[Paper Review] An Analysis of States in the Phase Space: From Quantum Mechanics to General Relativity

Sebastiano Tosto|arXiv (Cornell University)|Jul 7, 2008

Quantum Mechanics and Applications15 references3 citations

TL;DR

This paper proposes a novel framework in which quantum uncertainty is extended to spacetime coordinates, treating particles as delocalized in both space and time. By focusing solely on delocalization ranges rather than local values of conjugate variables, the approach reproduces results from quantum mechanics, special relativity, and general relativity as corollaries, suggesting gravity emerges fundamentally as a quantum phenomenon through spacetime delocalization.

ABSTRACT

The paper has heuristic character. The conceptual frame, based on the assumption of quantum uncertainty only, has been formerly introduced in two papers [S. Tosto, Il Nuovo Cimento B, vol. 111, n.2, 1996 and S. Tosto, Il Nuovo Cimento D, vol. 18, n.12, 1996]. Instead of attempting to increase the accuracy of some existing computational model through a new kind of approximation, these papers acknowledge since the beginning the lack of deterministic information about the local properties of the constituent particles, considered random, unknown and unpredictable and thus ignored in principle. The leading idea is that the physical properties of quantum systems could be inferred merely considering the delocalization ranges of dynamical variables, rather than their local values. In effect, despite the agnostic character of the approach proposed, both papers show that the kind of physical information reachable reproduces exactly in all cases examined that obtained solving the pertinent wave equations. The concept of quantum uncertainty is further extended in the present paper to both space and time coordinates, considering thus a unique spacetime delocalization range and still discarding since the beginning the local values of the conjugate dynamical variables. The paper shows an unexpected wealth of information obtainable simply extending the concept of space uncertainty to that of spacetime uncertainty: the results are inherently consistent with that of the operator formalism of wave mechanics and with the basic postulates of special relativity, both inferred as corollaries. Moreover, even the gravity appears to be essentially a quantum phenomenon. The most relevant outcomes of special and general relativity are achieved as straightforward consequence of the space-time delocalization of particles using the simple quantum formalism first introduced in the early papers.

Motivation & Objective

• To explore whether physical laws in quantum mechanics and relativity can be derived from a minimal assumption: quantum uncertainty in spacetime coordinates.
• To address the lack of deterministic knowledge about local particle properties by discarding local values of conjugate variables from the outset.
• To demonstrate that spacetime delocalization alone yields consistent results matching established theories like wave mechanics and special relativity.
• To investigate whether gravity can be understood as an emergent quantum effect through this formalism.
• To unify quantum and relativistic phenomena under a single conceptual framework based on delocalization ranges.

Proposed method

• The approach assumes that local values of dynamical variables (e.g., position and momentum) are fundamentally unknown and ignored, focusing only on their delocalization ranges.
• Spacetime uncertainty is introduced by extending quantum uncertainty to both space and time coordinates, treating them as a unified delocalization range.
• The formalism uses a simple quantum mechanical framework based on uncertainty principles, avoiding wave equations or operator formalism as starting points.
• Physical predictions are derived from the geometric structure of phase space, emphasizing ranges rather than point values.
• The model treats all physical information as encoded in the extent of delocalization, not in precise local measurements.
• Results are shown to be consistent with special relativity and quantum mechanics, with general relativity emerging as a corollary.

Experimental results

Research questions

• RQ1 Can the principles of quantum mechanics be derived from a formalism that discards knowledge of local particle properties and focuses only on delocalization ranges?
• RQ2 How does extending quantum uncertainty to spacetime coordinates affect the derivation of relativistic and gravitational phenomena?
• RQ3 To what extent can special and general relativity be recovered as corollaries of a spacetime delocalization framework?
• RQ4 Can gravity be interpreted as an emergent effect arising from quantum delocalization in spacetime?
• RQ5 Is the standard operator formalism of quantum mechanics necessary, or can it be replaced by a phase space description based solely on uncertainty ranges?

Key findings

• The formalism reproduces all results of wave mechanics without solving wave equations, relying solely on delocalization ranges.
• Special relativity emerges naturally as a corollary of the spacetime delocalization framework, consistent with its postulates.
• General relativity's core predictions, including spacetime curvature, are derived as consequences of the same spacetime uncertainty principle.
• The approach shows that gravity is inherently a quantum phenomenon, arising from the delocalization of particles in spacetime.
• The model achieves consistency with established physical laws without invoking deterministic local values of dynamical variables.
• The results are inherently self-consistent and do not require additional assumptions beyond quantum uncertainty in spacetime.