Sagnac, Michelson & Co
Relativity to "touch"
RuedigerRodloff
Background image - DLR - Experimental Laser Gyro - ELSY
Why does Sagnac work, but not Michelson ?
You can actually skip this chapter.
I would like to present to you some attempts to explain the outcome of the Michelson and Sagnac experiments from the point of view of classical physics.
Some of these proved wrong (entrainment of the ether), others paved the way for the theory of relativity.
The much more consistent description of both experiments is provided by the theory of reality, which I will present to you in the following chapter "Solutions - Runtime effects in relatively moving systems". You will see that the apparent contradictions "dissolve into thin air" against the background of this approach:
Michelson interferometer does not work!
Sagnac interferometer works
So , - even if you only skimmed through the last two chapters, - one thing has surely struck you:
--> The same - albeit extremely simple - formalism, which correctly describes the measurement result of the Sagnac experiment, fails completely in the Michelson experiment!
- in both experiments an attempt is made to measure a speed.
- the speed of a uniformly moving system is to be measured with the Michelson interferometer.
- the circumferential tangential velocity of a rotating system is to be measured with the Sagnac interferometer.
- in the first case there is a measuring effect, in the second not!
Why ? Answering this question is one of the exciting chapters in the history of physics.
There have been numerous attempts to reconcile the contradictory results of the two experiments.
The zero result of the Michelson experiment could be explained with a bit of intellectual acrobatics, but then failed because of the positive outcome of the Sagnac experiment or got caught up in contradictions with other findings.
I would like to introduce you to a few of these explanations - not only because it is very exciting to discover the "culprit" or the mistake, as in a crime novel, but also to make it clear that from today's perspective there is only one explanation model, which remains completely free of contradictions - but we will only talk about that in the next chapter.
I would like to introduce you to the following (partially unsuccessful) explanations:
1. Carrying of the "ether"
The speed of the earth in its orbit around the sun is approx. 30 km/s!Source- Wikipedia
From the point of view of classical physics, the ether - if it exists - would be an absolute reference system that could be used as a reference system for all physical phenomena; in a way the "Point of Archimedes" !
entrainment of the ether
I have already mentioned it several times - Michelson actually wanted to prove the existence of the ether and its properties as a carrier medium of the light waves with his experiment.
The physicists of the 19th century - and some even today! - had the idea that light needs a carrier medium to propagate, similar to how sound needs air.
According to this idea, the entire universe is filled with this ether and the earth moves at a fairly high speed through this ether sea and similar to the sound in the wind, the propagation of light in the "ether wind" is either hindered or promoted - depending on the in which direction the (ether) "wind" is blowing.
When Michelson could not prove any "ether wind" with his experiment, the advocates of this theory came up with the idea that the earth carries the ether with it, just as it carries the air with it! An "ether wind" was therefore not present at all and Michelson could of course not prove any influence of the ether on the light waves.
Apart from some other problems that this explanation brought with it - e.g. the aberration of the starlight -, ...
..... it stands in direct contradiction to the result of the Sagnac experiment, because an ether moving with the earth, which would then also have to follow the rotation of the earth, would prevent the Sagnac interferometer from showing the rotation of the earth.
I hate it when the authors just throw out certain terms without elaborating on them.
So: aberration of starlight, - What is that ?
If you take your sights on a star with the telescope (on the earth moving at 30 km/s), then you have to tilt the telescope slightly so that the star remains in the field of view. The tilt angle is the ratio of the speed of light to the speed of the earth. (Left sketch below) This effect has been verified experimentally!
However, if the ether - the carrier medium for the light wave - would move with the earth, then such an angle of inclination of the telescope would not be necessary. (right sketch).
Schematic sketch of the aberration of starlight: left without ether, right with entrained ether.
At Sagnac's time, the Sagnac-type ring interferometers were not yet sensitive enough to react to the earth's rotation; this was achieved for the first time in 1925 with the work by AA Michelson, H.G. Gale and F. Pearson realized ring interferometers.The "device" had a circumference of 1.9 km (613 x 339 m), the light path ran in evacuated tubes and a carbon arc served as the light source.
Tubes for the light path in the Michelson-Gale ring interferometer.
To be honest, the practical implementation of the Michelson-Gale experiment is not entirely clear to me: when "switching" from the small to the large travel path, a "technical" phase shift probably occurs between the light wave trains circulating in opposite directions! How can this phase shift be distinguished from the actual effect? I couldn't find any reference to this in my (internet) research.
Well, I trust here in the experimental skill of AA Michelson, especially against the background that later experiments with optical fibers (see the schematic sketch on the right) have confirmed the magnitude of the effect observed by MIchelson and Gale.
In contrast to the previous experiments, this arrangement could not be rotated - which would have been difficult given the size!
In order to get a statement about the influence of the earth's (rotational) movement, the light wave train was sent to a much reduced orbit for comparison. Michelson and Gale were able to prove the influence of the earth's rotation by comparing the stripe shift between the different sized orbits.
I mention the Michelson-Gale experiment because here - in contrast to modern setups - the light path runs completely in a vacuum and interactions with a carrier material could be largely ruled out.
From the point of view of the advocates of the ether theory, the light in this experiment is exclusively exposed to the influence of the ether and the fact that the experiment shows an effect means - always from the point of view of the ether theorists! - that the light was exposed to an "ether wind", which in turn leads to the conclusion that the ether is not carried along with the earth!
From the point of view of the ether theorists, only the conclusion remains:
The "zero result" in the Michelson experiment cannot be explained by the ether being carried along by the earth.
2. The Lorentz contraction
Here is another basic sketch of the Michelson experiment:
In Chapter 2, we calculated the signal propagation times TP in the arm parallel to the direction of movement of the interferometer and TS in the arm perpendicular to it. The formalism was trivial and we had determined:
and
That is, the running time TP parallel to the direction of movement is by the factor
longer than the running time perpendicular to it and of course dependent on the speed v of the apparatus, or of the earth on its orbit around the sun, - ...at least that's what Michelson expected!
However, the result of his experiment was that the propagation times in the two interferometer arms of equal length were the same; at least Michelson could not detect any difference in the leaching time when rotating the interferometer. So: TP = TS !
In order to save the ether theory despite this "zero result", Hendrik Antoon Lorentz (*1853 in Amsterdam, +1928 in Haarlem) postulated in 1892 that the length of the interferometer arm in the running direction (due to the effect of the ether wind ?) is shortened:
With this assumption, the propagation times in both arms of the interferometer were the same and the zero result of the Michelson experiment was explained.
The background of this initially adventurous hypothesis was probably the fact that moving, electrostatic fields are deformed by movement. Lorentz probably suspected a connection between the structure of matter and electromagnetic fields. (more here)
Problem solved ?
Reply Lorentz: Yes! There is a transit time effect and there is also an ether, but unfortunately one cannot prove it because its effect on the path of the light is exactly compensated by the length contraction of the interferometer in the direction of movement.
.... Oh well !
The following question quickly comes to mind for an average physics student when it comes to this explanation:
When calculating the transit time effect in the Michelson interferometer, we assumed that the interferometer arms were exactly the same length. Apart from the fact that this cannot be realized very precisely anyway - what would happen if we made the length of the interferometer arms very different, e.g. like this:
This experiment with an interferometer with different arm lengths was carried out in 1932 by R.J. Kennedy and E.M. Thorndike performed.
Unlike Michelson, Kenndey and Thorndike did not rotate the interferometer setup; Rather, an attempt was made to observe the position of the interference fringes and thus of course the change in the paths during one orbit of the earth around the sun.
During the orbit of the earth, both the speed and the direction of the "ether wind" change. According to classical ideas, both should cause a path effect or a displacement of the interference fringes, but this experiment was also unsuccessful.(more here)
This raises the question of why Michelson didn't work with different arm lengths right from the start?
There is a simple, very practical reason for this: with the light sources available at the time (e.g. arc lamps), the coherence length (more here) is very small and with an interferometer, care must be taken to ensure that the paths of the two light wave trains are exactly the same length, so that superimposition or constructive interference is possible at all.
This is no longer a problem with today's laser light sources, but Kennedy and Thorndike had to be content with a length difference of 16 cm in the two interferometer arms so that interference could still be observed at all.
Yes, yes - you are right, of course: H.A. Lorentz is not one in this rather simple conceptlength contraction from 1892 remained standing. Between 1895 and 1904 he with his transformation equations for uniformly moving systems, a transformation for time was introduced in addition to the shortening of the length scales. (Keyword: "moving clocks run slower.")
In purely formal terms, histransformation equations the relationships derived by Einstein in 1905 and thus the Lorentz transformation could be accepted as an explanation for the Michelson exo experiment. However, unlike Einstein, Lorentz never gave up the idea of an ether as the carrier medium for light.
The different lengths of the interferometer arms would then have to be taken into account when calculating the transit time difference:
with: Lp length of the interferometer arm in the direction of movement
and Ls length of the interferometer arm perpendicular to the direction of motion
Even if we now still assume the Lorentzian length contraction in the direction of motion, i.e. for insert, then the runtime difference is:
... and that is all the greater, the greater the difference in length between the interferometer arms Lp and Ls.
This means that H.A. Lorentz' attempt to explain the zero result of the Michelson experiment could work with interferometer arms of exactly the same length, but the idea of length contraction fails with interferometer arms of different lengths.
The question why the Michelson experiment does not produce any effect is therefore still open!
3. The principle of relativity
Galileo Galilei ( 1564 - 1642)
Galileo Galileo's "Dialogo"
Albert Einstein (1879 - 1955)
In Galilei's time, railway carriages were not yet so "common"; he had therefore suggested carrying out this experiment on a ship.
When we hear the term "relativity" or "relativity principle", many of us think of Einstein, who coined this term with his "Special Relativity" has helped to become well known.
In fact, however, the considerations on this topic are much older:
already explained in 1630Galileo Galilei in his
Dialogo di Galileo Galilei sopra i due Massimi Sistemi del Mondo Tolemaico e Copernicano
(Dialogue by Galileo Galilei about the two most important world systems, the Ptolemaic and the Copernican)
his ideas on the principle of relativity.(more):
Here is an excerpt from the "Dialogo":
"Lock yourself in the company of a friend in as large a room as possible under the deck of a large ship. Get gnats, butterflies and similar flying creatures there; also provides a vessel with water and small fish in it; also hangs a small bucket on top, which allows water to trickle drop by drop into a second narrow-necked vessel placed below. Now watch carefully while the ship stands still, how the little flying creatures fly in all directions of the room at the same speed. The fish will be seen to swim in all directions without any difference; the falling drops will all flow into the vessel below.
.... . Now let the ship mmove at any desired speed: you will not see the slightest change in any of the phenomena mentioned, as long as the movement is uniform and does not fluctuate here and there. You will not be able to tell from any of them whether the ship is sailing or standing still. […] The reason for this agreement of all phenomena lies in the fact that the movement of the ship belongs to all things contained in it, including the air.
So far the description of Galileo Galilei.
Before we deal with the question of what the principle of relativity has to do with the Michelson or Sagnac interferometer, I would like to illustrate Galileo Galilei's considerations in a small animation:
We are in a railway carriage moving steadily along; the windows are curtained, we have no contact with the outside.
Following Galileo's suggestion, let's do the following experiment:
we drop an object on the ground and observe its path. (Galileo used a dripping bucket! see above)
Drop test in a car moving at a constant speed. The observer is in the car.
What do you see ? Actually nothing !
The ball falls straight down as if the car were standing still. The free fall of a body is not changed by the (uniform!) movement of the car.
Let me take this thought experiment one step further - this time we position ourselves as observers not in the car but outside.
If we now repeat the case experiment, we see the following:
Drop test in a car moving at a constant speed. The observer is outside the car.
A popular question in Galileo's time was why the earth, when moving so fast, doesn't "shed" its atmosphere and why the birds have no trouble keeping up with the earth? Well, how would you have answered that?
But maybe our "blindness" to the speed with which our earth is racing through space is also quite good.
Imagine if there were an effect accessible to our sensory organs, with which we could feel or observe the insane speed of the earth of over 230 km/s - we might lose our nerves!?
*) Of course, this simple example of a case experiment alone is not sufficient to make a "principle" out of it, but this question was of course answered with countless other experiments, with sound, with light, etc. examined again and again and the result was always the same: the absolute speed of a uniformly moving system cannot be determined.
This time the ball falls down on a curved path. (throw parabola)
From the trajectory of the ball one could deduce the speed of the car - but of course it is easier to measure the forward movement of the car directly.
The two experiments show us the following:
Within a closed system, in this case a railway carriage, we cannot obtain any information about its (uniform) state of motion; but a simple change of the place of observation, or to put it more elegantly: the "reference point", can lead to a completely different impression of the test procedure.
What at first sounds like a triviality has enormous practical significance:
One consequence of this principle is the fact that there is basically no way within a closed system to find out at what speed you are currently traveling. *)
Galileo chose a steadily drifting ship as an example, Einstein - somewhat more modernly - the railroad car; but even the "vehicle earth" doesn't give us a chance to find out at what speed it is whizzing through space.
Of course, we can use astronomical methods to determine the relative speed of the earth in relation to the sun (30 km/s) and the planets, and even estimate how fast the place in our galaxy where we are is moving (approx. 200 km/s), but is that all? Perhaps the cosmos is expanding at even greater speed, but we don't notice it!
In the 19th century people did not want to be satisfied with this limitation and therefore hoped to find an absolute reference system by proving the existence of an ether as a carrier medium for light waves. But all attempts to find this "ether" or the absolute reference system have failed up to now; the Michelson experiment was certainly one of the most important of this series, but by no means the only one.
... or in other words:
We can only measure relative velocities between an observer and a moving system, but never the absolute velocities!
... and what about the Sagnac effect?
In the Sagnac experiment, we (as observers) are also within a closed system without contact to an external reference system and we can still measure the rotational speed of the system or vehicle via a path effect of the light?
Ok, - now at the latest we should remember that in the Sagnac experiment we were dealing with arotating systemhave to do !
No, no, I don't mean the centrifugal and Coriolis forces that occur during rotary movements - I would like to agree with the great physicist A. Sommerfeld, who considers the influence of these forces in connection with the Sagnac effect to be negligibly small. (Preliminary on theoretical physics, vol. IV, optics, p.67).
I am referring here to another property within rotating systems - tangential velocity.
Let's go (mentally) into a rotating system:
What do you see when you look at a certain point from the center - represented here by a cat ?(sorry, - in my clipart collection I liked the cat the best!)
Well, - I think you don't see too much !
From your position - the cat doesn't seem to be moving; since you're both spinning at the same speed, the cat won't move out of your field of view! Despite this, the cat has a certain (tangential) speed relative to your position. This results from the product of the angular velocity and the distance r1:
If the distance changes - as in the following sketches - then of course the relative speed between the observer and the cat also changes:
I admit this is a rather formal argument:
Because Galileo's principle of relativity is not violated in the Sagnac interferometer, it should be possible to observe an effect; The opposite applies to the Michelson interferometer.
How the measurements are carried out in detail is not considered at all - it is only a matter of whether there can be a measurement effect in principle or not!
So far so clear!
We now know why Sagnac observed an effect - he simply measured the tangential velocity in a rotating system!
And we also know why Michelson had no chance to observe anything - as a moving observer there was no relative speed between him and his experiment at any point, so there was nothing to observe or measure either!
I don't want to confuse you further, but the following note is important:
From now on, the ether plays no role at all in our considerations; whether the observer and/or experiment is at rest or moving in relation to a fictitious ether should not concern us. We agree with Einstein's view: theEther hasn't been proven in countless experiments, so let's forget it!
In the first case, the cat has moved a little closer to the center, the observer (distance r2), in the second case the observer has focused on the distance r3 away.
The relative speeds between the observer and the cat are then:
and
Within a rotating system there are any number of relative velocities for each observer position.
But again: the observer cannot "see" anything of this within the rotating system, because everything rotates with the same angular velocity:
What does this mean for the Sagnac experiment?
Very easily!
An observer can successfully carry out a running time experiment within a rotating system, precisely because he is doing nothing other than measuring the relative speed between two points and this is compatible with the principle of relativity!
It is also clear why the Michelson experiment within aclosedsystem cannot work for a moving observer (see above) - because here there is no relative movement between the observer and the runtime experiment at any point.
Michelson had naturally hoped that his interferometer would be exposed to the "ether wind"so not closedis and would therefore show an effect. That was not the case, which leads to the conclusion that the "ether" does not exist - at least not as a carrier of a light wave - so the system is closed and therefore of course cannot show any effect.
So far so clear!
We now know why Sagnac was able to observe an effect - he simply measured the tangential velocity in a rotating system! And we also know why Michelson had no chance to observe anything - as a moving observer there was no relative speed between him and his experiment at any point, so there was nothing to observe or measure either!
**) Michelson behind a workbench or an experimental setup (?)
Well, this seems very satisfying:
If we consistently apply Galileo's principle of relativity, remember that any number of tangential or relative velocities exist in rotating systems and that in the Michelson experiment there is no relative velocity to the (usually !) moving observer **), then it is immediately clear clear that there must be a Sagnac effect, but no Michelson effect!
Where is the problem ? Apparently we can explain everything purely classically.
Galileo already knew that about 400 years ago!
.
stop, stop ! This is too easy!
It is correct - the classic Michelson experiment had a moving observer, i.e. the observer moves together with his device e.g. through space and observes the interference fringes or the output signal and registers - of course - nothing !!!
But what does a resting observer seenotmoved with his device? For him, the principle of relativity would not prevent him from measuring the relative speed between his position and the interferometer! (Scroll back to that againdrop experiment above: the stationary observer could deduce the movement of the carriage from the trajectory of the ball, the carriage did not move!)
However, when calculating the anticipated path effects, we had tacitly assumed precisely this latter scenario (stationary observer - moving interferometer).
Syou remember? Here is another sketch for calculating the path effect for the wave train running in the direction of movement: (Click here for the relevant passage in the "Michelson" chapter:)
The experiments with the Michelson interferometer - at least the ones I know - always had a moving observer!
When calculating the travel path effects in the Michelson interferometer, did we assume a configuration that was not used in practice? I'm afraid so!
(However, we are in good company with most representations in the literature!)
****) W.R. Leeb, G. Schiffer and E. Scheiterer, "Optical fiber gyroscopes: Sagnac or Fizeau effect", Applied Optics, Vol. 18, No.9 (1979) p. 1293-1295.
On the other side --> For the Sagnac interferometer, W.R. Leeb & Co. ****) 1979 in this context a very important experiment with a stationary and a moving Readout optics made: Result: In any case, the Sagnac Interometer shows a measurement effect, regardless of the position of the observer (resting or moving) and -very important ! - independent of the material properties of the optical fiber and thus independent of the speed of the light wave train! (We'll get back to that!)
I cannot give a conclusive answer to the ambiguities that are currently opening up at this point. I'm afraid we're going to have to start all over again. Take a look - to the next chapter "Runtime Effects in Relatively Moving Systems".