We prove that associated with mass is spacetime curvature which leads to creation of volume and mass shells in every instance due to the energy equivalence principle. We put forth the relations between a point surface tension and a spacetime curvature. The conclusion is that the spacetime is of fluid nature. Finally we find the chi psi omega law and the action which is of central importance in quantum mechanics. From thereon we may estimate the true acceleration of the particle.
We prove that associated with mass is spacetime curvature which leads to creation of volume and mass shells in every instance due to the energy equivalence principle. We put forth the relations between a point surface tension and a spacetime curvature. The conclusion is that the spacetime is of fluid nature. Finally we find the chi psi omega law and the action which is of central importance in quantum mechanics. From thereon we may estimate the true acceleration of the particle.
Abstract In general relativity, the dynamics of objects is governed by the curvature of spacetime, which is caused by the presence of matter and energy. In contrast, in quantum mechanics, the dynamics is governed by the wavefunction, which completely describes the behavior of the particles. There is an ongoing effort to explore analogs of space and spacetime curvature in the context of quantum mechanics. Such analogies may reveal a deeper structure of quantum reality and its possible relations with Einstein’s theory of gravity. In this note, by coupling the non-relativistic Schrödinger equation with the heat equation and using the hydrodynamical formulation of quantum mechanics, we find that the dynamics of the particle is fully characterized by the normalized curvature of the wavefunction’s amplitude. Such a curvature obtains an analogy to the Ricci curvature of curved space in a Riemannian manifold. The proposed geometric correspondence provides a new pathway to explore quantum dynamics through the lens of differential geometry, the language of general relativity.
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.
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.
As was Einstein s original idea we suppose that the speed of light is altered in the presence of mass by a change in its dielectric susceptibility. Our explanation of the phenomena of quantum mechanics is a continuation of Einstein search for hidden variables. Mass induces a curvature in spacetime. This has two effects. New volume is created and this would mean that there is not exactly a point particle but matters in a way occupies some volume. Another result is that spacetime becomes cyclic and quantities like the action are quantized because they depend on angles through which the observer witnesses the events.
The equivalence postulate of quantum mechanics offers an axiomatic approach to quantum field theories and quantum gravity. The equivalence hypothesis can be viewed as adaptation of the classical Hamilton-Jacobi formalism to quantum mechanics. The construction reveals two key identities that underlie the formalism in Euclidean or Minkowski spaces. The first is a cocycle condition, which is invariant under D -dimensional Möbius transformations with Euclidean or Minkowski metrics. The second is a quadratic identity which is a representation of the D -dimensional quantum Hamilton-Jacobi equation. In this approach, the solutions of the associated Schrödinger equation are used to solve the nonlinear quantum Hamilton-Jacobi equation. A basic property of the construction is that the two solutions of the corresponding Schrödinger equation must be retained. The quantum potential, which arises in the formalism, can be interpreted as a curvature term. The author proposes that the quantum potential, which is always nontrivial and is an intrinsic energy term characterising a particle, can be interpreted as dark energy. Numerical estimates of its magnitude show that it is extremely suppressed. In the multiparticle case the quantum potential, as well as the mass, is cumulative.