WAVES AND PARTICLES—QUANTISATION OF THE INTERVAL BETWEEN EVENTS s_0

摘要

Mathematical analyses of such basic phenomena as interference and atomic reactions lead to two very different physical models, extensive waves and particles of atomic or subatomic dimensions, which have proved immensely difficult to reconcile. In this paper, the concept of a quantised unit of interval or space-time s_0 is introduced, simply related to the rest mass m_0 of a particle, s_0 = h/m_0c~2. This value follows directly from the relation between rest energy, mass and frequency E_0 = m_0c~2 = hv_0 = h/s_0. The interval s between events comprises n units s_0; s = n · s_0. Time t and distance between events are also quantised into units t_0 and r_0, but unlike s and s_0, do vary with relative velocity in accordance with relativity theory; t = n_t • t_0 and r =n_r • r_0. n_t and n_r vary with velocity but remain related to n; n = n_t - n_r. The de Broglie wavelength λ acquires a physical significance; it is the distance r_0 corresponding to unit interval s_0. The uncertainty principle for (time x energy) and (distance x momentum) also holds a simple meaning; it corresponds to an interval s = n • s_0 and cannot be measured to closer than one indivisible unit s_0. No physical waves need be involved. Interference and diffraction effects at the lowest intensity can require a single particle, e.g. an electron, to pass simultaneously through many widely-spaced slits. This is usually ascribed to an extensive wave nature which disappears physically on detection. With the present quantised s_0 model all interference beams comprise the same number n of s_0 units but shared differently between time and distance units n_t and n_r, always with n = n_t - n,. Beam maxima correspond to different integral values of n_t and n_r. These and other fundamental difficulties which have arisen in the physical interpretation of results deduced from quantum theory are ascribed to the assumption that, unlike many fundamental properties in physics, time and space are infinitely divisible even for a single particle at rest. With the theory considered here this assumption, which otherwise leads to wave concepts, is not required; an electron at rest has as unit time t_0 = 0.80932 x 10~(-20)s, with lower values for heavier particles. Units t_0 and r_0 vary with velocity in accordance with relativity. s_0 is more fundamental and for any particle the product of unit s_0 and rest-mass m_0 is constant; s_0 • m_0 = h/c~2 = 0.73725 x 10~(-50) kg • s. If rest mass is quantised so is interval s_0. There remains a fundamental scientific problem, the close relationship between mass m and frequency v or its reciprocal, the unit of time t_0 for any particle, whether at rest or in motion; m · c~2 = h · v =h/t_0.