The use of real clocks and measuring rods in quantum mechanics implies a natural loss of unitarity in the description of the theory. We briefly review this point and then discuss the implications it has for the measurement problem in quantum mechanics. The intrinsic loss of coherence allows to circumvent some of the usual objections to the measurement process as due to environmental decoherence.

The notion that the metric field in general relativity can be understood as a property of space-time rests on a feature of the theory sometimes called universal coupling—the claim that rods and clocks “measure” the metric in a way that is independent of their constitution. It is pointed out that this feature is not strictly a consequence of the central dynamical tenets of the theory, and argued that the metric field would better be regarded as a field in (...) space-time, rather than as the very fabric of space-time itself. (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)

Relative distance and velocity magnitudes between two arbitrarily moving particles are independent of an observer's reference frame, and may be used to construct theoretically a clock whose rate is Lorentz-invariant. This result is in accord with the principle of relativity, using the interaction interpretation: Relativistic changes arise in association with momentum-energy transfer, rather than in consequence of velocity-induced changes in measuring clocks and rods.

In a recent paper in this journal which was part of a panel discussion of Grünbaum's philosophy of science, M. G. Evans discusses the Lorentz-Fitzgerald contraction hypothesis and related matters [2]. The purpose of this note is to clarify and correct some of the points in Evans' paper.

In connection with another article by the author, we show how it might be possible to travel faster than the speed of light. We show that for clocks and rods moving faster than the speed of light, we get instead of “time dilation” and “Lorentz contraction,” respectively, “time contraction” and “Lorentz expansion,” respectively. It is shown that this paper is in confirmation with earlier articles dealing with this subject.

Between the microscopic domain ruled by quantum gravity, and the macroscopic scales described by general relativity, there might be an intermediate, “mesoscopic” regime, where spacetime can still be approximately treated as a differentiable pseudo-Riemannian manifold, with small corrections of quantum gravitational origin. We argue that, unless one accepts to give up the relativity principle, either such a regime does not exist at all—hence, the quantum-to-classical transition is sharp—, or the only mesoscopic, tiny corrections conceivable are on the behaviour of physical (...) fields, rather than on the geometric structures. (shrink)

Frank Jackson and Robert Pargetter propose a method for synchronizing clocks at rest at distant points of an inertial system in Euclidean space, which, they claim, does not depend on Einstein's signalling method and provides a basis for denying the conventionality of distant simultaneity. I am afraid, however, that the new method presupposes that the simultaneity of distant events relatively to the chosen inertial system has been already determined by Einstein's or some other method. Jackson and Pargetter describe their (...) method as follows: Let UA, UB be clocks at A, B, respectively. Let XY be an axis perpendicular to AB, passing through C, the midpoint of AB. Take a rigid straight rod A′B′ with midpoint C′ and length equal to the length AB. Move A′B′ with uniform velocity such that C′ travels along XY towards C, and A′B′ is perpendicular to XY ; then if the reading … on UA just when A′ coincides with A is the same as the reading … on UB just when B′ coincides with B, clocks UA and UB will be synchronous.. (shrink)

In the established space-time coordinate-transformation (STCT) interpretation of special relativity theory, relativistic changes are consequent upon the Lorentz transformation of coordinate clocks and rods between relatively moving systems. In the proposed alternative interpretation, relativistic changes occur only in association with physical interactions, and are direct alterations in the variables of the observed system. Since space-time and momentum-energy are conjugate four-vectors, transformation of a space or time variable of a system is to be expected only if there is a (...) concomitant transformation of the corresponding momentum or energy variable. The Lorentz invariance of the scalar entropy functionS supports the interaction interpretation; timet=f(S) of a macroscopic, entropy clock should give a Lorentz-invariant time measure, and an illustrative entropy clock is discussed. Noninteracting physical processes may be called Clausius processes, in contrast to Lorentz processes for which there is interaction and associated Lorentz transformation. Changes of energy and frequency, withE=hv, are instances of the parallel relativistic transformations. Likewise, the variation with velocity in decay time of mesons follows directly from the relativistic energy transformation of decay products; this relationship is shown for muons by a simple calculation with β-decay theory. (shrink)

A perverted space-time geodesy results from the notions of variable rods and clocks, which are taken to have their length and rates affected by the gravitational field. On the other hand, what we might call a concrete geodesy relies on the notions of invariable unit-measuring rods and clocks. In fact, this is a basic assumption of general relativity. Variable rods and clocks lead to a perverted geodesy in the sense that a curved space-time might (...) be seen as arising from the departure from the Minkowskian space-time as an effect of the gravitational field on the rate of clocks and the length of rods. In the case of a concrete geodesy we have “directly” a curved space-time whose curvature can be determined using (invariable) unit-measuring rods and clocks. In this paper, we will make the case for the plausibility that Einstein's views on geometry in relation to general relativity are permeated by a perverted geodesy. (shrink)

The Lorentz-formulae are deduced from three factual statements the physical meaning of which is explained in terms of operations with clocks, light-signals and measuring rods. These statements are: (1) The time-length of a process is invariant. (2) The velocity of light is the same in all inertial systems. (3) The velocity of light is independent of the source. It is also shown that these statements can be deduced from the Lorentz-formulae. They are the physical content of the latter. (...) The principle of relativity and the light-principle together, however, contain more physical meaning than the Lorentz-formulae. Operational definitions are given for all relevant concepts. (shrink)

An often repeated account of the genesis of special relativity tells us that relativity theory was to a considerable extent the fruit of an operationalist philosophy of science. Indeed, Einstein’s 1905 paper stresses the importance of rods and clocks for giving concrete physical content to spatial and temporal notions. I argue, however, that it would be a mistake to read too much into this. Einstein’s operationalist remarks should be seen as serving rhetoric purposes rather than as attempts to (...) promulgate a particular philosophical position --- in fact, Einstein never came close to operationalism in any of his philosophical writings. By focussing on what could actually be measured with rods and clocks Einstein shed doubt on the empirical status of a number of pre-relativistic concepts, with the intention to persuade his readers that the applicability of these concepts was not obvious. This rhetoric manoeuvre has not always been rightly appreciated in the philosophy of physics. Thus, the influence of operationalist misinterpretations, according to which associated operations strictly define what a concept means, can still be felt in present-day discussions about the conventionality of simultaneity. The standard story continues by pointing out that Minkowski in 1908 supplanted Einstein’s approach with a realist spacetime account that has no room for a foundational role of rods and clocks: relativity theory became a description of a four-dimensional ‘absolute world’. As it turns out, however, it is not at all clear that Minkowski was proposing a substantivalist position with respect to spacetime. On the contrary, it seems that from a philosophical point of view Minkowski’s general position was not very unlike the one in the back of Einstein’s mind. However, in Minkowski’s formulation of special relativity it becomes more explicit that the content of spatiotemporal concepts relates to considerations about the form of physical laws. If accepted, this position has important consequences for the discussion about the conventionality of simultaneity. (shrink)

Ideal rods and clocks are defined as an infinitesimal symmetry of the spacetime, at least in the non-quantum case. Since no a priori geometric structure is considered, all the possible models of spacetime are obtained.

There is no indication of time dilation of clocks or of length contraction of rods in Marzke and Wheeler's clock or in Desloge's metrosphere.

Prompted by Hasok Chang’s conception of the history and philosophy of science (HPS) as the continuation of science by other means, I examine the possibility of obtaining scientific knowledge through philosophical criticism and reflection, in the light of four historical cases, concerning (i) the role of absolute space in Newtonian dynamics, (ii) the purported contraction of rods and retardation of clocks in Special Relativity, (iii) the reality of the electromagnetic ether, and (iv) the so-called problem of time’s arrow. (...) In all four cases it is clear that a better understanding of such matters can be achieved —and has been achieved— through conceptual analysis. On the other hand, however, it would seem that this kind of advance has more to do with philosophical questions in science than with narrowly scientific questions. Hence, if HPS in effect continues the work of science by other means, it could well be doing it for other ends than those that working scientists ordinarily have in mind. (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)

We solve a question of McLaughlin by showing that if A is a regressive co-simple isol, there is a co-simple regressive isol B such that the intersection type of A and B is trivial. The proof is a nonuniform 0 priority argument that can be viewed as the execution of a single strategy from a 0-argument. We establish some limit on the properties of such pairs by showing that if AxB has low degree, then the intersection type of A and (...) B cannot be trivial. (shrink)

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.

A popular answer to the question of what, In addition to what a sentence means, Determines what a speaker who utters that sentence says, Is the context in which it is uttered. While this answer is often not developed in any detail, Paul ziff in "what is said" attempts to specify just what contextual features are relevant and how they operate. This paper argues that the factors ziff offers are in fact irrelevant to the determination of what is said. The (...) general outline of an alternative approach is briefly sketched. (shrink)

Traces the development of recursive functions from their origins in the late nineteenth century to the mid-1930s, with particular emphasis on the work and influence of Kurt Gödel.

We investigate the index sets associated with the degree structures of computable sets under the parameterized reducibilities introduced by the authors. We solve a question of Peter Cholakand the first author by proving the fundamental index sets associated with a computable set A, {e : W e ≤ q u A} for q∈ {m, T} are Σ4 0 complete. We also show hat FPT(≤ q n ), that is {e : W e computable and ≡ q n ?}, is Σ4 (...) 0 complete. We also look at computable presentability of these classes. (shrink)

In their book, Darwinism Evolving: Systems Dynamics and the Genealogy of Natural Selection, Depew and Weber argued for the need to address the relationship between self-organization and natural selection in evolutionary theory, and focused on seven “visions” for doing so. Recently, Batten et al. in a paper in this journal, entitled “Visions of evolution: self-organization proposes what natural selection disposes,” picked up the issue with the work of Depew and Weber as a starting point. While the efforts of both sets (...) of authors are to be commended, there are substantive errors in both the presentations of my work and of my work with colleagues that undermine theirs. My purpose here is to correct the errors in question, thereby removing the undermining effects and in so doing reassert the position my colleagues and I first advanced more than two decades ago, and that I still stand by and argue for today. The central points are as follows: Self-organization or spontaneous ordering is a process of selection; this selection process is governed by a “physical selection principle”; this principle is the law of maximum entropy production; and natural selection is a special case where the components are replicating. (shrink)

In Frege’s Puzzle, Nathan Salmon takes it to be obvious that the fact that names such as ‘Hesperus’ and ‘Phosphorus’ are coreferential is purely a matter of arbitrary linguistic convention, while the fact that Hesperus is Phosphorus is by no means a conventional matter. Salmon also takes these points to be ones to which Frege appeals in the opening paragraph of “On Sense and Reference,” and hence finds it ironic that these points undercut the theory of sense that Frege develops (...) in that paper. It is argued that the thesis that the coreferentiality of a pair of proper names is purely a matter of arbitrary linguistic convention is inconsistent with any plausible theory of reference. Salmon’s reading of Frege’s argument is also called into question. (shrink)

We prove that there exists a noncomputable c.e. real which is low for weak 2-randomness, a definition of randomness due to Kurtz, and that all reals which are low for weak 2-randomness are low for Martin-Löf randomness.

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)

Many of the figures in Thurnauer’s paintings who fix us with their gaze have been borrowed from the work of Manet, the artist who organized so many of his paintings around a face-to-face confrontation of viewer and work. The painting returns the viewer’s gaze with total impartiality, making us see our own motives and investments more than the illusion that the figure in the painting will accommodate them. Issues of language often surface literally in paintings by Thurnauer; written language appears (...) sometimes as part of the material fabric in which human figures move or recline. The textual elements are not superimposed on the figures but appear to exist in the world they inhabit, requiring the painter to relate figure to ground in a process of interlacing. When the viewer’s eye traverses the painting it falls under the magnetic influence of the text to the extent that viewing must succumb in some degree to the operations of reading with its specific rhythms and expectations. In these paintings, visual and verbal languages provide us with different maps of the same territory; and Thurnauer’s hybridized representations argue that the world can only be rendered through a dialogue, an interlocution of different forms, genres, media. We approach her work, not as viewers whose function is predicated through a gaze regulated according to the distorting demands of consumption or control, but as readers engaged in a critical activity seeing around the edges of historically produced versions of the self. (shrink)

Robert I. Soare, Automorphisms of the Lattice of Recursively Enumerable Sets. Part I: Maximal Sets.Manuel Lerman, Robert I. Soare, $d$-Simple Sets, Small Sets, and Degree Classes.Peter Cholak, Automorphisms of the Lattice of Recursively Enumerable Sets.Leo Harrington, Robert I. Soare, The $\Delta^0_3$-Automorphism Method and Noninvariant Classes of Degrees.

We characterize the class of c.e. degrees that bound a critical triple as those degrees that compute a function that has no ω-c.e. approximation.

The reputation of the Christian tradition has fared poorly in the literature on the history of attitudes to nonhuman animals. This is more a consequence of secularist prejudice than objective scholarship. The idea of "dominion" and the understanding of animal souls are almost universally misrepresented. There has been no firmer conclusion than that Charles Darwin's theory of evolution had a profoundly beneficial impact on the recognition of our similarities to, kinship with, and consequent moral obligations to, other species. In reality, (...) Darwinism had no such effect. That there was an essential kinship with, and homologies between, humans and other species had been attested to for centuries. In the first major ethical issue that arose after the publication of Darwin's The Descent of Man -- legislation to restrict vivisection -- Darwin and Huxley stood on the side of more or less unrestricted vivisection while many major explicitly Christian voices -- from Cardinal Manning to Lord Chief Justice Coleridge to the Earl of Shaftesbury -- demanded the most severe restrictions, in many cases abolition. The customary tale of how Christianity hindered the development of sensibilities to animals and how Darwinism occasioned a revolution in animal ethics needs to be rethought and retold. (shrink)

By inserting the dialogue between Einstein, Schlick and Reichenbach into a wider network of debates about the epistemology of geometry, this paper shows that not only did Einstein and Logical Empiricists come to disagree about the role, principled or provisional, played by rods and clocks in General Relativity, but also that in their lifelong interchange, they never clearly identified the problem they were discussing. Einstein’s reflections on geometry can be understood only in the context of his ”measuring rod (...) objection” against Weyl. On the contrary, Logical Empiricists, though carefully analyzing the Einstein–Weyl debate, tried to interpret Einstein’s epistemology of geometry as a continuation of the Helmholtz–Poincaré debate by other means. The origin of the misunderstanding, it is argued, should be found in the failed appreciation of the difference between a “Helmholtzian” and a “Riemannian” tradition. The epistemological problems raised by General Relativity are extraneous to the first tradition and can only be understood in the context of the latter, the philosophical significance of which, however, still needs to be fully explored. (shrink)

Despite the evidence showing the promise of HIV treatment as prevention (TasP) in reducing HIV incidence, a variety of ethical questions surrounding the implementation and “scaling up” of TasP have been articulated by a variety of stakeholders including scientists, community activists and government officials. Given the high profile and potential promise of TasP in combatting the global HIV epidemic, an explicit and transparent research priority-setting process is critical to inform ongoing ethical discussions pertaining to TasP.

Previous research has reported that ethical values of business students are lower than those of their peers in other majors. The purpose of this study was to investigate whether a self-selection bias with respect to ethical values exists among students enrolled as business majors when compared with students planning to enter the engineering profession. Engineering students are exposed to a similar technical orientation in academic curricula and also supply the market for managers.A survey instrument was administered to 195 students enrolled (...) in undergraduate business and engineering programs and a graduate business program. The research instrument measured how business and engineering students perceive their own ethical beliefs and actions and how they perceived the ethical beliefs and actions of their peers. (shrink)

We study a refined framework of parameterized complexity theory where the parameter dependence of fixed-parameter tractable algorithms is not arbitrary, but restricted by a function in some family . For every family of functions, this yields a notion of -fixed-parameter tractability. If is the class of all polynomially bounded functions, then -fixed-parameter tractability coincides with polynomial time decidability and if is the class of all computable functions, -fixed-parameter tractability coincides with the standard notion of fixed-parameter tractability. There are interesting choices (...) of between these two extremes, for example the class of all singly exponential functions. In this article, we study the general theory of -fixed-parameter tractability. We introduce a generic notion of reduction and two classes -W[P] and -XP, which may be viewed as analogues of NP and EXPTIME, respectively, in the world of -fixed-parameter tractability. (shrink)

For a set A of non-negative integers, let D be the set of non-negative differences of elements of A. Clearly, if A is computable, then D is computably enumerable. We show that every simple set which contains 0 is the difference set of some computable set and that every computably enumerable set is computably isomorphic to the difference set of some computable set. Also, we prove that there is a computable set which is the difference set of the complement of (...) some computably enumerable set but not of any computably enumerable set. Finally, we show that every arithmetic set is in the Boolean algebra generated from the computable sets by the difference operator D and the Boolean operations. (shrink)

Peter Klein claims to have explicated the notion of relative certainty and shown how it is related to the notion of absolute evidential certainty in his book Certainty. I argue that he has not succeeded at this because the account of relative certainty provided only applies to a subset of the pairs of propositions about which we make judgments of relative certainty.

This paper revisits some recent contributions on ‘Why Management Theory Needs Popper’ to the journal Philosophy of Management. It proposes that those discussions provided an appraisal of the relevance of Popper’s falsification schema to management theory, but that they did not thereby bring to the fore all of the issues pertinent to a balanced and well-rounded understanding of Popper’s philosophy of critical rationalism. It is argued that such an understanding requires a discussion of what Popper himself declared to be the (...) real lynchpin of his thought: fallibilism and a critical approach. It is noted that this represents a rejection of the historical problem situation of philosophy — that knowledge claims need to be positively justified as true. It is argued that this rejection implies an anti-authoritarian, non-justificational philosophy based on the use of critical reason. Its application to several different objects of criticism is demonstrated and its ethical dimensions are explored. The relevance of critical rationalism to management studies and practice is assessed and an inherent limitation on the prospects of its adoption in management practice is identified. … the appeal to authorities is the death of knowledge… the growth of knowledge depends entirely upon disagreement. (shrink)

The first edition, published by Acumen in 2000, became a prescribed textbook on modal logic courses. The second edition has been fully revised in response to readers' suggestions, including two new chapters on conditional logic, which was not covered in the first edition. "Modal Logics and Philosophy" is a fully comprehensive introduction to modal logics and their application suitable for course use. Unlike most modal logic textbooks, which are both forbidding mathematically and short on philosophical discussion, "Modal Logics and Philosophy" (...) places its emphasis firmly on showing how useful modal logic can be as a tool for formal philosophical analysis. In part 1 of the book, the reader is introduced to some standard systems of modal logic and encouraged through a series of exercises to become proficient in manipulating these logics. The emphasis is on possible world semantics for modal logics and the semantic emphasis is carried into the formal method, Jeffrey-style truth-trees. Standard truth-trees are extended in a simple and transparent way to take possible worlds into account. Part 2 systematically explores the applications of modal logic to philosophical issues such as truth, time, processes, knowledge and belief, obligation and permission. (shrink)

This work is an introduction to logic, covering what is most commonly taught in the first term of a two-term sequence in logic at four-year colleges and universities. It is designed for use by community college students who plan to transfer credits to four-year institutions. The material covered seeks to maintain logic's place in philosophical thought systems, and avoids political examples in order to appeal to reason and study rather than ill-conceived jokes that often offend students' varying policitcal beliefs. This (...) work concludes with studies in proof constructions and rules and provides explanations of various grading decisions commonly made in logic courses, a unique feature helpful to students and teachers alike. (shrink)