Abstract Starting from Louis de Broglie’s pilot wave-theory, this paper unifies gravity and quantum mechanics under a single mathematical field theory for all forces in Nature. Two families of potentials coexist as mathematical solutions for the homogeneous Klein-Gordon equation which is the same homogeneous classical wave equation: (a) Neo-Laplacian local time-independent background potentials, and (b) Novel time-distance entangled Q(q) potentials which are isomorph to distance-time-velocity transformations based on any of the competing relativistic theories (Lorentz, Poincaré or Einstein), or on the pre-relativistic Galilean invariant Doppler equations. This remarkable property makes present theory compatible with all previous empirical evidence, including experiments conventionally interpreted as supporting Einstein’s special relativity. We report explicit closed solutions for potentials solving the one-dimensional and three-dimensional classical wave equations, and describe in detail how to calculate time-independent neo-Laplacian background forces and relativistically isomorph time-dependent entangled forces. The scale of the problem appears as a required parameter, thus making our theory applicable to all scales of Nature from quarks to cosmos. A usually overlooked neo-Laplacian logarithmic potential predicts the observed high values of non-Keplerian tangential speeds at the galactic scale. At the human scale, calculations relative to hurricanes and tornadoes may be facilitated by the closed form of our unified forces. A novel torsion component of gravity automatically appears from our new solutions.
Abstract Starting from Louis de Broglie’s pilot wave-theory, this paper unifies gravity and quantum mechanics under a single mathematical field theory for all forces in Nature. Two families of potentials coexist as mathematical solutions for the homogeneous Klein-Gordon equation which is the same homogeneous classical wave equation: (a) Neo-Laplacian local time-independent background potentials, and (b) Novel time-distance entangled Q(q) potentials which are isomorph to distance-time-velocity transformations based on any of the competing relativistic theories (Lorentz, Poincaré or Einstein), or on the pre-relativistic Galilean invariant Doppler equations. This remarkable property makes present theory compatible with all previous empirical evidence, including experiments conventionally interpreted as supporting Einstein’s special relativity. We report explicit closed solutions for potentials solving the one-dimensional and three-dimensional classical wave equations, and describe in detail how to calculate time-independent neo-Laplacian background forces and relativistically isomorph time-dependent entangled forces. The scale of the problem appears as a required parameter, thus making our theory applicable to all scales of Nature from quarks to cosmos. A usually overlooked neo-Laplacian logarithmic potential predicts the observed high values of non-Keplerian tangential speeds at the galactic scale. At the human scale, calculations relative to hurricanes and tornadoes may be facilitated by the closed form of our unified forces. A novel torsion component of gravity automatically appears from our new solutions.
The relation between de Broglie’s double-solution approach to quantum dynamics and the hydrodynamic pilot-wave system has motivated a number of recent revisitations and extensions of de Broglie’s theory. Building upon these recent developments, we here introduce a rich family of pilot-wave systems, with a view to reformulating and studying de Broglie’s double-solution program in the modern language of classical field theory. Notably, the entire family is local and Lorentz-invariant, follows from a variational principle, and exhibits time-invariant, two-way coupling between particle and pilot-wave field. We first introduce a variational framework for generic pilot-wave systems, including a derivation of particle-wave exchange of Noether currents. We then focus on a particular limit of our system, in which the particle is propelled by the local gradient of its pilot wave. In this case, we see that the Compton-scale oscillations proposed by de Broglie emerge naturally in the form of particle vibrations, and that the vibration modes dynamically adjust to match the Compton frequency in the rest frame of the particle. The underlying field dynamically changes its radiation patterns in order to satisfy the de Broglie relation p=ℏk at the particle’s position, even as the particle momentum p changes. The wave form and frequency thus evolve so as to conform to de Broglie’s harmony of phases, even for unsteady particle motion. We show that the particle is always dressed with a Compton-scale Yukawa wavepacket, independent of its trajectory, and that the associated energy imparts a constant increase to the particle’s inertial mass. Finally, we see that the particle’s wave-induced Compton-scale oscillation gives rise to a classical version of the Heisenberg uncertainty principle.
A unified fluid and field theory containing all forces as special cases postulates that primordial fluid is formed by discrete, 3D-extended energy-like sagions obeying usual energy-momentum conservation laws. Contrary to Newtonian mechanics, mass and force are not primitive notions (hence, "Cartesian"), but the theory is atomistic (hence "neo"). Collective fluid behaviour obeys the homogeneous Klein-Gordon equation, or homogeneous 3D-wave equation, which besides usual harmonic periodic solutions has three families of quantized, Galilean-Lorentz isomorph, nonperiodic solutions discovered around 1995. Here, quantum mechanics is relativistic ab initio thus ensuring consistency with Einstein's general theory of relativity, which is extended to include effects upon gravity of chemical and nuclear composition, as indeed observed by Eötvös (1890s), and Majorana (1919). Planck constant is identified with the bit of minimum angular momentum in sagion-sagion interactions, thus introducing quantum features at the root of classical mechanics. Acceleration produced by successive pushes of a small projectile (say, a sagion, disagion, trisagion, 4-sagion) leads to a curve resembling Einstein's mass increase. This reinterprets one aspect of the restricted theory of relativity: rather than mass increase, Bertozzi experiment demonstrates inefficient transfer of linear momentum. The lower branch in our background universal acceleration curve is associated to static friction.
Almost 100 years ago, Erwin Schrödinger’s pioneering contributions provided the foundation for quantum mechanics, yet his deeper ontological vision of a purely wave-based reality was largely sidelined by the rise of the Copenhagen interpretation and its rejection of realism. This paper revisits and extends Schrödinger's wave-based ontology, exploring its potential evolution in light of contemporary physics challenges. The Quantum Ocean Theory (QOT) theory developed here reconceptualizes the quantum ocean as a dynamic, oscillatory field from which all physical phenomena emerge. Through a single wave equation, QOT describes particles as localized standing waves and forces as traveling waves of different frequencies of the underlying medium, with physical constants like the speed of light emerging naturally from the vacuum's underlying properties. All forces emerge organically from the wave equation. Drawing from Schrödinger's philosophical commitments and scientific insights, alongside complementary ideas from Einstein, Whitehead, Bohm, and Bell, we argue that QOT provides both a unified mathematical framework and coherent ontological foundation for physics. The framework offers novel solutions to persistent challenges in modern physics, including the Hubble tension, quantum measurement problem, and the quest for quantum gravity. It makes specific, testable predictions regarding galactic synchrony, early galaxy formation, and quantum coherence phenomena. Beyond its empirical implications, QOT represents a return to the kind of realist, deterministic physics that Einstein and Schrödinger advocated, while incorporating modern insights about non-locality and quantum behavior.
A new, very different physical model of the universe is proposed. Its virtues include unifying relativity and quantum mechanics, and particles with de Broglie waves. It also appears to provide a truly unified physical basis for electromagnetic, gravitational and nuclear forces. The basic system is a four-dimensional Euclidean space, containing an array of nonlinear "flow" waves. These repeat in one dimension, called [phi]. As in Newtonian mechanics, time is treated as an additional, unidirectional parameter describing the evolution of the system. Nevertheless, this wave system is shown be inherently relativistic. Further self-organizing patterns arise within the overall wave structure. Called "wavicles," these have intrinsic quantized fields, "spin," and rest energy, and represent elementary particles. Relativistic expressions are derived for particle behavior in scalar, vector and gravitational potentials. Proper representations of these potentials, based on the wave fields and associated [phi] flows of wavicles, are also obtained. As in the causal quantum mechanics of de Broglie and Bohm, wavicles exist continuously and follow definite, stochastic trajectories. Although experimentally equivalent to Einstein's special relativity, this theory differs fundamentally from his general relativity and the associated Big Bang model. According to Linde, the latter predict a large-scale space-time curvature roughly 60 orders of magnitude greater than observed values. Here a flat large-scale geometry is predicted, in agreement with the observed distribution of galaxies. This theory is also consistent with recent observations pertaining to the age of the universe.
Abstract We present a classical hydrodynamic analog of free relativistic quantum particles inspired by de Broglie's pilot wave theory and recent developments in hydrodynamic quantum analogs. The proposed model couples a periodically forced Klein-Gordon equation with a nonrelativistic particle dynamic equation. The coupled equations may represent both quantum particles and classical particles driven by the gradients of locally excited Faraday waves. Exact stationary solutions of the coupled system reveal a highly nonlinear mechanism responsible for the self-propulsion of free particles, leading to the onset of unsteady motion. Although the model is essentially nonrelativistic, a stabilizing mechanism for any particle traveling close to the wave signaling speed emerges through the coupling with the wavefield. Consequently, inline particle oscillations comparable to de Broglie's wavelength formula are realized through this fully-classical model, suggesting a new classical interpretation for the motion of relativistic quantum particles.
We propose a conceptual framework in which the pilot wave of de Broglie-Bohm quantum mechanics has a concrete physical substrate: dark matter existing in a fourth spatial dimension. Quantum superposition is reinterpreted as rapid physical oscillation — consistent with the Zitterbewegung predicted by the Dirac equation — rather than simultaneous existence in multiple classical states. Wave function collapse is correspondingly reinterpreted as physical interruption of this oscillation by detector interaction, rather than observation-dependent state reduction. The framework advances a coherence argument against the Many Worlds interpretation: real superposition, as evidenced by the ordered interference pattern in the double slit experiment, produces coherent identical behavior across superposed states rather than divergent branching. Divergent branches would produce detectable decoherence signatures inconsistent with observed interference; their absence constitutes evidence against branching interpretations by the same evidential standard used to establish superposition itself. The Born rule is proposed to be a relational property of the detector-system interaction rather than an intrinsic quantum axiom. Since detector physical constants — mass, charge, interaction energy — are fixed across measurements, probability distributions are determined by the interaction geometry rather than by unexplained features of the wave function alone. The squared amplitude relationship is identified as a universal property of wave energy mechanics appearing at quantum scale. The nonlocality problem of pilot wave theory is resolved by proposing that dark matter exists in a fourth spatial dimension. Particles entangled across cosmological distances in three-dimensional space may be geometrically adjacent in four-dimensional space, making instantaneous correlation a short-range 4D connection rather than superluminal 3D signaling. This is consistent with Kaluza-Klein dark matter proposals and brane cosmology. The inaccessibility of the wave medium to electromagnetic instruments follows naturally from the confinement of standard model forces to the three-dimensional brane. The framework makes several testable predictions: correlation between dark matter density and quantum coherence times; systematic shifts in Born rule probability distributions under varying detector parameters; and potential gravitational wave signatures of large-scale quantum collapse events. Mathematical formalization and experimental testing are identified as open problems.