A real Lorentz-FitzGerald contraction

Many condensed matter systems are such that their collective excitations at low energies can be described by fields satisfying equations of motion formally indistinguishable from those of relativistic field theory. The finite speed of propagation of the disturbances in the effective fields (in the simplest models, the speed of sound) plays here the role of the speed of light in fundamental physics. However, these apparently relativistic fields are immersed in an external Newtonian world (the condensed matter system itself and the laboratory can be considered Newtonian, since all the velocities involved are much smaller than the velocity of light) which provides a privileged coordinate system and therefore seems to destroy the possibility of having a perfectly defined relativistic emergent world. In this essay we ask ourselves the following question: In a homogeneous condensed matter medium, is there a way for internal observers, dealing exclusively with the low-energy collective phenomena, to detect their state of uniform motion with respect to the medium? By proposing a thought experiment based on the construction of a Michelson-Morley interferometer made of quasi-particles, we show that a real Lorentz-FitzGerald contraction takes place, so that internal observers are unable to find out anything about their `absolute ' state of motion. Therefore, we also show that an effective but perfectly defined relativistic world can emerge in a fishbowl world situated inside a Newtonian (laboratory) system. This leads us to reflect on the various levels of description in physics, in particular regarding the quest towards a theory of quantum gravity.Comment: 6 pages, no figures. Minor changes reflect published versio

Einstein's quantum theory of the monatomic ideal gas: non-statistical arguments for a new statistics

In this article, we analyze the third of three papers, in which Einstein presented his quantum theory of the ideal gas of 1924-1925. Although it failed to attract the attention of Einstein's contemporaries and although also today very few commentators refer to it, we argue for its significance in the context of Einstein's quantum researches. It contains an attempt to extend and exhaust the characterization of the monatomic ideal gas without appealing to combinatorics. Its ambiguities illustrate Einstein's confusion with his initial success in extending Bose's results and in realizing the consequences of what later became to be called Bose-Einstein statistics. We discuss Einstein's motivation for writing a non-combinatorial paper, partly in response to criticism by his friend Ehrenfest, and we paraphrase its content. Its arguments are based on Einstein's belief in the complete analogy between the thermodynamics of light quanta and of material particles and invoke considerations of adiabatic transformations as well as of dimensional analysis. These techniques were well-known to Einstein from earlier work on Wien's displacement law, Planck's radiation theory, and the specific heat of solids. We also investigate the possible role of Ehrenfest in the gestation of the theory.Comment: 57 pp

A spatially-VSL gravity model with 1-PN limit of GRT

A scalar gravity model is developed according the 'geometric conventionalist' approach introduced by Poincare (Einstein 1921, Poincare 1905, Reichenbach 1957, Gruenbaum1973). In principle this approach allows an alternative interpretation and formulation of General Relativity Theory (GRT), with distinct i) physical congruence standard, and ii) gravitation dynamics according Hamilton-Lagrange mechanics, while iii) retaining empirical indistinguishability with GRT. In this scalar model the congruence standards have been expressed as gravitationally modified Lorentz Transformations (Broekaert 2002). The first type of these transformations relate quantities observed by gravitationally 'affected' (natural geometry) and 'unaffected' (coordinate geometry) observers and explicitly reveal a spatially variable speed of light (VSL). The second type shunts the unaffected perspective and relates affected observers, recovering i) the invariance of the locally observed velocity of light, and ii) the local Minkowski metric (Broekaert 2003). In the case of a static gravitation field the model retrieves the phenomenology implied by the Schwarzschild metric. The case with proper source kinematics is now described by introduction of a 'sweep velocity' field w: The model then provides a hamiltonian description for particles and photons in full accordance with the first Post-Newtonian approximation of GRT (Weinberg 1972, Will 1993).Comment: v1: 11 pages, GR17 conf. paper, Dublin 2004, v2: WEP issue solved, section on acceleration transformation added, text improved, more references, same results, v3: typos removed, footnotes, added and references updated, v4: appendix added, improved tex

Entanglement, quantum phase transition and scaling in XXZ chain

Motivated by recent development in quantum entanglement, we study relations among concurrence $C$, SU$_q$(2) algebra, quantum phase transition and correlation length at the zero temperature for the XXZ chain. We find that at the SU(2) point, the ground state possess the maximum concurrence. When the anisotropic parameter $\Delta$ is deformed, however, its value decreases. Its dependence on $\Delta$ scales as $C=C_0-C_1(\Delta-1)^2$ in the XY metallic phase and near the critical point (i.e. $1<\Delta<1.3$) of the Ising-like insulating phase. We also study the dependence of $C$ on the correlation length $\xi$, and show that it satisfies $C=C_0-1/2\xi$ near the critical point. For different size of the system, we show that there exists a universal scaling function of $C$ with respect to the correlation length $\xi$.Comment: 4 pages, 3 figures. to appear in Phys. Rev.

Gravitation, electromagnetism and cosmological constant in purely affine gravity

The Ferraris-Kijowski purely affine Lagrangian for the electromagnetic field, that has the form of the Maxwell Lagrangian with the metric tensor replaced by the symmetrized Ricci tensor, is dynamically equivalent to the metric Einstein-Maxwell Lagrangian, except the zero-field limit, for which the metric tensor is not well-defined. This feature indicates that, for the Ferraris-Kijowski model to be physical, there must exist a background field that depends on the Ricci tensor. The simplest possibility, supported by recent astronomical observations, is the cosmological constant, generated in the purely affine formulation of gravity by the Eddington Lagrangian. In this paper we combine the electromagnetic field and the cosmological constant in the purely affine formulation. We show that the sum of the two affine (Eddington and Ferraris-Kijowski) Lagrangians is dynamically inequivalent to the sum of the analogous ($\Lambda$CDM and Einstein-Maxwell) Lagrangians in the metric-affine/metric formulation. We also show that such a construction is valid, like the affine Einstein-Born-Infeld formulation, only for weak electromagnetic fields, on the order of the magnetic field in outer space of the Solar System. Therefore the purely affine formulation that combines gravity, electromagnetism and cosmological constant cannot be a simple sum of affine terms corresponding separately to these fields. A quite complicated form of the affine equivalent of the metric Einstein-Maxwell-$\Lambda$ Lagrangian suggests that Nature can be described by a simpler affine Lagrangian, leading to modifications of the Einstein-Maxwell-$\Lambda$CDM theory for electromagnetic fields that contribute to the spacetime curvature on the same order as the cosmological constant.Comment: 17 pages, extended and combined with gr-qc/0612193; published versio

Maxwell equations in matrix form, squaring procedure, separating the variables, and structure of electromagnetic solutions

The Riemann -- Silberstein -- Majorana -- Oppenheimer approach to the Maxwell electrodynamics in vacuum is investigated within the matrix formalism. The matrix form of electrodynamics includes three real 4 \times 4 matrices. Within the squaring procedure we construct four formal solutions of the Maxwell equations on the base of scalar Klein -- Fock -- Gordon solutions. The problem of separating physical electromagnetic waves in the linear space \lambda_{0}\Psi^{0}+\lambda_{1}\Psi^{1}+\lambda_{2}\Psi^{2}+ lambda_{3}\Psi^{3} is investigated, several particular cases, plane waves and cylindrical waves, are considered in detail.Comment: 26 pages 16 International Seminar NCPC, May 19-22, 2009, Minsk, Belaru

Two Mathematically Equivalent Versions of Maxwell's Equations

This paper is a review of the canonical proper-time approach to relativistic mechanics and classical electrodynamics. The purpose is to provide a physically complete classical background for a new approach to relativistic quantum theory. Here, we first show that there are two versions of Maxwell's equations. The new version fixes the clock of the field source for all inertial observers. However now, the (natural definition of the effective) speed of light is no longer an invariant for all observers, but depends on the motion of the source. This approach allows us to account for radiation reaction without the Lorentz-Dirac equation, self-energy (divergence), advanced potentials or any assumptions about the structure of the source. The theory provides a new invariance group which, in general, is a nonlinear and nonlocal representation of the Lorentz group. This approach also provides a natural (and unique) definition of simultaneity for all observers. The corresponding particle theory is independent of particle number, noninvariant under time reversal (arrow of time), compatible with quantum mechanics and has a corresponding positive definite canonical Hamiltonian associated with the clock of the source. We also provide a brief review of our work on the foundational aspects of the corresponding relativistic quantum theory. Here, we show that the standard square-root and the Dirac equations are actually two distinct spin-$\tfrac{1}{2}$ particle equations.Comment: Appeared: Foundations of Physic

Radiation Reaction: General approach and applications, especially to electrodynamics

Radiation reaction (but, more generally, fluctuations and dissipation) occurs when a system interacts with a heat bath, a particular case being the interaction of an electron with the radiation field. We have developed a general theory for the case of a quantum particle in a general potential (but, in more detail, an oscillator potential) coupled to an arbitrary heat bath at arbitrary temperature, and in an external time-dependent $c$-number field. The results may be applied to a large variety of problems in physics but we concentrate by showing in detail the application to the blackbody radiation heat bath, giving an exact result for radiation reaction problem which has no unsatisfactory features such as the runaway solutions associated with the Abraham-Lorentz theory. In addition, we show how atomic energy and free energy shifts due to temperature may be calculated. Finally, we give a brief review of applications to Josephson junctions, quantum statistical mechanics, mesoscopic physics, quantum information, noise in gravitational wave detectors, Unruh radiation and the violation of the quantum regression theore