Symmetry and asymmetry in electrodynamics from Rowland to Einstein

Halfway through the paper in which he laid down the foundations for the theory of special relativity, Einstein concludes that “the asymmetry mentioned in the Introduction … disappears.” Making asymmetry disappear has proved to be one of Einstein's many significant moves in his annus mirabilis of 1905. This elimination of asymmetry has led many commentators to claim that Einstein was motivated by either an aesthetic or an epistemic argument which gives priority to symmetry over asymmetry. Following closely the development of electrodynamics in the period from 1880 to 1905 and the usage of the related terms reciprocity and symmetry, we suggest a different way of understanding Einstein's motivation and the path he took. In contrast to the received view, we argue that Einstein responded to a debate in the literature on electrodynamics and that he was concerned neither with an aesthetic nor with an epistemic argument; rather, his reasoning was physical in the best sense, and most original. We will show that by providing a new perspective on the relation between electricity and magnetism, Einstein succeeded in bringing the discussion of symmetry in electrodynamics to an end.     

Einstein's struggle for a Machian gravitation theory

The story of Einstein's struggle to create a general theory of relativity, and his early discontentment with the final form of the theory (1915), is well known in broad outline. Thanks to the work of John Norton and others, much of the fine detail of the story is also now known. One aspect of Einstein's work in this period has, however, been relatively neglected: Einstein's commitment to Mach's ideas on inertia, and the influence this commitment had on Einstein's work on general relativity from 1907 to 1918. In this paper published writings and archival material are examined, to try to reconstruct the details of Einstein's thinking about inertia and gravitation, and the role that Mach's ideas played in Einstein's crucial work on the general theory. By the end, a clear picture of Einstein's conceptions of Mach's ideas on inertia, and their philosophical motivations, will emerge. Several surprising conclusions also emerge: Einstein's desire for a Machian gravitation theory was the central force driving his work from 1912 to 1915, keeping him going despite numerous frustrating setbacks; Einstein's continued commitment to Mach's ideas in 1916–1917 kept him at work trying various strategies of modification of the field equations, in order to exclude anti-Machian solutions (including the addition of the cosmological constant in 1917); and as late as early 1918, Einstein was ready to call the whole General Theory a failure if no way of squaring it with Mach's ideas on inertia could be found. But by 1920 Einstein advocated a view that granted spacetime (under the name ‘ether’) independent existence with physical qualities of its own, a complete break with his earlier Machian views.     

狭义相对论与丁格尔时钟悖论 --对一场著名争论的回顾与再认识

1967年10月14日《自然》杂志发表了H 丁格尔教授反对狭义相对论的论证和W．H．麦克利教授对丁格尔论证的批评。本文指出麦克利对丁格尔的批评是不能成立的,因为麦克利为反对丁格尔观点而画出的时空图恰恰是支持丁格尔的,提出：丁格尔的论证就其反对爱因斯坦从狭义相对论引出的结论——“运动的钟比静止时走得慢”——是成立的,就其反对狭义相对论是不成立的：狭义相对论自身在逻辑上是无矛盾和完备的,而爱因斯坦从狭义相对论中得出“运动的钟变慢”的结论是不对的。文章阐明了狭义相对论与“钟慢效应实验证据”的正确关系。     

Did Einstein prove E=mc2?

Although Einstein's name is closely linked with the celebrated relation E=mc² between mass and energy, a critical examination of the more than half dozen “proofs” of this relation that Einstein produced over a span of forty years reveals that all these proofs suffer from mistakes. Einstein introduced unjustified assumptions, committed fatal errors in logic, or adopted low-speed, restrictive approximations. He never succeeded in producing a valid general proof applicable to a realistic system with arbitrarily large internal speeds. The first such general proof was produced by Max Laue in 1911 (for “closed” systems with a time-independent energy–momentum tensor) and it was generalized by Felix Klein in 1918 (for arbitrary time-dependent “closed” systems).     

Between autobiography and reality: Popper's inductive years

On the basis of his unpublished thesis ‘Gewohnheit und Gesetzerlebnis in der Erziehung’ (1926–7) a historical reconstruction is given of the genesis of Popper's ideas on induction and demarcation which differs radically from his own account in Unended quest. It is shown not only that he wholeheartedly endorses inductive epistemology and psychology but also that his ‘demarcation’ criterion is inductivistic. Moreover it is shown that his later demarcation thesis arises not from his worries about, on the one hand, Marxism and psychoanalysis and, on the other hand, Einstein's physics, but rather from his urgent preoccupation with providing pedagogy with a psychological foundation, which has its sources in Karl Bühler's cognitive psychology as well as, surprisingly, Adler's Characterology. Aside from Adler some lesser known psychologists, such as Karl Groos, will also be seen to have played a formative role on Popper's early thinking.     

Finding your marbles in wavefunction collapse theories

Lewis (Br. J. Philos. Sci. 48 (1997) 313) has recently presented an argument claiming that, under the Ghirardi–Rimini–Weber (GRW) theory of quantum mechanics, arithmetic does not apply to ordinary macroscopic objects such as marbles (known as the Counting Anomaly). In this paper, I disentangle two different lines of Lewis's argument, one devoted to what I call the standard GRW interpretation and the other to the mass density interpretation (MDI). I present both strains of Lewis's argument, and move on to criticise Lewis's position, focusing on his argument with respect to MDI. I analyse the structure of his argument, and follow this with a novel refutation of Lewis's argument, drawing on the original presentation of MDI as developed by Ghirardi et al. (Found. Phys. 25 (1995) 5). I briefly consider the debate that ensued between Bassi and Ghirardi and Clifton and Monton and interpret it within the context of my analysis. I conclude that Lewis's Counting Anomaly fails to generate a genuine problem.     

Comment on ‘Stapp's theorem without counterfactual commitment’

Michael Dickson has examined the ‘could’ version of my nonlocality theorem, and claims to have found a flaw. Several errors in his argument are pointed out. The main problem is that he replaces my locality criterion by a substitute that is too weak to do the job. His justification for making this change is critically flawed by a failure to differentiate my sufficient condition from the converse necessary condition. Nevertheless, Dickson succeeds in deriving all but the final step of my argument. My justification for this final crucial step is discussed here in some detail.     

Ludwig Boltzmann and his influence on science

The life of Ludwig Boltzmann (20 February 1844–5 September 1906) and his influence on science is reviewed. This great Austrian scientist was not only the founder of statistical mechanics and a gifted experimentalist, but his pioneering ideas influenced all the physical sciences. In his honour, many Austrian research institutes carry his name. He had great influence on Albert Einstein whose first papers were, according to his own words, in the spirit of Boltzmann, and intended to proved the reality and the size of certain atoms using the molecular fluctuations postulated by Boltzmann. Max Planck was converted from a ‘Saulus’ to a ‘Paulus’ when he had to use Boltzmann's method to derive his famous law of radiation. In fact, Boltzmann had already used discrete energy levels as early as 1872. Yet his work was heavily criticized by the neopositivists around Ernst Mach and seemed to receive very little attention in the last years of his life when a great number of physicists did not believe in atoms. It is the tragedy of Boltzmann's life that he did not experience the glorius victory of his ideas, but died under the gloomy vision that the work of his whole life was doomed to oblivion.     

On the “negative utility” of Ernst Cassirer׳s philosophy of physics: An application to the EPR argument

This paper tries to reconstruct Ernst Cassirer's potential reception of the EPR argument, as exposed by Einstein in his letter to Cassirer of March 1937. It is shown that, in conformity with his transcendental epistemology taking the conditions of accessibility as constitutive of the quantum object, Cassirer would probably have rejected the argument. Indeed, Cassirer would probably not have subscribed to its separability/local causality presupposition (which goes against his interpretation of the quantum formalism as a self-sufficient condition constitutive of the quantum object, without any reliance on spatial intuition), nor to its completeness requirement (as his partial endorsement of Bohr's complementarity, and his rejection of the Kantian "idea of complete determination", illustrate). By rejecting both of its premises, Cassirer's philosophy of physics thus enables to escape the EPR dilemma, and exhibits what, in Kantian terms, might be called a "negative utility" with respect to physical science. A further investigation of the anti-reductionist utility of Cassirer's systematic philosophy with respect to physics and other "symbolic forms" is finally suggested.     

`Nature is the Realisation of the Simplest Conceivable Mathematical Ideas': Einstein and the Canon of Mathematical Simplicity

Einstein proclaimed that we could discover true laws of nature by seeking those with the simplest mathematical formulation. He came to this viewpoint later in his life. In his early years and work he was quite hostile to this idea. Einstein did not develop his later Platonism from a priori reasoning or aesthetic considerations. He learned the canon of mathematical simplicity from his own experiences in the discovery of new theories, most importantly, his discovery of general relativity. Through his neglect of the canon, he realised that he delayed the completion of general relativity by three years and nearly lost priority in discovery of its gravitational field equations.     

Why the Afshar experiment does not refute complementarity

A modified version of Young's experiment by Shahriar Afshar demonstrates that, prior to what appears to be a “which-way” measurement, an interference pattern exists. Afshar has claimed that this result constitutes a violation of the Principle of Complementarity. This paper discusses the implications of this experiment and considers how Cramer's Transactional Interpretation easily accommodates the result. It is also shown that the Afshar experiment is analogous in key respects to a spin one-half particle prepared as “spin up along x”, subjected to a nondestructive confirmation of that preparation, and post-selected in a specific state of spin along z. The terminology “which-way” or “which-slit” is critiqued; it is argued that this usage by both Afshar and his critics is misleading and has contributed to confusion surrounding the interpretation of the experiment. Nevertheless, it is concluded that Bohr would have had no more problem accounting for the Afshar result than he would in accounting for the aforementioned pre- and post-selection spin experiment, in which the particle's preparation state is confirmed by a nondestructive measurement prior to post-selection. In addition, some new inferences about the interpretation of delayed choice experiments are drawn from the analysis.     

Paul Natorp and the emergence of anti-psychologism in the nineteenth century

This paper examines the anti-psychologism of Paul Natorp, a Marburg School Neo-Kantian. It identifies both Natorp’s principle argument against psychologism and the views underlying the argument that give it its force. Natorp’s argument depends for its success on his view that certain scientific laws constitute the intersubjective content of knowledge. That view in turn depends on Natorp’s conception of subjectivity, so it is only against the background of his conception of subjectivity that his reasons for rejecting psychologism make sense. This interpretation of Natorp suggests that attention paid to late nineteenth century theories of subjectivity and philosophy of psychology could improve our understanding of the emergence of anti-psychologism in that period.     

Gauge theories and holisms

Those looking for holism in contemporary physics have focused their attention primarily on quantum entanglement. But some gauge theories arguably also manifest the related phenomenon of nonseparability. While the argument is strong for the classical gauge theory describing electromagnetic interactions with quantum “particles”, it fails in the case of general relativity even though that theory may also be formulated in terms of a connection on a principal fiber bundle. Anandan has highlighted the key difference in his analysis of a supposed gravitational analog to the Aharonov–Bohm effect. By contrast with electromagnetism in the original Aharonov–Bohm effect, gravitation is separable and exhibits no novel holism in this case. Whether the nonseparability of classical gauge theories of nongravitational interactions is associated with holism depends on what counts as the relevant part–whole relation. Loop representations of quantized gauge theories of nongravitational interactions suggest that these conclusions about holism and nonseparability may extend also to quantum theories of the associated fields.     

Space–time philosophy reconstructed via massive Nordström scalar gravities? Laws vs. geometry,conventionality, and underdetermination

What if gravity satisfied the Klein–Gordon equation? Both particle physics from the 1920–30s and the 1890s Neumann–Seeliger modification of Newtonian gravity with exponential decay suggest considering a “graviton mass term” for gravity, which is algebraic in the potential. Unlike Nordström׳s “massless” theory, massive scalar gravity is strictly special relativistic in the sense of being invariant under the Poincaré group but not the 15-parameter Bateman–Cunningham conformal group. It therefore exhibits the whole of Minkowski space–time structure, albeit only indirectly concerning volumes. Massive scalar gravity is plausible in terms of relativistic field theory, while violating most interesting versions of Einstein׳s principles of general covariance, general relativity, equivalence, and Mach. Geometry is a poor guide to understanding massive scalar gravity(s): matter sees a conformally flat metric due to universal coupling, but gravity also sees the rest of the flat metric (barely or on long distances) in the mass term. What is the ‘true’ geometry, one might wonder, in line with Poincaré׳s modal conventionality argument? Infinitely many theories exhibit this bimetric ‘geometry,’ all with the total stress–energy׳s trace as source; thus geometry does not explain the field equations. The irrelevance of the Ehlers–Pirani–Schild construction to a critique of conventionalism becomes evident when multi-geometry theories are contemplated. Much as Seeliger envisaged, the smooth massless limit indicates underdetermination of theories by data between massless and massive scalar gravities—indeed an unconceived alternative. At least one version easily could have been developed before General Relativity; it then would have motivated thinking of Einstein׳s equations along the lines of Einstein׳s newly re-appreciated “physical strategy” and particle physics and would have suggested a rivalry from massive spin 2 variants of General Relativity (massless spin 2, Pauli and Fierz found in 1939). The Putnam–Grünbaum debate on conventionality is revisited with an emphasis on the broad modal scope of conventionalist views. Massive scalar gravity thus contributes to a historically plausible rational reconstruction of much of 20th–21st century space–time philosophy in the light of particle physics. An appendix reconsiders the Malament–Weatherall–Manchak conformal restriction of conventionality and constructs the ‘universal force’ influencing the causal structure.Subsequent works will discuss how massive gravity could have provided a template for a more Kant-friendly space–time theory that would have blocked Moritz Schlick׳s supposed refutation of synthetic a priori knowledge, and how Einstein׳s false analogy between the Neumann–Seeliger–Einstein modification of Newtonian gravity and the cosmological constant Λ generated lasting confusion that obscured massive gravity as a conceptual possibility.     

Mechanisms, principles, and Lorentz's cautious realism

I show that Albert Einstein's distinction between principle and constructive theories was predated by Hendrik A. Lorentz's equivalent distinction between mechanism- and principle-theories. I further argue that Lorentz's views toward realism similarly prefigure what Arthur Fine identified as Einstein's “motivational realism.”     

From natural history to political economy: the enlightened mission of Domenico Vandelli in late eighteenth-century Portugal

This article presents the main features of the work of Domenico Vandelli (1735–1816), an Italian-born man of science who lived a large part of his life in Portugal. Vandelli’s scientific interests as a naturalist paved the way to his activities as a reformer and adviser on economic and financial issues. The topics covered in his writings are similar to those discussed by Linnaeus, with whom Vandelli corresponded. They clearly reveal that the scientific preparation indispensable for a better knowledge of natural resources was also a fundamental condition for correctly addressing problems of efficiency in their economic allocation. The key argument put forward in this article is that the relationship between natural history and the agenda for economic reform and development deserves to be further analysed. It is indeed a central element in the emergence of political economy as an autonomous scientific discourse during the last decades of the eighteenth century.     

Experimentation in the cosmic laboratory

It might seem impossible to apply Ian Hacking's experimental argument for scientific realism to astrophysical objects; indeed Hacking himself expressed scepticism about extragalactic entities. Such astrophysical antirealism has been the subject of intense debate and is usually seen as an undesired consequence of experimental realism. In this paper, I claim that it is possible to recast the experimental argument by reference to James Woodward's non-anthropocentric account of experimentation so as to apply it to astrophysical entities, such as gravitational lenses. I also argue that this new formulation of the experimental argument solves several problems with Hacking's original version.     

The literature and the science of ‘two cultures’ historiography

This paper discusses the historiography of the ‘two cultures’ controversy. C. P. Snow’s lament about the ‘two cultures’, literary and scientific, has inspired a wide range of comment—much of which begins by citing Snow and his thesis, before going on to discuss very different things. This paper focuses upon one strand of this commentary, the historical analysis of the controversy itself. A ‘historical’ analysis is defined here as one that resists the impulse to enter the argument on behalf of Snow or Leavis, to conceive of their argument in the terms that Snow defined, or to invoke their argument as a precursor to some contemporary issue. Instead, a historical interpretation registers distance between that day and this, takes the controversy itself as its object of study, and explores the tensions and associations that came to be packed into those now familiar terms. As the fiftieth anniversary of Snow’s Rede Lecture nears, this approach—rather than the repetition of clichés about the bridging of cultures—offers both analytical perspective on the controversy and interpretive possibilities for its examination.