physical relativity space-time structure from a dynamical perspective feb 2006

[...]... in dynamical considerations, in which forces internal and external to the clock (rod) have to be compared Once again, such considerations ultimately depend on the quantum theory of the fundamental non-gravitational interactions involved in material structure In conclusion, the operational meaning of the metric is ultimately made possible by appeal to quantum theory, in general relativity as much as... other hand, the gµν field is an autonomous dynamical player, physically significant even in the absence of the usual ‘matter’ fields But its meaning as a carrier of the physical metrical relations between 10 Physical Relativity space-time points is a bonus, the gift of the strong equivalence principle and the clock (and rod) hypothesis The problem in general relativity is that the matter fields responsible... FitzGerald’s 1889 thinking based on the Heaviside result, summarized in section 1.2 above In fact it is essentially a generalization of that thinking to the case of accelerating bodies Finally, a word about time dilation It was seen above that Bell attributed its discovery to Joseph Larmor, who indeed had partially—very partially—understood the phenomenon in his 1900 Aether and Matter, a text based on papers... the non-gravitational interactions takes its usual Lorentz covariant form In short, as viewed from the perspective of the local freely falling frames, special relativity holds when the effects of space-time curvature—tidal forces—can be ignored It is this extra assumption, which brings in quantum physics even if this point is rarely emphasized, that guarantees that ideal clocks, for example, can both... in strong contrast with Lorentz’s treatment He went on to ask: ‘Should one, then, completely abandon any attempt to explain the Lorentz contraction atomistically?’ It may surprise some readers to learn that Pauli’s answer was negative Be that as it may, it is a question that deserves careful attention, and one that, if not haunting him, then certainly gave Einstein unease in the years that followed the... of the relativity principle, and that it is unclear whether Einstein himself appreciated this The main lesson that emerges, as I see it, is Overview 5 that the special theory of relativity is incomplete without the assumption that the quantum theory of each of the fundamental non-gravitational interactions— and not just electrodynamics—is Lorentz-covariant This lesson was anticipated as early as 1912... stance, the apparent underdetermination of the field equations that is a consequence of their general covariance evaporates 14 Physical Relativity of distinct marks and the set of points that is the space-time manifold Now this may not be considered a problem if the coordinates are used to label, first and foremost, the manifold points But this is both conceptually questionable (as we have seen) and... here that the extra structure being appealed to is the existence of ‘affine’ parameters τ in (2.1) such that the RHS of (2.2) vanishes in arbitrary coordinate systems and arbitrary reparametrization 18 Newton (1999) Physics of Coordinate Transformations 19 It is a notion dealt with by Newton with remarkable sophistication, more, arguably, than was the case with Einstein when in 1905 he also assumed... normal procedure, we were to learn general relativity prior to special relativity, wouldn’t we be puzzled to see apparently physical effects such as length contraction and time dilation emerge from the Lorentz transformations between local inertial coordinate systems? 1 Einstein (1920); English translation in Pfister (2004) 2 Rigden (1987) 12 Physical Relativity In his General Relativity from A to... at greater length below) has as its starting point a single atom built of an electron circling a much more massive nucleus Using not much more than Maxwellian electrodynamics (taken as valid relative to the rest frame of the nucleus), Bell determined that the orbit undergoes the familiar relativistic longitudinal contraction, and its period changes by the familiar ‘Larmor’ dilation Bell claimed that .