Michelson-Morley Research Articles

Special relativity as a simple geometry problem

The null result of the Michelson–Morley experiment and the constancy of the one-way speed of light in the ‘rest system’ are used to formulate a simple problem, to be solved by elementary geometry techniques using a pair of compasses and non-graduated rulers. The solution consists of a drawing allowing a direct visualization of all the fundamental effects of standard relativistic kinematics, namely time dilation, length contraction and relativity of simultaneity. Moreover, it also provides an immediate image of other important and more subtle aspects, often passed by in relativity courses, such as the conventionality of simultaneity thesis, possible non-invariance of the one-way speed of light and compatibility between the Lorentz–Poincaré and Einstein–Minkowski philosophies. The geometric scheme so constructed constitutes a powerful tool to clearly illustrate both traditional and not-so-traditional aspects of special relativity teaching.

The Mansouri–Sexl formalism for the Michelson–Morley experiment in nonvacuum media

In the present paper, we construct the complete Mansouri–Sexl formalism for the Michelson–Morley and Kennedy–Thorndike experiments executed in a refractive medium by extending their previous formalism derived for vacuum-based experiments. This is an important step since we will show that the experiments executed in a refractive medium give new possibilities for testing for Lorentz violations. In a previous paper, we developed the correct nonparametric treatment under the framework of special relativity, so no violation testing was possible. On the other hand, a parameterized theory, like that of Mansouri–Sexl is the standard way of testing for Lorentz symmetry violations. While other parameterized theories, like the Standard Model extension (SME) emerged in the late 1990s The Mansouri–Sexl formalism is still very much employed in experiments due to its relative simplicity and its lower number of parameters (three) versus the 19 parameters used in SME. This is why we are undertaking the novel step of constructing the corresponding Mansouri–Sexl formalism. Yet another novel attempt is to describe an unprecedented variation of the Kennedy–Thorndike experiment employing different refractive media for the interferometer arms. We will also demonstrate the advantages of deferring the expansion of the Mansouri–Sexl parameters a, b, and d as long as possible, thus obtaining a higher level of precision in deriving the violations.PACS No.: 03.30.+p

Michelson-Morley Experiment Within the Quantum Mechanics Framework

It is revisited the Michelson-Morley experiment within the quantum mechanics framework. One can define the wave function of photon in the whole space at a given moment of time. The phase difference between the source and receiver is a distance between the source and receiver at the time of reception hence it does not depend on the velocity of the frame. Then one can explain the null result of the Michelson-Morley experiment within the quantum mechanics framework.

Frequency-stable Nd:YAG lasers in Michelson — Morley experiment

Results of frequency stability of Nd:YAG lasers locked to resonances of high-Q Fabry-Perot sapphire interferometers are reported. The interferometers were mounted on a platform cooled down to the cryogenic temperature; this ensured high long-term laser stability in the Michelson-Morley experiment.

What Theory Is

The word theory covers a multitude of virtues and vices, sometimes counting as knowledge and sometimes contrasting with knowledge. But theory is as important as observation in science. We all take force, gravity, electrons, mass, and continental drift as genuine aspects of reality even though they are theoretical rather than observational (empirical) features. We all also recognize that the concept of luminiferous ether that was generally accepted at the outset of the nineteenth century is a theoretical concept that was discarded because of the Michelson-Morley experiment. The paradigm for scientific theory is Newton's theory of force, which incorporates the two theoretical concepts of force and gravity . Huygens formulated the laws of centrifugal force, Galileo the laws of freely-falling bodies, and Kepler the laws of planetary motion. Newton showed that each was a special case of the general laws of motion. He thereby integrated three apparently disparate fields of mechanics, explained the empirical laws by subsuming them under the general laws of the theory of force, and provided a heuristic model for further explanations. The best theories are explanatory, integrative, and heuristic. Most scholars recognize this paradigm. Nonetheless, theories today are too varied to come under any single rubric. A particular danger in the humanities and social sciences is that explanations there invariably have a moral dimension, raising the specter of moralism hidden in any and every theory. This essay articulates the paradigm and the cautions without attempting to evaluate grand theory in folkloristics.

Tests of Relativity by Complementary Rotating Michelson-Morley Experiments

We report relativity tests based on data from two simultaneous Michelson-Morley experiments, spanning a period of more than 1 yr. Both were actively rotated on turntables. One (in Berlin, Germany) uses optical Fabry-Perot resonators made of fused silica; the other (in Perth, Australia) uses microwave whispering-gallery sapphire resonators. Within the standard model extension, we obtain simultaneous limits on Lorentz violation for electrons (5 coefficients) and photons (8) at levels down to 10(-16), improved by factors between 3 and 50 compared to previous work.

Relativistic Effects of the Theory of Reference Frames.

The theory of reference frames is a new theory of relativity that represents the scientific evolution of Einstein’s relativity. In this essay the following points are examined: considerations about the theory of relativity of Albert Einstein, general notes on the theory of reference frames, the Michelson–Morley experiment, the new equations of space-time transformation, the kinematic principles of the theory of reference frames, the transformations of Maxwell’s equations for inertial systems, the Doppler effect, and the mystery of supernovas. The new theory responds to numerous and recent experimental results that are not confirmed by previous theories. In particular, the interpretation of the luminous phenomenon that causes supernovas is at variance with theoretical predictions of Einstein’s relativity but is in accordance with those of the theory of reference frames. The most important theoretical concept in this essay is the inertial time, which is a common time valid for all inertial reference frames that replaces Newtonian– Galilean absolute time and Einstein’s relativistic time.

Michelson-Morley Experiment Revisited

The idea of the Michelson-Morley experiment is theoretically reanalyzed. Elementary arguments are put forward to precisely derive the most general allowable form of the directional dependence of the one-way velocity of light.

On the Consistency between the Assumption of a Special System of Reference and Special Relativity

In a previous work, we have shown that the null result of the Michelson–Morley experiment in vacuum is deeply connected with the notion of time. The same is true for the postulate of constancy of the two-way speed of light in vacuum in all frames independently of the state of motion of the emitting body. The argumentation formerly given is very general and has to be true not only within Special Relativity and its “equivalence” of all inertial frames, but as well as in Lorentz-Poincare scenario of a preferred reference frame. This paper is the second of a trilogy intending to revisit the foundations of Special Relativity, and addresses the question of the constancy of the one-way speed of light and of the differences and similarities between both scenarios. Although they manifestly differ in philosophy, it is debated why and how the assumption of a “special system of reference experimentally inaccessible” is indeed compatible with Einstein’s Special Relativity, as beautifully outlined and discussed by Bell [Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1988)]. This rather trivial statement is still astonishing nowadays to a big majority of scientists. The purpose of this work is to bring such assertion into perspective, widening the somewhat narrow view of Special Relativity often presented in textbooks and scientific papers.

Analytical solution for the deformation of a cylinder under tidal gravitational forces

Quite a few future high precision space missions for testing special and general relativity will employ optical resonators which are used for laser frequency stabilization. These devices are basic for carrying out modern tests of the isotropy of light (Michelson–Morley experiment) and of the universality of the gravitational redshift. As the resonator frequency not only depends on the speed of light but also on the resonator length, the quality of these measurements is very sensitive to elastic deformations of the optical resonator itself. As a consequence, a detailed knowledge about the deformations of the cavity is necessary. Therefore, in this paper, we investigate the modelling of optical resonators in a space environment. Usually, for simulation issues, the finite element method (FEM) is applied in order to investigate the influence of disturbances on resonator measurements. However, for a careful control of the numerical quality of FEM simulations, a comparison with an analytical solution of a simplified resonator model is beneficial. In this paper we present an analytical solution for the problem of an elastic, isotropic, homogeneous free-flying cylinder in space under the influence of a tidal gravitational force. The solution is gained by solving the linear equations of elasticity for special boundary conditions. The applicability of using FEM codes for these simulations shall be verified through the comparison of the analytical solution with the results gained within the FEM code.

‘Time: What is it That it can be Measured?’

Experiments with the simple pendulum are easy, but its motion is nevertheless confounded with simple harmonic motion. However, refined theoretical models of the pendulum can, today, be easily taught using software like CALCODE. Similarly, the cycloidal pendulum is isochronous only in simplified theory. But what are theoretically equal intervals of time? Newton accepted Barrow’s even tenor hypothesis, but conceded that ‘equal motions’ did not exist – the refutability of Newtonian physics is independent of time measurement. However, time measurement was the key difficulty in reconciling Newtonian physics with electrodynamics. On Poincaré’s criterion of convenience, equal intervals of time ought be so defined as to make the enunciation of physics simple. Hence he postulated constancy of the speed of light. (The Michelson–Morley experiment was not critical.) The theory of relativity followed. But does there exist a proper clock?

Whispering modes in anisotropic and isotropic dielectric spherical resonators

The properties of degenerate whispering spherical modes within a fused silica and sapphire dielectric resonator have been investigated. However, departure from spherical symmetry occurs due to the support structure and anisotropy of the material. Finite element modeling is used to predicted the lifting of the frequency degeneracy, and is confirmed by experiment. Further optimization of the sapphire resonator to realize a Michelson–Morley experiment is discussed.

How Einstein discovered the Special Theory of Relativity

Contrary to what we learn in textbooks on the Special Theory of Relativity, Michelson-Morley experiment had no direct influence on Einstein’s discovery although he undoubtedly knew about it. At the age of only 16, Einstein imagined himself standing in front of a plane mirror while he himself together with the mirror was being carried forward with the velocity of light. He asked himself the question whether he would be able to see his image in the mirror in such a situation. In trying to solve this problem he thought over the whole foundation of physics with no assistance from any physicist. He, however, profited from some discussions with a few of his colleagues (the main person being Besso) who were unknown to the world of physics. Here we try to reconstruct in our own way the arguments that perhaps led Einstein to his goal. In our effort, we are guided by some of his utterances and interviews given to different people in his later life.

Graphical aids for visualising the space-time coordinates of events created by light signals emitted by moving sources

Relativistic space-time diagrams are presented, displaying in true values the space-time coordinates of events created by light signals emitted by moving sources, as detected from inertial reference frames in relative motion. The diagrams are used in order to solve the problem of the rays and mirrors in the Michelson-Morley experiment.

The conceptualization of time and the constancy of the speed of light

In this work, we show that the null result of the Michelson–Morley experiment in vacuum is deeply connected with the notion of time. It can be deduced, without any mathematics, from the assumption only that all good clocks can be used to measure time with the same results, independently of the machinery involved in their manufacturing. A second important assumption, intrinsic to the very notion of time, is that clocks measure time in the same way in different frames, i.e., the notion of time is the same in all inertial frames. Under this assumption, we point out that the ‘postulate’ of constancy of the ‘two-way’ speed of light in vacuum in all frames independently of the state of motion of the emitting body is also strongly related to the concept of time, together with the existence of a limit speed in the ‘rest frame’. This postulate simply results from the construction of clocks where ‘tic–tacs’ are made by objects travelling with the limit speed, taken to be the speed of light.

Test of Lorentz Invariance in Electrodynamics Using Rotating Cryogenic Sapphire Microwave Oscillators

We present the first results from a rotating Michelson-Morley experiment that uses two orthogonally orientated cryogenic sapphire resonator oscillators operating in whispering gallery modes near 10 GHz. The experiment is used to test for violations of Lorentz invariance in the framework of the photon sector of the standard model extension (SME), as well as the isotropy term of the Robertson-Mansouri-Sexl (RMS) framework. In the SME we set a new bound on the previously unmeasured kappa(ZZ)(e-) component of 2.1(5.7) x 10(-14), and set more stringent bounds by up to a factor of 7 on seven other components. In the RMS a more stringent bound of -0.9(2.0) x 10(-10) on the isotropy parameter, P(MM) = delta-beta + 1 / 2 is set, which is more than a factor of 7 improvement.

Projective Explanation: How Theories Explain Empirical Data in Spite of Theory-Data Incommensurability

In scientific explanations, the explanans theory is sometimes incommensurable with the explanandum empirical data. How is this possible, especially when the explanation is deductive in nature? This paper attempts to solve the puzzle without relying on any particular theory of reference. For us, it is rather obvious that the geometric idea of projection plays a key role in Kepler’s explanation of Tycho Brahe’s empirical data. We discover that a similar mechanism operates in theoretic explanations in general. In short, all theoretic explanations are “projective” explanations. If so, there should be no logical reason why explanans theories cannot be incommensurable with explanandum data. For illustration, we analyse Einstein’s explanation of the results of the Michelson–Morley experiment in some detail.

The OPTIS satellite – improved tests of Special and General Relativity

The OPTIS satellite mission is an international collaboration initiated by three German University institutes aiming at improving tests regarding the foundations of Special and General Relativity. The mission idea – which has already passed the state of the initial feasibility study – is to contribute to the most challenging project of physics in this century – the search for a Theory of Quantum Gravity. This theory should resolve the incompatibilities between the quantum theory and Einstein's General Relativity. All approaches for a Quantum Gravity Theory predict small deviations from Special and General Relativity. If such deviations could be found (e.g. an anisotropy of the speed of light, violations of the universality of gravitational red shift or of the universality of free fall) the way to a new understanding of the time and space structure of the universe would be open. Therefore the goal of the OPTIS satellite mission is an accuracy improvement of tests regarding the foundations of Special and General Relativity by up to three orders of magnitude. For that purpose several experiments will be carried out on board the OPTIS satellite testing (i) the isotropy of the speed of light, (ii) the independence of the speed of light from the velocity of the laboratory system, (iii) the universality of the gravitational redshift, (iv) the absolute gravitational redshift and (v) the special relativistic time-dilation. Furthermore, orbit analyses will be done in order to measure (vi) the Lense–Thirring effect and (vii) perigee advance as well as to test (viii) the Newtonian 1 r gravitational potential. The benefit from bringing these experiments into space is the nearly disturbance free environment allowing precise measurements and large measurement times. The OPTIS mission will use already available key technologies like optical cavities, highly stabilised lasers, atomic clocks, frequency combs, capacitive gravitational reference sensors, drag-free control, laser tracking and laser linking systems. For most of the proposed tests the measurements are done by comparing the rates of different clocks. For the test of the isotropy of the velocity of light (Michelson–Morley experiment) the frequencies of resonators (‘light clocks’) pointing in different directions are compared. Concerning the constancy of the speed of light (Kennedy–Thorndike experiment) a resonator and atomic clocks under varying velocities are compared. For tests of the time dilation the rates of clocks in different states of motion and for testing the universality of the gravitational redshift clocks at different positions in the gravitational field are compared. This paper will give an overview about the OPTIS satellite mission, including the science goals, science requirements, key technologies, measurement principles and devices.

Einstein?s Investigations of Galilean Covariant Electrodynamics Prior to 1905

Einstein learned from the magnet and conductor thought experiments how to use field transformation laws to extend the covariance to Maxwell’s electrodynamics. If he persisted in his use of this device, he would have found that the theory cleaves into two Galilean covariant parts, each with different field transformation laws. The tension between the two parts reflects a failure not mentioned by Einstein: that the relativity of motion manifested by observables in the magnet and conductor thought experiment does not extend to all observables in electrodynamics. An examination of Ritz’s work shows that Einstein’s early view could not have coincided with Ritz’s on an emission theory of light, but only with that of a conveniently reconstructed Ritz. One Ritz-like emission theory, attributed by Pauli to Ritz, proves to be a natural extension of the Galilean covariant part of Maxwell’s theory that happens also to accommodate the magnet and conductor thought experiment. Einstein's famous chasing a light beam thought experiment fails as an objection to an ether-based, electrodynamical theory of light. However it would allow Einstein to formulate his general objections to all emission theories of light in a very sharp form. Einstein found two well known experimental results of 18th and19th century optics compelling (Fizeau’s experiment, stellar aberration), while the accomplished Michelson-Morley experiment played no memorable role. I suggest they owe their importance to their providing a direct experimental grounding for Lorentz’ local time, the precursor of Einstein’s relativity of simultaneity, and do it essentially independently of electrodynamical theory. I attribute Einstein’s success to his determination to implement a principle of relativity in electrodynamics, but I urge that we not invest this stubbornness with any mystical prescience.

Doing Much About Nothing

One of the interesting problems concerning experimental results is what happens when an experiment gives a null result, when the phenomenon expected is not observed. Is it because the experimental apparatus and the associated analysis procedures cannot detect or measure the phenomenon in question or is it because the phenomenon is not present? This is a real problem in the practice of physics. In the Michelson-Morley experiment, one of the most famous experiments in modern physics, the experimenters expected to detect a fringeshift caused by the motion of the earth relative to the ether. They found no such fringeshift. Was it because the apparatus was faulty or because the earth’s velocity relative to the ether was zero? 1 In this paper I will discuss the Michelson