Musing on extreme quantity values in physics and the problem of removing infinity

Abstract

Many physical quantities display range values apparently extending to infinity (unbounded on one or on both sides). In this respect, unit systems and measurement conventions do not place any constraint to their validity for a maximum (or minimum) value. In general, this happens because such extreme values are far from being reached on the earth or yet are reached in experimental settings. Nevertheless, the issue of extreme values (not in the usual mathematical analysis meaning here) is not irrelevant, since the same units are used also in countless fields of physics, chemistry or technology where extreme values do occur—namely, in the description of the universe in one frame, and in pico/nano-scale or particle physics in another. The issue, of direct interest also of measurement science and specifically of metrology, is discussed here illustrating, as an example, our currently accepted concept of temperature, i.e., the kelvin temperature scale based on Lord Kelvin’s second definition, which encompasses the full range between bounds (0, +∞). In general, the occurrence of infinite values in physical equations, such as singularities in the description of black holes, is a painstaking problem that causes many theories to break down and/or being incapable of describing extreme events. Different methods, such as re-normalization (scaling) or logistic/geometrical, have been used in the assessment of physical observables in order to avoid the undesirable infinity.