Einsteins idea about solving the ether problem

Question

I'm struggling a bit with my Special Relativity course. Most exercises are quite trivial and can be done without much effort, but when you really start to think and analyse why and how certain things are, they can get really complicated and I often find myself thinking for hours about these things.

In Moore's work Six Ideas That Shaped Physics: The Laws of Physics are Frame-independent he explains a bit about what originally sparked Einsteins work. I will explain it as far as I understand it and then underline what I do not quite get.

• Maxwell published at the end of the 19th century a set of equations that describe the phenomena of electromagnetism. From these equations it can be concluded that the speed of electromagnetic waves are well defined since it depends on certain well established universal constants. This speed happens to be $c\approx 3.00 \cdot 10^8 \text{ m/s}$.
• It was known that the speed of light was very similar (no measurable significant difference) to the speed of electromagnetic waves and also that light behaved like a wave in certain situation (from work done by for example Fraunhover). Therefore it was assumed that light must also be an electromagnetic wave.
• Since there was no known isolated "carrier" for electromagnetic waves it was conjectured that some kind of ether must exist in which an electromagnetic wave could be produced, much like when you trow a rock in a pool it also creates ripples in carrier (water).
• The concept of ether was very unsatisfying to start with, since it was not measurable and had to be virtually everywhere. Michelson and Morley tried to prove the existence of this ether, since if it were to exist, it would produce an "ether wind" which would result in the speed of light being measured differently in the direction of rotation of the earth in comparison with the opposite direction of this rotation.
• However, nor Michelson and Morley nor any other physicist did find the existence of this "ether wind". They all found that the speed of light was measured exactly the same in each direction.
• Einstein concluded from this that the conjectured ether did not exist and that electromagnetic waves must therefore be able to travel trough vacuum, at the speed of light. Since no particular reference frame can be attached to vacuum we must conclude that the measured speed of light is independent of the reference frame and therefore that the Galilean transformations are incorrect (assuming the Maxwell equation and the postulate of relativity are true).

Now what I do not understand entirely (I do feel certain points a bit intuitively, but that is not enough for me):

• How did the experiment of Michelson and Morley disprove the existence of the conjectured ether? What if the ether moves along with the direction of the rotation of the earth?
• In the last point I phrased the book by saying "no particular reference frame can be attached to vacuum". Why can't we think of vacuum as an inertial reference frame with an absolute speed of 0? Why is vacuum assumed to be part of every reference frame (so that the speed of light must be measured the same in every frame)? Basically: what is the fundamental difference between the conjectured ether and vacuum?
• Why did the assumption that light does not travel equally fast in all directions not violate the principle of relativity? Was it because electromagnetic waves were assumed to travel in an other reference frame (the ether) and not in the frame that generated the emission (for example earth)?

When I am talking about reference frames, I assume - in the context of this question - that they are inertial (also assuming earth is practically inertial).

Thanks a lot for taking the time to answer my questions. Best wishes to you all!

Answer 1

How did the experiment of Michelson and Morley disprove the existence of the conjectured ether? What if the ether moves along with the direction of the rotation of the earth?

They tried the experiment at different times of year (when the Earth would have been moving in different directions in an inertial frame centered on the Sun) to try to rule this out. Some people did propose an Aether drag hypothesis in which the local Aether is dragged along with the Earth so it's always close to being at rest relative to Earth, but in order to be compatible with the negative result of experiments like Michelson-Morley, this model would make a number of other predictions that weren't compatible with observations--see the "problems of complete aether dragging" section in the wiki article.

In the last point I phrased the book by saying "no particular reference frame can be attached to vacuum". Why can't we think of vacuum as an inertial reference frame with an absolute speed of 0? Why is vacuum assumed to be part of every reference frame (so that the speed of light must be measured the same in every frame)?

Basically, because as long as relativity is correct that the laws of physics obey the same equations in all the inertial frames whose coordinates are related by the Lorentz transformation (i.e. the laws of physics have a symmetry known as "Lorentz invariance"), then there would be no experiment that could pick out a preferred frame. As a sort of philosophical interpretation similar to the interpretations of quantum mechanics (none of which make any distinct experimental predictions), you could still imagine that there was some frame representing absolute rest, but it would be invisible to all experiments.

Another way of putting it--suppose we assume as a matter of interpretation that there is an absolute frame, but that all physical means of measuring distance (say, the spacing between atoms in some kind of crystal) shrink according to the Lorentz contraction equation when the distance-measuring system is in motion relative to the absolute rest frame, and all physical clocks (like the average time for decay of some type of particle) slow down according to the time dilation equation when the clock is in motion relative to the absolute rest frame (an interpretation of SR where this happens is sometimes known as a Lorentz ether theory, although the terminology is confusing because sometimes this phrase is used to describe aether theories which do make distinct experimental predictions). Then if each observer constructs their own rulers and clocks to measure distance and time, and synchronizes their own clocks using the Einstein synchronization procedure (which will result in clocks moving relative to the absolute frame being out-of-sync in an absolute sense, according to this interpretation), then even with this assumption of an absolute frame, you'll still predict that each observer will measure the speed of a light ray as c relative to themselves (even if you say their measurements are 'objectively' incorrect because they're using rulers which are shrunk relative to the 'true' distance, and clocks which are slowed down and out-of-sync relative to 'true' time), and each observer will measure rulers moving relative to themselves to be shrunk in length, and clocks moving relative to themselves to be slowed down. So all their measurements will be completely symmetrical, and there'll be no way for them to decide experimentally which of their ruler/clock systems match the hypothesized absolute time and space.

Why did the assumption that light does not travel equally fast in all directions not violate the principle of relativity? Was it because electromagnetic waves were assumed to travel in an other reference frame (the ether) and not in the frame that generated the emission (for example earth)?

Prior to Michelson-Morley, but after the discovery of Maxwell's laws, I believe physicists tended to assume that the principle of relativity would just have to be false--Maxwell's laws would hold only in the rest frame of the aether, observers moving relative to this frame would not see light as traveling at the same speed in all directions as predicted by Maxwell's equations. But I suppose it's a matter of definition, if you were to rewrite Maxwell's equations to contain explicit reference to the velocity of the underlying ether, then you could put them in a form that would work in all frames even if there was no length contraction/time dilation (in the same way, the fact that sound waves only travel at the same speed in all directions in the rest frame of a medium like air isn't seen as a violation of the principle of relativity, because you can put the equations in a form that depends on the average velocity of the medium).