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The Unity of Microscopic and Macroscopic Regimes: Two Neglected Variables

Feng yvwen Fengdejian

Published Oct 3, 2026• 0 citations
Publisher

Abstract

Abstract Modern physics has long confronted the scale separation between microscopic quantum systems and macroscopic classical systems. This paper is built upon Feng’s unified field formula Φ = (εₓ · v² · t · T) / ε and its underlying axiomatic framework. It argues that this scale separation does not stem from a fundamental break in physical laws, but arises because established physical formulas systematically omit two key variables: temperature T and space compression coefficient ε. This work demonstrates that conventional formulas are limiting cases valid under specific conditions (constant T, ε≈1). When T and ε are restored as explicit variables, a continuous transition emerges between microscopic and macroscopic domains within a single framework, without discontinuity. Using the ground-state parameters of the hydrogen atom as a reference benchmark, this paper presents a continuous action spectrum ranging from the microscopic constant h to the macroscopic N·h. Testable quantitative predictions are proposed for future experimental verification, together with clear definitions of the newly introduced quantities Φ and ε.

DOI
10.5281/zenodo.23114149

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Abstract Modern physics has long confronted the scale separation between microscopic quantum systems and macroscopic classical systems. This paper is built upon Feng’s unified field formula Φ = (εₓ · v² · t · T) / ε and its underlying axiomatic framework. It argues that this scale separation does not stem from a fundamental break in physical laws, but arises because established physical formulas systematically omit two key variables: temperature T and space compression coefficient ε. This work demonstrates that conventional formulas are limiting cases valid under specific conditions (constant T, ε≈1). When T and ε are restored as explicit variables, a continuous transition emerges between microscopic and macroscopic domains within a single framework, without discontinuity. Using the ground-state parameters of the hydrogen atom as a reference benchmark, this paper presents a continuous action spectrum ranging from the microscopic constant h to the macroscopic N·h. Testable quantitative predictions are proposed for future experimental verification, together with clear definitions of the newly introduced quantities Φ and ε.
Abstract General relativity and quantum mechanics form two incompatible cornerstones of modern physics, artificially separating macroscopic and microscopic motion rules and attributing the trajectory uncertainty of microscopic particles to the intrinsic random property of particles. This paper takes the spatial compression coefficient as the core continuous variable to build a unified physical interpretation framework. The fundamental difference between macroscopic and microscopic states lies only in the continuous change of spatial compression coefficient, which determines the environmental density of universal irregular minimal matter units filling the whole space. Minimal matter units are irregular in shape with discrete moving speeds and collision forces. Microscopic particles have a similar scale to fundamental units, and continuous unobservable collisions lead to trajectory dispersion observed as randomness, while multi-directional collision disturbances on macroscopic objects offset each other to form deterministic motion. Wind tunnel multi-scale particle flow is adopted as a qualitative analogy to verify the medium disturbance mechanism. The theory eliminates artificial high/low-energy boundaries and the macro-micro rule division in conventional physics, and establishes a deterministic unified mass-energy theoretical system relying on spatial compression coefficient and omnipresent fundamental matter units. Keywords: spatial compression coefficient; spacetime density; universal fundamental matter units; microscopic particle trajectory; quantum uncertainty; medium disturbance; wind tunnel fluid analogy; unified mass-energy theory
Abstract The transition from microscopic reversible dynamics to macroscopic irreversible thermodynamics in statistical mechanics, the transformation from pure states to mixed states during quantum decoherence, and the transition from quantum superposition states to classical definite states in quantum measurement have long been regarded as three independent fundamental physical puzzles. This paper demonstrates that the three processes share a unified mathematical root: the filtering, truncation or projection of system degrees of freedom renders the information carried by partial degrees of freedom unreconstructable within the reduced description framework, and irreversibility spontaneously emerges in the remaining description space. Based on the rigorous derivation of Hilbert’s sixth problem proposed by Deng et al., Zurek’s environment-induced decoherence theory, and the three-stage model of temporal relativity proposed by the author, this paper extracts the mathematical structure of the three types of physical processes and constructs an axiomatic unified framework. This paper further clarifies that various filtering operations are essentially equivalent to the selection of reference frames by the observation system; any descriptive subject with finite information bandwidth must select a reference benchmark, and the arrow of time is an emergent characteristic of this selection behavior under reduced description. This paper distinguishes between global information conservation and local unreconstructable information, emphasizing that the theoretical framework does not violate unitary quantum evolution, and proposes quantitative predictions verifiable by attosecond physics and superconducting quantum experiments.
Abstract This paper takes quantum coherence as a unifying framework to establish a streamlined physical model that spans microscopic quantum phenomena, macroscopic motion, the four fundamental interactions, and conscious perception. Changes in an object’s motion state are fundamentally the transition and reconstruction of the system’s overall coherent mode. Electromagnetism, gravity, friction, contact forces, and the strong/weak interactions are all forms of coherent coupling at different scales. Macroscopic continuous motion is a sensory illusion of high-speed transitions between discrete coherent states, synthesized into a smooth temporal sequence by consciousness. Decoherence corresponds to the release of phase constraints, accompanied by energy release. From a dimensional perspective, the high-dimensional quantum coherent field is the underlying reality, and the macroscopic classical world is its low-dimensional projection after decoherence and conscious integration. Macroscopic physics is a simplified version of quantum physics, just as conventional calculus is a simplified version of its deeper mathematical foundations. This framework achieves a unified explanation of matter, force, energy, consciousness, and spacetime dimensions, with rigorous logical simplicity and self-consistency.
Macroscopic quantum phenomena refer to quantum features in objects of 'large' sizes, systems with many components or degrees of freedom, organized in some ways where they can be identified as macroscopic objects. This emerging field is ushered in by several categories of definitive experiments in superconductivity, electromechanical systems, Bose-Einstein condensates and others. Yet this new field which is rich in open issues at the foundation of quantum and statistical physics remains little explored theoretically (with the important exception of the work of A J Leggett [1], while touched upon or implied by several groups of authors represented in this conference. Our attitude differs in that we believe in the full validity of quantum mechanics stretching from the testable micro to meso scales, with no need for the introduction of new laws of physics.) This talk summarizes our thoughts in attempting a systematic investigation into some key foundational issues of quantum macroscopic phenomena, with the goal of ultimately revealing or building a viable theoretical framework. Three major themes discussed in three intended essays are the large N expansion [2], the correlation hierarchy [3] and quantum entanglement [4]. We give a sketch of the first two themes and then discuss several key issues in the consideration of macro and quantum, namely, a) recognition that there exist many levels of structure in a composite body and only by judicious choice of an appropriate set of collective variables can one give the best description of the dynamics of a specific level of structure. Capturing the quantum features of a macroscopic object is greatly facilitated by the existence and functioning of these collective variables; b) quantum entanglement, an exclusively quantum feature [5], is known to persist to high temperatures [6] and large scales [7] under certain conditions, and may actually decrease with increased connectivity in a quantum network [8]. We use entanglement as a measure of quantumness here and pick out these somewhat counter-intuitive examples to show that there are blind spots worthy of our attention and issues which we need to analyze closer. Our purpose is to try to remove the stigma that quantum only pertains to micro, in order to make way for deeper probes into the conditions whereby quantum features of macroscopic systems manifest.
This work presents a continuous, constraint-based interpretive framework for physical systems that unifies quantum behavior, classical structure, and cosmological evolution without introducing new forces or modifying established equations. Rather than treating quantum mechanics, electromagnetism, and general relativity as fundamentally separate domains, the paper proposes that these regimes can be understood as consistent descriptions of a shared underlying structure. The framework is built on three foundational elements: a non-geometric substrate (P_0) defining admissible configurations, interaction as the propagation of constraint, and geometry as the macroscopic record of accumulated interaction. Within this perspective, physical structure emerges through a continuous progression: distinctions enable gradients, gradients enable interaction, interaction accumulates as constraint, and constraint stabilizes into persistent configurations. The quantum–classical transition is interpreted as a continuous increase in interaction-induced constraint, while spacetime curvature reflects the large-scale organization of these interactions. The framework does not replace existing theories, but instead provides a unified conceptual interpretation that remains fully consistent with established physics across known regimes. Its value lies in clarifying relationships between domains, offering a continuous ontology of physical systems, and suggesting potential directions for further formalization.
The quantum–classical divide remains one of the most persistent conceptual challenges in modern physics. Conventionally, this transition is explained through decoherence— the environment-induced loss of phase coherence via interaction with external degrees of freedom. While phenomenologically successful, decoherence theory does not provide a fundamental mechanical substrate for why quantum behavior emerges preferentially at small scales and vanishes systematically at large ones. It remains a statistical account rather than a mechanistic one. The Absolute Medium (AM) framework offers an alternative foundation by re-conceptualizing spacetime not as an abstract arena, but as a Universal Force Continuum— a baseline of potential energy that precedes and underlies physical matter. In this formulation, the vacuum is characterized not by emptiness but by structured tension, where the “graininess” emerges from equilibrium conditions within the continuum itself.This graininess is quantified by the Energetic Net, defined by the fundamental length scale Lfund ≈ 3.34 nm. This scale represents the characteristic spacing at which the continuum’s tension reaches local equilibrium, creating a natural lattice structure. The continuum is neither rigid nor fluid in conventional terms, but exists in a state of dynamic equilibrium where its tension field supports both wave-like propagation and particle-like anchoring. This intrinsic structural property of the vacuum introduces a natural scale separation that defines two distinct dynamical regimes:• Slippage (Quantum) Regime (d < Lfund, m < mcrit): Particles interact with the continuum through local tension fluctuations without engaging its equilibrium structure. Their motion is governed by stochastic variations in the continuum’s potential field, yielding emergent quantum behavior.• Bulk-Coupled (Classical) Regime (d ≥ Lfund, m ≥ mcrit): Objects span multiple equilibrium nodes of the continuum, engaging its fundamental structure. They must displace the continuum’s equilibrium configuration, triggering deterministic volumetric coupling that recovers classical mechanics. This proposal replaces abstract decoherence with a concrete mechanical transition rooted in the continuum properties of the vacuum. It offers a first-principles explanation for the emergence of both quantum and classical dynamics from a unified energetic continuum, with the transition governed by intrinsic properties of the medium rather than external interactions.