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Harvey R. Brown

Publications and source records attributed to Harvey R. Brown.

17 recordsLinked to original sources
arXiv2021

Do symmetries "explain" conservation laws? The modern converse Noether theorem vs pragmatism

Noether's first theorem does not establish a one-way explanatory arrow from symmetries to conservation laws, but such an arrow is widely assumed in discussions of the theorem in the physics and philosophy literature. It is argued here that there are pragmatic reasons for privileging symmetries, even if they do not strictly justify explanatory priority. To this end, some practical factors are adduced as to why Noether's direct theorem seems to be more well-known and exploited than its converse, with special attention being given to the sometimes overlooked nature of Noether's converse result and to its strengthened version due to Luis Martínez Alonso in 1979 and Peter Olver in 1986.

physics.hist-ph↗
arXiv2020

Everettian probabilities, the Deutsch-Wallace theorem and the Principal Principle

This paper is concerned with the nature of probability in physics, and in quantum mechanics in particular. It starts with a brief discussion of the evolution of Itamar Pitowsky's thinking about probability in quantum theory from 1994 to 2008, and the role of Gleason's 1957 theorem in his derivation of the Born Rule. Pitowsky's defence of probability therein as a logic of partial belief leads us into a broader discussion of probability in physics, in which the existence of objective "chances" is questioned, and the status of David Lewis' influential Principal Principle is critically examined. This is followed by a sketch of the work by David Deutsch and David Wallace which resulted in the Deutsch-Wallace (DW) theorem in Everettian quantum mechanics. It is noteworthy that the authors of this important decision-theoretic derivation of the Born Rule have different views concerning the meaning of probability. The theorem, which was the subject of a 2007 critique by Meir Hemmo and Pitowsky, is critically examined, along with recent related work by John Earman. Here our main argument is that the DW theorem does not provide a justification of the Principal Principle, contrary to claims by Wallace and Simon Saunders. A final section analyses recent claims to the effect that that the DW theorem is redundant, a conclusion that seems to be reinforced by consideration of probabilities in "deviant' branches in the Everettian multiverse.

quant-ph↗
arXiv2016

Clarifying possible misconceptions in the foundations of general relativity

We discuss what we take to be three possible misconceptions in the foundations of general relativity, relating to: (a) the interpretation of the weak equivalence principle and the relationship between gravity and inertia; (b) the connection between gravitational redshift results and spacetime curvature; and (c) the Einstein equivalence principle and the ability to "transform away" gravity in local inertial coordinate systems.

physics.hist-ph↗
arXiv2014

Bell on Bell's theorem: The changing face of nonlocality

Between 1964 and 1990, the notion of nonlocality in Bell's papers underwent a profound change as his nonlocality theorem gradually became detached from quantum mechanics, and referred to wider probabilistic theories involving correlations between separated beables. The proposition that standard quantum mechanics is itself nonlocal (more precisely, that it violates `local causality') became divorced from the Bell theorem per se from 1976 on, although this important point is widely overlooked in the literature. In 1990, the year of his death, Bell would express serious misgivings about the mathematical form of the local causality condition, and leave ill-defined the issue of the consistency between special relativity and violation of the Bell-type inequality. In our view, the significance of the Bell theorem, both in its deterministic and stochastic forms, can only be fully understood by taking into account the fact that a fully Lorentz-covariant version of quantum theory, free of action-at-a-distance, can be articulated in the Everett interpretation.

quant-ph↗
arXiv2014

Ambiguities in order-theoretic formulations of thermodynamics

Since the 1909 work of Carathéodory, formulations of thermodynamics have gained ground which highlight the role of the the binary relation of adiabatic accessibility between equilibrium states. A feature of Carathéodory's system is that the version therein of the second law contains an ambiguity about the nature of irreversible adiabatic processes, making it weaker than the traditional Kelvin-Planck statement of the law. This paper attempts first to clarify the nature of this ambiguity, by defining the arrow of time in thermodynamics by way of the Equilibrium Principle ("Minus First Law"). It then argues that the ambiguity reappears in the important 1999 axiomatisation due to Lieb and Yngvason.

physics.class-ph↗
arXiv2014

The theory of the rise of sap in trees: some historical and conceptual remarks

The ability of trees to suck water from roots to leaves, sometimes to heights of over a hundred meters, is remarkable given the absence of any mechanical pump. This study deals with a number of issues, of both an historical and conceptual nature, in the orthodox Cohesion Tension theory of the ascent of sap in trees. The theory relies chiefly on the exceptional cohesive and adhesive properties of water, the structural properties of trees, and the role of evaporation (transpiration) from leaves. But it is not the whole story. Plant scientists have been aware since the inception of the theory in the late 19th century that further processes are at work in order to prime the trees, the main such process (growth itself) being so obvious to them that it is often omitted from the story. Other factors depend largely on the type of tree, and are not always fully understood. For physicists, in particular, it may be helpful to see the fuller picture, which is what this study attempts to provide in nontechnical terms.

physics.hist-ph↗
arXiv2013

Einstein, the reality of space, and the action-reaction principle

Einstein regarded as one of the triumphs of his 1915 theory of gravity --- the general theory of relativity --- that it vindicated the action--reaction principle, while Newtonian mechanics as well as his 1905 special theory of relativity supposedly violated it. In this paper we examine why Einstein came to emphasise this position several years after the development of general relativity. Several key considerations are relevant to the story: the connection Einstein originally saw between Mach's analysis of inertia and both the equivalence principle and the principle of general covariance, the waning of Mach's influence owing to de Sitter's 1917 results, and Einstein's detailed correspondence with Moritz Schlick in 1920.

physics.hist-ph↗
arXiv2008

Boltzmann's H-theorem, its limitations, and the birth of (fully) statistical mechanics

A comparison is made of the traditional Loschmidt (reversibility) and Zermelo (recurrence) objections to Boltzmann's H-theorem, and its simplified variant in the Ehrenfests' 1912 wind-tree model. The little-cited 1896 (pre-recurrence) objection of Zermelo (similar to an 1889 argument due to Poincare) is also analysed. Significant differences between the objections are highlighted, and several old and modern misconceptions concerning both them and the H-theorem are clarified. We give particular emphasis to the radical nature of Poincare's and Zermelo's attack, and the importance of the shift in Boltzmann's thinking in response to the objections as a whole.

physics.hist-ph↗
arXiv2006

Why special relativity should not be a template for a fundamental reformulation of quantum mechanics

In a comparison of the principles of special relativity and of quantum mechanics, the former theory is marked by its relative economy and apparent explanatory simplicity. A number of theorists have thus been led to search for a small number of postulates - essentially information theoretic in nature - that would play the role in quantum mechanics that the relativity principle and the light postulate jointly play in Einstein's 1905 special relativity theory. The purpose of the present paper is to resist this idea, at least in so far as it is supposed to reveal the fundamental form of the theory. It is argued that the methodology of Einstein's 1905 theory represents a victory of pragmatism over explanatory depth; and that its adoption only made sense in the context of the chaotic state state of physics at the start of the 20th century - as Einstein well knew.

quant-ph↗
arXiv2004

Minkowski space-time: a glorious non-entity

Einstein distinguished between ``principle'' and ``constructive'' theories in physics, and although he thought the latter were more explanatory than the former, he regarded his 1905 formulation of special relativity theory as a principle theory. Some have claimed that Minkowski space-time can serve as the deep structure within a constructive reformulation of special relativity. We criticise this claim, and argue that a satisfactory constructive version of special relativity must involve a dynamical treatment of the forces holding together the constitutive parts of moving rods and clocks.

physics.hist-ph↗
arXiv2000

Noether's Theorems and Gauge Symmetries

Consideration of the Noether variational problem for any theory whose action is invariant under global and/or local gauge transformations leads to three distinct theorems. These include the familiar Noether theorem, but also two equally important but much less well-known results. We present, in a general form, all the main results relating to the Noether variational problem for gauge theories, and we show the relationships between them. These results hold for both Abelian and non-Abelian gauge theories.

hep-th↗
arXiv1999

The origin of the spacetime metric: Bell's `Lorentzian pedagogy' and its significance in general relativity

The purpose of this paper is to evaluate the `Lorentzian pedagogy' defended by J.S. Bell in his essay ``How to teach special relativity'', and to explore its consistency with Einstein's thinking from 1905 to 1952. Some remarks are also made in this context on Weyl's philosophy of relativity and his 1918 gauge theory. Finally, it is argued that the Lorentzian pedagogy - which stresses the important connection between kinematics and dynamics - clarifies the role of rods and clocks in general relativity.

gr-qc↗
arXiv1998

Remarks on identical particles in de Broglie-Bohm theory

It is argued that the topological approach to the (anti-)symmetrisation condition for the quantum state of a collection of identical particles, defined in the `reduced' configuration space, is particularly natural from the perspective of de Broglie-Bohm pilot-wave theory.

quant-ph↗