A quantized approach to space-time

Abstract

Some consequences are traced of a simple approach to the concept of a quantized relativistic space-time. It is assumed that the basic unit of space-time s 0 depends on the rest-mass of the individual particle m 0 and that the location in space-time of the particle cannot be defined more closely than s 0, where s 0 equals h/ m 0 ic in space coordinates or h/ m 0 c 2 in time coordinates. This leads to the same expressions for the uncertainty in space and time, the de Broglie wavelength, basic frequency and energy levels, and phase velocity as in conventional quantum theory but without the need to introduce a physically significant wave function. This avoids the difficulty in accepting a probability explanation for the wave function and the apparently contradictory wave and particle concepts when dealing with interference and detection from large volumes at very low intensities as well as a possible inversion of cause and effect. Interference appears as the segregation of beams into different units of space-time, each with its own selection of quantum numbers n i of units s 0 along the four axes but with the same total Σ n i . The different beams correspond merely to a (quantized) change of axes. This approach is compared with that involved in the Schrodinger equation, which leads to an extensive wave function, and this must then be “reduced” by an observation or measurement to establish a localized particle. Prior to such a measurement, the nature of the particle, spread in some sense over the wave function raises questions of reality in unobserved objects. No such problems of reality need arise with the concept of quantized space-time, and the observer intervenes only by choosing the framework axes.