Planck Scale Physics and Newton's Ultimate Object Conjecture

Abstract

Abstract According to Newton, the ultimate building blocks of matter are hard frictionless spheres. This conjecture is here analyzed under different assumptions, which are: 1. The ultimate objects of matter are frictionless positive and negative Planck mass particles obeying nonrelativistic Newtonian mechanics. 2. The Planck mass particles interact with the Planck force c 4 /G (c velocity of light, G Newton's constant) locally within a Planck length r p , with the positive Planck mass particles exerting a repulsive and the negative Planck mass particles an attractive force. 3. Space if filled with an equal number of positive and negative Planck mass particles, whereby in the average each Planck length volume occupies one Planck mass particle. Making these three assumptions we derive: 1. Nonrelativistic quantum mechanics as an approximation with departures from this approxima-tion suppressed by the Planck length. 2. Lorentz invariance as a dynamic symmetry for energies small compared to the Plank energy. 3. The operator field equation for the previously proposed Planck aether model of a unified theory of elementary particles. In contrast to theories in which the ultimate objects are strings at the Planck scale, the alternative theory proposed here does not need a higher dimensional space, but rather can be formulated in 3 + 1 dimensions.