Michelson–Morley experiment

“ We might find some place on a railway where there is an echo from a place further along the railway—say a place where the railway goes into a tunnel—and when a train is traveling along the railway, let a man on the bank fire a gun. If the train is traveling towards the echo, the passengers will hear the echo sooner than the man on the bank; if it is traveling in the opposite direction, they will hear it later. But these are not quite the circumstances of the Michelson-Morley experiment. ”

“ I suppose that in stable times the practical consequences of this relativity are manifested chiefly in the minute fluctuations of foreign exchanges, which may be compared with the minute changes of length affecting delicate experiments like the Michelson-Morley experiment. Occasionally the consequences may be more sensational—a mark-exchange soaring to billions, a high-speed particle contracting to a third of its radius. ”

“ In our problem the body is supposed to move in a normal system of co-ordinates. By this our formula; simplify to [1]
When applied to a revolving body, these equations will enable us to determine the deformation that is produced, wholly independently of the theory of relativity, by centrifugal force, a deformation that will in reality far surpass the changes we want to consider. To get free from it we can consider the ideal case of a "rigid" body — i.e. a body for which the moduli of elasticity and in (6) are infinitely great. ”

“ On the ground of it we shall commit no error if, in determining the paths and of two rays that start from a point , and are made to interfere at a point , we take no account of the motion of the apparatus. The change in the difference of phase produced by the translation will be given by the difference between the values which the integral
takes for the lines and so determined. ”

“ Is the ether fixed, or does it move? Is it carried along with the earth in its motion round the sun, or does the ether pass through the atoms of material bodies as the sea passes through the meshes of a net? The elastic solid analogy, and the simplicity of the classical explanation of the aberration of light, are evidence in favour of a fixed ether. But the celebrated interference experiment of Michelson and Morley, which was capable of detecting a comparatively small relative velocity of earth and ether, gave a null result. ”

“ Néerl. xxi (1886) , p. 103. On the Michelson-Morley experiment cf. also Hicks, Phil. Mag. iii (1902) , p. 9. ↑ Cf. p. 413. ↑ Amer. Journ. Sci. (4) iii (1897) , p. 475. ↑ Phil. Trans. clxxxiv (1893) , p. 727. ↑ Ibid., clxxxix (1897) , p. 149. ↑ Archives Néerl. xxv (1892) , p. 363: the theory is given in ch. iv, pp. 132 et sqq. ↑ Cf. pp. 226, 231, 262. ↑ Some writers have inclined to use the term 'electron-theory' as if it were specially connected with Sir Joseph Thomson's justly celebrated discovery (cf. p. 407, supra) that all negative electrons have equal charges. ”

“ Then too, there are in electromagnetism certain equations of fundamental importance, known as the Maxwell equations, and it is perhaps just as important that the relativity theory retain these equations, as it is that it explain the Michelson and Morley experiment. ”

“ So, the interference experiment of Michelson and Morley is explained, furthermore that of Trouton and Noble on the angular momentum of a charged plate condenser, and also the unsuccessful double refraction experiments by Lord Rayleigh and Brace, because the theorem (already given earlier by the author up to magnitudes of second order) that brightness, darkness, and rays in the resting system, correspond to brightness, darkness, and rays in the moving transformed system, strictly applies to terms of all orders by the current transformation. ”

“ Thus we are, in consequence of the Michelson and Morley experiment, driven to the first fundamental postulate of relativity: The uniform velocity of a body can not be determined by experiments made by observers on the body. ”

“ If we put
the well-known expression for the potential energy of an isotropic elastic body, will be invariant for any change of co-ordinates.
As to the kinetic energy , it is to be replaced by an expression containing . Finally, we must write, instead of (3) ,
We have still to add the formula ”

“ If we leave for it, we must at the same time change the potentials , and if this is done the fundamental equation will certainly again lead to the result that is smaller than .
↑ If in (7) we replace by , omitting the constant term and neglecting , we are led back to the ordinary formula (3) . ”

“ Anyway, it seems undeniable that changes of the molecular forces and consequently of the body's size of order are possible. Michelson's experiment thus loses its verification power for the question at which it was aimed. If one assumes the theory of Fresnel, then its meaning rather lies in the fact, that we can learn something about the change of dimensions. ”

“ Under the new system of forces the molecules will have to find new positions of equilibrium; they become differently spaced; and it is therefore not surprising that the form of the rod changes. Without going beyond the classical laws of Maxwell we can anticipate theoretically what will be the new equilibrium state of the rod, and it turns out to be contracted to the exact amount required by the Michelson-Morley result. ”

“ If we would like to observe magnitudes so small, then we probably can hope to succeed only by an interference method. Thus we would have to work with two mutually perpendicular rods, and of two mutually interfering light beams, let one travel back and forth with respect to the first rod, and the other with respect to the second rod. By that we come again, however, to Michelson's experiment, and we wouldn't observe any displacement of the fringes during the rotation. ”

“ Michelson and Morley have shown that the ether close to and in the earth moves with the earth, which indicates that the ether does not move among atoms without some resistance corresponding to friction. The existence of an ether strain such as that in a leyden jar also shows that there is a resistance on the part of the ether to the kind of motion that takes place in the electric discharge. Ether has mass, since it conveys energy by waves which have a finite velocity. ”

“ In this way it can be seen, that when is the state of equilibrium of the body during the displacement in the aether, is the state of equilibrium when the displacement doesn't exist. One therefore comes exactly to the influence of motion on the dimensions, which was shown before to be necessary to explain Michelson's experiment.
Of course we cannot ascribe great importance to this result; the transfer to molecular forces of what we have found for electrical forces, may be too risky for some. ”

“ But in that case the inferences we draw from the Michelson experiment, in regard to the aspect of phenomena for observers in uniform different movements of translation, no longer suffice to explain to us the whole of reality. They need to be completed in such fashion that the universal invariant, the “Interval” of things, remains the same for an observer who is moving in any way whatever. ”

“ They can only be satisfied, when the periodic functions (10) and (13) representing both waves at point , are mutually connected by [3]
would be the phase transition at the reflection; if one neglects this, as it is done by Budde – this assumption is without influence on the result –, one additionally finds from (14)
Thus according to (12) , the returning oscillation is represented in the origin by
i.e., the phases require the time to traverse distance back and forth. Herein lies in my view the irrefutable justification of the present theory. ”

“ The more important fundamental laws and facts of physical science have all been discovered, and these are now so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote. Nevertheless, it has been found that there are apparent exceptions to most of these laws, and this is particularly true when the observations are pushed to a limit, i. e., whenever the circumstances of experiment are such that extreme cases can be examined. ”

“ If we now want to compare with each other the statements of the absolute theory and of relativity theory concerning the influence of the plate thickness under consideration of terms of second order in , then this would be a quite difficult task, because the absolute theory is only developed under consideration of terms of first oder. [11] However, the fortunate remark of Budde helps us here, by which the ratio of the plate thickness to the length of the arms of the interferometer, is of the same magnitude as . ”

“ Or in reality it is , so that the value of (5) is feigned by the deformation of the stone console (L) in the Michelson experiment. None of both assumptions may (in my view) be rejected by us for reasons of physical experience. The decision between the theories cannot be found here. ”