The thermodynamic behavior is analyzed of a single classical charged particle in thermal equilibrium with classical electromagnetic thermal radiation, while electrostatically bound by a fixed charge distribution of opposite sign. A quasistatic displacement of this system in an applied electrostatic potential is investigated. Treating the system nonrelativistically, the change in internal energy, the work done, and the change in caloric entropy are all shown to be expressible in terms of averages involving the distribution of the position coordinates alone. A convenient (...) representation for the probability distribution is shown to be the ensemble average of the absolute square value of an expansion over the eigenstates of a Schrödinger-like equation, since the heat flow is shown to vanish for each hypothetical “state.” Subject to key assumptions highlighted here, the demand that the entropy be a function of state results in statistical averages in agreement with the form in quantum statistical mechanics. Examining the very low and very high temperature situations yields Planck's and Boltzmann's constants. The blackbody radiation spectrum is then deduced. From the viewpoint of the theory explored here, the method in quantum statistical mechanics of statistically counting the “states” at thermal equilibrium by using the energy eigenvalue structure, is simply a convenient counting scheme, rather than actually representing averages involving physically discrete energy states. (shrink)

In this paper, I will attempt a defense of Hannah Arendt’s usage of the social/political distinction in her “Reflections on Little Rock,” demonstrating that not only is it tenable but also helpful. After distinguishing between her (in)famous distinction between the social and political spheres, I will use the notions of “power,” which is compatible with political freedom, and “force,” which is not, to analyze the strategy of governmentally enforced integration. What I hope to show is that althoughschools are of the (...) utmost political importance, governmental force cannot solve social prejudice, and it cannot legitimately be used outside of the sphere of establishing and protecting legal equality. I will further elucidate Arendt’s illustrative passage on how an integration effort might politically engage problems of exclusion and inequality in schools without having to resort to force to solve social problems and without reducing politics to instrumental administration. (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)

In the past, a few researchers have presented arguments indicating that a statistical equilibrium state of classical charged particles necessarily demands the existence of a temperature-independent, incident classical electromagnetic random radiation. Indeed, when classical electromagnetic zero-point radiation is included in the analysis of problems with macroscopic boundaries, or in the analysis of charged particles in linear force fields, then good agreement with nature is obtained. In general, however, this agreement has not been found to hold for charged particles bound in (...) nonlinear force fields. The point is raised here that this disagreement arising for nonlinear force fields may be a premature conclusion on this classical theory for describing atomic systems, because past calculations have not directed strict attention to electromagnetic interactions between charges. This point is illustrated here by examining the classical hydrogen atom and showing that this problem has still not been adequately solved. (shrink)

In this essay I defend Heidegger’s critique of technology against possible criticisms that he may be an anti-humanist and a mystic. This essay will show that Heidegger’s critique of technology is helpful in thinking about ecological questions; and his contributions to such questions is relevant and not radically separated from some of the work of other philosophers today including Karen Warren and Marilyn Frye.

In the game theory literature, Garrett Hardin’s famous allegory of the “tragedy of the commons” has been modeled as a variant of the Prisoner’s Dilemma, labeled the Herder Problem (or, sometimes, the Commons Dilemma). This brief paper argues that important differences in the institutional structures of the standard Prisoner’s Dilemma and Herder Problem render the two games different in kind. Specifically, institutional impediments to communication and cooperation that ensure a dominant strategy of defection in the classic Prisoner’s Dilemma are absent (...) in the Herder Problem. Their absence does not ensure that players will achieve a welfare-enhancing, cooperative solution to the Herders Problem, but does create far more opportunity for players to alter the expected payoffs through cooperative arrangements. In a properly modeled Herder Problem—along the lines of an assurance game—defection would not always be the dominant strategy. Consequently, the Herder Problem is not in the nature of a Prisoner’s Dilemma. (shrink)

In this paper, I elaborate the difference between the concept of infinity and the idea of infinity through Cantor's diagonalization proof to illuminate a passage in Kant's Critique of Judgment. Taking Lyotard's analysis of aesthetic judgments as the basis for my own project, I focus on the idea of a collapse of temporality required for objective cognition and its concomitant preclusion of cognitive subjectivity. Finally, after borrowing language from Hegel's Phenomenology of Spirit, I show that even though there is not (...) a cognitive subject in judgments of the sublime, there is nevertheless a subjectivity that consciousness is tasked with, even if it never fulfills this task when it is confronted with a mathematically sublime object, and it is an subjectivity that would transcend time in order to know the object in-itself. (shrink)

An analysis is carried out involving reversible thermodynamic operations on arbitrarily shaped small cavities in perfectly conducting material. These operations consist of quasistatic deformations and displacements of cavity walls and objects within the cavity. This analysis necessarily involves the consideration of Casimir-like forces. Typically, even for the simplest of geometrical structures, such calculations become quite complex, as they need to take into account changes in singular quantities. Much of this complexity is reduced significantly here by working directly with the change (...) in electromagnetic fields as a result of the deformation and displacement changes. A key result of this work is the derivation that for such cavity structures, classical electromagnetic zero-point radiation is the appropriate spectrum at a temperature of absolute zero to ensure that the reversible deformation operations obey both isothermal and adiabatic conditions. In addition, a generalized Wien displacement law is obtained from the demand that the change in entropy of the radiation in these arbitrarily shaped structures must be a state function of temperature and frequency. (shrink)