This paper represents an attempt to clarify a number of long-standing issues concerning the nature and status of the special and general principles of relativity in particular and symmetry or invariance principles in general. An analysis of the active and passive interpretations of symmetry operations is offered. This analysis yields an evaluation of the old covariance-invariance issue. It also demonstrates that the passive interpretation, insofar as it is not trivial, is parasitic on the active picture. Finally, the analysis (...) shows that grave difficulties lie in the way of any attempt to generalize the special principle of relativity in a manner like the one Einstein originally proposed. (shrink)

In this paper we define and examine frame constructions for the family of manyvalued modal logics introduced by M. Fitting in the '90s. Every language of this family is built on an underlying space of truth values, a Heyting algebra H. We generalize Fitting's original work by considering complete Heyting algebras as truth spaces and proceed to define a suitable notion of H-indexed families of generated subframes, disjoint unions and bounded morphisms. Then, we provide an algebraic generalization of the canonical (...) extension of a frame and model, and prove a preservation result inspired from Fitting's canonical model argument in [FIT 92a]. The analog of a complex algebra and of a principal ultrafilter is defined and the embedding of a frame into its canonical extension is presented. (shrink)

We describe a solution to the redundancy problem related to that proposed in Feldman & Levin's target article. We suggest that the system may use a fixed mapping between commands organized at the level of degrees of freedom and commands to individual muscles. This proposal eliminates the need to maintain an explicit representation of musculoskeletalgeometry in planning movements.

Most observers agree that modern physical theory attempts to provide objective representations of reality. However, the claim that these representations are based on conventional choices is viewed by many as a denial of their objectivity. As a result, objectivity and conventionality in representation are often framed as polar opposites. Offering a new appraisal of symmetry in modern physics, employing detailed case studies from relativity theory and quantum mechanics, Objectivity, Invariance, and Convention contends that the physical sciences, though dependent on (...) convention, may produce objective representations of reality. Talal Debs and Michael Redhead show that both realists and constructivists have recognized important elements of an understanding of science that may not be contradictory. The position--"perspectival invariantism"-- introduced in this book highlights the shortcomings of existing approaches to symmetry in physics, and, for the constructivist, demonstrates that a dependence on conventions in representation reaches into the domain of the most technical sciences. For the realist, it stands as evidence against the claim that conventionality must undermine objectivity. We can be committed to the existence of a single real ontology while maintaining a cultural view of science. (shrink)

A moda logic Λ is called invariant if for all automorphisms α of NExt K, α = Λ. An invariant ogic is therefore unique y determined by its surrounding in the attice. It wi be established among other that a extensions of K.alt1S4.3 and G.3 are invariant ogics. Apart from the results that are being obtained, this work contributes to the understanding of the combinatorics of finite frames in genera, something wich has not been done except for transitive frames. Certain (...) useful concepts will be established, such as the notion of a d-homogeneous frame. (shrink)

This article refines a foundational tenet of rational choice theory known as the principle of description invariance. Attempts to apply this principle to human agents with imperfect knowledge have paid insufficient attention to two aspects: first, agents’ epistemic situations, i.e. whether and when they recognize alternative descriptions of an object to be equivalent; and second, the individuation of objects of description, i.e. whether and when objects count as the same or different. An important consequence is that many apparent ‘ (...) class='Hi'>framing effects’ may not violate the principle of description invariance, and the subjects of these effects may not be irrational. (shrink)

A framing effect occurs when an agent's choices are not invariant under changes in the way a decision problem is presented, e.g. changes in the way options are described (violation of description invariance) or preferences are elicited (violation of procedure invariance). Here we identify those rationality violations that underlie framing effects. We attribute to the agent a sequential decision process in which a “target” proposition and several “background” propositions are considered. We suggest that the agent exhibits (...) a framing effect if and only if two conditions are met. First, different presentations of the decision problem lead the agent to consider the propositions in a different order (the empirical condition). Second, different such “decision paths” lead to different decisions on the target proposition (the logical condition). The second condition holds when the agent's initial dispositions on the propositions are “implicitly inconsistent,” which may be caused by violations of “deductive closure.” Our account is consistent with some observations made by psychologists and provides a unified framework for explaining violations of description and procedure invariance. (shrink)

The paper discusses the invariance view of reality: a view inspired by the relativity and quantum theory. It is an attempt to show that both versions of Structural Realism (epistemological and ontological) are already embedded in the invariance view but in each case the invariance view introduces important modifications. From the invariance view we naturally arrive at a consideration of symmetries and structures. It is often claimed that there is a strong connection between invariance and (...) reality, established by symmetries. The invariance view seems to render frame-invariant properties real, while frame-specific properties are illusory. But on a perspectival, yet observer-free view of frame-specific realities they too must be regarded as real although supervenient on frame-invariant realities. Invariance and perspectivalism are thus two faces of symmetries. Symmetries also elucidate structures. Because of this recognition, the invariance view is more comprehensive than Structural Realism. Referring to broken symmetries and coherence considerations, the paper concludes that at least some symmetries are ontological, not just epistemological constraints. (shrink)

We review several no-go theorems attributed to Gisin and Hardy, Conway and Kochen purporting the impossibility of Lorentz-invariant deterministic hidden-variable model for explaining quantum nonlocality. Those theorems claim that the only known solution to escape the conclusions is either to accept a preferred reference frame or to abandon the hidden-variable program altogether. Here we present a different alternative based on a foliation dependent framework adapted to deterministic hidden variables. We analyse the impact of such an approach on Bohmian mechanics and (...) show that retrocausation necessarily comes out without time-loop paradox. (shrink)

This paper examines some possibilities for the laws of nature changing over time. This is done within the context of recent literature on transformational emergence. Transformational emergence is a diachronic account of emergence that does not require the invariance of fundamental objects, properties, and laws. The requirement that no new laws are introduced after the first instance of the universe seems to indicate that all the laws of the universe are present from the outset. By using a dispositional approach (...) to fundamental properties, this restriction can be avoided. An argument appealing to quantitative laws of nature is then used to show that such laws are not, contrary to dispositional essentialism, metaphysically necessary. Further arguments are given to support the possibility of change of laws across time rather than across worlds and why the identity conditions for properties are different in the two cases. The paper is framed by an analysis of John Stuart Mill’s reasons for imposing the invariance requirement on fundamental laws. (shrink)

Judgment aggregation problems are language dependent in that they may be framed in different yet equivalent ways. We formalize this dependence via the notion of translation invariance, adopted from the philosophy of science, and we argue for the normative desirability of translation invariance. We characterize the class of translation invariant aggregation functions in the canonical judgment aggregation model, which requires collective judgments to be complete. Since there are reasonable translation invariant aggregation functions, our result can be viewed as (...) a possibility theorem. At the same time, we show that translation invariance does have certain normatively undesirable consequences (e.g. failure of anonymity). We present a way of circumventing them by moving to a more general model of judgment aggregation, one that allows for incomplete collective judgments. (shrink)

SummaryA concept of reality is sketched which claims to be metaphysically neutral. It is based on the criterion of invariance, invariance with respect to the observer, the reference frame, the state of the subject, time, mode of perception, kind of experience or language. This criterion is here used negatively: all that is invariant is not necessarily real, but in the explaining schema we make of the world, that which changes depending on the point of view, the mode of (...) perception or the knowledge of the subject cannot be considered real. The search for invariants allows efficient storage of information and prevision of events which have never been experienced. The concept of‘invariant limit' is introduced and the need of a suitable topology is stressed in order to speak of convergence of successive theories toward reality. (shrink)

Metaphysicians who are aware of modern physics usually follow Putnam (1967) in arguing that Special Theory of Relativity is incompatible with the view that what exists is only what exists now or presently. Partisans of presentism (the motto ‘only present things exist’) had very difficult times since, and no presentist theory of time seems to have been able to satisfactorily counter the objection raised from Special Relativity. One of the strategies offered to the presentist consists in relativizing existence to inertial (...) frames. This unfashionable strategy has been accused of counterfeiting, since the meaning of the concept of existence would be incompatible with its relativization. Therefore, existence could only be relativistically invariant. In this paper, I shall examine whether such an accusation hits its target, and I will do this by examining whether the different criteria of existence that have been suggested by the Philosophical Tradition from Plato onwards imply that existence cannot be relativized. (shrink)

Generalizing the notion that muscles are positional frames of reference, a high-dimensional muscle space is defined for multi-muscle systems with an embedded low-dimensional motor manifold of functional articulators. A central representation of such a manifold is proposed as computational body schema. The example of the jaw-tongue system is presented, discussing the relation of functional articulators with kinematic invariances and control problems.

Are shapes of objects intrinsic to them? The issue has been intensely debated. Special relativity (SR) adds a new dimension to it by relativizing three-dimensional (3D) shapes not just to times, but to times-in-frames. Arguably, however, such relativized spatial shapes are mere perspectival representations of an invariant, hence intrinsic, four-dimensional (4D) shape of an object in Minkowski spacetime. In a recent note, Matthew Davidson questions the intrinsicality of 4D shapes in SR. I show that his conclusion and the reasoning behind (...) it are in error. (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.

All the typical global quantum mechanical observables are complex relative phases obtained by interference phenomena. They are described by means of some global geometric phase factor, which is thought of as the “memory” of a quantum system undergoing a “cyclic evolution” after coming back to its original physical state. The origin of a geometric phase factor can be traced to the local phase invariance of the transition probability assignment in quantum mechanics. Beyond this invariance, transition probabilities also remain (...) invariant under the operation of complex conjugation. Most important, geometric phase factors distinguish between unitary and antiunitary transformations in terms of complex conjugation. These two types of invariance functions as an anchor point to investigate the role of loops and based loops in the state space of a quantum system as well as their links and interrelations. We show that arbitrary transition probabilities can be calculated using projective invariants of loops in the space of rays. The case of the double slit experiment serves as a model for this purpose. We also represent the action of one-parameter unitary groups in terms of oppositely oriented-based loops at a fixed ray. In this context, we explain the relation among observables, local Boolean frames of projectors, and one-parameter unitary groups. Next, we exploit the non-commutative group structure of oriented-based loops in 3-d space and demonstrate that it carries the topological semantics of a Borromean link. Finally, we prove that there exists a representation of this group structure in terms of one-parameter unitary groups that realizes the topological linking properties of the Borromean link. (shrink)

The standard argument for the Lorentz invariance of the thermodynamic entropy in equilibrium is based on the assumption that it is possible to perform an adiabatic transformation whose only outcome is to accelerate a macroscopic body, keeping its rest mass unchanged. The validity of this assumption constitutes the very foundation of relativistic thermodynamics and needs to be tested in greater detail. We show that, indeed, such a transformation is always possible, at least in principle. The only two assumptions invoked (...) in the proof are that there is at least one inertial reference frame in which the second law of thermodynamics is valid and that the microscopic theory describing the internal dynamics of the body is a field theory, with Lorentz invariant Lagrangian density. The proof makes no reference to the connection between entropy and probabilities and is valid both within classical and quantum physics. To avoid any risk of circular reasoning, we do not postulate that the laws of thermodynamics are the same in every reference frame, but we obtain this fact as a direct consequence of the Lorentz invariance of the entropy. (shrink)

This article surveys the latest research on risky-choice framing effects, focusing on the implications for rational decision-making. An influential program of psychological research suggests that people's judgements and decisions depend on the way in which information is presented, or ‘framed’. In a central choice paradigm, decision-makers seem to adopt different preferences, and different attitudes to risk, depending on whether the options specify the number of people who will be saved or the corresponding number who will die. It is standardly (...) assumed that such responses violate a foundational tenet of rational decision-making, known as the principle of description invariance. We discuss recent theoretical and empirical research that challenges the dominant ‘irrationalist’ narrative. These approaches typically pay close attention to how decision-makers represent decision problems (including their interpretation of numerical quantifiers or predicate choice) and they highlight the need for a more robust characterization of the description invariance principle. We conclude by indicating avenues for future research that could bring us closer to a complete—and potentially rationalizing—explanation of framing effects. (shrink)

We generalize two well-known model-theoretic characterization theorems from propositional modal logic to first-order modal logic. We first study FML-definable frames and give a version of the Goldblatt–Thomason theorem for this logic. The advantage of this result, compared with the original Goldblatt–Thomason theorem, is that it does not need the condition of ultrafilter reflection and uses only closure under bounded morphic images, generated subframes and disjoint unions. We then investigate Lindström type theorems for first-order modal logic. We show that FML has (...) the maximal expressive power among the logics extending FML which satisfy compactness, bisimulation invariance and the Tarski union property. (shrink)

A four-dimensional operator is shown to contain the operator-generators for rotation, scale, reflections, and boosts. The hypothesis is advanced that a physical system changes under this operator by at most a complex phase factor due to invariance against the choice of menial frame. A canonical transform gives a simple relation between space-time and energy-momentum. The basic conserved quantity is a four-dimensional angular momentum and/or coupling constant. The differential of this function contains a second-order differential product which is constrained as (...) a power series in the independent variable. The analysis explores the consequences of the model and shows its degree of correspondence to the standard models. (shrink)

Although Maxwell theory is O(3,1)-covariant, electrodynamics only transforms invariantly between Lorentz frames for special forms of the field, and the generator of Lorentz transformations is not generally conserved. Bérard, Grandati, Lages, and Mohrbach have studied the O(3) subgroup, for which they found an extension of the rotation generator that satisfies the canonical angular momentum algebra in the presence of certain Maxwell fields, and is conserved by the classical motion. The extended generator depends on the field strength, but not the potential, (...) and so is manifestly gauge invariant. The conditions imposed on the Maxwell field by the algebra lead to a Dirac monopole solution.In this paper, we study the generalization of the Bérard, Grandati, Lages and Mohrbach construction to the full Lorentz group in N dimensions. The requirements can be maximally satisfied in a three-dimensional subspace of the full Minkowski space; this subspace can be chosen to describe either an O(3)-invariant space sector, or an O(2,1)-invariant restriction of spacetime. The field solution reduces to the Dirac monopole found in the nonrelativistic case when the O(3)-invariant subspace is selected. When an O(2,1)-invariant subspace is chosen, the field strength can be associated with a Coulomb-like potential of the type A μ(x) = n μ/ρ, where ρ = (x μ x μ)1/2, similar to that used by Horwitz and Arshansky to obtain a covariant generalization of the hydrogen-like bound state. In the presence of these fields, which are determined entirely by symmetry considerations, without reference to a source equation, the extended generator is conserved under classical relativistic system evolution. (shrink)

An experiment aimed at detecting a DC voltage across a conductor induced by the steady magnetic field of a coil, carried out in 1998, provided a positive (although preliminary) evidence for such an effect, which might be interpreted as a breakdown of local Lorentz invariance. We repeated in 1999 the same experiment with a different experimental apparatus and a sensitivity improved by two orders of magnitude. The results obtained are discussed here in detail. They confirm the findings of the (...) previous experiment, and show, among the others, that the effect is independent of the direction of the current. A possible interpretation of the results is given in terms of a geometric description of the gravitational and the electromagnetic interactions by means of phenomenological, energy-dependent metrics. (shrink)

The frame associated with a classical point particle is generally noninertial. The point particle may have a nonzero velocity and force with respect to an absolute inertial rest frame. In time–position–energy–momentum-space {t, q, p, e}, the group of transformations between these frames leaves invariant the symplectic metric and the classical line element ds2 = d t2. Special relativity transforms between inertial frames for which the rate of change of momentum is negligible and eliminates the absolute rest frame by making velocities (...) relative but still requires the absolute inertial frame. The Lorentz group leaves invariant the symplectic metric and the line elements $ds^{2} = -dt^{2} + \frac{1}{c^{2}} dq^{2}$ and $d \mu^{2} = dp^{2}-\frac{1}{c^{2}}de^{2}$ . General relativity for particles under only the influence of gravity avoids the issue of noninertial frames as all particles follow geodesics and hence have locally inertial frames. For other forces, the question of the absolute inertial frame remains.) Born conjectured that the line element should be generalized to the pseudo-orthogonal metric $ds^{2} = -d t^{2}+\frac{1}{c^{2}} dq^{2} + \frac{1}{b^{2}}(dp^{2}-\frac{1}{c^{2}}de^{2})$ . The group leaving this metrics and the symplectic metric invariant is the pseudo-unitary group of transformations between noninertial frames. We show that these transformations also eliminate the need for an absolute inertial frame by making forces relative and bounded by b and so embodies a relativity that is shape reciprocal in the sense of Born. The inhomogeneous version of this group is naturally the semidirect product of the pseudo-unitary group with the nonabelian Heisenberg group. This is the quaplectic group. (shrink)

An unprocessed risk is a collection of simple lotteries with a reduction-rule that describes the actual-payoff to the decision-maker as a function of realized lottery outcomes. Experiments reveal that the willingness to pay for unprocessed risks is consistently biased toward the payoff-level in the unprocessed representation. The anchoring-to-frame bias in cases of positive framing is significantly weaker than in cases of negative framing suggesting that rational negativity bias may reflect in asymmetric violations of rationality.

We propose that observables in quantum theory are properly understood as representatives of symmetry-invariant quantities relating one system to another, the latter to be called a reference system. We provide a rigorous mathematical language to introduce and study quantum reference systems, showing that the orthodox “absolute” quantities are good representatives of observable relative quantities if the reference state is suitably localised. We use this relational formalism to critique the literature on the relationship between reference frames and superselection rules, settling a (...) long-standing debate on the subject. (shrink)

Philosophers of physics are split on whether foundational issues in relativistic quantum field theory should be framed within pragmatist approaches, which trade mathematical rigor for the ability to formulate non-trivial interacting models, or purist approaches, which trade the ability to formulate non-trivial interacting models for mathematical rigor. This essay addresses this debate by viewing it through the lens of the CPT theorem. I first consider two formulations of the CPT theorem, one purist and the other pragmatist, and extract from them (...) a set of problems that clarifies the distinction between pragmatism and purity. I then apply this distinction to Greenberg's influential claim that the violation of CPT invariance in an interacting RQFT entails the violation of Lorentz invariance. I show how this claim rests on an unsuccessful attempt to mediate between pragmatism and purity. I then evaluate another attempt at such mediation in the form of causal perturbation theory. This approach suggests that a focus on renormalized perturbation theory as a way of distinguishing pragmatists from purists may be misleading. (shrink)

A hypothesis about sensorimotor integration (the λ model) is described and applied to movement control and kinesthesia. The central idea is that the nervous system organizes positional frames of reference for the sensorimotor apparatus and produces active movements by shifting the frames in terms of spatial coordinates. Kinematic and electromyographic patterns are not programmed, but emerge from the dynamic interaction among the system s components, including external forces within the designated frame of reference. Motoneuronal threshold properties and proprioceptive inputs to (...) motoneurons may be cardinal components of the physiological mechanism that produces positional frames of reference. The hypothesis that intentional movements are produced by shifting the frame of reference is extended to multi-muscle and multi-degrees-of-freedom systems with a solution of the redundancy problem that allows the control of a joint alone or in combination with other joints to produce any desired limb configuration and movement trajectory. The model also implies that for each motor behavior, the nervous system uses a strategy that minimizes the number of changeable control variables and keeps the parameters of these changes invariant. Examples are provided of simulated kinematic and electromyographic signals from single- and multi-joint arm movements produced by suggested patterns of control variables. Empirical support is provided and additional tests of the model are suggested. The model is contrasted with others based on the ideas of programming of motoneuronal activity, muscle forces, stiffness, or movement kinematics. (shrink)

“Evidence” in the form of data collected and analysis thereof is fundamental to medicine, health and science. In this paper, we discuss the “evidence-based” aspect of evidence-based medicine in terms of statistical inference, acknowledging that this latter field of statistical inference often also goes by various near-synonymous names—such as inductive inference (amongst philosophers), econometrics (amongst economists), machine learning (amongst computer scientists) and, in more recent times, data mining (in some circles). Three central issues to this discussion of “evidence-based” are (i) (...) whether or not the statistical analysis can and/or should be objective and/or whether or not (subjective) prior knowledge can and/or should be incorporated, (ii) whether or not the analysis should be invariant to the framing of the problem (e.g. does it matter whether we analyse the ratio of proportions of morbidity to non-morbidity rather than simply the proportion of morbidity?), and (iii) whether or not, as we get more and more data, our analysis should be able to converge arbitrarily closely to the process which is generating our observed data. For many problems of data analysis, it would appear that desiderata (ii) and (iii) above require us to invoke at least some form of subjective (Bayesian) prior knowledge. This sits uncomfortably with the understandable but perhaps impossible desire of many medical publications that at least all the statistical hypothesis testing has to be classical non-Bayesian—i.e. it is not permitted to use any (subjective) prior knowledge. (shrink)

It is still perhaps not widely appreciated that in 1905 Einstein used his postulate concerning the ‘constancy’ of the light-speed in the ‘resting’ frame, in conjunction with the principle of relativity, to derive numerical light-speed invariance. Now a ‘weak’ version of the relativity principle (or, alternatively, appeal to the Michelson—Morley experiment) leads from Einstein's light postulate to a condition that we call universal light-speed constancy. which is weaker than light-speed invariance. It follows from earlier independent investigations (Robertson [1949]; (...) Steigler [1952]; Tzanakis and Kyritsis [1984]) that this condition is none the less sufficient to derive the Lorentz transformations up to a scale factor, given the well-known kinematic principle of ‘reciprocity’. In this paper, we follow Robertson and explore the kinematics consistent with universal light-speed constancy without imposing reciprocity, and we recover the Lorentz transformations by further appeal only to the weak relativity principle and spatial isotropy. (shrink)

The normative principle of description invariance presupposes that rational preferences must be complete. The completeness axiom is normatively dubious, however, and its rejection opens the door to rational framing effects. In this commentary, we suggest that Bermúdez's insightful challenge to the standard normative view of framing can be clarified and extended by situating it within a broader critique of completeness.

We investigate model theoretic characterisations of the expressive power of modal logics in terms of bisimulation invariance. The paradigmatic result of this kind is van Benthem’s theorem, which says that a first-order formula is invariant under bisimulation if, and only if, it is equivalent to a formula of basic modal logic. The present investigation primarily concerns ramifications for specific classes of structures. We study in particular model classes defined through conditions on the underlying frames, with a focus on frame (...) classes that play a major role in modal correspondence theory and often correspond to typical application domains of modal logics. Classical model theoretic arguments do not apply to many of the most interesting classes–for instance, rooted frames, finite rooted frames, finite transitive frames, well-founded transitive frames, finite equivalence frames–as these are not elementary. Instead we develop and extend the game-based analysis over such classes and provide bisimulation preserving model constructions within these classes. Over most of the classes considered, we obtain finite model theory analogues of the classically expected characterisations, with new proofs also for the classical setting. The class of transitive frames is a notable exception, with a marked difference between the classical and the finite model theory of bisimulation invariant first-order properties. Over the class of all finite transitive frames in particular, we find that monadic second-order logic is no more expressive than first-order as far as bisimulation invariant properties are concerned — though both are more expressive here than basic modal logic. We obtain ramifications of the de Jongh–Sambin theorem and a new and specific analogue of the Janin–Walukiewicz characterisation of bisimulation invariant monadic second-order for finite transitive frames. (shrink)

A completely Lorentz-invariant Bohmian model has been proposed recently for the case of a system of non-interacting spinless particles, obeying Klein-Gordon equations. It is based on a multi-temporal formalism and on the idea of treating the squared norm of the wave function as a space-time probability density. The particle’s configurations evolve in space-time in terms of a parameter σ with dimensions of time. In this work this model is further analyzed and extended to the case of an interaction with an (...) external electromagnetic field. The physical meaning of σ is explored. Two special situations are studied in depth: (1) the classical limit, where the Einsteinian Mechanics of Special Relativity is recovered and the parameter σ is shown to tend to the particle’s proper time; and (2) the non-relativistic limit, where it is obtained a model very similar to the usual non-relativistic Bohmian Mechanics but with the time of the frame of reference replaced by σ as the dynamical temporal parameter. (shrink)

Rotation in a general relativistic framework is examined. This concept, combined with the appropriate mechanical work concept, is used to show how the Euclidean group of transformations, serving as an invariance requirement associated with the principle of objectivity, can lead to erroneous conclusions.

Gender-neutral bathrooms are usually framed as an accommodation for trans and other gender-nonconforming individuals. In this paper, we show that the benefits of gender-neutral bathrooms are much broader. First, our simulations show that gender-neutral bathrooms reduce average waiting times: while waiting times for women go down invariably, waiting times for men either go down or slightly increase depending on usage intensity, occupancy-time differentials and the presence of urinals. Second, our result can be turned on its head: firms have an opportunity (...) to reduce the number of facilities and cut costs by making them all gender-neutral without increasing waiting times. These observations can be used to reframe the gender-neutral bathrooms debate so that they appeal to a larger constituency, cutting across the usual dividing lines in the ‘bathroom wars’. Finally, there are improved designs and behavioural strategies that can help overcome resistance. We explore what strategies can be invoked to mitigate the objections that gender-neutral bathrooms (1) are unsafe, (2) elicit discomfort and (3) are unhygienic. (shrink)

In this paper the Lorentz transformations (LT) and the standard transformations (ST) of the usual Maxwell equations (ME) with the three-dimensional (3D) vectors of the electric and magnetic fields, E and B, respectively, are examined using both the geometric algebra and tensor formalisms. Different 4D algebraic objects are used to represent the usual observer dependent and the new observer independent electric and magnetic fields. It is found that the ST of the ME differ from their LT and consequently that the (...) ME with the 3D E and B are not covariant upon the LT but upon the ST. The obtained results do not depend on the character of the 4D algebraic objects used to represent the electric and magnetic fields. The Lorentz invariant field equations are presented with 1-vectors E and B, bivectors EHv and BHv and the abstract tensors, the 4-vectors Ea and Ba. All these quantities are defined without reference frames, i.e., as absolute quantities. When some basis has been introduced, they are represented as coordinate-based geometric quantities comprising both components and a basis. It is explicitly shown that this geometric approach agrees with experiments, e.g., the Faraday disk, in all relatively moving inertial frames of reference, which is not the case with the usual approach with the 3D bf E and B and their ST. (shrink)

The idea that the world is made of particles — little discrete, interacting objects that compose the material bodies of everyday experience — is a durable one. Following the advent of quantum theory, the idea was revised but not abandoned. It remains manifest in the explanatory language of physics, chemistry, and molecular biology. Aside from its durability, there is good reason for the scientific realist to embrace the particle interpretation: such a view can account for the prominent epistemic fact that (...) only limited knowledge of a portion of the material universe is needed in order to make reliable predictions about that portion. Thus, particle interpretations can support an abductive argument from the epistemic facts in favor of a realist reading of physical theory. However, any particle interpretation with this property is untenable. The empirical adequacy of modern particle theories requires adoption of a postulate known as permutation invariance — the claim that interchanging the role of two particles of the same kind in a dynamical state description results in a description of the identical state. It is the central claim of this essay that PI is incompatible with any particle interpretation strong enough to account for the epistemic facts. This incompatibility extends across all physical theories. To frame and motivate the inconsistency argument, I begin by fixing the relevant notion of particle. To single out those accounts of greatest appeal to the realist, I develop the logically weakest particle ontology that entails the epistemic fact that the world is piecewise predictable, an ontology I call ‘minimal atomism’. The entire series of scientific conceptions of the particle, from Newton’s mechanically interacting corpuscles to the ‘centers of force’ in classical field theories, all comport with MA. As long as PI is left out, even quantum mechanics can be viewed this way. To assess the impact of PI on this picture, I present a framework for rigorously connecting interpretations to physical theories. In particular, I represent MA as a set of formal conditions on the models of physical theories, the mathematical structures taken to represent states of the world. I also formulate PI — originally introduced as a postulate of non-relativistic quantum mechanics — in theory independent terms. With all of these pieces in hand, I am then able to present a proof of the inconsistency of PI and MA. In the second part of the essay, I survey responses to the inconsistency result open to the scientific realist. The two most plausible approaches involve abandoning particles in one way or another. The first alternative interpretation considered takes the property bearing objects of the world to be regions of space rather than particles. In this view, the properties once attributed to particles in quantum states are attributed instead to one or more regions of space. PI no longer obtains in this case, at least not as a statement about the permutation symmetry of property bearers. Rather, the new interpretation naturally imposes an analogous constraint on quantum states. The second major approach to evading the inconsistency result is to dispense with objects altogether. This is the recommendation of so-called ‘Ontic Structural Realism’. The central OSR thesis is that structure rather than entities are the basic ontological components of the world. OSR is intended to embrace the ‘miracle’ argument in favor of scientific realism while avoiding the pessimistic meta-induction. I demonstrate that one principal motivation for OSR based on the under-determination of interpretations in QM is actually dissolved by the incompatibility result. At the same time, I suggest reasons to think that OSR fares no better with respect to the pessimistic meta-induction than traditional realism does. Thus, while PI and MA may be incompatible, object ontologies remain the best option for the realist. (shrink)

In this paper we scrutinize the so called Principle of Local Lorentz Invariance (PLLI) that many authors claim to follow from the Equivalence Principle. Using rigourous mathematics, we introduce in the General Theory of Relativity two classes of reference frames (PIRFs and LLRFγs) which as natural generalizations of the concept of the inertial reference frames of the Special Relativity Theory. We show that it is the class of the LLRFγs that is associated with the PLLI. Next we give a (...) definition of physically equivalent reference frames. Then, we prove that there are models of General Relativity Theory (in particular on a Friedmann universe) where the PLLI is false. However our finding is not in contradiction with the many experimental claims vindicating the PLLI, because theses experiments do not have enough accuracy to detect the effect we found. We prove moreover that PIRFs are not physically equivalent. (shrink)

The obvious metaphysical differences between Newton and Leibniz concerning space, time, and motion reflect less obvious differences concerning the relation between geometry and physics, expressed in the questions: what are the invariant quantities of classical mechanics, and what sort of geometrical frame of reference is required to represent those quantities? Leibniz thought that the fundamental physical quantity was “living force” (mv2), of which every body was supposed to have a definite amount; this notion violates the classical principle of relativity, since (...) it makes a physical distinction between uniform velocity and absolute rest. But Leibniz did not try to represent this physical quantity in a spatio-temporal reference frame, assuming, instead, that all such frames are equivalent so long as they agree on the relative motions (changes in the mutual Euclidean distances) among bodies. (shrink)

Gender-neutral bathrooms are usually framed as an accommodation for trans and other gender-nonconforming individuals. In this paper, we show that the benefits of gender-neutral bathrooms are much broader. First, our simulations show that gender-neutral bathrooms reduce average waiting times: while waiting times for women go down invariably, waiting times for men either go down or slightly increase depending on usage intensity, occupancy-time differentials and the presence of urinals. Second, our result can be turned on its head: firms have an opportunity (...) to reduce the number of facilities and cut costs by making them all gender-neutral without increasing waiting times. These observations can be used to reframe the gender-neutral bathrooms debate so that they appeal to a larger constituency, cutting across the usual dividing lines in the ‘bathroom wars’. Finally, there are improved designs and behavioural strategies that can help overcome resistance. We explore what strategies can be invoked to mitigate the objections that gender-neutral bathrooms (1) are unsafe, (2) elicit discomfort and (3) are unhygienic. (shrink)

The existence of sensory convergence does not establish that the senses function as a single unified perceptual system. Reality is fully specified only by a one:many mapping onto the totality of energy arrays, and these provide alternative frames of reference for movement. It is therefore possible that higher order crossmodal relationships are detected by skilled perceivers, but this has not been confirmed empirically.

The status of a causal approach to EPR-Bell nonlocal correlations in terms of a counterfactual framework for causation is considered. It is argued that when the relativistic spacetime structure of the events is taken into due account, the adoption of this approach is best motivated by the assumption of a preferred frame of reference, an assumption that seems even more in need of justification than the causal theory itself.

Expected Utility Theory (EUT) has anomalies when interpreted descriptively and tested empirically. Experiments show that the way in which options are formulated is, in most cases, relevant for decision-making. This kind of anomaly is directly related, however, not with a proper axiom of EUT but rather with the logical principle of extensionality and its decision theoretic version: the principle of invariance. This paper focuses on the phenomenon of framing effects (FE) and the associated failures of invariance. FE (...) arise when different descriptions of the same object lead to different preferences, beliefs, or choices. A formal reconstruction of the Gain–Loss (G-L) frame is proposed, expanding the domain of standard decision theory to incorporate not only prospects but also descriptions of prospects. The system is extended by adding non-monotonic logical resources so as to account for the ceteris paribus character of FE. Finally, the same method is applied to sketching a formal representation for an anomalous case that involves subjective probabilities. The logical method is a general one that can be applied to most cases of FE. The philosophical consequences of the strategy pursued are also discussed. (shrink)

A rigorous extension of the full Lorentz group is found which is parameterized by interframe velocities v(t) and which reduces to Special Relativity for acceleration-free cases and to Galilean relativity for low velocity cases. Full group properties are exhibited. Four-momentum is defined and particle masses are shown to be invariants. Four-force is introduced and pseudoforces are shown to enter the equations of particle dynamics. Maxwell's equations are shown to take on pseudocurrent terms in accelerating frames. A four-vector Green function solution (...) to the modified Maxwell equations is presented. Finally, a discussion is offered concerning philosophical questions such as the operational definition of time. (shrink)

The principle of relativity, that there is no preferred state of uniform motion, has recently come into conflict with certain cosmological observations. In an attempt to overcome this difficulty, an alternative formulation is explored in which this principle is replaced by the principle of universal time, while retaining the invariance of the speed of light. These two postulates lead to a well-defined world model in which one inertial frame has a preferred status. But the invariance properties of the (...) laws of physics are unaffected, and the model may be regarded as a modified form of special relativity which is in accordance with the new cosmological evidence. (shrink)

Charles Darwin found much in Australia to challenge and inform his thinking. This book explores the impact that Darwin’s short visit to Australia in 1836 had on the man himself and on the emerging nation. Now, more than 170 years later, Darwin continues to influence Australian attitudes to life and living.