Introduction to the Michelson Experiment

Albert A. Michelson in 1881,¹ just like George Biddell Airy in 1871,² did not set out to discover either a stationary or moving aether nor prove that the earth itself was either stationary or moving. Rather, he sought to determine (as indicated by the title of his paper) the relative motion of the earth and the luminiferous ether. In the nineteenth century, prior to Einstein’s (1905) special theory of relativlty,³ the aether was assumed to exist based on the undulatory theory of light. Also, whereas heliocentrism became hegemonic in the nineteenth century,⁴ Michelson assumed that the earth orbits the sun. Yet, as in the case of Airy, Michelson’s experimental results did not challenge the aether but obliterated heliocentrism.

Michelson’s paper begins with his acknowledgment of the existing aether-based undulatory theory of light as follows:

    The undulatory theory of light assumes the existence of a medium called the ether, whose vibrations produce the phenomena of heat and light, and which is supposed to fill all space. According to Fresnel, the ether, which is enclosed in optical media, partakes of the motion of these media, to an extent depending on their indices of refraction. For air, this motion would be but a small fraction of that of the air itself and will be neglected.⁵

Upon stating his assumptions that (a) the aether is at rest and (b) the earth is moving through said aether, Michelson establishes the basic parameters for measuring the relative motion of the earth and the aether:

    Assuming then that the ether is at rest, the earth moving through it, the time required for light to pass from one point to another on the earth’s surface, would depend on the direction in which it travels.
    Let \(V\) be the velocity of light.
          \(v=\) the speed of the earth with respect to the ether.
          \(D=\) the distance between the two points.
          \(d=\) the distance through which the earth moves,while light travels from one point to the other.
          \(d_1=\) the distance earth moves, while light passes in the opposite direction.
    Suppose the direction of the line joining the two points to coincide with the direction of earth’s motion, and let \(T=\) time required for light to pass from one point to the other, and \(T_1=\) time required for it to pass in the opposite direction. Further, let \(T_0=\) time required to perform the journey if the earth were at rest.

    Then \[T=\frac{D+d}{V}=\frac{d}{v};\]    and\[T_1=\frac{D-d}{V}=\frac{d_1}{v}\]    From these relations we find \(d=D\dfrac{v}{V-v}\) and \(d_1=D\dfrac{v}{V+v}\) whence \(T=\dfrac{D}{V-v}\) and \(T_1=\dfrac{D}{V+v};\)  \(T-T_1=2T_0\dfrac{v}{V}\) nearly\(,\) and \(v=V\dfrac{T-T_1}{2T_0}.\)
    If now it were possible to measure \(T-T_1\) since \(V\) and \(T_0\) are known, we could find \(v\) the velocity of the earth’s motion through the ether.⁶

Michelson’s Proof-of-Principle for the Experiment

Michelson subsequently carries out an analysis establishing the proof-of-principle of the experiment:

    The following is intended to show that, with a wave-length of yellow light as a standard, the quantity—if it exists—is easily measurable.
    Using the same notation as before we have \(T=\dfrac{D}{V-v}\) and \(T_1=\dfrac{D}{V+v}.\) The whole time occupied therefore in going and returning [is] \(T+T_1=2D\dfrac{V}{V^2-v^2}.\) If, however, the light had travelled in a direction at right angles to the earth’s motion it would be entirely unaffected and the time of going and returning would be, therefore, \(2\dfrac{D}{V}=2T_0.\) The difference between the times \(T+T_1,\) and \(2T_0\) is \[2DV\left(\dfrac{1}{V^2-v^2}-\dfrac{1}{V^2}\right)=τ\ ;\]\[τ=2DV\dfrac{v^2}{V^2(V^2-v^2)}\] or nearly \(2T_0\dfrac{v^2}{V^2}.\) In the time \(τ\) the light would travel a distance \(Vτ=2VT_0\dfrac{v^2}{V^2}=2D\dfrac{v^2}{V^2}.\)
    That is, the actual distance the light travels in the first case is greater than in the second, by the quantity \(2D\dfrac{v^2}{V^2}.\)
Considering only the velocity of the earth in its orbit, the ratio \(\dfrac{v}{V}=\dfrac{1}{10\ 000}\) approximately, and \(\dfrac{v^2}{V^2}=\dfrac{1}{100\ 000\ 000}.\) If \(D=1200\ \textrm{millimeters}\), or in the wave-lengths of yellow light, \(2\ 000\ 000,\) then in terms of the same unit, \(2D\dfrac{v^2}{V^2}=\dfrac{4}{100}.\)
    If, therefore, an apparatus is so constructed as to permit two pencils of light, which have travelled over paths at right angles to each other, to interfere, the pencil which has travelled in the direction of the earth’s motion, will in reality travel \(\frac{4}{100}\) of a wave-length farther than it would have done, were the earth at rest. The other pencil being at right angles to the motion would not be affected.
    If, now, the apparatus be revolved through \(90^\circ\) so that the second pencil is brought into the direction of the earth’s motion, its path will have lengthened \(\frac{4}{100}\) wave-lengths. The total change in the position of the interference bands would be \(\frac{8}{100}\) of the distance between the bands, a quantity easily measurable.⁷

Michelson’s Experimental Apparatus and Methodology

Whereas Michelson was a heliocentrist, his experimental design and arrangement not only accounted for the (alleged) orbital motion of the earth but also the (alleged) motion of the entire solar system ostensibly toward the constellation Hercules:

    At this time of the year, early in April, the earth’s motion in its orbit coincides roughly in longitude with the estimated direction of the motion of the solar system—namely, toward the constellation Hercules. The direction of this motion is inclined at an angle of about \(+26 ^\circ\) to the plane of the equator, and at this time of the year the tangent of the earth’s motion in its orbit makes an angle of \(-23\frac{1}2{}^\circ\) with the plane of the equator; hence we may say the resultant would lie within \(25^\circ\) of the equator.
    The nearer the two components are in magnitude to each other, the more nearly would their resultant coincide with the plane of the equator.
    In this case, if the apparatus be so placed that the arms point north and east at noon, the arm pointing east would coincide with the resultant motion, and the other would be at right angles. Therefore, if at this time the apparatus be rotated \(90^\circ\), the displacement of the fringes should be twice \(\frac{8}{100}\) or \(0.16\) of the distance between the fringes.
    If, on the other hand, the proper motion of the sun is small compared to the earth’s motion, the displacement should be \(\frac{6}{10}\) of \(.08\) or \(0.048\). Taking the mean of these two numbers as the most probable, we may say that the displacement to be looked for is not far from one-tenth [empasis added] the distance between the fringes.⁸

Readers interested in the overall technical details of Michelson’s interferometer and experimental arrangement are advised to refer to the original paper.⁹

A Graphical Display of the Results and Analysis of the Michelson Experiment

(a) Observed Geocentric Reality

Figure 1a. Graph of Michelson’s actual results indicating no fringe displacement outside the limits of experimental error (extracted and adapted from Michelson’s Figure 4).¹⁰

(b) Predicted Heliocentric Sophistry

NOTE: The cosinusoidal curve below represents the predicted fringe displacement based upon the heliocentric sophistry of the earth (allegedly) orbiting the sun in an eastward direction. Hence, the graph depicts maximum displacement (i.e., +0.05 and -0.05) occuring (hypothetically) on the four cardinal points (i.e., N, S, E, W) whereat one arm of the interferometer is pointed toward the east or west, the other arm (being at \(90^\circ\)) pointed north or south. Minimun displacemment (i.e., 0.00) would occur (hypothetically) on the four ordinal or intercardinal points (i.e., NE, SE, SW, NW) wherat one arm of the interferometer is pointed NE, SE, SW, or NW, the other arm (being at \(90^\circ\)) pointed (SE or NW), (SW or NE), (NW or SE), or (NE or SW) respectively, the effects of the (alleged) eastward motion of the earth being vectorially cancelled.

Figure 1b. Cosinusoidal curve representing the expected azimuthal fringe displacement if the earth were moving through the aether (extracted and adapted from Michelson’s Figure 4).¹¹

    The dotted curve is drawn on the supposition that the displacement to be expected is one-tenth of the distance between the fringes, but if this displacement were only \(\frac{1}{100},\) the broken line would still coincide more nearly with the straight line than with the curve.¹²

Conclusion

Michelson’s conclusion is unambiguous and definitive:

    The interpretation of these results is that there is no displacement of the interference bands. The result of the hypothesis of a stationary ether is thus shown to be incorrect, and the necessary conclusion follows that the hypothesis is erroneous. [emphasis added]
    This conclusion directly contradicts the explanation of the phenomenon of aberration which has been hitherto generally accepted, and which presupposes that the earth moves through the ether, the latter remaining at rest. [emphasis added]¹³

As a point of interest, it should be noted that this experiment was financed by Alexander Graham Bell.¹⁴

Denouement

Whereas geocentrism was experimentally confirmed by George Biddell Airy as far back as 1871 and here re-confirmed by Albert A. MIchelson in 1881 under entirely different experimental circumstances, it should not surprise readers that modern systems, e.g., commercial aviation, dependent upon the earth being stationary, re-confirm geocentrism on a daily basis. See Heliocentrism Refuted: Experimental Proof of a Stationary Earth.

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