[geistkiesel]

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I need a explanation done in flawless SR terms that shows me that SR leads to contradictions. All your current explanations were a mixup of classical view and SR view. When I look at the "two photons are emmited at the same point and reflected my mirrors"-scenario from the perspective of SR I can´t see any problems.

I cannot speculate on what you did, re SRT. Can you elaborate so I am able to make a coherent and rational reply? I am especially intersted in the "moving observer's point of view".
Thanx

[geistkiesel]

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OK, we can do a version of this.

We align a laser, with a spot size of a few microns into an aperture of similar size (a single-mode optical fiber) - the beam needs to be aligned to better than a micron, and deviation of a micron will cause a very noticeable drop in power.
We do this at a time of day when the earth's rotational motion is aligned with the 30 km/s motion, so the earth doesn't add a perpendicular component to the speed. (i.e. if the alignment is east-west, we do this at noon). The rotational speed is about 460 m/sec at the equator, and we do this a little further north, near 45 degrees, where the speed is around 333 m/sec. Make the laser path length 2m, so the transit time is 6.67 ns. After 6 hours, the speed vector will have changed by 90 degrees and will add this 333 m/sec vector component perpendicular to the beam, making it deflect by 2.2 microns. 12 hours after this, it will have deflected 2.2 microns in the other direction from the original spot, or a total of 4.4 microns maximum deflection. There's no way to keep the beam aligned into the optical fiber, according to your scenario.

Well, this experiment and ones like it are done routinely. In my lab we do this (except we don't bother to align it at a particular time of day that is most forgiving). And, not surprisingly to most, there is no deflection of the beam. Keeping it aligned all day long is simply not a problem.

So your theory makes a prediction which is not borne out by experiment. Time to discard the theory.

Your lasers are aligned in the east-west direction I take it. You are trying to emulate the Sagnac effect by watching the beam diverge from the initial target spot? Is this correct?
If you could provide a simple sketch I would be able to follow you more coherently.

AT this point though I do not see any reason for the beam to diverge and point off its original direction. The Sagnac effect will measure the E/W differences in earth rotation wrt to the east to west and west to east beams of light. That is the c + v and c- v relative speed, but I see no beam divergence at this point.

Orbital motion insignificant in Saganc effect, rotational motion is significant.Here is a link saying the rotational motion is significant in the Sagnac effect but earth bound experiments are not affected by orbital motion of the earth,

I cannot rationally respond further until I see the information I need to fully understand the arrangement at your lab. A sketch wouild certainly help.

[geistkiesel]

Johnny5, here is a good link to Dayton Miller who performed mopre than 200,000 MM experiments. Also included is an excellent and unbiased analysios of Miller's critic's especially Shanklandland that made an attempt to skuttle Miller's work.
Millers 1933 paper is invaluabel. Mine is dogged eared at this time. I keep reading it and finding things hidden.
So you want to play the game of physics? See out it is done behind closed doors.


This will cut down onn unnecessary speculations re MM, and Sagnac Effects.click for Miller

BTW, I do not see the direct Sagnac relationship re MM and Saganc that Swnsont mentioned. maybe I am splitting hairs, but Sagnac linearized is a detector for motion, The two dimensional rotational arrangement is an effective accelerometer, gyroscope. Some functional differences anyway.

[swansont]

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BTW, I do not see the direct Sagnac relationship re MM and Saganc that Swnsont mentioned. maybe I am splitting hairs, but Sagnac linearized is a detector for motion, The two dimensional rotational arrangement is an effective accelerometer, gyroscope. Some functional differences anyway.

One of the implications of SR is that the Michelson interferometer isn't a motion detector.

[swansont]

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Your lasers are aligned in the east-west direction I take it. You are trying to emulate the Sagnac effect by watching the beam diverge from the initial target spot? Is this correct?
If you could provide a simple sketch I would be able to follow you more coherently.

AT this point though I do not see any reason for the beam to diverge and point off its original direction. The Sagnac effect will measure the E/W differences in earth rotation wrt to the east to west and west to east beams of light. That is the c + v and c- v relative speed, but I see no beam divergence at this point.

Orbital motion insignificant in Saganc effect, rotational motion is significant.Here is a link saying the rotational motion is significant in the Sagnac effect but earth bound experiments are not affected by orbital motion of the earth,

I cannot rationally respond further until I see the information I need to fully understand the arrangement at your lab. A sketch wouild certainly help.

You're right, drawing a picture helped. The system would measure the 30 km/s speed.

If the system is aligned at noon or midnight, the earth's orbital velocity is in the plane of the laser. 6 hours later, it is perpendicular. The beam should deflect up or down. For the 2m path, that should be a 0.2 mm deflection.

Basically you'reletting the earth rotate the table, instead of doing it manually.

Attached image(s)

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[timo]

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I cannot speculate on what you did, re SRT [so that there´s no problem in SR]. Can you elaborate so I am able to make a coherent and rational reply? I am especially intersted in the "moving observer's point of view".
Thanx

The two photons are emmited at point A, hit the mirrors at point L and R, respectively, and meet again on point B. Different coordinate systems give different coordinates for those points but the points remain the same.

[swansont]

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Your statenment that the Sagnac aeffect is is inherently a rotaional effect iindicates a fundamental miisundersatnding indicated by your post. The post is not correct, not by a long shot: Oxymoron? read on Swansont.


Ron hatch discussing nonisotropic light motion in Sagnac conditions.

He is actually discussing relative motion of frame and photon wher thje relative velocity is C + v or c - v.The Sagnac effect shows that light signals emitted upon a rotating disc do not travel at the same speed with and against the direction of rotation of the disc. It has been long debated whether this same effect applies in the case were light signals are emitted upon a body in uniform translational motion. This paper shows that the Sagnac effect also applies in the latter case

Hatch describing that liner motion does not impose any changes in the Sagnac Effect wrt two dimensional motion.:

In the GPS system a non-rotating earth-centered isotropic-light-speed frame is assumed. Again, the motion of the receiver during the time the signal transits from the satellite to the receiver must be accounted for to obtain precise navigation results. In the GPS context, this effect is referred to as the one-way Sagnac effect and is blamed upon the rotation of the earth. But the receiver must account for its motion during the transit time no matter the source of the motion. It does not matter whether or not it follows a circular trajectory. The critical range which must be determined is the position of the satellite at the time the signal was transmitted and the position of the receiver at the time of its receipt. The path the receiver followed during the time of flight of the signal is completely irrelevant. This is consistent with the argument of Ives [3] that even the original Sagnac experimental results were not specifically due to rotation. Ives suggested an experimental proof designed to show the effect did not require rotation. In a beautiful modification of Ives suggestion, Ruyong Wang [4] has constructed what he calls a Fiber Optic Conveyer (FOC) which directly verifies that linear motion does not affect the speed of light.

.
The link shows the orbital motion is not signicificant in earth bound Sagnac effects, but the rotational motion is material.

When it is pointed out that those quantities do not refer to the speed of light, but rather to the sum and difference of the speed of light and the speed of some other object, both with respect to a single inertial coordinate system, which can be as great as 2c according to special relativity, the anti-scientific crackpots are undaunted, and merely proceed to construct progressively more convoluted and specious "objections". For example, they argue that each point on the perimeter of a rotating circular Sagnac device is always instantaneously at rest in some inertial coordinate system, and according to special relativity the speed of light is precisely c in all directions with respect to any inertial system of coordinates, so (they argue) the speed of light must be isotropic at every point around the entire circumference of the loop, and hence the light pulses must take an equal amount of time to traverse the loop in either direction. Needless to say, this "reasoning" is invalid, because the pulses of light are never (let alone always) at the same point in the loop at the same time during their respective trips around the loop in opposite directions.

You are saying
something like the above which is more completely described in this link

Abstract

The Sagnac effect shows that light signals emitted upon a rotating disc do not travel at the same speed with and against the direction of rotation of the disc. It has been long debated whether this same effect applies in the case were light signals are emitted upon a body in uniform translational motion. This paper shows that the Sagnac effect also applies in the latter case.
This describes some contradictory claims of SRT where in one direction the frame contrracts, but motion in the oppsite direction the frame nust expand!.
read this for more SRTcontradicitons The Abstractabove


A general derivation of the Sagnac formula is given for any shape of light path.

An interseting assortment of information


Or try google on "sagnac effect" for a plethora of Saqnac effect papers and discussion.

I don't see how you expect to show that the Sagnac effect is not due to rotation, when you can't go through an explanation of the effect without tripping over references to rotation.

Further, I find it interesting that you cited an explanation that seems to contradict your claim that a linear system showns a nonisotropic speed of light: Ruyong Wang [4] has constructed what he calls a Fiber Optic Conveyer (FOC) which directly verifies that linear motion does not affect the speed of light

[geistkiesel]

swansont]One of the implications of SR is that the Michelson interferometer [i]isn said:

a motion detector.

But only because the motion was "not detected"., not for any stated theoretical reasons, as far as I am able to determine (AFAIAATD). If there were any inherent systemdatici erriors in MM then the issue remains open.
And wouldn't you just predict it, I have found such an error.

[geistkiesel]

Atheist said:

The two photons are emmited at point A, hit the mirrors at point L and R, respectively, and meet again on point B. Different coordinate systems give different coordinates for those points but the points remain the same.

I hear what you are saying, but I am not quite following the maning of it all. As you have just stated it appears applicabnle to any situation, Atheist, I believe we have an understanding. I would say the same and have in different words: Photons emitted at point A strike parallel vertical mirrors at B and C and are reflected back to point A. Of course we can take this much farther and conclude with the Saganc effect as illyustrated in the opening post.

Let us assume the Saganc arrangement in this thread is but a tremporary flash and that there is some constructive uise fore ther dynamics of the whole process that occured only one time, thiat is one emission, one reflection. The process begins, is emplementyed and is concluded and we all go on to the next process or event, the Saganc effect just completed remains but a vague memjory so unremarkable was its affect, This doesn't lessen the propriety of the effect and the affect on existing theories, such as SRT. AS far as I know there is no physical law requiring eternal existence for all inertial frames as a finfdamental attribute of the physical accuracy or application of the frame. In other word a frame as copnstructed as inefficient and dificult to arrange, doe s not negate the status of the frame and thagt it be relageated tot he nearest theoretical trash bin.
.
I am still cautious on your meaning here as if I have missed something you are trying to say. The fact that the same points on A , B and C can be described by an infnite number of points and coordinate systems does not obscure the conlusions of tthe Saganc effect. If this were true no coordinant system would be safe. All someone would have to do is claim "an infinite number of coordinate points and frames also describe what one has described in formal scientific logic, and that this would effectively nullify the system, But we know such infinity rich states do not give dancing lesson to the host of angels dancing on the head. of a pin.

I read a treatise discussing scioentific analysis of the origin of religion and the effect of the scrutiny. One point hammered home consitently the scientific community is able to describe the origins of religion as if that explanation alone would be sufficent to bring about the downfall of religion. If I explain SRT will SRT crumble?

If we look at the matter from a sheer "utility " concern, the coordinate system that works apporpriately need never be repalced until a model comes along with such a significant benefit increase that the change becomes mandatory and crucial, absolutely mecessary.

The Ptolemy system of prediting the positions of stellar objects did not collapse one week aftyer Gallileo and Kepler publshed their famous documents. Ptolemy lasted approximately 150 years, plus, the reason for the survival after the grand awakening given the world by the K and G was that the Ptolemy system WORKED.

Soemhow I think I overkilled this response, What do you think?

[geistkiesel]

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I don't see how you expect to show that the Sagnac effect is not due to rotation, when you can't go through an explanation of the effect without tripping over references to rotation.

Further, I find it interesting that you cited an explanation that seems to contradict your claim that a linear system showns a nonisotropic speed of light: Ruyong Wang [4] has constructed what he calls a Fiber Optic Conveyer (FOC) which directly verifies that linear motion does not affect the speed of light

But look very closely what is being describeac as nonisotropic, SRT states that the relative velocity of frame and photon is always measured as C, correct" The nonisoptropic light motion is merely the recognition that the relative velocity of frame and photon is v - c or v + c. The speed of light wrt some Vf = 0 is still c. Nothing has really changed except the rhetoric. But no one is suggesting that light actually slows down or speeds up for the mere convenience of scientists constructing classical physical models of light motion. But that would be so cool if it did. :cool:

Swansot. histroically the Saganc effect came from experiments on rotaion. Only through time did the application generalize to not just rotation of circular wheels, but any turning shape was seen to give the same result. But while all this weas going on the mentality was thinking in terms that the system was a rotationall system, until even Einstein suggested that the Saganc unwrap the trajectories of the turning wheel and lineralize the effect.
So see the obedient result of that command by AE in the opening post of this thread.

I have concluded that the rotational Saganc effect is basically an accelerometer, the linear effect a motion indicattor, meaning uniform motion and perhaps measuring accelerating frame as well..

[swansont]

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But look very closely what is being describeac as nonisotropic, SRT states that the relative velocity of frame and photon is always measured as C, correct" The nonisoptropic light motion is merely the recognition that the relative velocity of frame and photon is v - c or v + c. The speed of light wrt some Vf = 0 is still c. Nothing has really changed except the rhetoric. But no one is suggesting that light actually slows down or speeds up for the mere convenience of scientists constructing classical physical models of light motion. But that would be so cool if it did. :cool:

Swansot. histroically the Saganc effect came from experiments on rotaion. Only through time did the application generalize to not just rotation of circular wheels, but any turning shape was seen to give the same result. But while all this weas going on the mentality was thinking in terms that the system was a rotationall system, until even Einstein suggested that the Saganc unwrap the trajectories of the turning wheel and lineralize the effect.
So see the obedient result of that command by AE in the opening post of this thread.

I have concluded that the rotational Saganc effect is basically an accelerometer, the linear effect a motion indicattor, meaning uniform motion and perhaps measuring accelerating frame as well..

A rotating frame is not an inertial one, which means that you can't blindly apply SR to it. And "any turning shape" still qualifies as rotational.

Can you point me to where Einstein suggested "unwrapping" it?

I think your conclusion that the linear effect is a motion indicator is wrong; as you note it predicts that beams will be deflected by motion, and this is not observed.

[swansont]

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If and when Johnny5 shows his detected frrame swapping error in MM, I will give you my detected error. Virtually all the literature descibes the leg orthogonal to the frame motion is reflected sin the triangular trajectory where the frame "carries the beam along"as this is often described.

The postulates of the light are clearly stated that the photon moves isotropically regardless of the motion of the sources of the light. Secondly, to use the "go along with" interpretation would be to impose a moving frame's momentum compoinent on the photon thereby increasing the velocity of the light to c' > c. If the mirrors are properly adjusted for accurate 180 degrees relectioopn the photon would would return on the same physical trajectory path of the downward directed beam. The photons of both legs would then approach the eyepiece parallel wrt each other.
If the earh is moving at 30 km/sec (as assumed) then in 32 meters of roundt rip time of flight, the orthogonal beam would move a distance as calualted by:
32/3x10⁸ = 10.6 x10^-8 seconds. This multiplied by the earth velocity of 30 km/sec returns a distance offset of .00318 meters = 3.18 mm.

MM should have been looking for 3.18 mm offset from the parallel (wrt the direction of motion) beam when the beams arrived at the eyepiece. This would be some sort of maximum offset. I betcha that MM & M adjuested the orthogonal mirror in oder to calaibrate the interferometer to a null positionj. After all they were using the wrong assumed physics for the reflection of light from an orthogonallyl moving mirror.

Let me confirm this: you think that in the interferometer's frame of reference, the orthogonal beam travels a triangular path if the device is properly adjusted? If so, what is the length of the base of the triangle?

Also, what "wrong assumed physics" were they using in deriving the equation?

[timo]

geistkiesel][indent said:

I hear what you are saying, but I am not quite following the maning of it all. As you have just stated it appears applicabnle to any situation, Atheist, I believe we have an understanding. I would say the same and have in different words: Photons emitted at point A strike parallel vertical mirrors at B and C and are reflected back to point A.

No, in the sense of relativity they are not reflected back to point A. I am talking about points in 4-dim space here. That is one misunderstanding of yours I´m complaining about all the time. But I admit I could have called the points in 4-space "events" for clearification. Just reread my post and replace "point" with "event".

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I am still cautious on your meaning here as if I have missed something you are trying to say.

Yes, see above. Don´t expect it to be a minor remark. The step to stop thinking in 3-space and to start thinking in 4-dim spacetime is no as easy as it sounds.

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If we look at the matter from a sheer "utility " concern, the coordinate system that works apporpriately need never be repalced until a model comes along with such a significant benefit increase that the change becomes mandatory and crucial, absolutely mecessary.

Not completely sure what you are talking about but sometimes it´s easier to tell someone "the bar is 50 meters up the road from that italian restaurant" than to give GPS coordinates.

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Soemhow I think I overkilled this response, What do you think?

I do think the same. That´s why I restricted my answer on the parts I understood. My main point is still that you seem to mix up classical view and relativisitic view.

[geistkiesel]

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Let me confirm this: you think that in the interferometer's frame of reference, the orthogonal beam travels a triangular path if the device is properly adjusted? If so, what is the length of the base of the triangle?

Also, what "wrong assumed physics" were they using in deriving the equation?

Thde base of the triangle is the length of the path of the interferometer during the tie the beam is translated down (1leg) and reflects at the apex then returns (2nd leg).
The beam of light reflecting from a flat surface perpendicular to the beam will reflect the beam back along the original trajectory of the beam whether the mirror is moving or at rest wrt the beam trajectory. This is where the beam is DRAWN HISTORICALLY AS A TERIANGLE, an error.

[geistkiesel]

swansont]One of the implications of SR is that the Michelson interferometer [i]isn said:

a motion detector.

What ever the MM results are there is the ever oresent ambiguities inherent in the results. Thje first is the cinsistent finding of the 8km/sec absolute motion (MM and Miller confirmed) together with the imposed error assumed by virtually all reviewers of the MM resuls (Miller included). Th error is the assumption that the orthogonal reflection on the moving mirror "dragez the beam along with the moving interferometer thus creating an extended path length for the reflected beam.

Until these questi8ons are fullt answered there is little valyue in using MM to prove one thing or another, or to impose any assumptions regarding SR and classical physics,
I have been reluctantly discussing these issues, with little ,if any, direct response. We can discuss the matters of MM all week long, but we are fancifying the progress of the discussions by our speculations.

[geistkiesel]

Atheist said:

No, in the sense of relativity they are not reflected back to point A. I am talking about points in 4-dim space here. That is one misunderstanding of yours I´m complaining about all the time. But I admit I could have called the points in 4-space "events" for clearification. Just reread my post and replace "point" with "event".

This much I gathered, however the use of the 4-dim world is SR structered is it not? The use of the coordinate systems of classical vs. 4-dim imposes ambiguities from the inherent differences imposed by the basic physical assumptions that are contradictory from the get go.

Were I to agree that the measure of relative velocity of frame and photon was always c for all uniformly moving frames I wouldn't be in this duiscussion, but i see the opposite. If we observe a duck flying in a straight line at uniform motion from any number of inertial fremes, we will not arrive at a duck version of SR, will we? It is only when we assume the constancy of the relative velocity of frame and ducks that we would construct such a model directly analogous to SR as we know it. Electromagetic dynamics is the only entity in the observeable universe that we make the constancy of the speed of light assumptions and this as an exception to all other motion. Because there was an inherent inability to consider situations and conditions that would allow one to measure the relative velocity of the speed of light measured from the frame, that got us where we are. This is the pnly reason why some discard the concept of absolute space and time. The moving frame is considered a special place in a universe where everthing is moving. Some are taught to reject the ratioanal and the observed and to believe in the mentally constructed which is based on the rejection of even attempting to measure the relative velocity of frame and photon. It has gotten to a point that any measurement of the absloute velocity of any entity is rejected by SR theorists, not from any inherent identifiable error in the experimental arrangement, but from a pure theoretical objection. Theory vs. Experimental results is where the battle is being raged, and all the philosophical rhetoric outlining the problem offers nothing to any resilutuion of the discussion.

I trust you can see my objections. If we are told that under no circumstances will any measurement of the relative velocity of frame and photon ever be measuarble as different than c, i.e. c - v, or c + v measuremnts as relative findings, are not true and accurate measurements. I expected no less of a response when I offered the example described in the opening post of this thread. I would think, as I did think, that if there was some intrinsic experimental error in the described system that that error would be so obvious that to point to the error would be a trivial task for the average SR theorist.

AS I described the system in the figure I see nothing that includes or discludes SR. The only assumption I made, the speed of light is independent of the motion of the source of light. I see this as used improperly when translated to mean the speed of light will always be measured as C wrt any source. This statement is a direct contradiction of the basis of SR. If the motion of light is independent of the motion of the souerce, then why make a statement that the speed of light will always be emasured as C from any frame. Why insert an exception to the independence piostualte of light?

This is an inaccurate meaning of the independent motion of light. No activity of the source will have any affect on the motion of the emitted light. is hoe I read it, but to then measure the speed of light wrt a point on a inertial frame moving at some v > 0 wrt Ve, embankment, that I must then jump thriough the SR hoops and effectively negate the velocity of the frame is too much. Every external observer to the frame making the measurement, from their external position, will come up with a relative velocity Vc - Vf = Vcf < C. The moving observer measures Vc - Vf = Vcf = Vc.

ATheist said:

Yes, see above. Don´t expect it to be a minor remark. The step to stop thinking in 3-space and to start thinking in 4-dim spacetime is no as easy as it sounds.

The difficulty to engage in that kind of thinking is indeed not easy. The writings I am familiar with state (in many versions), that one must give the learned "rational" thinking process and that what one observes is "not the reality" of the universe, are true statements. To accept SR one must discard rational observations.

Atheist said:

Not completely sure what you are talking about but sometimes it´s easier to tell someone "the bar is 50 meters up the road from that italian restaurant" than to give GPS coordinates.

the two examples you mentioned are from consistent coordinate systems, so if you are talking to the town drunk, or the astronaut, there may be the easiest way to give directions to one or the other.

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I do think the same. That´s why I restricted my answer on the parts I understood. My main point is still that you seem to mix up classical view and relativisitic view.

I make the attempt to determine which system is being used.We are in a debate, of sorts, each explaining their own perceptions and attempting to indicate the errors in the other's perceptions, so I agree it is not an easy task. Hiowever, we do agree, there is the bar down the road apiece, where we may all gather and discuss the matter, or we could just let St. Peter sort it all out.

[swansont]

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Thde base of the triangle is the length of the path of the interferometer during the tie the beam is translated down (1leg) and reflects at the apex then returns (2nd leg).
The beam of light reflecting from a flat surface perpendicular to the beam will reflect the beam back along the original trajectory of the beam whether the mirror is moving or at rest wrt the beam trajectory. This is where the beam is DRAWN HISTORICALLY AS A TERIANGLE, an error.

In the MM experiment, the beam path is not drawn as a triangle in the interferometer frame. The velocity addition is drawn that way, because that's how you add vectors.

It's drawn as a triangle in the ether frame, because it has to travel that path. If the mirror is moving wrt the ether frame, then you could assemble things so that the laser spot and mirror size were the same, or use an aperture to get the same effect. Under your scenario, the beams would be aligned in the interferometer frame, and the light would hit the mirror. But in the ether frame, the mirror would move and the light would miss. You can't have the light hit in one frame and miss in the other - either something happens or it doesn't. If it happens in one frame, it happens in all frames.

[swansont]

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What ever the MM results are there is the ever oresent ambiguities inherent in the results. Thje first is the cinsistent finding of the 8km/sec absolute motion (MM and Miller confirmed) together with the imposed error assumed by virtually all reviewers of the MM resuls (Miller included). Th error is the assumption that the orthogonal reflection on the moving mirror "dragez the beam along with the moving interferometer thus creating an extended path length for the reflected beam.

Until these questi8ons are fullt answered there is little valyue in using MM to prove one thing or another, or to impose any assumptions regarding SR and classical physics,
I have been reluctantly discussing these issues, with little ,if any, direct response. We can discuss the matters of MM all week long, but we are fancifying the progress of the discussions by our speculations.

Did Miller use some other equation for his experiments, or did he use the "incorrect" MM interferometer equation? What is the correct equation, according to you?

[geistkiesel]

swansont said:

Did Miller use some other equation for his experiments, or did he use the "incorrect" MM interferometer equation? What is the correct equation, according to you?

Miller used the incorrect equation. the correct equation will have the light reflected back up the trajectory of the down photon. The photon has traveled a total of 30 meters (miller's interferometer) in 30/3x10⁸ seconds, or 10^-7 sec. Assuming the earth frame moving at 30,000 m/sec the frame will have moved 30 x 10³ x 10^-7 = 3mm, if my arithmatic is correct.
The beams will be moving parallel to each other just before arriving at the scintillation screen. As Ching-Chuan Su has found that the Sagnac effect excludes influence of the orbital motion of the earth I(using global GPS data), the 3 mm is large by a factor of approxinmately 100. This places the expected offset of motion in the micron range and due exclusively to rotational motion of the earth.

[swansont]

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Miller used the incorrect equation. the correct equation will have the light reflected back up the trajectory of the down photon. The photon has traveled a total of 30 meters (miller's interferometer) in 30/3x10⁸ seconds, or 10^-7 sec. Assuming the earth frame moving at 30,000 m/sec the frame will have moved 30 x 10³ x 10^-7 = 3mm, if my arithmatic is correct.
The beams will be moving parallel to each other just before arriving at the scintillation screen. As Ching-Chuan Su has found that the Sagnac effect excludes influence of the orbital motion of the earth I(using global GPS data), the 3 mm is large by a factor of approxinmately 100. This places the expected offset of motion in the micron range and due exclusively to rotational motion of the earth.

If Miller used the wrong equation, how can you quote his results as being valid?

AFAIK GPS doesn't exclude the orbital Saganac due to nonexistence, it ignores it because it's small - 365 times smaller than the rotational Sagnac because the Sagnac effect depends on angular speed, not linear speed, and so it it excludes itself - the largest the rotational term can be is ~ 200 ns. But the MM interferometer does depend on linear speed, so it is a gross misapplication of results for you to apply the terms of one experiment to a completely different one.

It seems that your thesis is that there should be deflection of the perpendicular beam but not a speed correction. The example I gave before, with the fiber coupling, contradicts that argument. Are you going to continue to ignore this?