[Paper Review] Tensorial origin of the action function, nexus between Quantum physics and General Relativity

Enrique Ordaz Romay|ArXiv.org|Dec 6, 2002

Relativity and Gravitational Theory3 references3 citations

TL;DR

This paper proposes a tensorial action function as the fundamental origin of the scalar action used in the Hamiltonian principle, unifying quantum mechanics and general relativity. By linking the components of this tensorial action directly to spinorial components of higher-spin wave functions, it explains why non-quantum physics only observes a scalar action, thereby providing a geometric and dynamical nexus between quantum physics and relativity through a unified tensorial foundation.

ABSTRACT

The analytic physics, when it is development from aprioristic form, constructs all the laws from the Hamilton principle, also called action principle. According to this principle all systems are characterized by a magnitude called action which variation is equal to zero for the real evolution of the systems. At first, do not exist restrictions for the mathematical form of the action function, nonetheless, as in the a posteriori developer of the analytic physics, the traditional equations of the physics lead up to a scalar action, it is always sure that the action may be a scalar function. In this article we propose the existence of a tensorial function like origin of the traditional scalar action. First because it permits, without other argumens, to justify the own action principle and second because it permits connect the complementary principle of the Quantum physics with the analytic expressions of the nonquantum physics, including the General Relativity. We call tensorial action to this original function and their components are connecting, directly, with the tensorial (spinorial) componets of the wave function of the particles with spin higher than zero. For this reason we can understand why in the nonquantum physics only has significance a scalar action.

Motivation & Objective

• To establish a tensorial origin for the action function traditionally used in the Hamilton principle.
• To reconcile the principles of quantum mechanics with those of general relativity through a unified geometric framework.
• To explain why non-quantum physics only observes a scalar action, despite a deeper tensorial structure.
• To connect the components of the tensorial action directly with the spinorial components of higher-spin particles.
• To provide a theoretical foundation that justifies the action principle without ad hoc assumptions.

Proposed method

• Introduces a tensorial action function as the fundamental physical quantity, from which the traditional scalar action emerges.
• Uses the Hamilton principle as a variational principle applied to the tensorial action, leading to the equations of motion.
• Establishes a direct correspondence between components of the tensorial action and spinorial components of the wave function for particles with spin > 0.
• Applies this framework to derive the standard equations of motion in classical and relativistic physics from a unified tensorial foundation.
• Demonstrates that the scalar nature of action in non-quantum physics arises as a reduction of the underlying tensorial structure.
• Employs a formalism rooted in differential geometry and field theory to maintain consistency with general relativity and quantum mechanics.

Experimental results

Research questions

• RQ1 What is the fundamental origin of the action function in physical theories?
• RQ2 How can the action principle be derived from a more fundamental tensorial structure?
• RQ3 In what way does a tensorial action unify quantum mechanics and general relativity?
• RQ4 Why does non-quantum physics only observe a scalar action, despite the presence of spinorial degrees of freedom?
• RQ5 How are the components of the tensorial action related to the spinorial components of wave functions?

Key findings

• The tensorial action function provides a deeper, geometric origin for the scalar action used in the Hamilton principle.
• The components of the tensorial action are directly linked to the spinorial components of higher-spin wave functions in quantum theory.
• The scalar action observed in classical and relativistic physics emerges as a reduced form of the underlying tensorial action.
• The action principle is naturally justified as a consequence of the tensorial structure, without requiring additional assumptions.
• The framework offers a unified foundation connecting quantum mechanics and general relativity through a common tensorial action.
• The model explains the complementary nature of quantum physics as arising from the decomposition of the tensorial action into spinorial components.