Quantum Reality Redefined: New Theory Unifies Particle and Light Wave Behaviour

Scientists are increasingly scrutinising the fundamental nature of quantum states and whether they represent an underlying physical reality. Moncy V John from Mahatma Gandhi University, alongside colleagues, investigates this issue by tracing a path from classical to quantum mechanics, mirroring the established link between geometrical optics and electromagnetism. Their work reimagines the classical Hamilton-Jacobi equation as a wave equation, extending de Broglie’s wave-particle duality to encompass a broader range of wave function descriptions. This approach demonstrates the objectivity inherent in solutions to the Schrödinger equation and reveals that puzzles traditionally considered unique to quantum mechanics, such as entanglement, have roots in the nonlinearity of classical wave equations, potentially offering a new perspective on the interpretation of quantum phenomena.

Recent experiments suggest that models treating quantum states as mere information about a physical system contradict established quantum theory, prompting a deeper investigation into the reality of these states.

This work undertakes a fundamental approach, beginning with the Hamilton-Jacobi equation of classical mechanics and progressing to the Schrodinger equation of quantum mechanics, mirroring the historical transition from the eikonal equation in geometrical optics to the wave equation in electromagnetism. Researchers have rewritten the classical Hamilton-Jacobi equation as a wave equation, seeking to broaden de Broglie’s wave-particle duality.

This involves proposing that both particle and light waves can be described by any square-integrable function, allowing for superposition of matter wave functions. This generalisation facilitates the derivation of the Schrodinger equation, with its solution possessing an objectivity comparable to the classical mechanics wave function.

The study demonstrates that equations commonly used in quantum mechanics, including eigenvalue equations and energy state expansions, also have classical counterparts. The absence of wave function collapse or entanglement in the classical realm is attributed to the nonlinearity inherent in the classical wave equation.

These findings suggest that puzzles encountered in quantum mechanics are, in fact, present in classical mechanics in a latent form. This perspective offers a potential pathway to demystify quantum mechanics by revealing underlying connections to classical principles. By revisiting the foundations of both classical and quantum frameworks, this research aims to provide a more unified understanding of physical reality and the nature of wave functions.

From Hamilton-Jacobi formalism to a unified wave-based description of matter and electromagnetism emerges a compelling theoretical framework

Rewriting the classical Hamilton-Jacobi equation as a wave equation initiates this work, seeking to generalise de Broglie’s wave-particle duality by allowing both particle and light waves to be described by any square-integrable function. This generalisation, permitting superposition for matter wave functions, facilitates the derivation of the Schrodinger equation, positioning its solution as objectively real as the classical mechanics wave function.

The research demonstrates that several equations commonly used in mechanics, including eigenvalue equations for observables and series expansions of energy states, also have classical counterparts. The study begins by closely examining the connection between the eikonal equation, foundational to geometrical optics, and the electromagnetic wave equations underpinning wave optics.

Maxwell’s electromagnetic wave equations unified electric and magnetic phenomena, establishing a complete picture where geometrical optics emerges as a limiting case. A crucial element of this formalism is the superposition principle, valid for electromagnetic waves but absent in the eikonal equations, allowing electromagnetic signals to assume any square-integrable functional form while remaining solutions to Maxwell’s equations.

Subsequently, the work starts with the Hamilton-Jacobi equation in classical mechanics, noting its nonlinearity and lack of superposition. The classical Hamilton-Jacobi equation is recast into a wave equation, yielding a classical mechanics wave function that is also nonlinear and does not permit superposition.

The researchers then propose a generalised de Broglie principle, extending wave-particle duality to allow both photon and particle wave functions to be any function within the set of square-integrable functions, provided they satisfy their fundamental equation. This modification of the Hamilton-Jacobi equation, or the classical mechanics wave equation, ultimately yields the Schrodinger equation in quantum mechanics.

Furthermore, the Schrodinger equation can be expressed as a quantum Hamilton-Jacobi equation, closely resembling its classical counterpart and reducing to the latter when Planck’s constant approaches zero. The assignment of probabilities to particle positions, mirroring Born’s axiom, and to eigenvalues of observables, is also demonstrated within the classical framework. The work highlights that the principle of superposition is the key distinction between quantum and classical mechanics, suggesting that many quantum mechanical puzzles exist in a latent form within classical mechanics.

Hamilton-Jacobi and Schrödinger equations reveal a classical basis for quantum phenomena and their interconnectedness

Researchers demonstrate a direct correspondence between the classical Hamilton-Jacobi equation and the Schrödinger equation of quantum mechanics, establishing a fundamental link between the two frameworks. By rewriting the classical Hamilton-Jacobi equation as a wave equation, the study generalises de Broglie’s wave-particle duality to encompass both particle and light waves described by any square-integrable function.

This generalisation facilitates the derivation of the Schrödinger equation, positioning its solution as objectively real, akin to the classical mechanics wave function. The work reveals that equations commonly used in quantum mechanics, including eigenvalue equations for observables and series expansions of energy states, also have classical counterparts.

Absence of wave function collapse and entanglement in the classical realm originates from the nonlinearity inherent in the classical wave equation. These findings suggest that puzzles within quantum mechanics are also present, though dormant, within classical mechanics, potentially simplifying the understanding of quantum phenomena.

Starting from the eikonal equation of geometrical optics and its relation to the electromagnetic wave equation, the research highlights the importance of the superposition principle. Electromagnetic signals can adopt any square-integrable functional form while remaining solutions to Maxwell’s equations, a characteristic not shared by the eikonal equation.

The study proposes a generalised de Broglie principle, allowing both photon and particle wave functions to be any square-integrable function, provided they satisfy their respective fundamental equations. Modifying the classical wave equation through this principle yields the Schrödinger equation, demonstrating its emergence from classical mechanics.

Furthermore, the Schrödinger equation can be recast as a quantum Hamilton-Jacobi equation, closely resembling its classical analogue and converging towards it as Planck’s constant approaches zero. Probabilities can be assigned to particle positions using a Born-like axiom, and similarly to eigenvalues of observables, mirroring quantum mechanical approaches.

Classical foundations revealed through wave equation reformulations offer new insights into fundamental physics

Researchers have established a connection between classical and mechanics by reformulating the Hamilton-Jacobi equation of classical mechanics as a wave equation. This approach generalises de Broglie’s wave-particle duality, permitting both matter and light waves to be described by any square-integrable function, thereby allowing for superposition in matter wave functions.

The resulting Schrodinger equation, and associated equations governing observables, possess classical counterparts, suggesting that puzzles inherent in mechanics are also present, though often latent, within classical mechanics itself. This work demonstrates the objective nature of solutions to the Schrodinger equation, aligning them with the objectivity found in classical mechanical wave functions.

The preservation of normalisation of wave functions over time is proven using the Schrödinger equation and the Hermiticity of the Hamiltonian, confirming that the total probability of finding a particle remains constant. Furthermore, the expectation value of a particle’s position can be calculated directly from the probability density defined by the wave function, extending this principle to other observable quantities through the use of Hermitian operators.

These operators are shown to possess real eigenvalues and orthogonal eigenfunctions, properties crucial for consistent physical interpretations. Acknowledging the limitations inherent in any foundational investigation, the authors highlight that this work primarily focuses on establishing mathematical parallels between classical and mechanics.

While the analysis reveals a deeper connection and potentially demystifies some aspects of mechanics, it does not directly address the measurement problem or the interpretation of wave function collapse. Future research could explore the implications of this framework for understanding entanglement and other non-classical phenomena, potentially offering new insights into the foundations of physics and the nature of reality.