Physics Writ Small: Towards a Neo‑Classical Interpretation of Quantum Phenomena

J. Rogers, SE Ohio, 19 Apr 2025 1706
Abstract
This paper proposes a “Neo‑Classical” re-interpretation of physics at its smallest scales, asserting that observed “quantum” phenomena are direct consequences of fundamental reality (Layer 1/2) existing as packets possessing inherent wave properties, and exhibiting simple, fixed scaling proportionalities between their perceived facets (Mass, Frequency, Temperature, Energy, etc.). Concepts such as the Uncertainty Principle and quantized states are explained purely through the lens of classical wave mechanics principles—Fourier relationships and resonance under boundary conditions—applied to this packetized reality. Planck’s constant $h$ is identified as a pure unit scaling factor between human-defined measurement scales (Layer 3), such as Joules and Hertz, quantifying the simple Layer 1/2 equivalence $E = f$ in those units. It holds no intrinsic “quantum” significance; its numerical value is solely an artifact of our arbitrary unit choices. Similarly, constants like $\hbar = h/2\pi$ are simply alternative Layer 3 scaling factors based on mathematical conventions. Concepts like Energy are re-framed as Layer 4 descriptors of relationships and dynamics, not fundamental Layer 1/2 entities. This Neo‑Classical view simplifies physics writ small, attributing phenomena to the inherent nature and scaling of the packetized, wavelike stuff, rather than mysterious properties introduced by specific constants, offering a clearer path for fundamental inquiry.

---

1. Introduction: The Conceptual Puzzle of Quantum Mechanics

Quantum Mechanics (QM) stands as one of the most successful scientific theories, accurately describing the behavior of particles and fields at microscopic scales. However, its conceptual foundations often remain deeply counter-intuitive, marked by paradoxes such as wave-particle duality, intrinsic uncertainty, non-locality, and seemingly arbitrary quantized properties. These phenomena are commonly attributed to a fundamental “quantumness” embodied by Planck’s constant $h$, often presented as a “quantum of action” that dictates the discrete, probabilistic nature of the universe at its smallest scales.

While mathematically successful, this interpretation breeds mysteries: Why does $h$ have its specific value? How do continuous classical phenomena emerge from a fundamentally discrete quantum reality? What is the true nature of a particle that is also a wave?

This paper proposes a “Neo‑Classical” interpretation of physics writ small. It synthesizes elements traditionally associated with classical physics (specifically, wave dynamics and relational thinking) with a core non-classical premise (the fundamental existence of reality as packets). We argue that many of the conceptual puzzles of QM arise from misinterpreting the role of descriptive tools (units, constants, derived concepts) and applying a classical point-particle intuition where a wave-packet understanding is required. By clarifying the layers of scientific description and the true function of constants, we can apply the powerful explanatory principles of wave mechanics to the behavior of fundamental particles, leading to a clearer, more unified understanding. We aim to remove the unnecessary mysticism surrounding constants like $h$ and clarify where the true, non-classical nature of reality resides.

2. The Neo‑Classical Foundation: Packet‑Waves and Direct Equivalences

Our proposed interpretation rests on a fundamental premise about reality (Layer 1/2) that departs from both classical point particles and classical continuous fields:

Fundamental reality consists of packets. These packets are the irreducible quanta of “stuff.” Crucially, these packets inherently possess wave properties. They are not point particles that also happen to wave; they are entities whose very nature includes spatio-temporal extent and oscillatory behavior. This is the fundamental “quantumness” – the universe’s inherent protocol of existence in bundled, wavelike units.

Within this Layer 1/2 reality of packets and waves, perceived facets of these packets are not fundamentally different entities, but exhibit simple, direct, and fixed proportional equivalences. What we perceive as Energy ($E$), Frequency ($f$), Mass ($m$), and Temperature ($T$) are all equivalent measures of the state of the same underlying stuff’s packets. This inherent scaling means

$$E \leftrightarrow f \leftrightarrow m \leftrightarrow T.$$

Similarly, concepts like Length ($L$) and Time duration ($T_{duration}$) are directly equivalent facets

$$L \leftrightarrow T_{duration},$$

as are Momentum ($p$) and ordinary spatial frequency (cycles per meter, $\nu$):

$$p \leftrightarrow \nu.$$

These proportionalities are quantified by fundamental, Layer 1/2 physical constants ($c, h, k$, etc.). These constants represent the fixed, inherent scaling rules within this wave-packet reality. They state the ratio inherent in reality itself.

3. $h$ as Pure Unit Scaling: Demystifying the Constant

Drawing from frameworks like PUCS, the numerical values of constants like $c, h, k$ in human-defined unit systems (Layer 3), such as SI, are identified as pure unit scaling factors. They exist because the arbitrary scales chosen for the base units (kilogram, meter, second, Kelvin, etc.) and derived units (Joule, Hertz) were selected without regard for the fundamental Layer 1/2 proportional equivalences.

For instance, the numerical value of $h$ in J·s is simply the multiplier needed to convert a measurement in Hertz to its equivalent value in Joules, as dictated by the fundamental $E \leftrightarrow f$ proportionality. $h$ holds no intrinsic “quantum” significance; it does not inject quantumness into physics. Its value is solely a Layer 3 artifact of our unit system relative to the inherent Layer 1/2 proportionality. Similarly, the common notation $\hbar = h/2\pi$ is merely an alternative Layer 3 scaling factor used when relating quantities based on angular conventions (like angular frequency).

The specific numerical values of $c, h, k$ in SI quantify the network of Layer 1/2 proportionalities

$$L \leftrightarrow T, e ↔…$$

by acting as Layer 3 scaling factors between the chosen unit axes of the SI system (meter ↔ second, Joule ↔ Hertz, Joule ↔ kilogram, Joule ↔ Kelvin).

4. Neo‑Classical Explanation of Quantum Phenomena (Wave Dynamics Writ Small)

With the foundation of wave-like packets and constants as unit scaling, we re-interpret quantum phenomena using the well-developed tools of classical wave mechanics:

4.1 Wave‑Particle “Duality”

This is a misnomer. There is no duality between two fundamentally different types of entities. The fundamental entities are inherently wavelike packets (Layer 1/2). What we call “particle” behavior is simply the manifestation of a wave packet’s properties when localized in space-time. What we call “wave” behavior is the manifestation of its extended, oscillatory properties (interference, diffraction). $h$ appears in $E = h f$ and $p = h \nu$ purely as the Layer 3 scaling factor to convert between measurements of the Energy/Momentum facets and the Frequency/Wavelength facets of the packet.

4.2 Quantization (e.g., Atomic Energy Levels)

Discrete energy levels in bound systems are not the result of $h$ sprinkling “quantum dust,” but are analogous to resonance in classical wave systems. When an inherently wavelike entity (like an electron packet) is confined by boundary conditions (like the electromagnetic potential of an atom), only specific wavelengths/frequencies (modes) can exist as stable standing waves. These allowed modes correspond to the system’s discrete energy levels via the fundamental proportionality $E \leftrightarrow f$. $h$ is present only as the Layer 3 unit converter between the frequency and energy units used to label these resonant states.

4.3 The Certainty of Uncertainty: A Neo‑Classical View from Wave Dynamics

The Uncertainty Principle is a property of all waves, captured by the Fourier Transform. A wave packet localized in space ($\Delta x$) requires a spread in ordinary spatial frequencies ($\Delta \nu$):

$$\Delta x\;\Delta \nu \;\ge\; \frac{1}{4\pi}.$$

Since ordinary frequency and momentum relate by $\nu = p/h$, substituting gives:

$$\Delta x\;\bigl(\tfrac{\Delta p}{h}\bigr) \;\ge\; \frac{1}{4\pi}.$$

Here, $h$ stays on the left‑hand side exactly as the converter from momentum to cycles‑per‑meter, and the right‑hand side remains the pure geometric constant $1/(4\pi)$.

5. Relational Concepts and the Role of Energy

Concepts like mass (as a source of gravity), charge, force, and energy, which carry compound units (Layer 4), are interpreted as descriptors of the relationships and dynamics between the fundamental Layer 1/2 packets, rather than intrinsic properties of isolated packets. They quantify how packets interact and change their state relative to each other.

As the “It Takes Two Particles to Tango” idea suggests, concepts like gravity and charge only gain meaning in the context of interaction; they describe the way packets relate. Similarly, Energy is a powerful Layer 4 descriptor of the state of interaction, motion, or configuration of the wave-packet stuff. The fundamental equivalences $E = m c^2 = h f = k T$ express the fixed proportional scaling between the energy descriptor and the other perceived facets ($m,f,T$) of the stuff involved in the interaction or state change. The constants ($c^2, h, k$) are the necessary Layer 3 scaling factors to bridge our units for these different facets according to the Layer 1/2 proportionalities.

6. Implications for Fundamental Physics: A Unit-Aware, Wave-Centric View

The “Neo‑Classical” interpretation offers a powerful alternative lens through which to view physics writ small. By starting with the premise that reality consists of wave-like packets (a fundamentally non‑classical idea) and applying the robust principles of classical wave dynamics, combined with a clear understanding of constants as Layer 3 unit scaling factors quantifying Layer 1/2 proportionalities, many of the conceptual mysteries of standard QM are clarified.

• Wave-particle duality becomes the inherent nature of the packet.

• Quantization is understood as wave resonance within boundaries.

• Uncertainty is recognized as a fundamental property of wave packets ($\Delta x\;\tfrac{\Delta p}{h} \ge 1/4\pi$), with $h$ remaining a unit-converter on the left side.

• Constants like $h$ and $k$ are seen as quantifiers of inherent scaling relationships ($E\leftrightarrow f, E\leftrightarrow T$), not mysterious introducers of “quantumness.”

This Neo‑Classical view doesn’t deny the empirical results of quantum mechanics; it re-interprets their underlying meaning. It proposes that physics writ small is not fundamentally strange due to forces or constants, but because the fundamental “stuff” exists as packets and behaves as waves, adhering to precise scaling rules. This changes the unification problem’s nature: it’s about describing the single Layer 1/2 reality of wave-like packets and their inherent scaling, rather than reconciling arbitrary unit-based constants. By providing a clearer conceptual landscape, the Neo‑Classical approach offers a potentially more intuitive path to understanding the universe at its most fundamental level.

---