Proof of Special Relativity w/ Michelson–Morley Experiment

[FMJalink]

TL;DR Summary

Where is the observer located in the Michelson-Morley experiment?

Dear readers,
Maybe someone can enlighten me on the understanding of the proof given by the Michelson–Morley experiment on the special relativity.

Just as introduction to detail the setting: There are 2 coordinate systems A and B. A stands still and B moves with the velocity v along one of mutual axis. The standard description with the experiment. The light beam in system B is split up in a beam perpendicular to the velocity v of system B and in a beam in the direction of the velocity v. The distance from splitting mirror to return mirror is equal on both physical trajectories. They come back and the interference of the 2 beams is examined. There is no difference in phase witnessed by the observer, so is assumed the light rays traveled the distance in equal time.

In texts the observer is placed in system A, which does not move, which leads to the well known formulas. As at the time of the experiments no space ships were available, I think the observer formed part of system B (the Earth rushing along with velocity v) and for him the system B was completely at rest, which should also explain the result of the experiment and to my opinion not proof anything. Can someone tell me where I am going wrong?

 

[BvU]

Hallo @FMJalink ,

$\qquad$!​

Yes, the observer reference system was stationary on planet earth. That moves and rotates through the aether as was imagined in those days. So the expected results took a sine wave shape, which was not observed.

So: end of necessity of aether existence.

$\$

 

[Dale]

Summary:: Where is the observer located in the Michelson-Morley experiment?

I think the observer formed part of system B (the Earth rushing along with velocity v) and for him the system B was completely at rest, which should also explain the result of the experiment

Sure, but the speed of the apparatus relative to some observer is only relevant to relativity. So your analysis is the relativity analysis.

The MMX was performed 18 years prior to the advent of relativity. It was designed to test the aether theory. In the aether theory speeds are measured with respect to the luminiferous aether, not relative to an observer. So the description you read is a correct description of how the MMX was intended to work under the extant theory.

 

[Orodruin]

To be nitpicking: MM does not prove relativity. It disproves aether as it was imagined. Generally, you cannot prove that a model is true in an empirical science. It is all about trying to test predictions (those predictions may turn out to be true but that does not prove the theory, it just raises our confidence in the theory being a good description of Nature).

 

[jartsa]

Summary:: Where is the observer located in the Michelson-Morley experiment?

In texts the observer is placed in system A, which does not move, which leads to the well known formulas. As at the time of the experiments no space ships were available, I think the observer formed part of system B (the Earth rushing along with velocity v) and for him the system B was completely at rest, which should also explain the result of the experiment and to my opinion not proof anything. Can someone tell me where I am going wrong?

You have a point there. Ether filling the solar system could move with the earth. I mean all of the ether could move with the earth. Then observer in a spaceship hovering next to sun would observe the effects of the moving ether. While observer on Earth could not observe any effects of moving ether, except by using a telescope in order to observe the Michelson-Morley experiment conducted on a spaceship.Well actually they knew that ether filling the solar system does not move with the earth. They saw it in the propagation of sunlight in the solar system. Like in this experiment: https://www.amnh.org/learn-teach/curriculum-collections/cosmic-horizons-book/ole-roemer-speed-of-light

 

[A.T.]

Maybe someone can enlighten me on the understanding of the proof given by the Michelson–Morley experiment on the special relativity.

M&M doesn't prove SR. It disproves the aether, but is still consistent with theories other than SR. You need additional observation to rule these out:

https://en.wikipedia.org/wiki/Emission_theory

 

[cianfa72]

So M&M does not disprove an aether always 'at rest' in the rest frame of the M&M apparatus (i.e. an aether dragged from the apparatus).

 

[A.T.]

So M&M does not disprove an aether always 'at rest' in the rest frame of the M&M apparatus (i.e. an aether dragged from the apparatus).

Yes, an Earth fixed aether is not ruled out by M&M alone either. But M&M is also consistent with emission theories which don't have an aether or a preferred frame (and thus satisfy Galilean Invariance). Ruling those out requires additional observation.

 

[cianfa72]

But M&M is also consistent with emission theories which don't have an aether or a preferred frame (and thus satisfy Galilean Invariance). Ruling those out requires additional observation.

AFAIK in Emission theory there is no aether at all and the light speed is the constant $c$ w.r.t. the light source (i.e. light is like a projectile thrown with velocity $c$ w.r.t. the source).

Since in M&M the light source is at rest w.r.t. the apparatus then its null result is actually expected.

 

[A.T.]

AFAIK in Emission theory there is no aether at all and the light speed is the constant $c$ w.r.t. the light source (i.e. light is like a projectile thrown with velocity $c$ w.r.t. the source).

Since in M&M the light source is at rest w.r.t. the apparatus then its null result is actually expected.

Yes, that's what I said.

 

[FMJalink]

Thanks to all for your replies. Maybe I did phrase some parts of my question not correctly. I am quite familiar with the reason why the MM experiment was done. The negative result made scientists think of an explanation. The interference result is often used in texts to come to the well known formulas. That basis (proof) is to my opinion not founded on solid ground, as the observer seeing no difference forms part of the moving reference system. Main point with SR theory is that light (electromagnetic waves) has the same speed in all (constant speed) moving reference frames. In the mean time I stumbbled over an article by Kenneth Khan mentioning that space (dimensions) and time are not principle entities. Just an idea that I intend to investigate further is, if there was a Big Bang, than that electromagnetic waves blast, with its velocity is the basis from which dimensions and time follow.

 

[A.T.]

The interference result is often used in texts to come to the well known formulas.

Please provide a reference to what you are talking about. What formulas are derived solely from the M&M result?

That basis (proof) is to my opinion not founded on solid ground,

Proof of what? As already explained above, the M&M alone doesn't imply SR. You need additional observations to rule out other potential explanations.

 

[phinds]

Just an idea that I intend to investigate further is, if there was a Big Bang, than that electromagnetic waves blast, with its velocity is the basis from which dimensions and time follow.

Before doing so here on PF you should read the rules, particularly the one about personal theories being a no-no.

 

[Dale]

That basis (proof) is to my opinion not founded on solid ground, as the observer seeing no difference forms part of the moving reference system.

Please cite the specific proof you reference which is not founded on solid ground.
There are indeed many incorrect proofs, and you may have been exposed to a poor source. There are also many correct proofs from good sources. At this point we cannot tell if you are generalizing from a poor proof or misunderstanding a valid one.

In either case, SR is well founded. Both experimentally and theoretically.

 

[Bernadette]

Hello

How Michelson does his experience. And what did he think before.

At that time, it was thought that light needed a support to move. Ether. Assumed immobile (first assumption that MM (Michelson Morley) will hijack. By floating their interferometer on a bath of mercury to be able to turn it easily). Second assumption: the Earth is supposed to move in the ether. But without knowing if at a moment of its rotation around the sun, it is not immobile in the ether. MM will take measurements at monthly intervals to be sure not to be in this situation. Earth and ether immobile relative to each other !
MM were also unable to construct the two arms of their interferometer (distances traveled by each of the two beams of light) to within one wavelength. It is very small as a tolerance. They therefore opted for the interference phenomenon to observe whether the path traveled by the first beam and the second varied when they rotated the interferometer on its mercury bath. They should have varied if the speed of light combined with that of its support. But MM did not observe any change in the interferences.

The installation of MM on his mercury "bath". Consider the following displacement of the interferometer in ether. And we assume - it's possible - that the two arms of the interferometer are strictly identical (the two optical paths to be precise)

MM see in the detector the combination of two waves which have traveled the same distance and therefore in the same duration both. And it's "in-phase" interference.

MM rotates their interferometer, let say 20°. One of the two optical paths lengthens. And the other shortens (if there is speeds composition). And so the interference of the two "waves" that MM perceives in the detector should change.

Except that. Since one of the paths lengthens, this "wave" must leave the source before the other. Who travels a shorter path and therefore leaves the source after the other.

And MM see the combination of two waves that did not leave the source at the same time. Is it all in the equations?

What do you think?

Bernadette

 

[Ibix]

What do you think?

I think that's an unusual way of conceptualising why the waves arrive out of phase. Normally you consider waves leaving at the same time and arriving at different times, since it's easier to impose the condition that the phases be consistent at emission. There's nothing wrong with looking at it the other way as you have done, but the maths is messier.

 

[Bernadette]

In a "classical" diffraction experiment. The two holes of Young for example. There are particular points on the observation screen. Those for which the two optical paths have the same length. (and here the same duration). This is the center straight.
The two "bright" lines (therefore in phase) (and which are no longer straight lines) to the left and to the right of this straight line, have a path difference (path length through the first hole minus path length through the second hole) of 1 wavelength. That can be expressed in duration here. And so, if we increase one of the distances (if we move one of the holes), we see scrolling at the observation point that we have chosen a light zone then a dark zone... Etc. MM looks at the same point in their detector. I chose a particular configuration for beginning. The two arms are at 45° in the movement of the ether. And they are exactly the same length. So, it's the same wave that interferes with itself (if we can say it like that).

When MM turns their interferometer, they "slow down" the light in one arm and speed it up in the other (just a little, I'm aware). It's like experiencing young's holes in the water. And then that we "removed" in one of the two paths a thickness of water. The speed of light increases in this space. And that we added in the other way, a material that slows down the light. It seems to me that this is correct?

I will review Fizeau's experience in the water. See you.

Bernadette

 

[Ibix]

Perhaps you should write down some maths, because I don't understand what you think you are doing.

 

[Bernadette]

Hello Ibix

(i must say that sometimes, i do not understand about what you write. When you write "serial of Fourrier" in an other post. But i am sure you see the "things" in an other way than i. More with equations and mathematics. What is not easy for me)

I try to resume. (And English is not my normal langage, lot of difficulty between us)...

With the experience of Young's holes, I understand that it does not matter to calculate the phase shift on one side or the other. On the side of the light source or on the side of the receiver (a point on the observation screen). Ligth doesn't move in the ether. And speed of ligth is the same everwhere. But the reality is that the two "rays" of ligth interfer at the same place and at the same time. So the two rays do not leave the source at the same time (except for the straight line on the screen, Identical optical paths.

In the MM experience, the equations i see most often (always...) do not take care of some parameters i think.
And the equations calculate an interference between two rays of light that are not in the same place at the same time. I think. The ligth move in the ether (hypothese of this time. Speed are not the same).

Yesterday, i have a look on Fizeau experience with flowing water. With an interferometer. And i read (google translate:" More than half a century passed before a satisfactory explanation for Fizeau's unexpected measure was developed with the advent of Albert Einstein's special theory of relativity. Einstein later emphasized the importance of the experiment for special relativity, in which it corresponds to the relativistic velocity addition formula when restricted to small velocities.". And some information about a Fresnel experience. Also with water.Trying to find the historical path that forged our knowledge is difficult. But exciting I find.

Good Thursday.

 

[Ibix]

In the MM experience, the equations i see most often (always...) do not take care of some parameters i think.
And the equations calculate an interference between two rays of light that are not in the same place at the same time. I think. The ligth move in the ether (hypothese of this time. Speed are not the same).

The only thing that matters is the phase difference between the two beams at the interferometer output. The usual way to calculate this is to calculate the flight time of a light pulse along each arm, then the difference $\Delta t$. Consider two wave crests entering the interferometer at the same time. When one exits the interferometer then the other must be $\Delta t$ away, so the phase difference between the crest that's arrived and the part of the other wave currently arriving is $2\pi f\Delta t$.

You seem to prefer to say that the two parts of the wave now exiting the interferometer must have entered at times $\Delta t$ apart, so the phase difference is $2\pi f\Delta t$. The maths is the same.

Trying to find the historical path that forged our knowledge is difficult. But exciting I find.

There are books on this. Someone posted a reference once - unfortunately I don't remember the poster or the book. If you start a new thread in the relativity forum asking about it someone may be able to supply it.

 

[Bernadette]

Hello Ibix

Thank you for your interventions. I will go back to my reading. The arrival of RR and RG is quite simply a fascinating subject. When A Einstein was employed in the patent office in Zurich, Switzerland, he complained by post to a friend of his that he did not have access to many books: the opening hours of the library were the same as those of his job... This is no longer the case today...

Bernadette