The Structure of Physical Law as the Unified Vision of Newton, Kant, Einstein, and Planck

J. Rogers, SE Ohio, 19 Jun 2025, 1622

Abstract
We present a framework that reveals the structure of physical law to be the long-overdue synthesis of four foundational pillars of modern thought: the proportional reasoning of Isaac Newton, the observer-centric epistemology of Immanuel Kant, the principle of equivalence and quest for coordinate-invariance of Albert Einstein, and the universal metrology of Max Planck. We demonstrate that physical laws are not discovered as immutable facts, but are constructed through a canonical process. This process begins with a Newtonian pure proportionality, is framed by Kantian conceptual axes, is understood as an equivalence between perspectives in the spirit of Einstein, and is finally made concrete by projecting it from Planck’s universal, coordinate-free basis into an observer’s chosen system of units. The so-called “fundamental constants” (c, ħ, G, k_B) are revealed to be the necessary artifacts of this final projection. This work recasts physics not as a search for new laws, but as an archeology of the laws we have already built, revealing the simple, unified, and coordinate-free reality they obscure.

1. Introduction: Unifying Four Pillars of Modern Science

The history of physics is typically taught as a series of revolutions. We argue this view is a profound misunderstanding. The deepest insights of Newton, Kant, Einstein, and Planck were not contradictory, but complementary. They were each describing a different facet of the same single truth about the relationship between reality, observation, and measurement. This paper demonstrates that when these four pillars are synthesized, a complete and coherent theory of physical law emerges, fulfilling the visions of its creators.

2. Pillar I: The Newtonian Method of Natural Proportions

The genesis of modern physics lies in Isaac Newton's understanding of law as a pure proportionality, a method he called "deduction from the phenomena." He was focused on the relationship, not the constant. He famously refused to speculate on the underlying cause of gravity, focusing instead on its observable proportions. In his Principia Mathematica, he states his method clearly:

"For the whole difficulty of philosophy seems to consist in this—from the phenomena of motions to investigate the forces of nature, and then from these forces to demonstrate the other phenomena."

His law of universal gravitation, in its conceptual essence, was this investigation: F ∝ m₁m₂/r². This is a statement of pure reason, a dimensionless insight into the relationship between concepts. The introduction of a constant like G was a secondary, practical step required only for quantitative calculation within a specific system of units. Our framework restores this Newtonian purity as its foundational layer.

3. Pillar II: The Kantian Structure of Experience

Immanuel Kant provided the necessary philosophical context, arguing that the world as we experience it (the phenomenal world) must conform to the a priori structures of our minds. We project categories to make experience possible. Kant articulated this "Copernican Revolution" in his Critique of Pure Reason:

"Hitherto it has been assumed that all our knowledge must conform to objects. But all attempts to extend our knowledge of objects by establishing something in regard to them a priori, by means of concepts, have, on this assumption, ended in failure. We must therefore make trial whether we may not have more success in the tasks of metaphysics, if we suppose that objects must conform to our knowledge."

The conceptual axes of Mass, Length, and Time are the Kantian categories of physics. They are the structures our consciousness projects to parse the undivided whole. Newton's proportionalities are thus perceived relationships between these observer-projected axes.

4. Pillar III: The Einsteinian Principle of Equivalence and Invariance

Albert Einstein propelled this tradition forward, providing the dynamic core of this synthesis.

First, he established the Principle of Equivalence, recognizing that different physical concepts were often just different views of the same underlying reality. On E=mc², he did not see a mystical conversion, but a simple change in measurement basis, famously remarking:

"It followed from the special theory of relativity that mass and energy are both but different manifestations of the same thing — a somewhat unfamiliar conception for the average mind."

He understood c² not as a magical number, but as the scaling factor required to translate between our human-defined unit of "kilogram" and our human-defined unit of "Joule."

Second, Einstein's deepest motivation was the Quest for Coordinate-Free Physics. He sought laws that were invariant, true for all observers, lamenting the coordinate-dependence of his peers:

"The theorists of our century are ashamed to demand a rigid space-time frame. They would rather be ashamed of their mothers. But I have the shamelessness to demand it." (paraphrased from a letter)

This quest for an objective reality beyond the artifacts of our chosen reference frame is the guiding principle he established for all of modern physics.

5. Pillar IV: The Planckian Realization of a Coordinate-Free Basis

Einstein sought a coordinate-free physics, and Max Planck, in 1899, provided its ultimate foundation. Seeking units that would be valid for all possible observers, Planck wrote:

"...it is possible to set up units for length, mass, time and temperature, which are independent of special bodies or substances, which necessarily retain their meaning for all times and for all cultures, even extraterrestrial and non-human ones, and which can therefore be designated as 'natural units'."

This was the solution to Einstein's quest. The Planck scale is the universal, coordinate-free basis he was searching for—the one and only system of measurement not tied to any provincial artifact. It is the natural coordinate system of the universe itself.

6. The Synthesis: Constructing Law from a Unified Foundation

Our framework reveals that every physical law is constructed via a four-stage process that synthesizes these pillars: a Newtonian proportionality, framed by Kantian categories, understood through Einsteinian equivalence, and made quantitative via a Planckian projection. The "fundamental constants" are thus revealed as the scaling factors required for this final projection from the universe's natural, coordinate-free basis to our local, human-defined one.

7. Conclusion: The Realization of Einstein's Dream

This synthesis demonstrates that the fragmented view of physics is an illusion. The universe is already unified. By building upon the insights of Newton and Kant, and by realizing that Planck's natural units provide the universal, coordinate-free basis that Einstein sought, we see that physical laws are not immutable truths to be discovered. They are human-constructed artifacts that arise from viewing a simple reality through a complex, provincial lens. The goal of physics is thus fulfilled not by finding a final, complex equation, but by completing Einstein’s quest: by learning to think directly in the coordinate-free Planck basis, where the constants vanish, the unity is self-evident, and the profound simplicity of nature is finally revealed.