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The (failed) goal of the Michelson-Morley experiment was to detect the motion of the Earth with respect to the hypothetical ether. As far as I understand (e.g. from the exposition in Feynman’s textbook, Ch. 15.3, and some other textbooks) the only property of ether which was used is that the constant $c$ from the Maxwell equations is equal to the speed of light in vacuum with respect to the ether. Its numerical value was supposed to be known and equal approximately to 300,000 km/s.

However, as far as I understand, this numerical value of the speed of light was measured experimentally with respect to the Earth (e.g. in Fizeau’s experiment). Moreover it cannot be measured directly with respect the ether in principle since nobody knew where the ether was (in fact, a posteriori ether does not exist).

My question is how to find the numerical value of the speed of light with respect to the ether (assuming it exists) from its values with respect to the Earth.
I think it is necessary in order to complete the argument in Feynman’s textbook.

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    $\begingroup$ You ask for a way to ‘find the numerical value of the speed of light with respect to the ether (assuming it exists) from its values with respect to the Earth’. That is exactly what the experiment of Michelson and Morley is. Do you have any reason to doubt their approach? $\endgroup$
    – my2cts
    Commented Jan 6 at 10:22
  • $\begingroup$ @my2cts: I do not doubt their approach, I just want to understand it. I want to understand the argument why their experiment implies that ether does not exist. $\endgroup$
    – MKO
    Commented Jan 6 at 10:58
  • $\begingroup$ Perhaps you should rephrase your question as: Why does the Michelson&Morley experiment imply that the aether does not exist. For example, what if the aether rotates around the sun in the same obit as Earth? $\endgroup$
    – my2cts
    Commented Jan 6 at 11:29
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    $\begingroup$ At the risk of sounding pedantic, the concept is called 'aether'. en.wikipedia.org/wiki/Aether_(classical_element) $\endgroup$
    – my2cts
    Commented Jan 6 at 11:35

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If you assume the Earth moves relative to the ether at some unknown speed, and if you assume light moves at a fixed speed relative to the ether, then you can't determine the speed of light relative to the ether from knowing the speed of light relative to the Earth. However, what you can do is to measure the speed of light relative to the Earth at opposite points on the Earth's orbit around the Sun, and if you find there is no difference, you can either rule out the idea of light moving at a fixed speed relative to the ether, or rule out the idea of the Earth moving relative to the ether. Indeed, some people entertained the idea of 'ether drag', which meant that the Earth was pulling some ether along with it so the speed of the Earth relative to the ether was always zero locally.

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Moreover it cannot be measured directly with respect the ether in principle

Michelson-Morley experiment was specifically designed so that if Earth would move inside ether, then along one interferometer arm ether would "drag light" hereby changing it's speed to $c \pm v_{ether}$ while in other interferometer arm (perpendicular to ether flow)- it would not change light speed. Experiment hasn't found any light speed differences between interferometer arms, so called null result. And so it was concluded that ether doesn't exist.

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  • $\begingroup$ The point was how to determine the numerical value of $c$ if it is the speed of light with respect to ether. This data was not determined during Michelson-Morley experiment, but was supposed to be known previously. $\endgroup$
    – MKO
    Commented Jan 6 at 14:14
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    $\begingroup$ This experiment goal was not to measure light speed, but rather change in light speed value across interferometer arms as light travels different optical paths across ether. This should reflect in shifted interference pattern, but it was found none. So you miss experiment design idea - it doesn't use absolute light speed value $c$ at all. $\endgroup$
    – Agnius Vasiliauskas
    Commented Jan 6 at 15:01
  • $\begingroup$ In this case, what properties of ether are used in the experiment design? I thought this is the numerical value of the speed of light with respect to ether. Some properties of ether must be used. $\endgroup$
    – MKO
    Commented Jan 6 at 16:05
  • $\begingroup$ I think i already explained it in the post and multiple comments. Basic property was "light dragging", a similar process when light enters medium with refractive index greater that 1,- light speed drops then. If you move such medium really fast (fiber for example) then you will drag light with it together, because now electrons inside which re-emit light are dragged together, so light speed relative to stationary observer now depends on this medium movement speed. If you measure light speed in perpendicular to movement direction, no such drag exist. So they lookup for $\Delta v$ instead of $c$ $\endgroup$
    – Agnius Vasiliauskas
    Commented Jan 6 at 17:38
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"the only property of ether which was used is that the constant c from the Maxwell equations is equal to the speed of light in vacuum with respect to the ether"

In other words, Michelson and Morley assumed that the speed of light is independent of the speed of the emitter, and accordingly calculated different times of arrival of the two beams. The null result of the experiment disproved the assumption, so theoreticians should have concluded that the speed of light does depend on the speed of the emitter:

"Emission theory, also called emitter theory or ballistic theory of light, was a competing theory for the special theory of relativity, explaining the results of the Michelson–Morley experiment of 1887...The name most often associated with emission theory is Isaac Newton. In his corpuscular theory Newton visualized light "corpuscles" being thrown off from hot bodies at a nominal speed of c with respect to the emitting object, and obeying the usual laws of Newtonian mechanics, and we then expect light to be moving towards us with a speed that is offset by the speed of the distant emitter (c ± v)." https://en.wikipedia.org/wiki/Emission_theory

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