The Third Way to General Relativity: Einstein and Mach in Context

Abstract

If I let all things disappear from the world, then, according to Newton, the Galilean inertial space remains, while according to my view, nothing is left. Albert Einstein, 9 January 1916 Space, brought to light by the corporeal object, made a physical reality by Newton, has in the last few decades swallowed ether and time and seems about to swallow also the field and the corpuscles, so that it remains as the sole medium of reality. Albert Einstein, 1930

Introducing General Relativity in High Schools: a proposal for a Teaching-Learning Module

“…In fact, the inclusion of historical, philosophical and Nature of Science (NoS) aspects in physics education has been repeatedly advocated by researchers, also in the context of GR [5,6]. Our track partially retraces the early conceptual development of GR, which took place from 1907 on [9,10,11], while keeping in mind that the basic concepts and principles of GR can be stated without resorting to the geometric point of view (interestingly, the views of Einstein himself were much less geometrical than commonly thought, as argued in [12]). This point of view is also shared by several modern approaches to GR, as e.g.…”

“…In the 19th century, the possibility that Newton's law is in fact only a static limit of a more general theory of gravity (as Coulomb's law is the static limit of Maxwell's theory) was investigated by many physicists. After special relativity, the need for such a theory became of course much more compelling, and several physicists struggled to find a theory of gravity fully consistent with special relativity ( [11], voll. [3][4].…”

Progress and Gravity: Overcoming Divisions Between General Relativity and Particle Physics and Between Physics and HPS

“…Such a result sounds rather dramatic when expressed in modern vocabulary. But coordinate inequalities are old [Hilbert, 2007], familiar [Møller, 1972], and not very dramatic classically; coordinates can have qualitative physical meaning while lacking a quantitative one. A principal square root is related to the avoidance of negative eigenvalues of g µν η νρ [Higham, 1987, Higham, 1997.…”

Gauge-invariant localization of infinitely many gravitational energies from all possible auxiliary structures

“…Constructing a gauge-invariant set by collecting together an expression in every gauge works even if one quantifies only over all elements satisfying some suitable condition, perhaps some inequalities restricting the allowed coordinates [50,51] or allowed bimetric gauges [47]: the gauge-invariant collection is found by collecting the complexes for all the allowed gauges or coordinates. One then has only a (Brandt) groupoid, not a group, of gauge transformations [47]: the allowed transformations depend on the configuration, so not every pair of elements can be multiplied.…”