Nonlocal observables and lightcone-averaging in relativistic thermodynamics

The unification of relativity and thermodynamics has been a subject of considerable debate over the last 100 years. The reasons for this are twofold: (i) Thermodynamic variables are nonlocal quantities and, thus, single out a preferred class of hyperplanes in spacetime. (ii) There exist different, seemingly equally plausible ways of defining heat and work in relativistic systems. These ambiguities led, for example, to various proposals for the Lorentz transformation law of temperature. Traditional 'isochronous' formulations of relativistic thermodynamics are neither theoretically satisfactory nor experimentally feasible. Here, we demonstrate how these deficiencies can be resolved by defining thermodynamic quantities with respect to the backward-lightcone of an observation event. This approach yields novel, testable predictions and allows for a straightforward-extension of thermodynamics to General Relativity. Our theoretical considerations are illustrated through three-dimensional relativistic many-body simulations.Comment: typos in Eqs. (12) and (14) corrected, minor additions in the tex

On the Foundation of the Relativistic Dynamics with the Tachyon

The theoretical foundation of the object moving faster than light in vacuum ({\it tachyon}) is still missing or incomplete. Here we present the classical foundation of the relativistic dynamics including the tachyon. An anomalous sign-factor extracted from the transformation of ${ \sqrt{1-u^{2}/c^{2} } }$ under the Lorentz transformation, which has been always missed in the usual formulation of the tachyon, has a crucial role in the dynamics of the tachyon. Due to this factor the mass of the tachyon transforms in the unusual way although the energy and momentum, which are defined as the conserved quantities in all uniformly moving systems, transform in the usual way as in the case of the object moving slower than light ({\it bradyon}). We show that this result can be also obtained from the least action approach. On the other hand, we show that the ambiguities for the description of the dynamics for the object moving with the velocity of light ({\it luxon}) can be consistently removed only by introducing a new dynamical variable. Furthermore, by using the fundamental definition of the momentum and energy we show that the zero-point energy for any kind of the objects, {\it i.e.}, the tachyon, bradyon, and luxon, which has been known as the undetermined constant, should satisfy some constraints for consistency, and we note that this is essentially another novel relativistic effect. Finally, we remark about the several unsolved problems.Comment: 39 pages, latex, 15 figures avaliable upon reques

Theory of quantum radiation observed as sonoluminescence

Sonoluminescence is explained in terms of quantum radiation by moving interfaces between media of different polarizability. In a stationary dielectric the zero-point fluctuations of the electromagnetic field excite virtual two-photon states which become real under perturbation due to motion of the dielectric. The sonoluminescent bubble is modelled as an optically empty cavity in a homogeneous dielectric. The problem of the photon emission by a cavity of time-dependent radius is handled in a Hamiltonian formalism which is dealt with perturbatively up to first order in the velocity of the bubble surface over the speed of light. A parameter-dependence of the zero-order Hamiltonian in addition to the first-order perturbation calls for a new perturbative method combining standard perturbation theory with an adiabatic approximation. In this way the transition amplitude from the vacuum into a two-photon state is obtained, and expressions for the single-photon spectrum and the total energy radiated during one flash are given both in full and in the short-wavelengths approximation when the bubble is larger than the wavelengths of the emitted light. It is shown analytically that the spectral density has the same frequency-dependence as black-body radiation; this is purely an effect of correlated quantum fluctuations at zero temperature. The present theory clarifies a number of hitherto unsolved problems and suggests explanations for several more. Possible experiments that discriminate this from other theories of sonoluminescence are proposed.Comment: Latex file, 28 pages, postscript file with 3 figs. attache