Lorentz and Poincaré Invariance

The following sections are included:

• Preface

• CONTENTS

• Acknowledgements

• Remarks on the Development of the Lorentz and Poincaré Invariance

The following sections are included:

• First proposal of the universal speed of light by Voigt in 1887

• The Ether and the Earth's Atmosphere

• GENERAL PROBLEM OF MOVING MATTER TREATED IN RELATION TO THE INDIVIDUAL MOLECULES

• MOVING MATERIAL SYSTEM : APPROXIMATION CARRIED TO THE SECOND ORDER

• In Pursuit of the Electrodynamics for Moving Bodies

The following sections are included:

• Electromagnetic Phenomena in a System Moving with any Velocity less than that of Light

• Poincaré's Rendiconti Paper on Relativity. Part I

• Poincaré's Rendiconti Paper On Relativity. Part II

• On the Electrodynamics of Moving Bodies

• The Principle of Relativity and the Fundamental Equations of Mechanics

• SPACE AND TIME

• The Theory of Relativity and Science

• Einstein's first paper on relativity

• On the Origins of the Special Theory of Relativity

The following sections are included:

• The Postulate of the Constancy of the Speed of Light. Ritz's and Related Theories

• Critical Researches on General Electrodynamics

The following sections are included:

• The Philosophy of Space and Time: Simultaneity

• Special Relativity in Anisotropic Space

• Four-dimensional symmetry of taiji relativity and coordinate transformations based on a weaker postulate for the speed of light. - I

• Four-dimensional symmetry of taiji relativity and coordinate transformations based on a weaker postulate for the Speed of light. - II

The following sections are included:

• The Quantum Theory of the Emission and Absorption of Radiation

• The Quantum Theory of the Electron

• The Radiation Theories of Tomonaga, Schwinger, and Feynman

The following sections are included:

• Symmetries, Quantum Lorentz Transformation and The Poincaré Algebra

• Lorentz Group in Feynman's World –Wigner's Little Groups and Their Applications

The following sections are included:

• Test Theories of Special Relativity

The following sections are included:

• Common Time in a Four-Dimensional Symmetry Framework

• Questions on Universal Constants and Four-Dimensional Symmetry from a Broad Viewpoint - I.

• NEWS AND VIEWS (Extract) (On Common Time and Common Relativity)

The following sections are included:

• Is there an Æther ?

• VACUUM AS THE SOURCE OF ASYMMETRY

• The New Ether

The following sections are included:

• Can one derive the Lorentz Transformation from precision experiments?

• A physical theory based solely on the first postulate of relativity

Historically, the first ether theory describing the propagation of light rays in moving media was developed by A. J. Fresnel beginning in 1818 [1]. He made calculations which were able to explain the phenomena of polarization, diffraction and interference. The interference of light was originally investigated by T. Young in 1801-1804. Young's results supported the wave theory of light developed by C. Huygens in his book ”Treatise on Light” (1690). They also suggested the existence of a medium, called aether (or ether) for the vibrations of light waves…

The famous and ingenious Michelson experiment in 1881 was stimulated by a suggestion of C. Maxwell in 1879. Maxwell believed in the existence of the aether and was eager to find out the earth's motion through the aether. In his letter to Todd of the U.S. Nautical Almanac Office (Washington), Maxwell suggested a terrestrial experiment on the (2-way) speed of light, since the (first order) effect related to the eclipses of Jupter's moon was very difficult to observe, as pointed out by Todd. Maxwell said that the effect due to the earth's motion in terrestrial experiments is of the second order v²/c² ∼ 10⁻⁸, which would be too small to observed. Fortunately, Maxwell's letter to Todd was also read by Michelson (a young naval instructor.) Michelson was, however, not deterred by the difficulty and, two years later, came up with an ingenious device (the Michelson interferometer) with unprecedented sensitivity to measure this very small second order effect…

Long before 1905, electromagnetic phenomena for moving bodies (especially, magnetic dielectric materials) were difficult problems that had been investigated by many people. In 1831 M. Faraday [1] first studied the socalled “unipolar induction”. He found that a stable electric current was produced in a stationary conducting wire when placed near a rotating magnet. Although this discovery had been widely applied to engineering for production of the electric generator (i.e., unipolar machine), many different explanations of the “unipolar induction” were in dispute for a long time [2,3]…

In 1932, R. J. Kennedy and E. M. Thorndike [1] performed an important variation of the Michelson-Morley experiment. There were two main differences of their experiment from that of Michelson and Morley:

(a) The difference in length of the two arms in the Michelson interferometer was made large.

(b) The interferometer was held fixed in a single direction in the laboratory, and the interference fringes were observed over a period of months…

The Doppler effect can be derived from the transformation of the wave 4-vector (k₀,k). In particular, we have

where , , k′ = 2π/λ′ and k =| k |= 2π/λ. In special relativity, one has the relations β = ν/c, and k₀ = ω/c. However, equation (15.1) holds for all relativity theories with the 4-dimensional symmetry of the Lorentz and Poincaré groups. In other words, 4-dimensional symmetry dictates that (15.1) results from the transformaton of the wave 4-vector (k₀, k)…

Let us consider a particle 1 which decays into particles 2 and 3, 1 → 2+3, in a general inertial frame F(w,x,y,z). Within special relativity, one has the relation w = ct. The time dilation of special relativity implies that the mean decay lifetime of particle 1 moving with a velocity ν₁ would increase by a factor of compared to that of the particle 1 at rest. Experimentally, the quantity which is actually measured in particle-decay in flight is the decay-length rather than time. Thus, these experiments can also be interpreted in terms of the dilation of the mean decay-length…

There are many experiments which purport to test the second postulate of special relativity, i.e., the universal constancy of the (one-way) speed of light. Many of these experiments use moving light sources such as binary star systems, stars, the sun, extragalactic systems, moving media, and gamma ray sources…

The mass-velocity relation is one of the fundamental and important predictions of special relativity. It is given by

where m_o is the constant (rest) mass of a particle and u is its velocity in an inertial frame. This relation was obtained and discussed by Lorentz before the creation of special relativity in 1905. It appears that this was the first physical “prediction” of relativity theory and was tested by an experiment using β rays by W. Kaufmann around 1905 [1]. Such an experimental test helped to raise interest in relativity among physicists at that time, even though the results of this early experiment were not in favor of relativity and were controversal [2]…

The equivalence of mass and energy is one of the most important results of the special theory of relativity. This is probably the best known formula in physics. Its validity has been demonstrated by the powerful explosion of the atomic bomb. Within the framework of special relativity, a free particle with the energy E has the inertial mass m. The connection of the magnitudes of E and m is given by Einstein's famous formula

where the mass m is the inertial mass…

Let us consider experimental measurements of the (g − 2) factor of the electron. Suppose an electron moves in a uniform magnetic field B. Let the velocity v of the electron be perpendicular to the magnetic field B…

The following sections are included:

• Woldemar Voigt (1850-1919)

• George Francis FitzGerald (1851-1901)

• Abbreviated Biographical Sketch of Walter Ritz (1878-1909)

• Hans Reichenbach (1891-1953): Principal Dates [1]

• The Most General Linear-Acceleration Transformation of Spacetime Based on Limiting 4-Dimensional Symmetry