Poincaré’s Relativistic Physics: Its Origins and Nature

Henri Poincaré (1854–1912) developed a relativistic physics by elevating the empirical inability to detect absolute motion, or motion relative to the ether, to the principle of relativity, and its mathematics ensured that it would be compatible with that principle. Although Poincaré’s aim and theory were similar to those of Albert Einstein (1879–1955) in creating his special theory of relativity, Poincaré’s relativistic physics should not be seen as an attempt to achieve Einstein’s theory but as an independent endeavor. Poincaré was led to advance the principle of relativity as a consequence of his reflections on late nineteenth-century electrodynamics; of his conviction that physics should be formulated as a physics of principles; of his conventionalistic arguments on the nature of time and its measurement; and of his knowledge of the experimental failure to detect absolute motion. The nonrelativistic theory of electrodynamics of Hendrik A.Lorentz (1853–1928) of 1904 provided the means for Poincaré to elaborate a relativistic physics that embraced all known physical forces, including that of gravitation. Poincaré did not assume any dynamical explanation of the Lorentz transformation, which followed from the principle of relativity, and he did not seek to dismiss classical concepts, such as that of the ether, in his new relativistic physics. Shaul Katzir teaches in the Graduate Program in History and Philosophy of Science, Bar Ilan University.     

Reply to comay’s "relativity versus the longitudinal magnetic field of the photon"

Poincaré group electrodynamics is {ie255-1} conserving and Lorentz covariant under all conditions by definition. Examples are given of these properties. Comay’s comment is incorrect: any {ie255-2} conserving field theory that is Lorentz covariant is consistent with special relativity, whose underlying group is the Poincaré group.     

Standing Waves in the Lorentz-Covariant World

When Einstein formulated his special relativity, he developed his dynamics for point particles. Of course, many valiant efforts have been made to extend his relativity to rigid bodies, but this subject is forgotten in history. This is largely because of the emergence of quantum mechanics with wave-particle duality. Instead of Lorentz-boosting rigid bodies, we now boost waves and have to deal with Lorentz transformations of waves. We now have some nderstanding of plane waves or running waves in the covariant picture, but we do not yet have a clear picture of standing waves. In this report, we show that there is one set of standing waves which can be Lorentz-transformed while being consistent with all physical principle of quantum mechanics and relativity. It is possible to construct a representation of the Poincaré group using harmonic oscillator wave functions satisfying space-time boundary conditions. This set of wave functions is capable of explaining the quantum bound state for both slow and fast hadrons. In particular it can explain the quark model for hadrons at rest, and Feynman’s parton model hadrons moving with a speed close to that of light.     

On the difference between Poincaré and Lorentz gravity

The Poincaré invariance of GR is usually interpreted as Lorentz invariance plus diffeomorphism invariance. In this paper, by introducing the local inertial coordinates (LIC), it is shown that a theory with Lorentz and diffeomorphism invariance is not necessarily Poincaré invariant. Actually, the energy–momentum conservation is violated there. On the other hand, with the help of the LIC, the Poincaré invariance is reinterpreted as an internal symmetry. In this formalism, the conservation law is derived, which has not been sufficiently explored before.     

Poincaré, Einstein,et l’inertie de l’énergie

The mystery surrounding the discovery of the inertia of energy is solved by considering its connection with an older problem: the effect of uniform, global motion on the forces acting in an electric System. From Maxwell's and his disciples’ point of view this effect confirmed the existence of the ether. From Poincaré’ s point of view, it was paradoxical for it contradicted the relativity principle and went with a violation of the principle of reaction. The inertia of energy, as Einstein proposed it in 1905, answered these paradoxes in the framework of special relativity and in Poincaré’s style of reasoning.     

De Sitter Relativity: a New Road to Quantum Gravity?

The Poincaré group generalizes the Galilei group for high-velocity kinematics. The de Sitter group is assumed to go one step further, generalizing Poincaré as the group governing high-energy kinematics. In other words, ordinary special relativity is here replaced by de Sitter relativity. In this theory, the cosmological constant Λ is no longer a free parameter, and can be determined in terms of other quantities. When applied to the whole universe, it is able to predict the value of Λ and to explain the cosmic coincidence. When applied to the propagation of ultra-high energy photons, it gives a good estimate of the time delay observed in extragalactic gamma-ray flares. It can, for this reason, be considered a new paradigm to approach the quantum gravity problem.     

The Lorenz Number and the Lorenz Gauge—Known Concepts,Unknown Physicist

Ludvig Lorenz was Denmark's first theoretical physicist of international recognition. Despite his important contributions to a broad range of experimental and theoretical physics, he generally appears as a somewhat peripheral figure in histories of late‐nineteenth‐century physics and is completely overshadowed by his near‐namesake H. A. Lorentz. Herein, a selected number of Lorenz's works is introduced with an eye on those which are still of relevance to modern physics and today eponymously associated with his name. These contributions are known as the Lorenz number, the Lorenz gauge, the Lorenz–Lorentz law or formula, and the Lorenz–Mie scattering theory.     

Poincaré gauge theory from self-coupling

Poincaré gauge theory is derived from a linear theory by the method suggested by Gupta for deriving Einstein’s general relativity from the linear theory of a spin-2 field. Non-linearity is introduced by requiring that a set of tensor fields be coupled to the Noether currents of the Poincaré group (energy-momentum and spin).     

The deformation of Poincar subgroups concerning very special relativity

We investigate here various kinds of semi-product subgroups of Poincar group in the scheme of Cohen-Glashow’s very special relativity along the deformation approach by Gibbons-Gomis-Pope.For each proper Poincar subgroup which is a semi-product of proper lorentz group with the spacetime translation group T(4),we investigate all possible deformations and obtain all the possible natural representations inherited from the 5-d representation of Poincar′e group.We find from the obtained natural representation that rotation operation may have additional accompanied scale transformation when the original Lorentz subgroup is deformed and the boost operation gets the additional accompanied scale transformation in all the deformation cases.The additional accompanied scale transformation has a strong constrain on the possible invariant metric function of the corresponding geometry and the field theories in the spacetime with the corresponding geometry.     

Einstein's ‘Zürich Notebook’ and his journey to general relativity

On the basis of his ‘Zürich Notebook’ I shall describe a particularly fruitful phase in Einstein's struggle on the way to general relativity. These research notes are an extremely illuminating source for understanding Einstein's main physical arguments and conceptual difficulties that delayed his discovery of general relativity by about three years. Together with the ‘Entwurf’ theory in collaboration with Marcel Grossmann, these notes also show that the final theory was missed late in 1912 within a hair's breadth. The Einstein‐Grossmann theory, published almost exactly hundred years ago, contains, however, virtually all essential elements of Einstein's definite gravitation theory.     

E. Cartan’s attempt at bridge-building between Einstein and the Cosserats – or how translational curvature became to be known as torsion

Élie Cartan’s “généralisation de la notion de courbure” (1922) arose from a creative evaluation of the geometrical structures underlying both, Einstein’s theory of gravity and the Cosserat brothers generalized theory of elasticity. In both theories groups operating in the infinitesimal played a crucial role. To judge from his publications in 1922–24, Cartan developed his concept of generalized spaces with the dual context of general relativity and non-standard elasticity in mind. In this context it seemed natural to express the translational curvature of his new spaces by a rotational quantity (via a kind of Grassmann dualization). So Cartan called his translational curvature “torsion” and coupled it to a hypothetical rotational momentum of matter several years before spin was encountered in quantum mechanics.

     

相对论的协变场是虚构

基于洛伦兹电子论和洛伦兹磁力,否定法拉第定律和相对论电磁学,暨揭示广义洛伦兹磁力的科学研究之五:相对论的协变场是荒唐。本文基于洛伦兹电子论和洛伦兹磁力,论证表明:协变换出来的磁力线成为直线,它违背客观事实;协变换出来的环形电力线更荒唐;协变换出来的电磁场成为无穷大,广义洛伦兹磁力才是真谛;两电荷对撞时协变换出来的排斥力成为虚数,它违背客观事。     

The language of Einstein spoken by optical instruments

The mathematics of Lorentz transformations, called the Lorentz group, continues to play an important role in optical sciences. It is the basic mathematical language for coherent and squeezed states. It is noted that the six-parameter Lorentz group can be represented by two-by-two matrices. Since the beam transfer matrices in ray optics are largely based on two-by-two matrices or ABCD matrices, the Lorentz group is bound to be the basic language for ray optics, including polarization optics, interferometers, lens optics, multilayer optics, and the Poincaré sphere. Because the group of Lorentz transformations and ray optics are based on the same two-by-two matrix formalism, ray optics can perform mathematical operations that correspond to transformations in special relativity. It is shown, in particular, that one-lens optics provides a mathematical basis for unifying the internal space-time symmetries of massive and massless particles in the Lorentz-covariant world.     

Electromagnetic Field Theory Without Divergence Problems 1. The Born Legacy

Born's quest for the elusive divergence problem-free quantum theory of electromagnetism led to the important discovery of the nonlinear Maxwell–Born–Infeld equations for the classical electromagnetic fields, the sources of which are classical point charges in motion. The law of motion for these point charges has however been missing, because the Lorentz self-force in the relativistic Newtonian (formal) law of motion is ill-defined in magnitude and direction. In the present paper it is shown that a relativistic Hamilton–Jacobi type law of point charge motion can be consistently coupled with the nonlinear Maxwell–Born–Infeld field equations to obtain a well-defined relativistic classical electrodynamics with point charges. Curiously, while the point charges are spinless, the Pauli principle for bosons can be incorporated. Born's reasoning for calculating the value of his aether constant is re-assessed and found to be inconclusive.     

On the structure of the relativistic many-body problem and the construction of effective many-hadron theories

The general structure of the bound state problem posed by a Poincaré-invariant quantum field theory is discussed. It is pointed out that the only present-day method which promises to solve this problem is a nonperturbative regularisation and a check of scaling in the continuum limit. It is demonstrated that perturbation procedures like the Green's function methods of “quantum hadro-dynamics” are inconsistent with respect to covariance and do not solve the bound state problem. As a consequence we propose to use for an effective many-hadron theory a regularised Hamiltonian including form factors, the arbitrariness of which may be essentially restricted by a “minimal relativity” condition. Examples for such effective theories are discussed.     

Reconsidering a Scientific Revolution: The Case of Einstein <Emphasis Type="Italic">versus</Emphasis> Lorentz

The relationship between Albert Einstein's special theory of relativity and Hendrik A. Lorentz's ether theory is best understood in terms of competing interpretations of Lorentz invariance. In the 1890s, Lorentz proved and exploited the Lorentz invariance of Maxwell's equations, the laws governing electromagnetic fields in the ether, with what he called the theorem of corresponding states. To account for the negative results of attempts to detect the earth's motion through the ether, Lorentz, in effect, had to assume that the laws governing the matter interacting with the fields are Lorentz invariant as well. This additional assumption can be seen as a generalization of the well-known contraction hypothesis. In Lorentz's theory, it remained an unexplained coincidence that both the laws governing fields and the laws governing matter should be Lorentz invariant. In special relativity, by contrast, the Lorentz invariance of all physical laws directly reflects the Minkowski space-time structure posited by the theory. One can use this observation to produce a common-cause argument to show that the relativistic interpretation of Lorentz invariance is preferable to Lorentz's interpretation.     

Friedmann cosmology with torsion

For the cosmological field equations of the Poincaré gauge theory a universal appearance of the Friedmann equations of general relativity is shown. Some exact solutions with torsion are presented.     

Note on the gravitational analogue of the magnetic force

Aspects of the transformation properties of Newton's law of gravitation under Lorentz transformations and the occurrence of velocity dependent gravitational forces are discussed in the framework of the general theory of relativity.     

The field equations of the Poincaré gauge theory of gravitation

We define local active Poincaré transformations of matter fields and the corresponding invariance. Only kinematical notions of special relativity enter these definitions. We are straightforwardly led to a first order form of the gravitational field equations with momentum and spin as sources.