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.

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)

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)

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)

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)

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)

Every so often a book comes along that transforms one’s perspective on a major development in the history of science. Kenneth Caneva’s is one of them. Built upon decades of immersion in the primary...

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)

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)

Evan Fales has recently argued that, although I provide the most promising approach for those concerned to defend belief in divine intervention, I nevertheless fail to show that such belief can be rational. I argue that Fales’ objections are unsuccessful.

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)

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)

Many contemporary thinkers seeking to integrate theistic belief and scientific thought reject what they regard as two extremes. They disavow deism in which God is understood simply to uphold the existence of the physical universe, and they exclude any view of divine influence that suggests the performance of physical work through an immaterial cause. Deism is viewed as theologically inadequate, and acceptance of direct immaterial causation of physical events is viewed as scientifically illegitimate. This desire to avoid both deism and (...) any positing of God as directly intervening in the physical order has led to models of divine agency that seek to defend the reality of divine causal power yet affirm the causal closure of the physical. I argue, negatively, that such models are unsuccessful in their attempts to affirm both the reality of divine causal power acting in the created world and the causal closure of the physical and, positively, that the assumption that underlies these models, namely that any genuine integration of theistic and scientific belief must posit the causal closure of the physical on pain of violating well-established conservation principles, is mistaken. (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)

We discuss a new theory of the universe in which the vacuum energy is of classical origin and dominates the energy content of the universe. As usual, the Einstein equations determine the metric of the universe. However, the scale factor is controlled by total energy conservation in contrast to the practice in the Robertson–Walker formulation. This theory naturally leads to an explanation for the Big Bang and is not plagued by the horizon and cosmological constant problem. (...) It naturally accommodates the notion of dark energy and proposes a possible explanation for dark matter. It leads to a dual description of the universe, which is reminiscent of the dual theory proposed by Milne in 1937. On the one hand one can describe the universe in terms of the original Einstein coordinates in which the universe is expanding, on the other hand one can describe it in terms of co-moving coordinates which feature in measurements. In the latter representation the universe looks stationary and the age of the universe appears constant. The paper describes the evolution of this universe. It starts out in a classical state with perfect symmetry and zero entropy. Due to the vacuum metric the effective energy density is infinite at the beginning, but diminishes rapidly. Once it reaches the Planck energy density of elementary particles, the formation of particles can commence. Because of the quantum nature of creation and annihilation processes spatial and temporal inhomogeneities appear in the matter distributions, resulting in residual proton (neutron) and electron densities. Hence, quantum uncertainty plays an essential role in the creation of a diversified complex universe with increasing entropy. It thus seems that quantum fluctuations play a role in cosmology similar to that of random mutations in biology. Other analogies to biological principles, such as recapitulation, are also discussed. (shrink)

Energy nonconservation is a serious problem of dynamical collapse theories. In this paper, we propose a discrete model of energy-conserved wavefunction collapse. It is shown that the model is consistent with existing experiments and our macroscopic experience.

An infinite number of elastically colliding balls is considered in a classical, and then in a relativistic setting. Energy and momentum are not necessarily conserved globally, even though each collision does separately conserve them. This result holds in particular when the total mass of all the balls is finite, and even when the spatial extent and temporal duration of the process are also finite. Further, the process is shown to be indeterministic: there is an arbitrary parameter in the general (...) solution that corresponds to the injection of an arbitrary amount of energy (classically), or energy-momentum (relativistically), into the system at the point of accumulation of the locations of the balls. Specific examples are given that illustrate these counter-intuitive results, including one in which all the balls move with the same velocity after every collision has taken place. (shrink)

In his recent authoritative Helmholtz and the Conservation of Energy, Kenneth Caneva has claimed that earlier authors had invoked the principle of conservation of living force only in cases of a system returning to an earlier state, or of one without Newtonian forces. Relaying on texts in the tradition of the French Analytical Mechanics form Lagrange to Coriolis, I argue that this was not the case, and that the principle had been formulated and used for cases where (...) living force proper (mv2) was not conserved but its sum with an integral function (refers today as potential) was constant. In addition. I show that contrary to Caneva’s claim, the principle had been connected to the impossibility of creating power out of nothing. The two points indicate a stronger link between the analytical tradition and Helmholtz and his readers than usually portrayed, and the significant contribution of mechanics to the emergence of energy conservation. On a methodological level the use of living force shows that a common term and even a concept, like energy, is not always needed for its successful employment. (shrink)

Supertasks recently discussed in the literature purport to display a failure ofenergy conservation and determinism in Newtonian mechanics. We debatewhether these supertasks are admissible as Newtonian systems, with Earmanand Norton defending the affirmative and Alper and Bridger the negative.

We study the conservation of energy, or lack thereof, when measurements are performed in quantum mechanics. The expectation value of the Hamiltonian of a system changes when wave functions collapse in accordance with the standard textbook treatment of quantum measurement, but one might imagine that the change in energy is compensated by the measuring apparatus or environment. We show that this is not true; the change in the energy of a state after measurement can be arbitrarily (...) large, independent of the physical measurement process. In Everettian quantum theory, while the expectation value of the Hamiltonian is conserved for the wave function of the universe, it is not constant within individual worlds. It should therefore be possible to experimentally measure violations of conservation of energy, and we suggest an experimental protocol for doing so. (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)