This inaugural handbook documents the distinctive research field that utilizes history and philosophy in investigation of theoretical, curricular and pedagogical issues in the teaching of science and mathematics. It is contributed to by 130 researchers from 30 countries; it provides a logically structured, fully referenced guide to the ways in which science and mathematics education is, informed by the history and philosophy of these disciplines, as well as by the philosophy of education more generally. The first handbook to cover the (...) field, it lays down a much-needed marker of progress to date and provides a platform for informed and coherent future analysis and research of the subject. -/- The publication comes at a time of heightened worldwide concern over the standard of science and mathematics education, attended by fierce debate over how best to reform curricula and enliven student engagement in the subjects There is a growing recognition among educators and policy makers that the learning of science must dovetail with learning about science; this handbook is uniquely positioned as a locus for the discussion. -/- The handbook features sections on pedagogical, theoretical, national, and biographical research, setting the literature of each tradition in its historical context. Each chapter engages in an assessment of the strengths and weakness of the research addressed, and suggests potentially fruitful avenues of future research. A key element of the handbook’s broader analytical framework is its identification and examination of unnoticed philosophical assumptions in science and mathematics research. It reminds readers at a crucial juncture that there has been a long and rich tradition of historical and philosophical engagements with science and mathematics teaching, and that lessons can be learnt from these engagements for the resolution of current theoretical, curricular and pedagogical questions that face teachers and administrators. (shrink)

Thought experiments are described in which the one-way velocity of light appears as a physical quantity. A rotating shaft is used to define distant synchrony for a system of clocks along the shaft. In this context Einstein's definition of distant simultaneity is seen as based on a physical assumption (and not merely on an overwhelmingly sensible choice in a range of conventional possibilities).

Timelines is an inquiry into the nature of time, both as an apparent feature of the external physical world and as a fundamental feature of our experience of ourselves in the world. The principal argument of Timelines is that our coventional ideas about time are largely mistaken and that what we think of as independent physical time is actually our calibration of a certain relation between events. Namely, the relation between time-keeping events and the causal sequential differences of physical processes (...) which are real and independent of us. (shrink)

In this paper we recall, improve, and extend several definitions, properties and applications of our previous 2019 research referred to NeutroAlgebras and AntiAlgebras (also called NeutroAlgebraic Structures and respectively AntiAlgebraic Structures). Let <A> be an item (concept, attribute, idea, proposition, theory, etc.). Through the process of neutrosphication, we split the nonempty space we work on into three regions {two opposite ones corresponding to <A> and <antiA>, and one corresponding to neutral (indeterminate) <neutA> (also denoted <neutroA>) between the opposites}, which may (...) or may not be disjoint – depending on the application, but they are exhaustive (their union equals the whole space). A NeutroAlgebra is an algebra which has at least one NeutroOperation or one NeutroAxiom (axiom that is true for some elements, indeterminate for other elements, and false for the other elements). A Partial Algebra is an algebra that has at least one Partial Operation, and all its Axioms are classical (i.e. axioms true for all elements). Through a theorem we prove that NeutroAlgebra is a generalization of Partial Algebra, and we give examples of NeutroAlgebras that are not Partial Algebras. We also introduce the NeutroFunction (and NeutroOperation). (shrink)

Abstract.Einstein learned from the magnet and conductor thought experiment how to use field transformation laws to extend the covariance of Maxwell’s electrodynamics. If he persisted in his use of this device, he would have found that the theory cleaves into two Galilean covariant parts, each with different field transformation laws. The tension between the two parts reflects a failure not mentioned by Einstein: that the relativity of motion manifested by observables in the magnet and conductor thought experiment does not extend (...) to all observables in electrodynamics. An examination of Ritz’s work shows that Einstein’s early view could not have coincided with Ritz’s on an emission theory of light, but only with that of a conveniently reconstructed Ritz. One Ritz-like emission theory, attributed by Pauli to Ritz, proves to be a natural extension of the Galilean covariant part of Maxwell’s theory that happens also to accommodate the magnet and conductor thought experiment. Einstein’s famous chasing a light beam thought experiment fails as an objection to an ether-based, electrodynamical theory of light. However it would allow Einstein to formulate his general objections to all emission theories of light in a very sharp form. Einstein found two well known experimental results of 18th and 19th century optics compelling (Fizeau’s experiment, stellar aberration), while the accomplished Michelson-Morley experiment played no memorable role. I suggest they owe their importance to their providing a direct experimental grounding for Lorentz‘ local time, the precursor of Einstein’s relativity of simultaneity, and doing it essentially independently of electrodynamical theory. I attribute Einstein’s success to his determination to implement a principle of relativity in electrodynamics, but I urge that we not invest this stubbornness with any mystical prescience. (shrink)

In this article I argue for an empiricist view on laws. Some laws are fundamental in the sense that they are the result of inductive generalisations of observed regularities and at the same time in their formulation contain a new theoretical predicate. The inductive generalisations simul- taneously function as implicit definitions of these new predicates. Other laws are either explicit definitions or consequences of other previously established laws. I discuss the laws of classical mechanics, relativity theory and electromagnetism in detail. (...) Laws are necessary, whereas acciden- tal generalisations are not. But necessity here is not a modal concept, but rather interpreted as short for the semantic predicate “... is necessarily true”. Thus no modal logic is needed. The neces- sity attributed to law sentences is in turn interpreted as “necessary condition for the rest of the the- ory”, which is true since fundamental laws are implicit definitions of theoretical predicates use in the theory. (shrink)

In her articles on the clock paradox and the relativity of time Luise Lange (1891–1978) defends the theory of relativity against philosophical refutations, by showing that the apparent clock paradox is not a paradox, but merely conflicts with common sense and is based on a misunderstanding of the theory. The following study explores, contextualizes and analyzes Lange’s clear and sophisticated contribution to the debate on the clock paradox for the first time.

The mind of man is central to the structure and functioning of the physical world. Modern physical theory indicates that the mind stands in a relationship of equals to the physical world. Both are fundamental, neither can be reduced to the other, and both require each other for their full understanding. This thesis is at odds with the view of the universe found in Newtonian mechanics as well as the generally held view among contemporary physicists of modern physical theory. Since (...) the Renaissance, man has come to understand a great deal about the physical world, and he has gained significant control over it. This increased power over the physical world has occurred hand in hand with the assumption that the structure and functioning of the physical world is essentially independent from his cognitive functioning. According to this assumption, if man’s cognitive capacity did not exist, the functioning of the physical world would not be fundamentally altered. This last statement is not in fact correct, and modern physical theory, and even fundamentals underlying Newtonian mechanics, provide evidence to attest to this. Nonetheless, contemporary physicists for the most part do not see that the relationship of human cognition to the physical world is radically altered in their own modern theory, theory that is supported by a great deal of empirical data. Instead, attempting to preserve the thesis that the structure and functioning of the physical world is independent of the mind while on a practical level relying on modern theory that contradicts this thesis, physicists have placed themselves in the position of wondering at times exactly what is the nature of the physical world at the same time they obtain experimental results concerning the physical world that can only be labeled astonishing in their precision and the scope of their implications. Modern physical theory consists of three main components: 1) the special and general theories of relativity; 2) quantum mechanics; and 3) statistical mechanics. There are very successful theories that have been developed on the basis of these three bedrock areas. An example of one is quantum electrodynamics. But these theories owe their conceptual foundation to the three components mentioned. The basic issues at the core of these three components also are expressed in these later theories. In addition, there are new unresolved issues of a fundamental nature concerning the conceptual integrity of these later theories that do not apply to quantum mechanics, relativity theory, and statistical mechanics. Quantum mechanics and relativity theory are areas I have written about for over twelve years. The nature of statistical mechanics has also been of interest to me during this time. But when I took a serious look in 1993 at Tolman’s (1938) The Principles of Statistical Mechanics, it became clear that the mind is linked to the physical world in statistical mechanics, a relationship I had found earlier in both relativity theory and quantum mechanics. It was after reading Tolman’s justification of the method of statistical mechanics in the original that I decided to write this book. When I found that the three components of modern physical theory all pointed to the same relationship between mind and the physical world, it became clear that the fundamental isolation of the mind from the physical world that has characterized our experience since the development of Newtonian mechanics is unfounded. Based on empirically supported principles of modern physical theory, I determined that the appropriate assumption for one’s experience, that the mind is linked to the physical world, could be stated with confidence. The impact of this change in assumption concerning the relationship of man to the cosmos in modern physical theory will find its way into our everyday experience. It will perhaps have no greater effect than in reducing the sense of isolation of man from the world that has characterized modern existence. (shrink)

The ArgumentEinstein's concept of causality as analyzed in this paper is a thick concept comprised of: (a) regularity; (b) locality; (c) symmetry considerations leading to conservation laws; (d) mutuality of causal interaction. The main theses are: 1. Since (b)–(d) are not elements of Hume's concept of causality, Einstein's concept, the concept embedded in the theory of relativity, is manifestly non–Humean. 2. On a Humean conception, Newtonian mechanics is a paradigmatically causal theory. Einstein, however, regarded this theory as causally deficient, for (...) it fails to comply with both (b) and (d). Special relativity was (partly) motivated by the wish to correct the first of these failures; general relativity the second. 3. Ironically, general relativity, based on the thick concept of causality, opens the way for a conventionalist understanding of that concept. 4. With regard to human freedom, Einstein professed to be a Spinozist. However, he suggested a version of soft determinism, not found in Spinoza. (shrink)

In this article, I limn the remarkable ascent of Albert Einstein and Wassily Kandinsky into our cultural pantheon. I depict how both figures mastered and transcended their respective fields, and how they called into question long-established disciplinary assumptions and practices. I also demonstrate how the creative works of Einstein and Kandinsky constructed, and were constructed by, the reality we now call "modern.".

In relativistic theories, the assumption of proper mass constancy generally holds. We study gravitational relativistic mechanics of point particle in the novel approach of proper mass varying under Minkowski force action. The motivation and objective of this work are twofold: first, to show how the gravitational force can be included in the Special Relativity Mechanics framework, and, second, to investigate possible consequences of the revision of conventional proper mass concept (in particular, to clarify a proper mass role in the divergence (...) problem). It is shown that photon motion in the gravitational field can be treated in terms of massless refracting medium, what makes the gravity phenomenon compatible with SR Mechanics framework in the variable proper mass approach.Specifically, the problem of point particle in the spherical symmetric stationary gravitational field is studied in SR-based Mechanics, and equations of motion in the Lorentz covariant form are obtained in the relativistic Lagrangean problem formulation. The dependence of proper mass on potential field strength is derived from the Euler-Lagrange equations as well. One of new results is the elimination of conventional 1/r divergence, which is known to be not removable in Schwarzschild gravitomechanics. Predictions of particle and photon gravitational properties are in agreement with GR classical tests under weak-field conditions; however, deviations rise with potential field strength. The conclusion is made that the approach of field-dependent proper mass is perspective for development of SR gravitational mechanics and further studies of gravitational problems. (shrink)

Ernst Mach is the only person whom Einstein included on both the list of physicists he considered his true precursors, and the list of the philosophers who had most affected him. Einstein scholars have been less generous in their estimation of Mach's contributions to Einstein's work, and even amongst the more generous of them, Mach's great achievements in physics are seldom mentioned in this context. This is odd, considering Mach was nominated for the Nobel Prize in Physics three times. In (...) this paper, I examine some of Mach's work in physics that bears conceptually on Einstein's 1905 paper on Special Relativity ("On The Electrodynamics of Moving Bodies"). Mach was the first to give the correct explanation of the Doppler Effect, and he presented it in a way that Einstein echoes in his 1905 paper: laying out two apparently contradictory principles and showing how both can be retained. It is also notable that Mach's explanation was explicit about not relying on the existence of a medium of transmission for the propagation of light waves. In his work on supersonic shock waves, Mach invokes the constancy of the velocity of sound (i.e., its independence of the motion of the sound source) , just as he had invoked the constancy of the velocity of light in his work on the Doppler Effect for Light. I examine the analogies between light and sound that were drawn upon by Einstein and Mach, as well as one analogy that Einstein could have, but did not make: Cherenkov radiation, or "singing electrons", i.e., cases in which the sound of light in the medium of transmission is exceeded, which results in an optical analogue of supersonic shock waves. (shrink)

Extensionalism, as I understand it here, is the view that physical reality consists exclusively of extensional entities. On this view, intensional entitities must either be eliminated in favor of an ontology of extensional entities, or be reduced to such an ontology, or otherwise be admitted as non-physical. In this paper I argue that extensionalism is a misguided philosophical doctrine. First, I argue that intensional phenomena are not confined to the realm of language and thought. Rather, the ontology of such phenomena (...) is intimately entwined with the ontology of properties. After providing some evidence to the popularity of extensionalism in contemporary analytic philosophy, I investigate the motivating reasons behind it. Considering several explanations, I argue that the main motivating reason is rooted in the identification of matter with extension, an identification which is one of the hallmarks of the mechanistic conception of nature inherited from the founding fathers of our modern scientific outlook. I then argue that such a conception is not only at odds with a robust ontology of properties but is also at odds with our best contemporary physics. Rather than vindicating extensionalism contemporary science undermines the position, and the lesson to be drawn from this surprising fact is that extensionalism needs no longer be espoused as a regulative ideal of naturalistic philosophy. I conclude by showing that the ontological approach to intensional phenomena advocated throughout the paper also gains support from an examination of the historical context within which ‘intension’ was first introduced as a semantic notion. (shrink)

Modern readers turning to Einstein’s famous 1905 paper on special relativity may not find what they expect. Its title, “On the electrodynamics of moving bodies,” gives no inkling that it will develop an account of space and time that will topple Newton’s system. Even its first paragraph just calls to mind an elementary experimental result due to Faraday concerning the interaction of a magnet and conductor. Only then does Einstein get down to the business of space and time and lay (...) out a new theory in which rapidly moving rods shrink and clocks slow and the speed of light becomes an impassable barrier. This special theory of relativity has a central place in modern physics. As the first of the modern theories, it provides the foundation for particle physics and for Einstein’s general theory of relativity; and it is the last point of agreement between them. It has also received considerable attention outside physics. It is the first port of call for philosophers and other thinkers, seeking to understand what Einstein did and why it changed everything. It is often also their last port. The theory is arresting enough to demand serious reflection and, unlike quantum theory and general relativity, its essential content can be grasped fully by someone merely with a command of simple algebra. It contains Einstein’s analysis of simultaneity, probably the most celebrated conceptual analysis of the century. (shrink)

The aim of this paper is to elucidate the question of whether Newtonian mechanics can be derived from relativity theory. Physicists agree that classical mechanics constitutes a limiting case of relativity theory. By contrast, philosophers of science like Kuhn and Feyerabend affirm that classical mechanics cannot be deduced from relativity theory because of the incommensurability between both theories; thus what we obtain when we take the limit c in relativistic mechanics cannot be Newtonian mechanics sensu stricto. In this paper I (...) focus on the alleged change of reference of the term mass in the transition from one theory to the other. Contradicting Kuhn and Feyerabend, special relativity theory supports the view that the mass of an object is a characteristic property of the object, that it has the same value in whatever frame of reference it is measured, and that it does not depend on whether the object is in motion or at rest. Thus mass preserves the reference through the change of theory, and the existence of a Newtonian limit of relativity theory provides a good example of the rationality of theory change in mathematical physics. (shrink)

Einstein learned from the magnet and conductor thought experiments how to use field transformation laws to extend the covariance to Maxwell’s electrodynamics. If he persisted in his use of this device, he would have found that the theory cleaves into two Galilean covariant parts, each with different field transformation laws. The tension between the two parts reflects a failure not mentioned by Einstein: that the relativity of motion manifested by observables in the magnet and conductor thought experiment does not extend (...) to all observables in electrodynamics. An examination of Ritz’s work shows that Einstein’s early view could not have coincided with Ritz’s on an emission theory of light, but only with that of a conveniently reconstructed Ritz. One Ritz-like emission theory, attributed by Pauli to Ritz, proves to be a natural extension of the Galilean covariant part of Maxwell’s theory that happens also to accommodate the magnet and conductor thought experiment. Einstein's famous chasing a light beam thought experiment fails as an objection to an ether-based, electrodynamical theory of light. However it would allow Einstein to formulate his general objections to all emission theories of light in a very sharp form. Einstein found two well known experimental results of 18th and19th century optics compelling (Fizeau’s experiment, stellar aberration), while the accomplished Michelson-Morley experiment played no memorable role. I suggest they owe their importance to their providing a direct experimental grounding for Lorentz’ local time, the precursor of Einstein’s relativity of simultaneity, and do it essentially independently of electrodynamical theory. I attribute Einstein’s success to his determination to implement a principle of relativity in electrodynamics, but I urge that we not invest this stubbornness with any mystical prescience. (shrink)

Two books on Whitehead, a major study by the noted philosopher of science, Isabelle Stengers, and a shorter one by Didier Debaise are reviewed, along with two earlier mathematical and scientific works by Whitehead himself, which have been re-issued. This provides the basis for a wide-ranging discussion of the relationships between Whitehead's love of poetry and Heidegger's approach to it, Whitehead's background in mathematics and theoretical physics and his attitude to empirical science and more general problems of the philosophy of (...) the event, in particular how radical change can come about. (shrink)

The convention that the one-way velocity of light is isotropic is shown to be independent of the postulates of relativity in a globally Minkowskian continuum, but not in a continuum which is only locally Minkowskian.

One of the reasons for relativistic attitudes toward science is the impossibility of justifying scientists’ decisions in the face of alternative theories. According to this paper, an alternative theory can challenge scientific rationality only if the conditions of “methodological shortcomings of scientists” and the “existence of alternative theories” are met at a specific time. A commonly used technique to counter relativism is to try to supplement and equip scientists’ methodologies when confronted with alternative theories. However, this paper focuses on evaluating (...) the possibility of “existence an alternative theory.” To this end, by referring to the different definitions of being alternative, we try to show that only “after the decision” and “the conversion of the scientific community” can a theory be considered justifiably “alternative.” Therefore, the relativistic claim is inconsistent because relativists must first accept the validity of scientists’ decisions to attribute being alternative to a theory. In this work, we provide evidence for our claim using a historical example. We also defend conservatism as a corollary of our discussion. (shrink)

The paper offers a historical overview of Einstein's oscillating attitude towards a "phenomenological" and "dynamical" treatment of rods and clocks in relativity theory. Contrary to what it has been usually claimed in recent literature, it is argued that this distinction should not be understood in the framework of opposition between principle and constructive theories. In particular Einstein does not seem to have plead for a "dynamical" explanation for the phenomenon rods contraction and clock dilation which was initially described only "kinematically". (...) On the contrary textual evidence shows that, according to Einstein, a realistic microscopic model of rods and clocks was needed to account for the very existence of measuring devices of "identical construction" which always measure the same unit of time and the same unit of length. In fact, it will be shown that the empirical meaningfulness of both relativity theories depends on what, following Max Born, one might call the "principle of the physical identity of the units of measure". In the attempt to justify the validity of such principle, Einstein was forced by different interlocutors, in particular Hermann Weyl and Wolfgang Pauli, to deal with the genuine epistemological, rather then physical question whether a theory should be able or not to described the material devices that serve to its own verification. (shrink)

A number of physical processes and experimental procedures are listed which appear to be inexplicable in the context of the conventionality thesis of Reichenbach and Grünbaum. Distant synchrony can be produced by procedures based on the free displacement or rotation of elastic solids. Results are expected to agree with Einstein's definition of distant synchrony (by means of light signals, assuming isotropy). The one-way velocity of light can be measured using a rotating shaft, slotted disks, and one stationary clock.

Values of some arbitrary parameters appearing in a geometrical model for elementary particles developed by MacGregor are compared with quantities associated with classical properties of blocks of charges±e interacting via Coulomb forces and hard-sphere repulsion only. If it is assumed that masses and radii of individual charged particles are related bymc 2=(2/3)(e 2/r) and thatmc 2=6.87 MeV, then the self-energiesM andM ± of 24-particle neutral blocks and 25-particle charged blocks composed of layers of three octagons and of a square sandwiched (...) by two distorted octagons satisfyM=70.1 MeV,M ±=74.2 MeV. The binding energyB nn of pairs of neutral blocks is given byB nn=4.9 MeV, and the maximum radius of the neutral block is 0.60 F. These four calculated parameter values lie within an average of 1% of the corresponding quantities for nonspinning quarks determined empirically by MacGregor. (shrink)

A theoretical device, which incorporates the functions of clock, rod, nonrotating platform, and accelerometer, and whose operation depends on the properties of light rays and free particles, is defined. The device, which we call a metrosphere, is simple enough that it can be introduced at the starting point of relativity theory and versatile enough that it can serve as an aid in the development and conceptualization of the theory. Relative to an inertial frame, a moving metrosphere undergoes a Lorentz-Fitzgerald contraction (...) and the associated clock exhibits a Lorentz-Larmor rate retardation. From this fact and the assumption that there exists one inertial frame, it is possible to generate the kinematical results of special relativity. A metrosphere provides an observer with a local frame of reference, hence it is well adapted to the needs of general relativity, allows the equivalence principle to be introduced in a straightforward manner, and permits a smooth transition from special relativity to general relativity. (shrink)

The aim of this paper is to address, from a fresh perspective, the question of whether Newtonian mechanics can legitimately be regarded as a limiting case of the special theory of relativity, or whether the two theories should be deemed so radically different as to be incommensurable in the sense of Feyerabend and Kuhn. Firstly, it is argued that focusing on the concept of mass and its transformation across the two varieties of mechanics is bound to leave the issue unsettled. (...) On the one hand, the idea of a speed-dependent ‘relativistic mass’, which has been invoked in support of incommensurability claims, results from a particular, often innocuous but unnecessary and inappropriate reading of certain basic formulae. On the other hand, the existence of an invariant rest mass in STR does not warrant its identification with the Newtonian mass, be it in a suitable limit. This invariant notwithstanding, those who follow Feyerabend and Kuhn can still uphold their views with regard to the two theories. It is shown, however, that the two mechanics embody relativistic frameworks that are direct consequences of the same set of assumptions. As a result, if Newton’s mechanics cannot simply be regarded as a limiting case of STR, the possibility of ‘recovering’ from the latter some elements of the former can be traced to a common source, belying claims of logical disconnection between the two theories. (shrink)

I discuss the idea of relativistic causality, i.e., the requirement that causal processes or signals can propagate only within the light-cone. After briefly locating this requirement in the philosophy of causation, my main aim is to draw philosophers' attention to the fact that it is subtle, indeed problematic, in relativistic quantum physics: there are scenarios in which it seems to fail. I set aside two such scenarios, which are familiar to philosophers of physics: the pilot-wave approach, and the Newton-Wigner representation. (...) I instead stress two unfamiliar scenarios: the Drummond-Hathrell and Scharnhorst effects. These effects also illustrate a general moral in the philosophy of geometry: that the mathematical structures, especially the metric tensor, that represent geometry get their geometric significance by dint of detailed physical arguments. (shrink)

As the past-future asymmetry – that fact that we have records of the past but not the future – is still a puzzle the aim of this paper is twofold: a) to explain the asymmetry and its status in philosophy and physics and to critically review the proposed solutions to this puzzle; b) to advance a dynamic solution to the puzzle in terms of the ‘universality’ of the entropy relation in statistical mechanics.