concepts of Newtonian physics, we see that Time and Length, which we know instinctively, are no exceptions. The modern physics challenges our classical understandings of them too. Relativity theory argues that Time and Space are of equal ontological status; the reality is the 4-dimensional unity of Space-Time. Physics could no longer be understood as Space by itself, and Time by itself. It also states that simultaneity is relative, so there is no objective way to define a “Now” that would be the same for all states of motion which substantially affects the idea of causality. In addition, this Space-Time is not flat but rather curved due to the material and energy contained in it and not static but dynamic. Time and Space are neither uniform nor absolute.

The missing part of the so-called Theory of Everything is the quantum gravity, which attempts to develop scientific models that unify quantum mechanics describing three of the four known fundamental interactions with general relativity describing the fourth, gravity. The following quotation is from one of the leading quantum gravity researcher, Carlo Rovelli, stated in 1997:

“I believe that we are going through a period of profound confusion, in which we lack a general coherent picture of the physical world capable of embracing what or at least most of what, we have learned about it. The fundamental scientific view of the world of the present time is characterized by an astonishing amount of perplexity, and disagreement, about what time, space, matter, and causality are. But if a new synthesis is to be reached, I believe that philosophical thinking will be once more one of its ingredients. Due to the vastness of the problem involved, the generality and accuracy of philosophical thinking and its capacity to clarify conceptual premises are probably necessary to help physics out of a situation in which we have learned so much about the world, but no longer know what matter, time, space, and causality are.“

Lee Smolin, another theoretical physicist named as #21 on Foreign Policy Magazine’s 2008 list of Top 100 Public Intellectuals, stated the following in 2001:

“Atoms do fall, so the relationship between gravity and the quantum is not a problem for nature. If it is a problem for us, it must be because somewhere in our thinking there is at least one, and possibly several, wrong assumptions. At the very least, these assumptions involve our concept of space and time and the connection between the observer and the observed.”

It is true that quantum mechanics and the theory of relativity were born and are growing in the nontraditional atmosphere of the scientific enterprise. Thus, they can be considered as sharing the reductionist character of the Newtonian physics by having no direct reference to the hierarchy of physical and metaphysical existence. Nevertheless, we consider them as an improvement since they took the modern scientific community to the boundary of the two realms, by asking the old question of ancients about the nature of the fundamental physical dimensions. The mystery of them is still an open question resting, we believe, on the related areas of science and metaphysics.