arXiv subjects

J. Brian Pitts

Publications and source records attributed to J. Brian Pitts.

At least 19 recordsLinked to original sources

arXiv2022

First-Class Constraints, Gauge Transformations, de-Ockhamization, and Triviality: Replies to Critics, Or, How (Not) to Get a Gauge Transformation from a Second-Class Primary Constraint

Recently two pairs of authors have aimed to vindicate the longstanding conventional claim that a first-class constraint generates a gauge transformation in typical gauge theories such as electromagnetism, Yang-Mills and General Relativity, in response to the Lagrangian-equivalent reforming tradition, in particular Pitts, _Annals of Physics_ 2014. Both pairs emphasize the coherence of the extended Hamiltonian formalism against what they take to be core ideas in Pitts 2014, but both overlook Pitts 2014's sensitivity to ways that one might rescue the claim in question, including an additive redefinition of the electrostatic potential. Hence the bulk of the paper is best interpreted as arguing that the longstanding claim about separate first-class constraints is _either false or trivial_ -- de-Ockhamization (using more when less suffices by splitting one quantity into the sum of two) being trivial. Unfortunately section 9 of Pitts 2014, a primarily verbal argument that plays no role in other works, is refuted. Pooley and Wallace's inverse Legendre transformation to de-Ockhamized electromagnetism with an additively redefined electrostatic potential, however, opens the door to a precisely analogous calculation introducing a photon mass, which shows that a _second-class primary_ constraint generates a gauge transformation in the exactly same sense -- a reductio ad absurdum of the claim that a first-class constraint generates a gauge transformation and a second-class constraint does not. Gauge freedom by de-Ockhamization does not require any constraints at all, first-class or second-class, because any dynamical variable in any Lagrangian can be de-Ockhamized into exhibiting trivial additive artificial gauge freedom by splitting one quantity into the sum of two. Physically interesting gauge freedom, however, is typically generated by a tuned sum of first-class constraints.

physics.hist-ph↗

arXiv2022

Peter Bergmann on Observables in Hamiltonian General Relativity: A Historical-Critical Investigation

The problem of observables and their supposed lack of change has been significant in Hamiltonian quantum gravity since the 1950s. This paper considers the unrecognized variety of ideas about observables in the thought of Peter Bergmann, who invented observables. Whereas initially he required a constrained Hamiltonian formalism to be mathematically equivalent to the Lagrangian, in 1953 Bergmann and Schiller introduced a novel postulate, motivated by facilitating quantum gravity: observables were _invariant_ under transformations generated by _each individual_ first-class constraint. While modern works rely on Bergmann's authority and sometimes speak of "Bergmann observables," he had much to say about observables, plausible but not all consistent or remembered. At times he required observables to be locally defined (not changeless and global); at times he wanted them independent of the Hamiltonian formalism (not essentially involving separate first-class constraints). But typically he took observables to have vanishing Poisson bracket with each first-class constraint, purportedly justified by electrodynamics. He expected observables to be analogous to the transverse true degrees of freedom of electromagnetism. Hence there is no coherent concept of observables which he reliably endorsed. A revised definition of observables that satisfies the requirement that equivalent theories should have equivalent observables using the Rosenfeld-Anderson-Bergmann-Castellani gauge generator $G$, a tuned sum of first-class constraints that changes the canonical action $\int dt(p\dot{q}-H)$ by a boundary term. Bootstrapping from theory formulations with no first-class constraints, the "external" coordinate symmetry of GR calls for covariance ($4$-dimensional Lie derivative), not invariance ($0$ Poisson bracket), under $G$ (not each first-class constraint).

gr-qc↗

arXiv2022

What Represents Space-time? And What Follows for Substantivalism \emph{vs.} Relationalism and Gravitational Energy?

The questions of what represents space-time in GR, the status of gravitational energy, the substantivalist-relationalist issue, and the (non)exceptional status of gravity are interrelated. If space-time has energy-momentum, then space-time is substantival. Two extant ways to avoid the substantivalist conclusion deny that the energy-bearing metric is part of space-time or deny that gravitational energy exists. Feynman linked doubts about gravitational energy to GR-exceptionalism; particle physics egalitarianism encourages realism about gravitational energy. This essay proposes a third view, involving a particle physics-inspired non-perturbative split that characterizes space-time with a constant background _matrix_ (not a metric), avoiding the inference from gravitational energy to substantivalism: space-time is (M, eta), where eta=diag(-1,1,1,1) is a spatio-temporally constant numerical signature matrix (already used in GR with spinors). The gravitational potential, bearing any gravitational energy, is g_(munu)(x)-eta (up to field redefinitions), an _affine_ geometric object with a tensorial Lie derivative and a vanishing covariant derivative. This non-perturbative split permits strong fields, arbitrary coordinates, and arbitrary topology, and hence is pure GR by almost any standard. This razor-thin background, unlike more familiar ones, involves no extra gauge freedom and so lacks their obscurities and carpet lump-moving. After a discussion of Curiel's GR exceptionalist rejection of energy conservation, the two traditional objections to pseudotensors, coordinate dependence and nonuniqueness, are explored. Both objections are inconclusive and getting weaker. A literal interpretation of Noether's theorem (infinitely many energies) largely answers Schroedinger's false-negative coordinate dependence problem. Bauer's nonuniqueness (false positive) objection has several answers.

physics.hist-ph↗

arXiv2021

Change in Hamiltonian General Relativity with Spinors

In Hamiltonian GR, change has seemed to be missing, defined only asymptotically, or otherwise obscured at best. By construing change as essential time dependence, can one find change locally in Hamiltonian GR with spinors? This paper is motivated by tendencies in space-time philosophy to slight fermionic/spinorial matter, in Hamiltonian GR to misplace changes of time coordinate, and in treatments of the Einstein-Dirac equation to include a gratuitous local Lorentz gauge symmetry. Spatial dependence is dropped in most of the paper. To include all and only the coordinate freedom, the Einstein-Dirac equation is investigated using the Schwinger time gauge and Kibble-Deser symmetric triad condition as a $3+1$ version of the DeWitt-Ogievetsky-Polubarinov nonlinear group realization formalism that dispenses with a tetrad and local Lorentz gauge freedom. Change is the lack of a time-like stronger-than-Killing field for which the Lie derivative of the metric-spinor complex vanishes. An appropriate $3+1$-friendly form of the Rosenfeld-Anderson-Bergmann-Castellani gauge generator $G$, a tuned sum of first class-constraints, changes the canonical Lagrangian by a total derivative and implements changes of time coordinate for solutions.

gr-qc↗

arXiv2020

The Field-Theoretic Approach in General Relativity and Other Metric Theories. A Review

GR and other metric theories of gravity are formulated with an arbitrary auxiliary curved background in a Lagrangian formalism. A new sketch of how to include spinor fields is included. Conserved quantities are obtained using Noether's theorem and expressed as divergences of antisymmetric densities, connecting local perturbations with quasi-local conserved quantities. The background's arbitrariness matches the so-called non-localizability of gravitational energy (infinity of localizations). The formalism has two partly overlapping uses: practical applications of pure GR (with fictitious background) and foundational considerations in which background causality facilitates quantization. The Schwarzschild solution is a primary application. Various possibilities for calculating the mass using surface integration are given. A field-theoretic curved spacetime is given from spatial infinity to the horizon and even to the true singularity. Trajectories of test particles in the Schwarzschild geometry are gauge-dependent in that even breakdowns at the horizon can be suppressed (or generated) by naive gauge transformations. This fact illustrates the auxiliary nature of the background metric and the need for some notion of maximal extension---much as with coordinate transformations in geometric GR. A continuous collapse to a point mass in the field-theoretic framework is given. The field-theoretic method is generalized to arbitrary metric theories in $D$ dimensions. The results are developed in the framework of Lovelock gravity and applied to calculate masses of Schwarzschild-like black holes. The bimetric formalism makes it natural to consider a graviton mass. Babak and Grishchuk's numerical and hence nonperturbative work sheds light on questions of a (dis)continuous massless limit for massive pure spin-2 and the classical (in)stability of spin-2/spin-0 theory.

gr-qc↗

arXiv2019

Historical and Philosophical Insights about General Relativity and Space-time from Particle Physics

Historians recently rehabilitated Einstein's "physical strategy" for General Relativity (GR). Independently, particle physicists similarly re-derived Einstein's equations for a massless spin 2 field. But why not a light \emph{massive} spin 2, like Neumann and Seeliger did to Newton? Massive gravities are bimetric, supporting conventionalism over geometric empiricism. Nonuniqueness lets field equations explain geometry but not \emph{vice versa}. Massive gravity would have blocked Schlick's critique of Kant's synthetic \emph{a priori}. Finally in 1970 massive spin 2 gravity seemed unstable or empirically falsified. GR was vindicated, but later and on better grounds. However, recently dark energy and theoretical progress have made massive spin 2 gravity potentially viable again.

physics.hist-ph↗

arXiv2019

How Dualists Should (Not) Respond to the Objection from Energy Conservation

The principle of energy conservation is widely taken to be a serious difficulty for interactionist dualism (whether property or substance). Interactionists often have therefore tried to make it satisfy energy conservation. This paper examines several such attempts, especially including E. J. Lowe's varying constants proposal, showing how they all miss their goal due to lack of engagement with the physico-mathematical roots of energy conservation physics: the first Noether theorem (that symmetries imply conservation laws), its converse (that conservation laws imply symmetries), and the locality of continuum/field physics. Thus the "conditionality response", which sees conservation as (bi)conditional upon symmetries and simply accepts energy non-conservation as an aspect of interactionist dualism, is seen to be, perhaps surprisingly, the one most in accord with contemporary physics (apart from quantum mechanics) by not conflicting with mathematical theorems basic to physics. A decent objection to interactionism should be a posteriori, based on empirically studying the brain.

physics.hist-ph↗

arXiv2019

Cosmological Constant $Λ$ vs. Massive Gravitons: A Case Study in General Relativity Exceptionalism vs. Particle Physics Egalitarianism

The renaissance of General Relativity witnessed considerable progress regarding both understanding and justifying Einstein's equations. Both general relativists and historians of the subject tend to share a view, General Relativity exceptionalism. But does some of the renaissance progress in understanding and justifying Einstein's equations owe something to particle physics egalitarianism? If so, how should the historiography of gravitation and Einstein's equations reflect that fact? The idea of a graviton mass has a 19th century Newtonian pre-history in Neumann's and Seeliger's long-distance modification of gravity, which (especially for Neumann) altered Poisson's equation to give a potential $e^{-mr}/r$ for a point mass, improving convergence for homogeneous matter. Einstein reinvented the idea before introducing his faulty analogy with $Λ$. This confusion was first critiqued by Heckmann in the 1940s (without effect) and by Trautman, DeWitt, Treder, Rindler, and Freund et al. in the 1960s, and especially more recently by Schücking, but it has misled North, Jammer, Pais, Kerszberg, the Einstein Papers, and Kragh. The error is difficult to catch if one has an aversion to perturbative thinking, but difficult to make if one thinks along the lines of particle physics. The $Λ$-graviton mass confusion not only distorted the interpretation of Einstein's theory, but also obscured a potentially serious particle physics-motivated rivalry (massless vs. massive spin 2). How could one entertain massive spin 2 gravity if $Λ$ is thought already analogous to the Neumann-Seeliger scalar theory? Historiography, like physics, is best served by overcoming the divide between the two views of gravitation.

physics.hist-ph↗

arXiv2019

General Relativity, Mental Causation, and Energy Conservation

The conservation of energy and momentum have been viewed as undermining Cartesian mental causation since the 1690s. Modern discussions of the topic tend to use mid-19th century physics, neglecting both locality and Noether's theorem and its converse. The relevance of General Relativity (GR) has rarely been considered. But a few authors have proposed that the non-localizability of gravitational energy and consequent lack of physically meaningful local conservation laws answers the conservation objection to mental causation: conservation already fails in GR, so there is nothing for minds to violate. This paper is motivated by two ideas. First, one might take seriously the fact that GR formally has an infinity of rigid symmetries of the action and hence, by Noether's first theorem, an infinity of conserved energies-momenta (thus answering Schrödinger's 1918 false-negative objection). Second, Sean Carroll has asked (rhetorically) how one should modify the Dirac-Maxwell-Einstein equations to describe mental causation. This paper uses the generalized Bianchi identities to show that General Relativity tends to exclude, not facilitate, such Cartesian mental causation. In the simplest case, Cartesian mental influence must be spatio-temporally constant, and hence 0. The difficulty may diminish for more complicated models. Its persuasiveness is also affected by larger world-view considerations. The new general relativistic objection provides some support for realism about gravitational energy-momentum in GR (taking pseudotensor laws seriously). Such realism also answers an objection to theories of causation involving conserved quantities, because energies-momenta would be conserved even in GR.

physics.hist-ph↗

arXiv2019

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

Reflective equilibrium between physics and philosophy, and between GR and particle physics, is fruitful and rational. I consider the virtues of simplicity, conservatism, and conceptual coherence, along with perturbative expansions. There are too many theories to consider. Simplicity supplies initial guidance, after which evidence increasingly dominates. One should start with scalar gravity; evidence required spin 2. Good beliefs are scarce, so don't change without reason. But does conservatism prevent conceptual innovation? No: considering all serious possibilities (Feynman, Weinberg, etc.) could lead to Einstein's equations. (The rehabilitation of massive gravity shows that 'progress' isn't unidirectional.) GR is surprisingly intelligible. Energy localization makes sense if one believes Noether mathematics: an infinity of symmetries shouldn't produce just one energy. Hamiltonian change results from Lagrangian-equivalence. Causality poses conceptual questions. For GR, what are canonical 'equal-time' commutators? For massive spin 2, background causality exists but is violated. Both might be cured by engineering a background null cone respected by a gauge groupoid. Perturbative expansions can enlighten. They diagnose Einstein's 1917 'mass'-Lambda analogy. Ogievetsky-Polubarinov (1965) invented an infinity of massive spin 2 gravities -- including ghost-free de Rham-Gabadadze-Tolley (2010) theories! -- perturbatively, and achieved the impossible (c.f. Weyl, Cartan): spinors in coordinates.

physics.hist-ph↗

arXiv2019

What Are Observables in Hamiltonian Einstein-Maxwell Theory?

Is change missing in Hamiltonian Einstein-Maxwell theory? Given the most common definition of observables (having weakly vanishing Poisson bracket with each first-class constraint), observables are constants of the motion and nonlocal. Unfortunately this definition also implies that the observables for massive electromagnetism with gauge freedom (Stueckelberg) are inequivalent to those of massive electromagnetism without gauge freedom (Proca). The alternative Pons-Salisbury-Sundermeyer definition of observables, aiming for Hamiltonian-Lagrangian equivalence, uses the gauge generator G, a tuned sum of first-class constraints, rather than each first-class constraint separately, and implies equivalent observables for equivalent massive electromagnetisms. For General Relativity, G generates 4-dimensional Lie derivatives for solutions. The Lie derivative compares different space-time points with the same coordinate value in different coordinate systems, like 1 a.m. summer time vs. 1 a.m. standard time, so a vanishing Lie derivative implies constancy rather than covariance. Requiring equivalent observables for equivalent formulations of massive gravity confirms that $G$ must generate the $4$-dimensional Lie derivative (not $0$) for observables. These separate results indicate that observables are invariant under internal gauge symmetries but covariant under external gauge symmetries, but can this bifurcated definition work for mixed theories such as Einstein-Maxwell theory? Pons, Salisbury and Shepley have studied $G$ for Einstein-Yang-Mills. For Einstein-Maxwell, both $F_{μν}$ and $g_{μν}$ are invariant under electromagnetic gauge transformations and covariant (changing by a Lie derivative) under $4$-dimensional coordinate transformations. Using the bifurcated definition, these quantities count as observables, as one would expect on non-Hamiltonian grounds.

gr-qc↗

arXiv2018

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

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 \emph{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.

physics.hist-ph↗

arXiv2018

Equivalent Theories and Changing Hamiltonian Observables in General Relativity

Change and local spatial variation are missing in Hamiltonian General Relativity according to the most common definition of observables (0 Poisson bracket with all first-class constraints). But other definitions have been proposed. Seeking Hamiltonian-Lagrangian equivalence, Pons, Salisbury and Sundermeyer use the Anderson-Bergmann-Castellani gauge generator G, a tuned sum of first-class constraints. Kuchař waived the 0 Poisson bracket condition for the Hamiltonian constraint to achieve changing observables. A systematic combination of the two reforms might use the gauge generator but permit non-zero Lie derivative Poisson brackets. One can test definitions by calculation using two formulations of a theory, one without gauge freedom and one with it, which must have equivalent observables. For de Broglie-Proca non-gauge massive electromagnetism, all constraints are second-class, so everything is observable. Demanding equivalent observables from gauge Stueckelberg-Utiyama electromagnetism, one finds that the usual definition fails while the Pons-Salisbury-Sundermeyer definition with G succeeds. This definition does not readily yield change in GR, however. Should GR's external gauge freedom of General Relativity share with internal gauge symmetries the 0 Poisson bracket (invariance), or is covariance (a transformation rule) sufficient? A graviton mass breaks the gauge symmetry (general covariance), but it can be restored by parametrization with clock fields. By requiring equivalent observables, one vindicates the Lie derivative as the Poisson bracket of observables with the gauge generator G.

physics.gen-ph↗

arXiv2017

Space-time Constructivism vs. Modal Provincialism: Or, How Special Relativistic Theories Needn't Show Minkowski Chronogeometry

In 1835 Lobachevski entertained the possibility of multiple (rival) geometries. This idea has reappeared on occasion (e.g., Poincaré) but didn't become key in space-time foundations prior to Brown's \emph{Physical Relativity} (at the end, the interpretive key to the book). A crucial difference between his constructivism and orthodox "space-time realism" is modal scope. Constructivism applies to all local classical field theories, including those with multiple geometries. But the orthodox view provincially assumes a unique geometry, as familiar theories (Newton, Special Relativity, Nordström, and GR) have. They serve as the orthodox "canon." Their historical roles suggest a story of inevitable progress. Physics literature after c. 1920 is relevant to orthodoxy mostly as commentary on the canon, which closed in the 1910s. The orthodox view explains the behavior of matter as the manifestation of the real space-time geometry, which works within the canon. The orthodox view, Whiggish history, and the canon relate symbiotically. If one considers a theory outside the canon, space-time realism sheds little light on matter's behavior. Worse, it gives the wrong answer when applied to an example arguably in the canon, massive scalar gravity with universal coupling. Which is the true geometry---the flat metric from the Poincaré symmetry, the conformally flat metric exhibited by material rods and clocks, or both---or is the question bad? How does space-time realism explain that all matter fields see the same curved geometry, given so many ways to mix and match? Constructivist attention to dynamical details is vindicated; geometrical shortcuts disappoint. The more exhaustive exploration of relativistic field theories (especially massive) in particle physics is an underused resource for foundations.

physics.hist-ph↗

arXiv2017

Equivalent Theories Redefine Hamiltonian Observables to Exhibit Change in General Relativity

Change and local spatial variation are missing in canonical General Relativity's observables as usually defined, part of the problem of time. Definitions can be tested using equivalent formulations, non-gauge and gauge, because they must have equivalent observables and everything is observable in the non-gauge formulation. Taking an observable from the non-gauge formulation and finding the equivalent in the gauge formulation, one requires that the equivalent be an observable, constraining definitions. For massive photons, the de Broglie-Proca non-gauge formulation observable A_μ is equivalent to the Stueckelberg-Utiyama gauge formulation quantity A_μ+\partial_μ ϕ. Thus observables must have 0 Poisson bracket not with each first-class constraint, but with the Rosenfeld-Anderson-Bergmann-Castellani gauge generator G, a tuned sum of first-class constraints, in accord with the Pons-Salisbury-Sundermeyer definition of observables. The definition for external gauge symmetries can be tested using massive gravity, where one can install gauge freedom by parametrization with clock fields X^A. The non-gauge observable g^{μν} has the gauge equivalent X^A,_μ g^{μν} X^B,_ν. The Poisson bracket of X^A,_μ g^{μν} X^B,_ν with G turns out to be not 0 but a Lie derivative. This non-zero Poisson bracket refines and systematizes Kuchar's proposal to relax the 0 Poisson bracket condition with the Hamiltonian constraint. Thus observables need covariance, not invariance, in relation to external gauge symmetries. The Lagrangian and Hamiltonian for massive gravity are those of General Relativity + Lambda + 4 scalars, so the same definition of observables applies to General Relativity. Local fields such as g_{μν} are observables. Thus observables change. Requiring equivalent observables for equivalent theories also recovers Hamiltonian-Lagrangian equivalence.

gr-qc↗

arXiv2016

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

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 \emph{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.

physics.hist-ph↗

arXiv2016

Permanent Underdetermination from Approximate Empirical Equivalence in Field Theory: Massless and Massive Scalar Gravity, Neutrino, Electromagnetic, Yang-Mills and Gravitational Theories

Classical and quantum field theory provide not only realistic examples of extant notions of empirical equivalence, but also new notions of empirical equivalence, both modal and occurrent. A simple but modern gravitational case goes back to the 1890s, but there has been apparently total neglect of the simplest relativistic analog, with the result that an erroneous claim has taken root that Special Relativity could not have accommodated gravity even if there were no bending of light. The fairly recent acceptance of nonzero neutrino masses shows that widely neglected possibilities for nonzero particle masses have sometimes been vindicated. In the electromagnetic case, there is permanent underdetermination at the classical and quantum levels between Maxwell's theory and the one-parameter family of Proca's electromagnetisms with massive photons, which approximate Maxwell's theory in the limit of zero photon mass. While Yang-Mills theories display similar approximate equivalence classically, quantization typically breaks this equivalence. A possible exception, including unified electroweak theory, might permit a mass term for the photons but not the Yang-Mills vector bosons. Underdetermination between massive and massless (Einstein) gravity even at the classical level is subject to contemporary controversy.

physics.hist-ph↗

arXiv2016

Einstein's Physical Strategy, Energy Conservation, Symmetries, and Stability: "but Grossmann & I believed that the conservation laws were not satisfied"

Recent work on the history of General Relativity by Renn, Sauer, Janssen et al. shows that Einstein found his field equations partly by a physical strategy including the Newtonian limit, the electromagnetic analogy, and energy conservation. Such themes are similar to those later used by particle physicists. How do Einstein's physical strategy and the particle physics derivations compare? What energy-momentum complex(es) did he use and why? Did Einstein tie conservation to symmetries, and if so, to which? Einstein used an identity from his assumed linear coordinate covariance x'= Mx to relate it to the canonical tensor. Usually he avoided using matter Euler-Lagrange equations and so was not well positioned to use or reinvent the Herglotz-Mie-Born understanding that the canonical tensor was conserved due to translation symmetries, a result with roots in Lagrange, Hamilton and Jacobi. Whereas Mie and Born were concerned about the canonical tensor's asymmetry, Einstein did not need to worry because his Entwurf Lagrangian is modeled not so much on Maxwell's theory as on a scalar theory. As a result, it also has 3 ghosts, failing a 1920s-30s a priori particle physics stability test with antecedents in Lagrange's and Dirichlet's stability work. This critique of the Entwurf theory can be compared with Einstein's 1915 critique of his Entwurf theory for not admitting rotating coordinates and not getting Mercury's perihelion right. Particle physics also can be useful in the historiography of gravity and space-time. This topic can be a useful case study in the history of science on recently reconsidered questions of presentism, whiggism and the like.

physics.hist-ph↗