Relativity in brief... or in detail..

# Some more details on the Michelson Morley experiment

The Michelson Morley experiment is not consistent with Galilean/Newtonian relativity, as the introductory film clip shows. Its results are explained using Einstein's principle of relativity. A non-quantitative introduction is given here. This page gives a simple quantitative analysis.

Schematically, a beam of monochromatic light is divided by a beam splitter (a partially transparent sheet positioned at an angle). The divided beams reach two mirrors, are returned and recombined by respectively transmission and reflection at the beam splitter. Their relative phase produces an interference pattern in the combined beam.

Schematic of the Michelson-Morley experiment. A beam of light (actually continuous, not pulsed as in the animation below) is split when it strikes a transparent plate: part is transmitted, part reflected. When the two divided beams return to the block, partial reflection and partial transmission also combines them.

Following Galilean/Newtonian physics, let us suppose that light travels (at c) with respect to a 'stationary' medium (called the æther). For our purposes, suppose that it bid set up with l1 = l2 and that the whole spectrometer be stationary with respect to the æther, the medium that supports the wave motion of light. Let's consider a point in the interference pattern at which the phase difference is zero. This is the situation shown at left.

Now let it move to the right at speed v with respect to æther. Picture this from a frame at rest in the æther (middle diagram). The transit times are no longer equal, but for the horizontal and near vertical directions are given by:

By rotating the spectrometer 90 degrees, one can compare the effect of speed through the putative æther on one of the beams. Then by making measurements six months apart, one can add or subtract the speed of the Earth through æther. The speed of the Earth in its orbit around the sun is v = 30 km/s. Substituting in the equations above (and using l = 11 m ..., yes wow, for an optical spectrometer, it was seriously large!) the phase difference expected would be
Δφ = 2πΔt(c/λ) = 2.3 radians = 0.4 fringes.
The spectrometer was easily sensitive enough to see this*. However, the result was: 0.00 plus or minus 0.01 fringes.

michelson_rotate_html

The simplest interpretation of the results is that light travelled at the same speed with respect to the lab, whether or not the arm of the spectrometer were travelling with the Earth through the aether or at right angles to it. (One could also make explanations in which the speed of light varied, but the shape of the spectrometer changed according to its orientation, in such a way that it exactly cancelled the effect of the lab's motion, or that the Earth dragged the æther around with it.)

Many further experiments have been performed to look for variations in the speed of light with respect to relative motion. Like Michelson and Morley, researchers usually look for differences in the speed in different direction. Measurements by Stephan Schiller's team in Dusseldorf give an upper limit of 6 parts in 1016. (Reported in Nature's research highlights, 9/6/2005 — relativity's centenary year.) The important conclusion is that no-one has yet found a case in which the speed of light in vacuum is different.

"But it can't be so." "It just doesn't make sense." These are common responses - and they were certainly my response when I first read about relativity. The answer to the first is simply that it is not up to us to decide in advance what is and what is not so (in spite of what Plato might have said). That is the job for observation and experiment (as Plato's student Aristotle, and even more emphatically Galileo, might have told Plato). To the second objection, we might say that it is not up to us to tell the universe what to do. The universe just is. It is up to us to make sense of it. For scientists, this means finding theories and laws whose predictions are in agreement with what we observe in the universe. Relativity is a theory that has been very thoroughly and precisely tested, and whose predictions are in spectacularly good agreement with the behaviour of the universe. Most people who claim to disagree with relativity are troubled not so much by the theory but by the results of experiments such as this one. Deep down, I think that such people are saying "It may be true, but it wouldn't be true if I had designed the universe" or "I don't like it that the universe behaves thus". To this objection, the universe is unlikely to register offence. It seems that you have three options: either (i) accept it, (ii) forget about it or (iii) go and live in a universe where it isn't true.

• Michelson, A.A. and Morley, E.W. (1887) "On the relative motion of the earth and the luminiferous ether", Am. J. Science. 34, 333. A facsimile of the paper is here.
• I should point out that a number of reports claim that, while the speed of gas in vacuum and in a solid is isotropic, the speed of light in a gas is not isotropic. The claimed effect is very small compared with that expected from a stationary aether, so the data are not immediately persuasive. For example, this paper by Reg Cahill of Flinders University puts the case for retaining the Lorentz equations but abandoning Einstein's principle of special relativity.
* I should mention that, when we discuss wave motion in moving systems, we should normally talk of the Doppler shift, the effect that makes a car horn sound sharper in pitch when it approaches you and flat when it recedes. However, what we are interested in here is the difference in the transmission between the beam splitter, one of the mirrors and the beam splitter again. The relative motion among those is zero. (By the way, the analogy between sound and light is incomplete. To start with, sound requires a medium.)

* I should also mention that, although the spectrometer was sensitive enough to detect, in principle, the variation during a year of its speed through the aether, it was not sensitive enough to detect the putative daily effect due to the earth's rotation. In this sense, our animation may be misleading, for which I apologise.

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