This paper argues that unitary time evolution — the continuous, deterministic, reversible evolution of the wave function via the Schrodinger equation — is not a fundamental feature of quantum reality but a continuous approximation of an underlying discrete process, structurally parallel to how Newtonian mechanics approximates discrete molecular dynamics. The measurement problem is identified not as a feature of quantum reality but as an artifact of imposing continuous formalism on discrete physics. A continuous equation cannot produce discrete events; this is mathematical, not mysterious. Caldirola's finite-difference quantum mechanics is cited as the formal precedent. Companion paper to DOI: 10.5281/zenodo.19540088.
This paper argues that unitary time evolution — the continuous, deterministic, reversible evolution of the wave function via the Schrodinger equation — is not a fundamental feature of quantum reality but a continuous approximation of an underlying discrete process, structurally parallel to how Newtonian mechanics approximates discrete molecular dynamics. The measurement problem is identified not as a feature of quantum reality but as an artifact of imposing continuous formalism on discrete physics. A continuous equation cannot produce discrete events; this is mathematical, not mysterious. Caldirola's finite-difference quantum mechanics is cited as the formal precedent. Companion paper to DOI: 10.5281/zenodo.19540088.
This work proposes that the discreteness observed in quantum mechanics is not a property of objective reality but an artifact of humanly bounded measurement frameworks. By distinguishing between the Ontic State — what exists — and the Epistemic Observation — what can be measured — the framework demonstrates that the continuous deterministic evolution of the Schrödinger equation represents the true underlying reality, while discrete eigenvalues emerge only through the spectral decomposition of measurement operators. The work further argues that quantum jumps are continuous transitions bounded by the decoherence timescale of the measuring apparatus, that quantum randomness is a dimensional projection loss rather than fundamental chaos, and that the contradiction between General Relativity and Quantum Mechanics is a measurement framework artifact rather than a property of nature. A testable prediction is proposed — that finite continuous transition time during quantum state changes is detectable in principle through attosecond spectroscopy.
This paper is a conceptual and interpretive companion to "The Dynamics of Discrete Fact: A Phase-Transition Theory of Wavefunction Collapse" (doi:10.5281/zenodo.18748601), which develops a phase-transition theory of wavefunction collapse in full mathematical detail. The interpretive claims made here rest on the physical model established there. The paper identifies a structural conflation at the root of the quantum measurement problem. The standard formulation treats measurement simultaneously as a physical process and as an experiential event without distinguishing between the two. We formalize this distinction as two complementary descriptive frames — a Reality Frame (F_R) for the continuous dynamics of the system–apparatus field, and an Observer Frame (F_O) for the discrete outcomes recorded by an embedded observer — connected by a calculable critical threshold γ_c derived from the companion paper's phase-transition model. The frame distinction is applied to the three sub-problems of measurement, to five foundational paradoxes (Wigner's friend, Frauchiger–Renner, Schrödinger's cat, delayed choice, and EPR), and to seven major interpretations of quantum mechanics, each shown to privilege one frame while neglecting the other. A Frame Complementarity Principle is conjectured as a testable constraint on the simultaneous accessibility of process information and outcome definiteness.
Quantum mechanics presents a profound conceptual challenge: it describes a world that is mathematically continuous but observationally discrete. The equations governing quantum systems are smooth differential equations, yet the physical reality they predict appears relentlessly quantized: energy comes in steps, particles are countable, and measurements register as distinct, indivisible events. This whitepaper proposes a unified taxonomy that organizes all known sources of quantum discreteness into five mutually exclusive, collectively exhaustive categories. We demonstrate that approximately 60% of observed discreteness appears to emerge from geometric and topological constraints on continuous wave dynamics, 25% stems from the mathematical structure of symmetry, and only 15% remains uncertain in its ontological status. By systematizing these mechanisms, this synthesis suggests that quantum discreteness may rarely be a fundamental property of nature's substrate but predominantly a consequence of selective stability: continuous wave dynamics, when subjected to global self-consistency constraints, can only sustain certain resonant patterns characterized by integers.
Abstract Modern physics has achieved extraordinary predictive success through continuous mathematical formulations. However, the underlying nature of space, time, and physical processes remains conceptually open. This work presents a conceptual framework in which physical reality is interpreted as a discrete phase-supported structure. Space is considered as a lattice of elementary units separated at approximately the Planck scale, while time emerges through successive phase-closure events. Within this picture, energy transport, quantum coherence, and observable events are not continuous processes but arise from structured phase propagation. A triadic propagation mechanism naturally generates hexagonal connectivity, while phase closure defines the emergence of physical events. Rather than proposing new physical laws, this work suggests a broader interpretational perspective, encouraging reconsideration of continuity-based assumptions and inviting exploration of phase-based descriptions of physical reality. Author’s Perspective : I would like to submit the attached manuscript entitled: “Quantum Phase, Discrete Space, and the Limits of Continuity: A Conceptual Framework Toward a Phase-Based Interpretation of Physical Reality” for consideration as a conceptual or perspective article in your journal. The work presents a unified interpretational framework in which physical processes are described in terms of discrete phase propagation and phase closure. Rather than introducing new physical laws, the manuscript offers a geometrical and phase-based perspective that aims
Abstract Quantum mechanics admits two distinct evolutions: deterministic unitary dynamics governed by the Schrödinger equation and the probabilistic collapse of the wave function. We show that the continuous collapse of a quantum state under measurement can, on a trajectory-by-trajectory basis, be equivalently described as unitary evolution generated by a time- and state-dependent Hermitian Hamiltonian with stochastic parameters. While the ensemble dynamics remains non-unitary, each individual trajectory thus admits a unitary representation. We derive explicit forms of such Hamiltonians for projective measurements on arbitrary n -level systems and for continuous position measurements of a harmonic oscillator, and we propose experimental schemes to test these predictions. Our framework provides a new approach to modeling and controlling continuously monitored quantum systems using only state-dependent unitary resources.
The debate instigated by the seminal works of Einstein, Podolsky, Rosen, and Bell put the notions of realism and nonlocality at the core of almost all philosophical and physical discussions underlying the foundations of quantum mechanics. However, while experimental criteria and quantifiers are by now well established for nonlocality, there is no clear quantitative measure for the degree of reality associated with continuous variables such as position and momentum. This work aims at filling this gap. Considering position and momentum as effectively discrete observables, we implement an operational notion of projective measurement and, from that, a criterion of reality for theses quantities. Then we introduce a quantifier for the degree of irreality of a discretized continuous variable which, when applied to the conjugated pair position-momentum, is shown to obey an uncertainty relation, meaning that quantum mechanics prevents classical realism for conjugated quantities. As an application of our formalism, we study the emergence of elements of reality in an instance where a Gaussian state is submitted to the dissipative dynamics implied by the Caldirola-Kanai Hamiltonian. In particular, at equilibrium, we make some links with the measurement problem and identify aspects that can be taken as the quantum counterpart for the notion of rest.