Massive Nordström scalar (density) gravities from universal coupling

2017

Erkenn

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Kantian philosophy of space, time and gravity is significantly affected in three ways by particle physics. First, particle physics deflects Schlick's General Relativity-based critique of synthetic a priori knowledge. Schlick argued that since geometry was not synthetic a priori, nothing was-a key step toward logical empiricism. Particle physics suggests a Kant-friendlier theory of space-time and gravity presumably approximating General Relativity arbitrarily well, massive spin-2 gravity, while retaining a flat space-time geometry that is indirectly observable at large distances. The theory's roots include Seeliger and Neumann in the 1890s and Einstein in 1917 as well as 1920s-30s physics. Such theories have seen renewed scientific attention since 2000 and especially since 2010 due to breakthroughs addressing early 1970s technical difficulties.Second, particle physics casts additional doubt on Friedman's constitutive a priori role for the principle of equivalence. Massive spin-2 gravity presumably should have nearly the same empirical content as General Relativity while differing radically on foundational issues. Empirical content even in General Relativity resides in partial differential equations, not in an additional principle identifying gravity and inertia.Third, Kant's apparent claim that Newton's results could be known a priori is undermined by an alternate gravitational equation. The modified theory has a smaller (Galilean) symmetry group than does Newton's. What Kant wanted from Newton's gravity is impossible due its large symmetry group, but is closer to achievable given the alternative theory.

Section: B) Local Problemsmentioning

confidence: 74%

Kant, Schlick and Friedman on Space, Time and Gravity in Light of Three Lessons from Particle Physics

2017

Erkenn

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“…Such issues are relevant to whether it is epistemically possible for us now that such a theory is true of the actual world. If one is interested only in whether theories with similar features are metaphysically possible, and epistemically possible as of the 1910s rather than 2016, then one can use a massive scalar theory instead [Pitts, 2011b, Pitts, 2011a, Pitts, 2016b, doing to Nordström's theory what Hugo von Seeliger and Carl Neumann in the 1890s had done and Einstein in 1917 [Einstein, 1923] would do to Newton's theory. Hence the general philosophical idea of Freund, Maheshwari and Schonberg manifestly could be realized for scalar gravity theories, whether or not it could be for tensor theories such as they considered.…”

Section: B) Local Problemsmentioning

confidence: 99%

“…More definitively troublesome is the fact, that Norton's (3) is false even within what is presumably a sector of Special Relativity, namely, universally coupled massive scalar gravity, which is just Poincaré-invariant. These theories, though they have roots in the 1890s in the work of Seeliger and Neumann, and would have gravity satisfy the rather familiar Klein-Gordon equation in the lowest approximation, have hardly ever been studied thoroughly, especially for philosophical lessons, until recently [Pitts, 2011a, Pitts, 2011b, Pitts, 2016b. One cannot assume that physicists have already done all the work that philosophy requires.…”

Section: Massive Scalar Gravity Vs Space-time Realismmentioning

confidence: 99%

Space-time constructivism vs. modal provincialism: Or, how special relativistic theories needn't show Minkowski chronogeometry

Studies in History and Philosophy of Science Part B: Studies in

2019

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Already in 1835 Lobachevski entertained the possibility of multiple (one might say "rival") geometries of the same type playing a role. This idea of rival geometries has reappeared from time to time (including Poincaré and several 20th century authors) but had yet to become a key idea in space-time philosophy prior to Brown's Physical Relativity. Such ideas are emphasized towards the end of Brown's book, which I suggest as the interpretive key. A crucial difference between Brown's constructivist approach to space-time theory and orthodox "space-time realism" pertains to modal scope. Constructivism takes a broad modal scope in applying (at least) to all local classical field theories-modal cosmopolitanism, one might say, including theories with multiple geometries. By contrast the orthodox view is modally provincial in assuming that there exists a unique geometry, as the familiar theories (Newtonian gravity, Special Relativity, Nordström's gravity, and Einstein's General Relativity) have. These theories serve as the "canon" for the orthodox view. Their historical roles also suggest a Whiggish story of inevitable progress. Physics literature after c. 1920 is relevant to orthodoxy primarily as commentary on the canon, which closed in the 1910s. The orthodox view explains the spatio-temporal behavior of matter in terms of the manifestation of the real geometry of space-time, an explanation works fairly well within the canon. The orthodox view, Whiggish history, and the canon have a symbiotic relationship.If one happens to philosophize about a theory outside the canon, space-time realism sheds little light on the spatio-temporal behavior of matter. Worse, it gives the wrong answer when applied to an example arguably within the canon, a sector of Special Relativity, namely, massive scalar gravity with universal coupling. Which is the true geometry-the flat metric from the Poincaré symmetry group, the conformally flat metric exhibited by material rods and clocks, or both-or is the question faulty? * To appear in the special issue of Studies in History and Philosophy of Modern Physics on Harvey Brown's Physical Relativity 10 years later. 1How does space-time realism explain the fact that all matter fields see the same curved geometry, when so many ways to mix and match exist? Constructivist attention to dynamical details is vindicated; geometrical shortcuts can disappoint. The more exhaustive exploration of relativistic field theories in particle physics, especially massive theories, is a largely untapped resource for space-time philosophy.

“…It is not coincidental that universal coupling derivations for massive scalar gravity using the canonical tensor have led only to a single theory (Freund and Nambu, 1968), because one needs to use the freedom to add a curl to the canonical tensor to accommodate second derivatives except in one case (Pitts, 2011a). The ideal might be to use the Belinfante-Rosenfeld equivalence the identity to permit using the Rosenfeld definition for calculations and the Belinfante tensor (or it plus terms vanishing on-shell) for conceptual purposes.…”

Section: Particle Physics Spin 2 Derivation(s)mentioning

confidence: 99%

Einstein׳s Equations for Spin 2 Mass 0 from Noether׳s Converse Hilbertian Assertion

Studies in History and Philosophy of Science Part B: Studies in

2016

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An overlap between the general relativist and particle physicist views of Einstein gravity is uncovered. Noether's 1918 paper developed Hilbert's and Klein's reflections on the conservation laws. Energy-momentum is just a term proportional to the field equations and a "curl" term with identically zero divergence. Noether proved a converse "Hilbertian assertion": such "improper" conservation laws imply a generally covariant action. Later and independently, particle physicists derived the nonlinear Einstein equations assuming the absence of negative-energy degrees of freedom ("ghosts") for stability, along with universal coupling: all energy-momentum including gravity's serves as a source for gravity. Those assumptions (all but) imply (for 0 graviton mass) that the energy-momentum is only a term proportional to the field equations and a symmetric curl, which implies the coalescence of the flat background geometry and the gravitational potential into an effective curved geometry. The flat metric, though useful in Rosenfeld's stress-energy definition, disappears from the field equations. Thus the particle physics derivation uses a reinvented Noetherian converse Hilbertian assertion in Rosenfeld-tinged form.The Rosenfeld stress-energy is identically the canonical stress-energy plus a Belinfante curl and terms proportional to the field equations, so the flat metric is only a convenient mathematical trick without ontological commitment. Neither generalized relativity of motion, nor the identity of gravity and inertia, nor substantive general covariance is assumed. The more compelling criterion of lacking ghosts yields substantive general covariance as an output. Hence the particle physics derivation, though logically impressive, is neither as novel nor as ontologically laden as it has seemed.