The conservation laws do not establish the central premise within the argument from causal overdetermination – the causal completeness of the physical domain. Contrary to David Papineau, this is true even if there is no non-physical energy. The combination of the conservation laws with the claim that there is no non-physical energy would establish the causal completeness principle only if, at the very least, two further causal claims were accepted. First, the claim that the only way (...) that something non-physical could affect a physical system is by affecting the amount of energy or momentum within it, or redistributing the energy and momentum within it. Second, the claim that redistribution of energy and momentum cannot be brought about without supplying energy or momentum. Both of these claims, however, are exceedingly difficult to defend in the context of the argument. (shrink)

The conservation of energy law, a law of physics that states that the total energy of any closed system is always conserved, is a bedrock principle that has achieved both broad theoretical and experimental support. Yet if interactive dualism is correct, it is thought that the mind can affect physical objects in violation of the conservation of energy. Thus, some claim, the conservation of energy grounds an argument for physicalism. Although critics of the (...) argument focus on the implausibility of causation requiring the transference of energy, I argue that even if causation requires the transference of energy, once we accept the other required premises of the argument that lie behind any supposed argument from the conservation of energy the law of the conservation of energy is revealed as irrelevant to the question of whether the mental is physical. (shrink)

Misconceptions about energy conservation abound due to the gap between physics and secondary school chemistry. This paper surveys this difference and its relevance to the 1690s–2010s Leibnizian argument that mind-body interaction is impossible due to conservation laws. Justifications for energy conservation are partly empirical, such as Joule’s paddle wheel experiment, and partly theoretical, such as Lagrange’s statement in 1811 that energy is conserved if the potential energy does not depend on time. In 1918 (...) Noether generalized results like Lagrange’s and proved a converse: symmetries imply conservation laws and vice versa. Conservation holds if and only if nature is uniform. The rise of field physics during the 1860s–1920s implied that energy is located in particular places and conservation is primordially local: energy cannot disappear in Cambridge and reappear in Lincoln instantaneously or later; neither can it simply disappear in Cambridge or simply appear in Lincoln. A global conservation law can be inferred in some circumstances. Einstein’s General Relativity, which stimulated Noether’s work, is another source of difficulty for conservation laws. As is too rarely realized, the theory admits conserved quantities due to symmetries of the Lagrangian, like other theories. Indeed General Relativity has more symmetries and hence more conserved energies. An argument akin to Leibniz’s finally gets some force. While the mathematics is too advanced for secondary school, the ideas that conservation is tied to uniformities of nature and that energy is in particular places, are accessible. Improved science teaching would serve the truth and enhance the social credibility of science. (shrink)

Consensus in the contemporary philosophical literature has it that conserved quantity theories of causation such as that of Dowe [2000]—according to which causation is to be analysed in terms of the exchange of conserved quantities (e.g., energy)—face damning problems when confronted with contemporary physics, where the notion of conservation becomes delicate. In particular, in general relativity it is often claimed that there simply are no conservation laws for (say) total-stress energy. If this claim is correct, it (...) is difficult to see how conserved quantity theories of causation could survive. In this article, we resist the above consensus and defend conserved quantity theories from this conclusion, at least when focusing on the apparent problems posed by general relativity. We argue that this approach to causation can continue to be defended in general relativity, once one appreciates (a) the availability of approximate symmetries in generic general relativistic spacetimes, and (b) the role of modelling and idealisation in that theory. Given these points, conserved quantity theories of causation must stand or fall on other grounds. (shrink)

Automatic conservation of energy-momentum and angular momentum is guaranteed in a gravitational theory if, via the field equations, the conservation laws for the material currents are reduced to the contracted Bianchi identities. We first execute an irreducible decomposition of the Bianchi identities in a Riemann-Cartan space-time. Then, starting from a Riemannian space-time with or without torsion, we determine those gravitational theories which have automatic conservation: general relativity and the Einstein-Cartan-Sciama-Kibble theory, both with cosmological constant, and the (...) nonviable pseudoscalar model. The Poincaré gauge theory of gravity, like gauge theories of internal groups, has no automatic conservation in the sense defined above. This does not lead to any difficulties in principle. Analogies to 3-dimensional continuum mechanics are stressed throughout the article. (shrink)

The theory of the conservation of energy and the Second Law of Thermodynamics have been described as the two most firmly established “findings” of modern science. Scientists frequently refer to them, not as theories or assumptions, but as facts. During the last two decades of the nineteenth century, however, Edmund Montgomery—an unsung Texas philosopher—repeatedly challenged, not only the notions that energy is convertible and is indestructible, but the very idea that there is such a thing as (...) class='Hi'>energy which can be imposed ab extra upon matter. For his trouble he received censure and ridicule on every hand; friends usually apologized for this eccentricity of his. Montgomery, of course, has not been entirely alone in criticizing the theory of the conservation of energy, though he was the first to make a persistent attack on the merits of the theory as a principle of scientific explanation. Busse, for one, contended that if, as he thought likely, the theory were incompatible with psychophysical interactionism, it should be discarded on the grounds that the evidence in its behalf is far from compelling. Emergent evolutionists remind us occasionally that it is still within the province of reason to question this great dogma notwithstanding the fact that it is a god at whose feet many scientists worship with blind and jealous devotion. Of all these critics Montgomery attacked the theory where its greatest weaknesses lie. (shrink)

Many have thought that symmetries of a Lagrangian explain the standard laws of energy, momentum, and angular momentum conservation in a rather straightforward way. In this paper, I argue that the explanation of conservation laws via symmetries of Lagrangians involves complications that have not been adequately noted in the philosophical literature and some of the physics literature on the subject. In fact, such complications show that the principles that are commonly appealed to to drive explanations of (...) class='Hi'>conservation laws are not generally correct without caveats. I hope here to give a clearer picture of the relationship between symmetries and conservation laws in Lagrangian mechanics via an examination of the bearing that results in the inverse problem in the calculus of variations have on this topic. (shrink)

An actual infinity of colliding balls can be in a configuration in which the laws of mechanics lead to logical inconsistency. It is argued that one should therefore limit the domain of these laws to a finite, or only a potentially infinite number of elements. With this restriction indeterminism, energy nonconservation and creatio ex nihilo no longer occur. A numerical analysis of finite systems of colliding balls is given, and the asymptotic behaviour that corresponds to the potentially infinite system (...) is inferred. (shrink)

Since Leibniz's time, Cartesian mental causation has been criticized for violating the conservation of energy and momentum. Many dualist responses clearly fail. But conservation laws have important neglected features generally undermining the objection. Conservation is _local_, holding first not for the universe, but for everywhere separately. The energy in any volume changes only due to what flows through the boundaries. Constant total energy holds if the global summing-up of local conservation laws converges; it (...) probably doesn't in reality. Energy conservation holds if there is symmetry, the sameness of the laws over time. Thus, if there are time-places where symmetries fail due to nonphysical influence, conservation laws fail there and then, while holding elsewhere, such as refrigerators and stars. Noether's converse first theorem shows that conservation laws imply symmetries. Thus conservation trivially nearly entails the causal closure of the physical. But expecting conservation to hold in the brain simply assumes the falsehood of Cartesianism. Hence Leibniz's objection begs the question. Empirical neuroscience is another matter. So is Einstein's General Relativity: far from providing a loophole, General Relativity makes mental causation _harder_. (shrink)

The conservation of energy and momentum have been viewed as undermining Cartesian mental causation since the 1690s. Modern discussions of the topic tend to use mid-nineteenth century physics, neglecting both locality and Noether’s theorem and its converse. The relevance of General Relativity has rarely been considered. But a few authors have proposed that the non-localizability of gravitational energy and consequent lack of physically meaningful local conservation laws answers the conservation objection to mental causation: conservation (...) already fails in GR, so there is nothing for minds to violate. This paper is motivated by two ideas. First, one might take seriously the fact that GR formally has an infinity of rigid symmetries of the action and hence, by Noether’s first theorem, an infinity of conserved energies-momenta. Second, Sean Carroll has asked how one should modify the Dirac–Maxwell–Einstein equations to describe mental causation. This paper uses the generalized Bianchi identities to show that General Relativity tends to exclude, not facilitate, such Cartesian mental causation. In the simplest case, Cartesian mental influence must be spatio-temporally constant, and hence 0. The difficulty may diminish for more complicated models. Its persuasiveness is also affected by larger world-view considerations. The new general relativistic objection provides some support for realism about gravitational energy-momentum in GR. Such realism also might help to answer an objection to theories of causation involving conserved quantities, because energies-momenta would be conserved even in GR. (shrink)

According to history texts, philosophers searched for a unifying natural law whereby natural phenomena and numbers are related. More than 2300 years ago, Aristotle postulated that nature requires minimum energy. More than 220 years ago, Euler applied the minimum energy postulate. More than 200 years ago, Lagrange provided a mathematical “proof” of the postulate for conservative systems. The resulting Principle of Least Action served only to derive the differential equations of motion of a conservative system. Then, 170 years (...) ago, Hamilton presented what he claimed to be a “general method in dynamics.” Hamilton's resulting “Law of Varying Action” was supposed to apply to both conservative and non-conservative systems and was supposed to yield either the differential equations of motion or the integrals of those differential equations. However, no direct evaluation of the integrals of motion ever resulted from Hamilton's law of varying action. In 1975, a scant 29 years ago, following five years of controversy with engineer mechanicians, Dr. Wolfgang Yourgrau, Editor, Foundations of Physics, published my first paper based on Aristotle's postulate, without mathematical proof. That and subsequent papers present, through applications, a true “general method in dynamics.” In this essay, I present the mathematical proof that is missing from my 1975 and subsequent papers. Six fundamental integrals of analytical mechanics are derived from Aristotle's postulate. First, however, Hamilton must be revisited to show why his H function and his “force function” prevents the law of varying action from being the general method in dynamics that he claimed it to be. I have found that Hamilton’s Law of Varying Action (HLVA), as Hamilton presented it, cannot be applied to systems for which the force function is non-integrable. In 1972, Dr. B.E. Gatewood and Dr. D.P. Beres (then a graduate student) discovered that the end-point term associated with the principle of least action does not vanish. I named the new equation, “the general energy equation.” In 1973, because I was doing with it what Hamilton claimed could be done with HLVA, I simply assumed that this new equation was HLVA. I gave the new equation the misnomer HLVA. In 2001, I learned that I had made a grave mistake. I found that HLVA is at most a special case of the general energy equation. My interpretation of Aristotle's postulate permits one to by-pass the differential equations of motion completely for both conservative and non-conservative systems (no calculus of variations). (shrink)

We emphasize that the pressure related work appearing in a general relativistic first law of thermodynamics should involve proper volume element rather than coordinate volume element. This point is highlighted by considering both local energy momentum conservation equation as well as particle number conservation equation. It is also emphasized that we are considering here a non-singular fluid governed by purely classical general relativity. Therefore, we are not considering here any semi-classical or quantum gravity which apparently suggests thermodynamical (...) properties even for a (singular) black hole. Having made such a clarification, we formulate a global first law of thermodynamics for an adiabatically evolving spherical perfect fluid. It may be verified that such a global first law of thermodynamics, for a non-singular fluid, has not been formulated earlier. (shrink)

Joule’s Energy Conservation Law was the first “meta-law”: a general principle that all physical equations must satisfy. It has led to many important and useful physical discoveries. However, a recent analysis seems to indicate that this meta-law is inconsistent with other principles—such as the existence of free will. We show that this conclusion about inconsistency is based on a seemingly reasonable—but simplified—analysis of the situation. We also show that a more detailed mathematical and physical analysis of the situation (...) reveals that not only Joule’s principle remains true—it is actually strengthened: it is no longer a principle that all physical theories should satisfy—it is a principle that all physical theories do satisfy. (shrink)

During the period 1860-1880, a number of physicists and mathematicians, including Maxwell, Stewart, Cournot and Boussinesq, used theories formulated in terms of physics to argue that the mind, the soul or a vital principle could have an impact on the body. This paper shows that what was primarily at stake for these authors was a concern about the irreducibility of life and the mind to physics, and that their theories can be regarded primarily as reactions to the law of (...) class='Hi'>conservation of energy, which was used among others by Helmholtz and Du Bois-Reymond as an argument against the possibility of vital and mental causes in physiology. In light of this development, Maxwell, Stewart, Cournot and Boussinesq showed that it was still possible to argue for the irreducibility of life and the mind to physics, through an appeal to instability or indeterminism in physics: if the body is an unstable or physically indeterministic system, an immaterial principle can act through triggering or directing motions in the body, without violating the laws of physics. (shrink)

The topics of gravitational field energy and energy-momentum conservation in General Relativity theory have been unjustly neglected by philosophers. If the gravitational field in space free of ordinary matter, as represented by the metric g ab itself, can be said to carry genuine energy and momentum, this is a powerful argument for adopting the substantivalist view of spacetime.This paper explores the standard textbook account of gravitational field energy and argues that (a) so-called stress-energy of (...) the gravitational field is well-defined neither locally nor globally; and (b) there is no general principle of energy-momentum conservation to be found in General Relativity. I discuss the nature and justification of the zero-divergence law for ordinary stress-energy, and its possible connection with the failure of General Relativity to realise Mach's principle. (shrink)

The examples of dynamic supertasks analyzed to date in the philosophical literature, in which both determinism and the classical laws of conservation of energy and momentum are violated, all share the important limitation of requiring material systems of infinite mass. This paper demonstrates that this limitation is not necessary. This has important consequences for the scope and meaning of such violations.

Recent work on the history of General Relativity by Renn, Sauer, Janssen et al. shows that Einstein found his field equations partly by a physical strategy including the Newtonian limit, the electromagnetic analogy, and energy conservation. Such themes are similar to those later used by particle physicists. How do Einstein's physical strategy and the particle physics derivations compare? What energy-momentum complex did he use and why? Did Einstein tie conservation to symmetries, and if so, to which? (...) How did his work relate to emerging knowledge of the canonical energy-momentum tensor and its translation-induced conservation? After initially using energy-momentum tensors hand-crafted from the gravitational field equations, Einstein used an identity from his assumed linear coordinate covariance x'=Mx to relate it to the canonical tensor. Usually he avoided using matter Euler-Lagrange equations and so was not well positioned to use or reinvent the Herglotz-Mie-Born understanding that the canonical tensor was conserved due to translation symmetries, a result with roots in Lagrange, Hamilton and Jacobi. Whereas Mie and Born were concerned about the canonical tensor's asymmetry, Einstein did not need to worry because his Entwurf Lagrangian is modeled not so much on Maxwell's theory as on a scalar theory. Einstein's theory thus has a symmetric canonical energy-momentum tensor. But as a result, it also has 3 negative-energy field degrees of freedom. Thus the Entwurf theory fails a 1920s-30s a priori particle physics stability test with antecedents in Lagrange's and Dirichlet's stability work; one might anticipate possible gravitational instability. This critique of the Entwurf theory can be compared with Einstein's 1915 critique of his Entwurf theory for not admitting rotating coordinates and not getting Mercury's perihelion right. One can live with absolute rotation but cannot live with instability. Particle physics also can be useful in the historiography of gravity and space-time, both in assessing the growth of objective knowledge and in suggesting novel lines of inquiry to see whether and how Einstein faced the substantially mathematical issues later encountered in particle physics. This topic can be a useful case study in the history of science on recently reconsidered questions of presentism, whiggism and the like. Future work will show how the history of General Relativity, especially Noether's work, sheds light on particle physics. (shrink)

It is emphasized that the collapse postulate of standard quantum theory can violate conservation of energy-momentum and there is no indication from where the energy-momentum comes or to where it goes. Likewise, in the Continuous Spontaneous Localization (CSL) dynamical collapse model, particles gain energy on average. In CSL, the usual Schrödinger dynamics is altered so that a randomly fluctuating classical field interacts with quantized particles to cause wavefunction collapse. In this paper it is shown how to (...) define energy for the classical field so that the average value of the energy of the field plus the quantum system is conserved for the ensemble of collapsing wavefunctions. While conservation of just the first moment of energy is, of course, much less than complete conservation of energy, this does support the idea that the field could provide the conservation law balance when events occur. (shrink)

The principle of energy conservation is widely taken to be a se- rious difficulty for interactionist dualism (whether property or sub- stance). Interactionists often have therefore tried to make it satisfy energy conservation. This paper examines several such attempts, especially including E. J. Lowe’s varying constants proposal, show- ing how they all miss their goal due to lack of engagement with the physico-mathematical roots of energy conservation physics: the first Noether theorem (that symmetries imply (...) conservation laws), its converse (that conservation laws imply symmetries), and the locality of continuum/field physics. Thus the “conditionality re- sponse”, which sees conservation as (bi)conditional upon symme- tries and simply accepts energy non-conservation as an aspect of interactionist dualism, is seen to be, perhaps surprisingly, the one most in accord with contemporary physics (apart from quantum mechanics) by not conflicting with mathematical theorems basic to physics. A decent objection to interactionism should be a posteri- ori, based on empirically studying the brain. (shrink)

The notions of conservation and relativity lie at the heart of classical mechanics, and were critical to its early development. However, in Newton’s theory of mechanics, these symmetry principles were eclipsed by domain-specific laws. In view of the importance of symmetry principles in elucidating the structure of physical theories, it is natural to ask to what extent conservation and relativity determine the structure of mechanics. In this paper, we address this question by deriving classical mechanics—both nonrelativistic and relativistic—using (...) relativity and conservation as the primary guiding principles. The derivation proceeds in three distinct steps. First, conservation and relativity are used to derive the asymptotically conserved quantities of motion. Second, in order that energy and momentum be continuously conserved, the mechanical system is embedded in a larger energetic framework containing a massless component that is capable of bearing energy (as well as momentum in the relativistic case). Imposition of conservation and relativity then results, in the nonrelativistic case, in the conservation of mass and in the frame-invariance of massless energy; and, in the relativistic case, in the rules for transforming massless energy and momentum between frames. Third, a force framework for handling continuously interacting particles is established, wherein Newton’s second law is derived on the basis of relativity and a staccato model of motion-change. Finally, in light of the derivation, we elucidate the structure of mechanics by classifying the principles and assumptions that have been employed according to their explanatory role, distinguishing between symmetry principles and other types of principles (such as compositional principles) that are needed to build up the theoretical edifice. (shrink)

Thermodynamic implications of anisotropic gas-surface interactions in a closed molecular flow cavity are examined. Anisotropy at the microscopic scale, such as might be caused by reduced-dimensionality surfaces, is shown to lead to reversibility at the macroscopic scale. The possibility of a self-sustaining nonequilibrium stationary state induced by surface anisotropy is demonstrated that simultaneously satisfies flux balance, conservation of momentum, and conservation of energy. Conversely, it is also shown that the second law of thermodynamics prohibits anisotropic gas-surface interactions (...) in “equilibrium”, even for reduced dimensionality surfaces. This is particularly startling because reduced dimensionality surfaces are known to exhibit a plethora of anisotropic properties. That gas-surface interactions would be excluded from these anisotropic properties is completely counterintuitive from a causality perspective. These results provide intriguing insights into the second law of thermodynamics and its relation to gas-surface interaction physics. (shrink)

This article examines three aspects of the problem of understanding Benjamin Libet’s idea of conscious will causally interacting with certain neural activities involved in generating overt bodily movements. The first is to grasp the notion of cause involved, and we suggest a definition. The second is to form an idea of by what neural structure(s) and mechanism(s) a conscious will may control the motor activation. We discuss the possibility that the acts of control have to do with levels of supplementary (...) motor area activity and with the activation of populations of excitatory and inhibitory interneurons. The third aspect is to conceive of the main features of Libet’s proposed conscious mental field (CMF). We consider both an ontological and an epistemological interpretation of the CMF being nonphysical. In an attempt to refute the idea that Libet’s dualist mind–brain interactionism would violate the law of conservation of energy, we suggest that a CMF may alter the probability of the ion-channel gating by influencing structures of a size to which quantum mechanics needs to be applied. We argue that given the suggested definition of cause, and given the epistemological interpretation of the CMF being nonphysical, nothing would necessarily rule out that an element of a CMF, conscious will, may causally interact with neural activities in the brain. This defense of the idea of conscious will being causally efficacious has a bearing not only on the understanding of the mind–brain relation but also on the free will debate. (shrink)

In a recent article, Neil MacGill criticizes my claim (See "Water Into Wine", MacGill-Queen’s University Press, 1988) that miracles, understood as a transcendent agent overriding the usual course of nature, can conceivably occur without violating or suspending any of the laws of nature. MacGill feels that my account of miracles implies the violation of at least one law of nature, the Principle of the Conservation of Energy. In my reply, I point out that he is mistaken and that (...) my original claim has not, therefore, been refuted. (shrink)

Cross-term conservation relationships for electromagnetic energy, linear momentum, and angular momentum are derived and discussed here. When two or more sources of electromagnetic fields are present, these relationships connect the cross terms that appear in the traditional expressions for the electromagnetic (1) energy, (2) linear momentum, and (3) angular momentum, over to, respectively, (1) the sum of the rates of work, (2) the sum of the forces, and (3) the sum of the torques, that are due to (...) the fields of each charge or current source acting upon the other charge and current sources. These relationships, although not new, appear to be rarely recognized and used in the physics literature. As shown here, they can be extremely helpful for solving and gaining a deeper physical understanding into a rather diverse range of interesting problems in electrodynamics, including (1) aspects of Poynting's theorem when applied to charged point particles, (2) the detailed physical basis of electrostatic analysis, (3) understanding the connection between different techniques used in the past for solving Casimir force problems, and (4) reconciling the invalidity of Newton's third law in electrodynamics. (shrink)

Recently, the correspondence between the air track scenario and quantum database search algorithm was revealed. The conservation laws of linear momentum and nonlinear kinetic energy in the former case, which involve sequential elastic collisions, have their analogs in the latter case. Obviously, probability normalization combined with the Born rule serves as an analog for kinetic energy conservation. Here we explore the linear conservation laws in a generic quantum database search. Regarding the non-uniform distribution of the (...) marked state, the uneven state is initially prepared. In this way, the Grover diffusion operator results in a linear but nonphysical conservation law. On the other hand, in the CTC-assisted database search with the vast reduction of query complexity, the nonlinear instead of linear conservation laws are found. Finally, we conjecture that there are no conservation laws in the generalized Grover’s algorithm including the imaginary number i. (shrink)

It will be argued that Minkowski's implementation of distances is inconsistent. An alternative implementation will be proposed. In the new model the proper time of an object is taken as its fourth coordinate. Distances will be measured according to a four dimensional Euclidean metric. In the present approach mass is a constant of motion. A mass can therefore be ascribed to photons and neutrinos. Mechanics and dynamics will be reformulated in close correspondence with classical physics. Of particular interest is the (...) equation of motion for the proper time momentum. In the classical limit it reduces to the classical law of conservation of (kinetic+potential) energy. In the relativistic limit it is similar to the conservation of energy of the theory of relativity. The conservation of proper time momentum allows for an alternative explanation for Compton scattering and pair annihilation. On the basis of the proper time formulation of electrodynamics also an alternative explanation will be offered for the spectra of hydrogenic atoms. The proper time formulation of gravitational dynamics leads to the correct predictions of gravitational time dilation, the deflection of light and the precession of the perihelia of planets. For this no curvature will be needed. That is, spacetime is flat everywhere, even in the presence of sources of gravitation. Some cosmological consequences will be discussed. The present approach gives a new notion to energy, antiparticles and the structure of spacetime. The contents of the present paper will have important implications for the foundations of physics in general. (shrink)

Wolfgang Pauli first suggested the existence of what we now call the neutrino in order to preserve the law of conservation of energy. Previously, in 1911, James Chadwick had demonstrated that in the radioactive process called beta decay the emitted "beta particle" (now known to be an electron) was emitted with some random amount of its kinetic energy missing. Instead of the expected sharp spike of well-defined kinetic energy, a sample of many such emitted electrons showed (...) that their kinetic energies were distributed over a broad bump-like distribution. (shrink)

We consider several subtle aspects of the theory of neutrino oscillations which have been under discussion recently. We show that the S-matrix formalism of quantum field theory can adequately describe neutrino oscillations if correct physics conditions are imposed. This includes space-time localization of the neutrino production and detection processes. Space-time diagrams are introduced, which characterize this localization and illustrate the coherence issues of neutrino oscillations. We discuss two approaches to calculations of the transition amplitudes, which allow different physics interpretations: (i) (...) using configuration-space wave packets for the involved particles, which leads to approximate conservation laws for their mean energies and momenta; (ii) calculating first a plane-wave amplitude of the process, which exhibits exact energy-momentum conservation, and then convoluting it with the momentum-space wave packets of the involved particles. We show that these two approaches are equivalent. Kinematic entanglement (which is invoked to ensure exact energy-momentum conservation in neutrino oscillations) and subsequent disentanglement of the neutrinos and recoiling states are in fact irrelevant when the wave packets are considered. We demonstrate that the contribution of the recoil particle to the oscillation phase is negligible provided that the coherence conditions for neutrino production and detection are satisfied. Unlike in the previous situation, the phases of both neutrinos from Z 0 decay are important, leading to a realization of the Einstein-Podolsky-Rosen paradox. (shrink)

If one demystifies entropy the second law of thermodynamics comes out as an emergent property entirely based on the simple dynamic mechanical laws that govern the motion and energies of system parts on a micro-scale. The emergence of the second law is illustrated in this paper through the development of a new, very simple and highly efficient technique to compare time-averaged energies in isolated conservative linear large scale dynamical systems. Entropy is replaced by a notion that is much more transparent (...) and more or less dual called ectropy. Ectropy has been introduced before but we further modify the notion of ectropy such that the unit in which it is expressed becomes the unit of energy. The second law of thermodynamics in terms of ectropy states that ectropy decreases with time on a large enough time-scale and has an absolute minimum equal to zero. Zero ectropy corresponds to energy equipartition. Basically we show that by enlarging the dimension of an isolated conservative linear dynamical system and the dimension of the system parts over which we consider time-averaged energy partition, the tendency towards equipartition increases while equipartition is achieved in the limit. This illustrates that the second law is an emergent property of these systems. Finally from our large scale linear dynamic model we clarify Loschmidt’s paradox concerning the irreversible behavior of ectropy obtained from the reversible dynamic laws that govern motion and energy at the micro-scale. (shrink)

I argue against Barbara Montero's claim that Conservation of Energy has nothing to do with physicalism. I reject her reconstruction of the argument for physicalism from CoE, and offer an alternative reconstruction that better captures the intuitions of those who believe that there is a conflict between interactionist dualism and CoE.

The 3D Prandtl fluid flow through a bidirectional extending surface is analytically investigated. Cattaneo–Christov fluid model is employed to govern the heat and mass flux during fluid motion. The Prandtl fluid motion is mathematically modeled using the law of conservations of mass, momentum, and energy. The set of coupled nonlinear PDEs is converted to ODEs by employing appropriate similarity relations. The system of coupled ODEs is analytically solved using the well-established mathematical technique of HAM. The impacts of various physical (...) parameters over the fluid state variables are investigated by displaying their corresponding plots. The augmenting Prandtl parameter enhances the fluid velocity and reduces the temperature and concentration of the fluid. The momentum boundary layer boosts while the thermal boundary layer mitigates with the rising elastic parameter strength. Furthermore, the enhancing thermal relaxation parameter ) reduces the temperature distribution, whereas the augmenting concentration parameter drops the strength of the concentration profile. The increasing Prandtl parameter declines the fluid temperature while the augmenting Schmidt number drops the fluid concentration. The comparison of the HAM technique with the numerical solution shows an excellent agreement and hence ascertains the accuracy of the applied analytical technique. This work finds applications in numerous fields involving the flow of non-Newtonian fluids. (shrink)

By means of a Clebsch representation which differs from that previously applied to electromagnetic field theory it is shown that Maxwell's equations are derivable from a variational principle. In contrast to the standard approach, the Hamiltonian complex associated with this principle is identical with the generally accepted energy-momentum tensor of the fields. In addition, the Clebsch representation of a contravariant vector field makes it possible to consistently construct a field theory based upon a direction-dependent Lagrangian density (it is this (...) kind of Lagrangian density that may arise when developing the Finslerian extension of general relativity). The corresponding field equations are proved to be independent of any gauge of Clebsch potentials. The law of energy-momentum conservation of the field appears to be covariant and integrable in a rather wide class of direction-dependent Lagrangian densities. (shrink)

P. Busch has formulated a particular measurement process in order to show that predictable position measurements are impossible in general. Here we apply his formulation to studying the characteristics of various quantum measurements under the limitations which are imposed by the universal conservation laws and prove some theorems related to Busch's theorem. A simple approximate model measuring momentum is analyzed to investigate the roles of energy and momentum conservation. The results reveal the importance of the role of (...) Galilei's principle of relativity. (shrink)

References to energy of the universe have focussed upon the matter contribution, whereas the conservation laws must include a gravitational contribution as well. The conservation laws as applied to FRW cosmologies suggest a zero total energy irrespective of the spatial curvature when the value of the cosmological constant is taken to be zero. This result provides a useful constraint on models of the early universe and lends support to currently studied theories of the universe arising as (...) a quantum fluctuation of the vacuum. (shrink)

A ‘scientific worldview’ is commonly seen as contradictory to belief in supernatural forces, and there is little research on the supernatural beliefs of individuals who identify with science. In this article, we investigate the supernatural explanations of science-oriented individuals in domains of fundamental concern (suffering, death, and origins), and how supernatural causality is reconciled with belief in science. The open-ended responses of 387 Finns were analysed. The results show that science-oriented Finns endorsed both religion-related and more secular supernatural beliefs (such (...) as belief in evolution as a purposeful process). Following the coexistence model, science-oriented Finns applied synthetic and target-dependent reasoning. In addition, many who invoked supernatural explanations integrated supernatural causality with science. Two forms of integrated reasoning were found: 1) supernatural agency as the ultimate cause and scientific theory as the proximate cause, and 2) a similarity-based heuristic, as seen in afterlife beliefs appealing to the law of conservation of energy. (shrink)

Alsatian engineer Gustave-Adolphe Hirn is best known to historians of science for his experimental determination of the mechanical equivalent of heat, first published in 1855. Since the 1840s, that equivalent has been closely associated with the conservation of energy, indeed often conflated with it. Hirn was one of Thomas Kuhn’s twelve ‘pioneers’ whose work he deemed relevant to the ostensible ‘simultaneous discovery’ of energy conservation. Yet Hirn never wholeheartedly embraced energy conservation. After reviewing his (...) experimental work, his philosophical reflections, and his response to developments in heat theory, this article identifies three factors as having played central roles in this regard: Hirn’s deepest concerns were ontological, not energetic; none of the concepts basic to his natural philosophy were appropriate stand-ins for a quantitatively conserved energy; and, accurately reflecting the most common interpretation of the principle of the conservation of energy from the 1860s on – as exemplified already by Helmholtz in 1847 – Hirn associated its corpuscular-mechanical underpinning with the despiritualizing materialism he saw as dominating contemporary science. Hence although Hirn’s natural philosophy embraced sentiments quite in the spirit of the conservation of energy, he never explicitly subscribed to that principle. (shrink)

The mathematical framework of Relativistic Schrödinger Theory (RST) is generalized in order to include the self-interactions of the particles as an integral part of the theory (i.e. in a non-perturbative way). The extended theory admits a Lagrangean formulation where the Noether theorems confirm the existence of the conservation laws for charge and energy–momentum which were originally deduced directly from the dynamical equations. The generalized RST dynamics is applied to the case of some heavy helium-like ions, ranging from germanium (...) (Z=32) to bismuth (Z=83), in order to compute the interaction energy of the two electrons in their ground-state. The present inclusion of the electron self-energies into RST yields a better agreement of the theoretical predictions with the experimental data. (shrink)

Samuel Lytler Metcalfe was an American chemist and physician who wrote a voluminous work, Caloric Its Mechanical Chemical and Vital Agencies in the Phenomena of Nature ; attempting to account for all natural phenomena in terms of caloric. The book came out at the time when the concept of caloric was being gradually discarded and the law of conservation of energy was about to appear. Metcalfe was convinced that caloric would be the key to unlock the secrets of (...) nature; in order to develop the practical implications of his views he made research trips twice to England , and there he completed Caloric. (shrink)

Compared to approach motivation, avoidance motivation evokes vigilance, attention to detail, systematic information processing, and the recruitment of cognitive resources. From a conservation of energy perspective it follows that people would be reluctant to engage in the kind of effortful cognitive processing evoked by avoidance motivation, unless the benefits of expending this energy outweigh the costs. We put forward three empirically testable propositions concerning approach and avoidance motivation, investment of energy, and the consequences of such investments. (...) Specifically, we propose that compared to approach-motivated people, avoidance-motivated people (a) carefully select situations in which they exert such cognitive effort, (b) only perform well in the absence of distracters that occupy cognitive resources, and (c) become depleted after exerting such cognitive effort. (shrink)

One of the major reasons underlying the widespread rejection of the theory that the mind is an immaterial substance distinct from the body, But which nevertheless acts on the body, Is that it is felt that such a theory commits one to denying the principle of the conservation of energy. My aim in this article is to assess the strength of this objection. My thesis is that the usual replies are inadequate, But--Strong as this objection appears--Some important logical (...) distinctions have been overlooked and when these are taken into account its force vanishes. (shrink)

It is not known whether consciousness can affect the physical world, as a result of a free will action or in some other way. To do so, it must be able to produce physical changes that cannot be accounted for by physical laws, an ability we will refer to as causal action, and several issues relevant to this possibility are discussed. 1) Until recently it was thought that the conservation laws of physics would prohibit causal action. It has now (...) been found that such is not the case, but other problems remain. 2) Observations of brain activity show that most of the process for determining a decision is done by the brain. However, the question of whether the final determination is done by mind or the brain is still open. The issue then arises that given the large amount of processing the brain can do, why would mind do this final step and if it does, why would the amount done by mind be so small? (shrink)

The explicit history of the “hidden variables” problem is well-known and established. The main events of its chronology are traced. An implicit context of that history is suggested. It links the problem with the “conservation of energy conservation” in quantum mechanics. Bohr, Kramers, and Slaters (1924) admitted its violation being due to the “fourth Heisenberg uncertainty”, that of energy in relation to time. Wolfgang Pauli rejected the conjecture and even forecast the existence of a new and (...) unknown then elementary particle, neutrino, on the ground of energy conservation in quantum mechanics, afterwards confirmed experimentally. Bohr recognized his defeat and Pauli’s truth: the paradigm of elementary particles (furthermore underlying the Standard model) dominates nowadays. However, the reason of energy conservation in quantum mechanics is quite different from that in classical mechanics (the Lie group of all translations in time). Even more, if the reason was the latter, Bohr, Cramers, and Slatters’s argument would be valid. The link between the “conservation of energy conservation” and the problem of hidden variables is the following: the former is equivalent to their absence. The same can be verified historically by the unification of Heisenberg’s matrix mechanics and Schrödinger’s wave mechanics in the contemporary quantum mechanics by means of the separable complex Hilbert space. The Heisenberg version relies on the vector interpretation of Hilbert space, and the Schrödinger one, on the wave-function interpretation. However the both are equivalent to each other only under the additional condition that a certain well-ordering is equivalent to the corresponding ordinal number (as in Neumann’s definition of “ordinal number”). The same condition interpreted in the proper terms of quantum mechanics means its “unitarity”, therefore the “conservation of energy conservation”. In other words, the “conservation of energy conservation” is postulated in the foundations of quantum mechanics by means of the concept of the separable complex Hilbert space, which furthermore is equivalent to postulating the absence of hidden variables in quantum mechanics (directly deducible from the properties of that Hilbert space). Further, the lesson of that unification (of Heisenberg’s approach and Schrödinger’s version) can be directly interpreted in terms of the unification of general relativity and quantum mechanics in the cherished “quantum gravity” as well as a “manual” of how one can do this considering them as isomorphic to each other in a new mathematical structure corresponding to quantum information. Even more, the condition of the unification is analogical to that in the historical precedent of the unifying mathematical structure (namely the separable complex Hilbert space of quantum mechanics) and consists in the class of equivalence of any smooth deformations of the pseudo-Riemannian space of general relativity: each element of that class is a wave function and vice versa as well. Thus, quantum mechanics can be considered as a “thermodynamic version” of general relativity, after which the universe is observed as if “outside” (similarly to a phenomenological thermodynamic system observable only “outside” as a whole). The statistical approach to that “phenomenological thermodynamics” of quantum mechanics implies Gibbs classes of equivalence of all states of the universe, furthermore re-presentable in Boltzmann’s manner implying general relativity properly … The meta-lesson is that the historical lesson can serve for future discoveries. (shrink)

This paper argues that nonphysical souls would violate fundamental physical laws if they were able to influence brain events. Though we have no idea how nonphysical souls might operate, we know quite a bit about how brains work, so we can consider each of the ways that an external force could interrupt brain processes enough to control one’s body. It concludes that there is no way that a nonphysical soul could interact with the brain—neither by introducing new energy into (...) the physical world, nor by borrowing existing energy from it—without apparently violating one or more basic laws of physics, such as the law of conservation of energy. And despite widespread appeals to quantum mechanics to give interactionism an air of scientific respectability, the essential randomness of quantum processes prohibits the distinctly nonrandom influence that a nonphysical soul must have on brain events in order to control the body, and quantum mechanical uncertainty is not great enough to allow neurons to fire action potentials. -/- 1. Introduction -- 2. How the Brain Works -- 3. Mind-Brain Interaction Mechanisms - 3.1 Opening Sodium Channels - 3.2 Altering Voltage Gradients - 3.3 Synaptic Transmission - 3.3.1 The Presynaptic Neuron - 3.3.2 The Post-Synaptic Neuron - 3.3.3 The Beck and Eccles Models - 3.4 Neuronal Modulation - 3.5 Self-Generation of Action Potentials by Neurons -- 4. Harnessing Energy -- 5. How Many Action Potentials for a Volitional Act? -- 6. Input: From Brain to Nonphysical Mind -- 7. Discussion -- Appendix A: Opening Gates on Membrane Channels - A.1 Directly Opening Gates - A.2 Changing Voltage Across the Membrane -- Appendix B: The Biochemical Approach. (shrink)

Standard lore holds that magnetic forces are incapable of doing mechanical work. More precisely, the claim is that whenever it appears that a magnetic force is doing work, the work is actually being done by another force, with the magnetic force serving only as an indirect mediator. However, the most familiar instances of magnetic forces acting in everyday life, such as when bar magnets lift other bar magnets, appear to present manifest evidence of magnetic forces doing work. These sorts of (...) counterexamples are often dismissed as arising from quantum effects that lie outside the classical regime. In this paper, we show that quantum theory is not needed to account for these phenomena, and that classical electromagnetism admits a model of elementary magnetic dipoles on which magnetic forces can indeed do work. In order to develop this model, we revisit the foundational principles of the classical theory of electromagnetism, showcase the importance of constraints from relativity, examine the structure of the multipole expansion, and study the connection between the Lorentz force law and conservation of energy and momentum. (shrink)