The universe presents itself as very characteristic environment, governed by explicit laws and definitive classes of forces and matter. At first these characteristics seem quite arbitrary (gold weighs roughly twice as much as silver), but throughout the 20th century, we confirmed that the characteristics of the universe were virtue of more fundamental particles that made up matter. Gold and silver, for example, are made up of elementary atoms. After the atom came the elementary sub-atomic particle in the early 20th century and then elementary quarks in the mid-20th century. But discovering an elementary particle only to break it apart further becomes yet another paradoxical infinite regression; if quarks are elementary, what are quarks made of?
As physicists are studying the subatomic world, a world they will never be able to touch or see, they must represent it with abstract mathematical models. Having no direct observation, various interpretations attempt to unify the mathematics. This leads to speculative theories of the true nature of these particles. For example, what exactly is an electron? Is it a little round marble flying around space? As per the double-slit experiments and consequent wave-particle duality, the humble electron is an enigma that defies all intuition. Some theories have become very successful at modelling the universe, albeit incomplete.
Quantum Field Theory (QFT) models the universe as a set of permeating fields that conduct distinct mediums within which elementary particles can exist. Each elementary particle is therefore a quantized, discrete disturbance of its corresponding field. Electrons are quantized disturbances in the electron field, while photons are quantized disturbances of the electromagnetic field.
Based on the Standard Model, a “work-in-progress” catalog of discovered particles, there are various fields with varying levels of interaction, all characteristic in their own way. Their properties range from the energy potential of their quanta, to the ways in which they can interact with each other. For example, the electron field when changing energy states can trigger a photon from having disturbed the electromagnetic field, thus a light bulb can emit light.
When any particle is proclaimed to be elementary, it begs the question as to whether it really is indivisible and fundamental. For example, when learning of QFT, it is natural for a lay person to ask the obvious question: what are fields made of? We might visualise a quantum field as an ether-like proto-substance that permeates the universe, or we might think of them as mathematical models of something inexplicable, closely tied into the very fabric of reality. In either case, or in any case, no explanation is sufficient to explain them because the way they interact must be defined by something more transcendant.
Whether quantum fields are truly fundamental or not brings to scrutiny the very notion of an elementary particle or substance. The nature of a fundamental particle must be that it is an indivisible, raw existence, not composite of anything more elementary. If the universe is made up of multiple distinct fundamentals (such as the various fields in QFT), this would imply a defining property or characteristic that would make them distinct from each other, however such characterics must arise from some underlying building block to give it such properties. For example, gold has the property of a greater mass than silver virtue of the quantity of its more fundamental building blocks: electrons, protons, and neutrons. Building blocks do not necessarily require a physical substance to define it. For example, a screwdriver’s orientation relative to its screw will determine if it can lock in with the head of the screw, just as the spin of the electron is governed by an inexplicable dimension. Even such intrinsic properties require that something more fundamental is able to define such a property. Even something as humble as orientation requires the deep implications of spatial dimensions to give rise to it.
Thus, the idea of a “Theory of Everything” in classic scientific terms is an impossible goal, for the theory requires a “Theory of the Theory of Everything” to give rise to it. Each degree of being fundamental requires something more fundamental to define it’s characteristics.
Reducing the Paradox of a Fundamental
The Paradox of a Fundamental is logically the same as the First-mover Paradox only it could be considered a vertical infinite regression of properties. The First-mover Paradox simply points out the infinite regression of cause and effect, especially in regards to the procession of events over time. The Paradox of a Fundamental however, uses the infinite regression of any theoretical fundamental particle requiring a more fundamental particle to exist, thus the paradox. This also ties in with the Paradox of Assymetry, which can be reduced to the fact that the universe has properties (spacial, quantative, and qualitive), thus cannot be the product of any fundamental proto-substance. Thats for another article.