Understanding the MMX Calculation Problem: Vertical vs. Horizontal Analysis"

[Kanesan]

There is no reason to assume that you are at rest in a "rest frame", you are free to assume that you are co-moving with a "moving frame".

I am thinking that all co-movers are in same frame! Not to confuse with too many frames if they are co-moving. Is it wrong?

That is effectively the same as assuming that at that moment the apparatus is in rest in the ether.

I have difficulty grasping this. If we assume rest (temporarily or permanently), doesn't that mean velocity is zero?

We calculated what in two different states of motion the result of the experiment will be

We have calculated only once. Just one experiment (one view) needed two calculations as one experiment can need several individual calculations.

Today I am thinking that may be I am mixing up some aether and SR expectations! May be in aether theory everything is supposed to be absolute and calculation from either view should be same (unlike from SR). Can you see if that was my mistake?

According to special relativity, we should expect the same results for an interferometer in rest as for a moving interferometer.

But this one suggests that my above conclusion was wrong as well!

Thanks Harold.

 

[harrylin]

I am thinking that all co-movers are in same frame! Not to confuse with too many frames if they are co-moving. Is it wrong?

I don't understand that. A "frame" is just jargon for an infinite number of reference systems that are in rest relative to each other (they can have their origin at other positions, etc.). In SR, an inertial reference system tracks the position as function of time of everything in the universe. So, if you consider 10 inertial reference systems that are all in different states of motions, then you are in all those reference systems but you can at most be co-moving with one of them.

I have difficulty grasping this. If we assume rest (temporarily or permanently), doesn't that mean velocity is zero?

Yes. In particular, this implies that all light is supposed to propagate at speed v=c in all directions with respect to that system.

Hopefully you are familiar with classical physics which similarly uses rest systems and moving systems, with the same principle of relativity for mechanics. You can choose any inertial system and call it "rest system"; co-moving objects have zero momentum and zero kinetic energy based on that assumption. It is said that such physical quantities are "relative". In special relativity much more is "relative" in that sense.

We have calculated only once. Just one experiment (one view) needed two calculations as one experiment can need several individual calculations.

Oops yes you are right, in this calculation there's only one state of motion considered. https://en.wikipedia.org/wiki/Michelson–Morley_experiment#Light_path_analysis_and_consequences

However that calculation was meant for an experiment in different states of motion. It's alluded to in that section as follows "Any slight change in the spent time would then be observed as a shift in the positions of the interference fringes." In fact it's explained clearly in the section "Michelson–Morley experiment (1887)":
"The mercury trough allowed the device to turn with close to zero friction, so that once having given the sandstone block a single push it would slowly rotate through the entire range of possible angles to the "aether wind," while measurements were continuously observed by looking through the eyepiece. The hypothesis of aether drift implies that because one of the arms would inevitably turn into the direction of the wind at the same time that another arm was turning perpendicularly to the wind, an effect should be noticeable even over a period of minutes."

Thus, for a change of the spent time they observed:
- the interference pattern of the interferometer fast moving in one direction (at least at one time of the year)
- the same with the interferometer moving in a direction perpendicular to it.
For that means the apparatus was rotated, and the changes in the interference were recorded.

It explains what Michelson expected to find, based on Maxwell's theory of optics, combined with Newton's theory of mechanics. In fact those two theories are incompatible, but neither Maxwell nor Michelson had realized that.

PS. I now notice that also the issue of mirror reflection angle is discussed there, under the header "Mirror reflection".

Today I am thinking that may be I am mixing up some aether and SR expectations! May be in aether theory everything is supposed to be absolute and calculation from either view should be same (unlike from SR). Can you see if that was my mistake? [...]

Probably you mixed them up, but it's just the other way round! In ether theory combined with Newton's mechanics, a detectable effect of motion relative to the ether was predicted, but it was not found. That is explained in the Wikipedia article.

This is also referred to in a general way in Einstein's introduction: "the unsuccessful attempts to discover any motion of the Earth relatively to the “light medium”"
- http://fourmilab.ch/etexts/einstein/specrel/www/

Apart of the introduction, also the first line of §1 is useful, as it uses "stationary system" just as in classical mechanics.