Generalization of Heisenberg uncertainty principle for strong interactions

Conference · 01 April 1981 · Hadronic J.; (United States)

OSTI ID:6648552

Santilli, R M

We propose a unified form of possible generalizations of Heisenberg uncertainty principle for strong interactions, which is based on the product of the envelope of the dynamical equations representing wave packets under conditions of mutual overlapping and nonlocal non-Hamiltonian forces. For conventional associative products of operators, we recover the conventional Heisenberg relations for particles under long range electromagnetic interactions and no appreciable wave overlapping. For nonassociative Lie-admissible products of operators we have (a) a number of generalizations of Heisenberg's equations of increasing algebraic complexity; (b) the capability of representing a correspondingly progressive increase of conditions of wave overlapping and nonlocal, non-Hamiltonian forces; and (c) a corresponding, rather inevitable sequence of generalizations of Heisenberg uncertainty relations. All these possibilities are expressed in a unified way by postulating generalized uncertainty relations whereby the product of operators is that of the envelope of the dynamical equations. For conditions of minimal wave overlapping under strong interactions, such as in the nuclear structure, we expect a very small nonlocal non-Hamiltonian component of the force and a minimal departure from Heisenberg principle. For progressive increase of wave overlappings, such as in the structure of hadrons, or in the structure of stars undergoing gravitational collapse, we expect a corresponding progressive replacement of Heisenberg principle with more general principles. The problem of the experimental resolution of the exact or only approximate validity of Heisenberg principle under strong interactions is considered for a more detailed treatment in a separate paper.

• Research Organization: Inst. for Basic Research, Cambridge, MA
• DOE Contract Number: AC02-80ER10651
• OSTI ID: 6648552
• Report Number(s): CONF-8008162-
• Conference Information: Journal Name: Hadronic J.; (United States) Journal Volume: 4:3
• Country of Publication: United States
• Language: English

Related Subjects

645204* -- High Energy Physics-- Particle Interactions & Properties-Theoretical-- Strong Interactions & Properties
657002 -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BASIC INTERACTIONS
DIFFERENTIAL EQUATIONS
ELEMENTARY PARTICLES
EQUATIONS
HADRONS
INTERACTIONS
LIE GROUPS
MATHEMATICAL OPERATORS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM OPERATORS
STARS
STRONG INTERACTIONS
SYMMETRY GROUPS
UNCERTAINTY PRINCIPLE
WAVE EQUATIONS
WAVE PACKETS