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.
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.
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.
Starting from three fundamental duality relations (time-energy, space-momentum, angle-angular momentum), we establish an integral equation of quantum action and its dual counterpart. This integral equation directly links the evolution of the wave function to the accumulated action of spacetime and rotational degrees of freedom, forming a unified framework for quantum theory. Through semiclassical expansion, local approximation, and relativistic covariance, we rigorously derive the Schr\"odinger equation, Klein-Gordon equation, Dirac equation, Heisenberg equation, Schwinger-Dyson equation, Feynman path integral, Yang-Mills equations, Einstein field equations, and the Friedmann and Schwarzschild solutions. The framework also yields the kinematic effects of special relativity (time dilation, length contraction, mass-energy equivalence) as consequences of the duality structure. Moreover, the nonlocal kernel in the integral equation gives an exponential damping factor in momentum space, providing an intrinsic regularization mechanism for ultraviolet divergences. We extend the framework to quantum electrodynamics (QED), quantum chromodynamics (QCD), the electroweak theory, the full Standard Model, and quantum gravity, obtaining dual formulations for each. From the integral equation and its dual, we automatically derive quantization conditions for energy, momentum, angular momentum, and their duals, and propose experimental schemes to observe these discrete effects. All derivations are complete and rigorous, based on the same integral equation, providing a possible answer to Dirac's criticism that "quantum electrodynamics lacks a fundamental equation" and opening a new path toward a unified theory.
Inverted Relativistic Phase-Fluid Mechanics on Curved Spacetime introduces a covariant matter-phase model in which the phase field defines the local four-momentum, written in readable form as: p_mu = hbar * nabla_mu phi or equivalently: four-momentum = Planck constant × phase gradient The density n weights the conserved phase current and determines how strongly the phase flow contributes to the stress-energy tensor and therefore to spacetime curvature. In the minimal model, n has no independent gradient term. It acts as an algebraic density variable enforcing a relativistic Hamilton-Jacobi or mass-shell relation. This gives an inverted relativistic phase fluid: the phase determines motion, while the density weights its physical and gravitational effect. The model is then extended through the Madelung decomposition: psi = sqrt(n) * exp(i phi) This adds the amplitude-gradient term and produces the relativistic quantum-pressure contribution: Q_rel = - hbar^2 * Box(sqrt(n)) / sqrt(n) where Box is the covariant d’Alembert operator on curved spacetime. In this way, the minimal phase-fluid picture becomes connected to the full Klein-Gordon/Madelung quantum-fluid structure on curved spacetime. The paper provides a covariant bridge between: proper-time matter phase, de Broglie momentum-phase relations, relativistic fluid mechanics, Madelung quantum hydrodynamics, quantum pressure, stress-energy generation, and gravitational curvature. The model does not replace general relativity and does not claim to be a completed theory of quantum gravity. Instead, it formulates a compact theoretical framework in which matter phase, density, quantum amplitude structure and spacetime curvature are coupled without introducing a preferred reference frame. A compact summary of the construction is: The phase carries the motion, the density carries the weighting, the quantum pressure carries the wave nature, and the metric carries gravity. This preprint is intended as a theory note and starting point for further analytical and numerical work, including fixed-background simulations, weak gravitational backreaction, and full Einstein-Klein-Gordon/Madelung evolution.
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.
Inverted Relativistic Phase-Fluid Mechanics on Curved Spacetime introduces a covariant matter-phase model in which the phase field defines the local four-momentum, written in readable form as: p_mu = hbar * nabla_mu phi or equivalently: four-momentum = Planck constant × phase gradient The density n weights the conserved phase current and determines how strongly the phase flow contributes to the stress-energy tensor and therefore to spacetime curvature. In the minimal model, n has no independent gradient term. It acts as an algebraic density variable enforcing a relativistic Hamilton-Jacobi or mass-shell relation. This gives an inverted relativistic phase fluid: the phase determines motion, while the density weights its physical and gravitational effect. The model is then extended through the Madelung decomposition: psi = sqrt(n) * exp(i phi) This adds the amplitude-gradient term and produces the relativistic quantum-pressure contribution: Q_rel = - hbar^2 * Box(sqrt(n)) / sqrt(n) where Box is the covariant d’Alembert operator on curved spacetime. In this way, the minimal phase-fluid picture becomes connected to the full Klein-Gordon/Madelung quantum-fluid structure on curved spacetime. The paper provides a covariant bridge between: proper-time matter phase, de Broglie momentum-phase relations, relativistic fluid mechanics, Madelung quantum hydrodynamics, quantum pressure, stress-energy generation, and gravitational curvature. The model does not replace general relativity and does not claim to be a completed theory of quantum gravity. Instead, it formulates a compact theoretical framework in which matter phase, density, quantum amplitude structure and spacetime curvature are coupled without introducing a preferred reference frame. A compact summary of the construction is: The phase carries the motion, the density carries the weighting, the quantum pressure carries the wave nature, and the metric carries gravity. This preprint is intended as a theory note and starting point for further analytical and numerical work, including fixed-background simulations, weak gravitational backreaction, and full Einstein-Klein-Gordon/Madelung evolution.