Mapping in inertial frames
World space mapping in inertial frames is used to examine the Lorentz covariance of symmetry operations. It is found that the Galilean invariant concepts of simultaneity (S), parity (P), and time reversal symmetry (T) are not Lorentz covariant concepts for inertial observers. That is, just as the concept of simultaneity has no significance independent of the Lorentz inertial frame, likewise so are the concepts of parity and time reversal. However, the world parity (W) (i.e., the space-time reversal symmetry (P-T)) is a truly Lorentz covariant concept. Indeed, it is shown that only those mapping matrices M that commute with the Lorentz transformation matrix L (i.e., (M,L) = 0) are the ones that correspond to manifestly Lorentz covariant operations. This result is in accordance with the spirit of the world space Mach's principle. Since the Lorentz transformation is an orthogonal transformation while the Galilean transformation is not an orthogonal transformation, the formal relativistic space-time mapping theory used here does not have a corresponding non-relativistic counterpart. 12 refs.
- Research Organization:
- Princeton Univ., NJ (USA). Plasma Physics Lab.
- DOE Contract Number:
- AC02-76CH03073
- OSTI ID:
- 6035249
- Report Number(s):
- PPPL-2619; ON: DE89013320
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
657002 -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
657003* -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COMMUTATION RELATIONS
EIGENVALUES
FIELD THEORIES
FUNCTIONS
GALILEI TRANSFORMATIONS
GENERAL RELATIVITY THEORY
INVARIANCE PRINCIPLES
LORENTZ INVARIANCE
LORENTZ TRANSFORMATIONS
MAPPING
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MINKOWSKI SPACE
PARITY
PARTICLE PROPERTIES
QUANTUM OPERATORS
RELATIVITY THEORY
SPACE
SPACE-TIME
T INVARIANCE
TRANSFORMATIONS
WAVE FUNCTIONS
657003* -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COMMUTATION RELATIONS
EIGENVALUES
FIELD THEORIES
FUNCTIONS
GALILEI TRANSFORMATIONS
GENERAL RELATIVITY THEORY
INVARIANCE PRINCIPLES
LORENTZ INVARIANCE
LORENTZ TRANSFORMATIONS
MAPPING
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MINKOWSKI SPACE
PARITY
PARTICLE PROPERTIES
QUANTUM OPERATORS
RELATIVITY THEORY
SPACE
SPACE-TIME
T INVARIANCE
TRANSFORMATIONS
WAVE FUNCTIONS