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Springer eBooks

Space, Time and Motion

Helmut Günther, V. Müller

Published Jan 1, 2019• 0 citations
Publisher
DOI
10.1007/978-981-13-7783-9_1

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Ordinarily, the Jacobi formulation of classical mechanics describes a system by giving the path of a “system point” in “configuration space,” the path being a geodesic if a metric is suitably defined. Nothing is said, however, about the motion in time. It is suggested here that, by adding a degree of freedom in uniform motion to serve as a clock, and identifying the time with the coordinate of that degree of freedom, the configuration space can be extended to a space-time, in which the motion is completely described, both in space and in time, as being along a geodesic. Also, by this representation, the idea of “absolute time” is made unnecessary. A representation such as this is, of course, normal in relativistic theory, but its use here in nonrelativistic mechanics is believed to have some novelty.
We show that the natural motion of particles in continuous space-time (CSTM) is not classical continuous motion (CCM), but one kind of essentially discontinuous motion, the wave function in quantum mechanics is the very mathematical complex describing this kind of motion, and Schrodinger equation is just its simplest nonrelativistic motion equation, we call such motion quantum discontinuous motion or quantum motion; furthermore, we show that, when considering gravity the space-time will be essentially discrete, and the motion in discrete space-time (DSTM) will naturally result in the collapse process of the wave function, this finally brings about the appearance of classical continuous motion (CCM) in macroscopic world.
We present a theory of discontinuous motion of particles in continuous space-time. We show that the simplest nonrelativistic evolution equation of such motion is just the Schroedinger equation in quantum mechanics. This strongly implies what quantum mechanics describes is discontinuous motion of particles. Considering the fact that space-time may be essentially discrete when considering gravity, we further present a theory of discontinuous motion of particles in discrete space-time. We show that its evolution will naturally result in the dynamical collapse process of the wave function, and this collapse will bring about the appearance of continuous motion of objects in the macroscopic world.