Open AccessA contribution to modern ideas on the quantum theory
Publication year - 1927
Publication title -
proceedings of the royal society of london. series a, containing papers of a mathematical and physical character
Language(s) - English
Resource type - Journals
eISSN - 2053-9150
pISSN - 0950-1207
DOI - 10.1098/rspa.1927.0086
Subject(s) - geodesic , theory of relativity , physics , mathematical physics , notation , gravitation , general relativity , extension (predicate logic) , classical mechanics , quantum mechanics , theoretical physics , mathematics , geometry , computer science , arithmetic , programming language
The relativity theory of gravitation indicates that space-time is a four dimensional continuum in which the line element is measured by the equation (ds )2 =gmn dxm dxn , (1) the notation being that generally adopted. The world-lines or natural tracks of free particles in this space are geodesics. From (1) we havegmn dxm /ds.dxn /ds= 1, (2) the quantity on the left being an expression corresponding to the kinetic energy of ordinary dynamics for a particle of unit mass. This correspondence is readily appreciated if it be noted thatdxm /dsis the natural extension of the velocity,dxm /dt.