Predicting the motion of particles in Newtonian mechanics and special relativity

✍ Scribed by Jan Hendrik Schmidt

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 308 KB
• Volume: 29
• Category: Article
• ISSN: 1355-2198
• DOI: 10.1016/s1355-2198(97)00029-4

✦ Synopsis

This paper and its predecessor (Schmidt, 1997) are about the question: 'Are the events in the entire universe encoded in and predictable from any of its parts?' To approach a positive answer in classical physics, the following result is proved and commented on: in Newton's theory of gravitation, the entire trajectory of a particle can be predicted given any segment of it, regardless of how the other particles are moving-provided that there is only a finite number of particles and that their speeds remain bounded. (It is this condition, together with a set of parameters characterising the motion of the other particles, which enables us to estimate the effect of the other particles on the trajectory of the given particle.) The extension of this result to other theories, in particular to special relativity, is discussed.