Assuming First Principles

Physics is rooted in empirical observation, but inherently it must rely on certain ontological principles as a precondition to ground it. Physics is unable to provide its own foundation and must look to metaphysics. All physical theories inevitably rest upon these metaphysical foundations as the fundamental assumptions about the nature of existence. However, they are often left implicit and unexamined. The purpose of this work is to make these foundational assumptions explicit. 

If it does not, it will simply begin, having assumed these metaphysical principles.

This is particularly evident in quantum mechanics, where empirical results are interpreted with multiple metaphysical frameworks. This leads to moving beyond empirical facts to establishing ontological statements without real grounding. eg. “a particle has superposition”

Starting with fundamental ontological commitments is not a philosophical luxury but a scientific necessity. Without these principles, we risk losing the ability to distinguish between different aspects of reality, thereby compromising the intelligibility of our scientific discourse. These principles are more than just axioms; they are essential for ensuring any discourse, scientific or philosophical, can meaningfully engage with the nature of reality.

Goals

We will demonstrate that the physical phenomena we experience, particularly the core structures described by Relativity and Quantum Mechanics, are not arbitrary discoveries but rather the direct and necessary consequences of these unavoidable first principles.

This approach aims to achieve several critical goals:

1. To reveal precisely where ontology (the study of being and existence) ends and physics begins.
2. To explain why quantum mechanics must necessarily turn to the language of probability when probing reality beyond the constraints imposed by fundamental discreteness (i.e., beyond the Planck scale).
3. Crucially, the primary aim of this relational approach is not merely to provide an alternative description of physical reality but to solve a fundamental problem: the inherent tension between the discrete descriptions mandated by quantum theory and the continuous descriptions inherent in relativistic spacetime.

By rooting the theory in absolute metaphysical first principles, the approach tackles a different, more fundamental issue than standard physical theories—namely, identifying and making explicit the underlying assumptions that any viable physical theory must build upon. This is not intended as a rehash of existing physical methods or interpretations, but rather as a clear attempt to solve the central paradoxes of modern physics by reframing their deepest foundations. We posit that understanding these necessary metaphysical preconditions reveals why the universe possesses the specific structures (like c and ħ) that it does.

Methodological Commitment: We do not begin with appeals to empirical evidence, but with what cannot be rationally denied. We will start with only the most basic ontological commitments as this necessary foundation.

First Principles

Metaphysical Foundations

Fundamental Principles

Identity: Each entity is itself  ( A = A ). 

Difference: Each entity is not another ( A ≠ B ).

Relation: Entities can stand in relation to one another ( R ( A, B ) ).

Causality:This describes that one entity can influence another through their relationship. This involves real patterns of changes, where the actualization of one entity depends on another. ( A → B )

Noncontradiction (PNC): An entity cannot simultaneously be and not be in the same respect, at the same time (A cannot be both A and not-A). It also establishes that contradictory states cannot coexist in the same entity. Ontologically, this principle preserves the coherence of entities and the integrity of identity in reality. It establishes the most fundamental logical and ontological opposition (Being vs. Non-being, Is vs. Is Not), which is the absolute bedrock for any possible distinction or intelligibility.
( ¬( p ∧ ¬p ) )

Derived First Principles

Distinction: Identity and difference provide the foundation for distinction, which is the boundary between entities. Discrete identity allows entities to be distinguished from each other, creating ontological boundaries necessary for their existence as unique entities. Distinction fundamentally arises from negation (is vs. is not).

Emergent Properties: This ontology posits the real ontological status of relationships and the emergent properties of relationships and collections of relationships. Entities, relationships, and properties are all real, but not reducible to the same.

Unity in Multiplicity: Many entities form coherent relational connections.

Causal Precedence: The ordering of influence between entities. This is a primitive feature of relations between causal events, not derived from physical laws.

Causal Capacity: The ability to affect and be affected. Ground causality in primitive relational influence rather than in physical laws. We avoid defining causation through the very laws we’re trying to derive.

Irrefutability

First principles cannot be proven, otherwise they would not be first principles. However, we also do not need to accept these axioms blindly. We can demonstrate their necessity.

First, if we do not posit the truth of these principles, then reality, knowledge, science, and math break down into incomprehension and irreality. Physics can pretend to accept a different set of metaphysical presuppositions, but in practice it must accept a minimum of realist principles (Identity, difference, relation, noncontradiction, and causality) for any empirical science to even be possible.

Second, these premises are particularly certain, since they are inherent in human thought and communication. We cannot interact with the world, think, or communicate without implicitly validating them. So, one cannot coherently argue against them without first assuming them as the very basis for what they seek to disprove. This can be shown ontologically and as a principle of thought by our use of language.

For example, even the mundane act of going home from work ontologically demonstrates these principles. The office exists (Identity) and it is not home (Difference). There is a real spatial relation between these locations (Relation). The car’s motion causes your position to change (Causality). And fundamentally, being at home and not being at home are not the same thing (Noncontradiction). Even going home necessarily requires these ontological principles as an inescapable feature of physical reality.

Second, even stating they must be tentative proves the point. To say these principles are “tentative” requires we distinguish them from other statements (Identify & Difference). It requires the relationship between this statement and other potential truths (Relation). It assumes a cause for such tentativeness (Causality). Using the term “tentative” must demarcate what is provisional and what is firmly established (Distinction). And this only matters if the principles cannot be both tentative and non-tentative in the same way at the same time (Noncontradiction).

So clearly, without at least this minimum collection of principles we cannot distinguish reality, speak of anything meaningful, or do physics at all. These ontological principles are not merely axiomatic, but indispensable for any coherent discourse, intelligibility, or reality. These are not empirical findings derived from the physical world; rather, they are the preconditions for any possible physical world that can be coherently conceived or described.

Realism and Quantum Mechanics

Quantum mechanics presents apparent challenges to traditional metaphysical principles, but closer examination reveals these principles remain intact at a fundamental level.

Identity: Quantum superposition seems to describe particles existing in multiple states simultaneously until measurement. However, this wouldn’t negate identity. The very concept of a “particle” in superposition presupposes an entity with a coherent identity. There must be something capable of existing in this complex state. Rather than abandoning identity, some quantum mechanics theories would assert an identity that can encompass potentiality and actuality simultaneously. 

Difference: Quantum entanglement can be interpreted as particles exhibiting instantaneously correlated states across distances. Even if there is strong interconnectedness, this still requires distinct entities to be entangled. The phenomenon doesn’t erase difference, because entanglement experiments presuppose our ability to distinguish between entangled pairs.

Causality: The probabilistic nature of quantum mechanics challenges a fully deterministic causality, but not causality itself. Quantum events follow probabilistic patterns governed by precise mathematical laws. The wave function evolves causally according to the Schrödinger equation until measurement. Quantum mechanics does not show the absence of causality, but a more nuanced understanding of it.

Noncontradiction: Concepts like wave-particle duality may appear to violate noncontradiction, but this misunderstands both the principle and quantum phenomena. Electrons aren’t simultaneously waves and particles in the same respect. They exhibit wave-like or particle-like properties depending on the experimental context. The principle of noncontradiction remains intact. Even if they could be a wave-particle, that would assert noncontradiction saying it is that and not something else. 

These principles remain foundational even in quantum mechanics—not as empirical discoveries but as necessary conditions for the intelligibility of quantum phenomena themselves.

Ontological Categories

Our framework begins with entities that possess primary ontological status. They establish relations with other entities while maintaining an identity that persists independent of reference frames. Relations between these entities have secondary ontological status. They are real but cannot exist independently of the entities they connect. Properties, which characterize either entities or relations, have tertiary ontological status. They are real but entirely dependent on what they characterize.

This ontological hierarchy provides the foundation for understanding how seemingly absolute concepts like space and time emerge from the complex interplay of relations between entities, while still maintaining that something real exists independent of how it is observed or related to.

Overview – Moderate Relational Realism

Ontological Plurality: Entities, relations, and properties all have an ontological status as real.

Ontological Distinction: Entities, relations, and properties are ontologically different

Non-Reductive Approach: Entities, relations, and properties are not reduced to each other.

Entities

Entities possess primary ontological status as foundational beings. An entity can be thought of as a substance that exists in itself, not in another or between others. Entities serve as the basis for identity and the capacity for entering into relations, providing the ontological anchor for all further categories.

Core Features:

• Identity Persistence: Entities maintain a stable identity that is independent of any particular reference frame or relations. This persistence allows entities to endure through changes without losing their core nature.
• Causal Agency: Entities can be both sources and recipients of causal influence.
• Capacity for Relation: While entities exist in themselves, they are not isolated. They have the potential to enter into relations with other entities.
• Irreducibility: An entity is not reducible to the sum of its relations or properties. An entity retains primacy even as its features and connections change.

Examples: Human beings, chairs, atoms, and other macroscopic objects. The ontological status of spacetime, subatomic particles (photons, bosons, etc), and fields is not assumed at this point.

Relations

Relations have secondary, dependent ontological status. A relation is real, but exists between two or more entities. While relations do not exist independently, they are not mere conceptual constructs. They are ontologically real and exert significant influence on the structure of reality.

Key Characteristics:

• Ontological Dependence: Relations cannot exist except in virtue of the entities they connect. Without corresponding entities, a relation has no persistence.
• Distinctness: Every relation is ontologically distinct from the entities it connects and their properties. A relation is not an entity, nor is it reducible to a property.
• Foundational for Structure: Relations ground key structural and organizational features of reality, such as ordering, comparison, difference, and connectivity that cannot be reduced solely to the intrinsic nature of entities.
• Frame-Dependence: A relation may vary with reference frame and is not absolute or frame-invariant.
• Precondition for Causality: Although relations do not “cause” anything by themselves, they are necessary for causal events and interactions to occur.

Examples: The spatial position between two objects, the cause for an effect, a change of position over time.

Properties

Properties possess tertiary ontological status as features that characterize either entities or relations. Properties are real, but their existence is entirely dependent—properties do not exist in isolation but always as aspects or features of some underlying entity or relation.

Types and Features:

• Classification: Properties may be intrinsic (inhering directly in a substance, such as mass or charge), dispositional (reflecting tendencies or capacities, such as reactivity or fragility), or relational (arising out of multiple interactions, such as velocity, energy, or distance).
• Dependence: Intrinsic properties “inhere in” an entity; extrinsic or relational properties depend on a specific relational context. All properties, including those ascribed to relations, are ultimately dependent on entities and/or their interactions.
• Measurability: Physical science accesses and measures properties (such as length, duration, temperature, or velocity) always through comparisons or ratios—no property is meaningful independently of a relevant standard or relational framework.
• Stability and Variability: Some properties endure through changes (as with essential or proper accidents), while others arise or vanish with shifts in relational configuration (such as force, energy transfers, or spatial arrangement).

Key Note: In modern physics, properties such as position, momentum, and energy—once classified as simple accidents of substance—are better understood as relational properties, instantiated only through specific interactions.

Examples: Mass, charge, velocity, electric charge

Moderate Relational Realism – A Middle Ground

Some physicists do not take relativity to its full metaphysical conclusion. They hold an epistemological relativity, and admit that all measurement is frame-dependent. But they quietly assume that physical reality itself is somehow unaffected. Velocity is a real property of an object independent of a frame of reference.

On the other extreme, some may push relativity and quantum mechanics to another limit and claim that only relations exist. There are no real entities, only webs of interaction. In both cases, the reality of what actually exists is lost. Pure relationalism fails to account for the persistence and identity of the entities that relations presuppose.

Our position is moderate relational realism. We fully accept that all measurable properties (mass, motion, energy, distance, energy) are fundamentally relational. They exist only through the interplay between entities and a frame of reference. However, these properties are always properties of real relationships and real entities. Relations require something to exist between and cannot exist on their own. Reality is not dissolved into pure relation, nor is it untouched by the frame-dependence that modern physics reveals. Our ontology preserves both: without real entities, there is no reality, and without real relations, there is no physics.

Math

The extraordinary success of mathematics in physics arises not because nature “is mathematics,” but because the regularities and structures present in reality can be faithfully captured through mathematical abstraction. Mathematics, properly used, allows us to predict, analyze, and uncover relational structures across physical systems.

Mathematics is an abstraction, which does not have independent existence. It is a rigorously structured language created by reason to describe, model, and quantify the real features, patterns, and relations within the world.

Thus, mathematics is indispensable for science and description, but always as an abstraction rooted in reality, not the substance of reality itself.

Emergence of Physical Laws

Physical laws are not mysterious rules stamped onto reality from outside. Rather, laws are descriptions of the consistent patterns and regularities that emerge from the relationships among real entities. What we call a “law of nature” is our best mathematical and conceptual summary of how entities interact and how their properties change in relation to one another.

This approach stands in contrast to views that imagine physical laws as pre-existing frameworks into which reality fits. Instead, we propose that every genuine law of physics emerges from and can’t not exist without the concrete reality of entities and the relationships between them.

Philosophical Implications

This hierarchical view of ontological realness:

1. Avoids both extremes: Neither reducing everything to relations (extreme relationalism) nor treating all properties as intrinsic (naive realism)
2. Explains persistence and change: Accounts for how things can both change (in their relations and properties) and persist (in their fundamental identity)
3. Grounds physical laws: Physical laws describe patterns in how ontologically real entities relate to each other, giving laws an ontological basis without making them absolute
4. Supports scientific realism: Maintains that science studies something real while acknowledging the relational nature of scientific knowledge
5. Clarifies emergence: Provides a framework for understanding how higher-level properties can emerge from relations between entities

This approach gives our relational physics a solid metaphysical foundation that respects both the insights of traditional metaphysics and the discoveries of modern physics.

Measurements

Measurement is inherently relational and comparative, never absolute. When we measure any physical quantity, we are not accessing some intrinsic, absolute value, but rather establishing a relationship between the measured property and another property chosen as a reference standard. This comparative nature is not a practical limitation but reflects a deeper epistemological principle: knowledge of physical properties is fundamentally relational.

All measurements resolve to ratios between properties. We do not measure spatial position in any absolute sense; rather, we determine distance as a proportion of some standard unit (meter, light-year, etc.). Similarly, we do not measure time directly, but compare durations against reference intervals. Even seemingly intrinsic properties like mass or charge are known only through their relational effects and measured by comparison to established standards.

Ontological and Epistemological Constraints

Our epistemological framework is bounded by our ontological commitments, creating a hierarchical relationship:

Ontology → Epistemology → Formalism

The direction of explanation flows from what exists (ontology) to how we can know it (epistemology) to how we can represent it (formalism). While epistemological limitations and formal structures can place practical constraints on our theories, they cannot override fundamental ontological commitments.

For instance, our ontological commitment to entities with relational capacities necessitates an epistemology based on signal exchange and interaction. This, in turn, requires transformation rules (such as Lorentz transformations) that preserve relational consistency across different frames of reference. The mathematical formalism emerges as a consequence of these more fundamental commitments, not as their foundation.