Dear Ziaedin Shafiei,

Your problem has been encountered by anyone trying to understand

the meaning of Einstein's relativity theory, in general due to

unclear or even mistaken formulations in early papers and even

textbooks. In particular Lorentz contraction is an issue: is this

contraction real or only apparent?

In order to be able to answer this question you should carefully

consider what Einstein actually did in 1905. He did define `time'

in such a way that the speed of light is the same for each observer

(he had to do so in order to be able to encompass the Maxwell equations

in his newly to be developed theory, c being in this theory a

scalar property of the medium in which light propagates). For this

reason he calibrated clocks in such a way that this condition is

satisfied. It turned out that this requirement is fulfilled

precisely if the Lorentz transformations are fulfilled.

You should now be aware that this definition of `time' is only

fulfilled on the basis of a certain calibration procedure of

clocks. You could use other calibration procedures (for instance

Newton's one). But then you would be unable to use Maxwell's

classical theory of electromagnetism, which seems to be

unattractive.

Using Einstein's procedure you, hence, should be aware that `time'

is not some abstract property but just something corresponding to

the `pointers of clocks that have been calibrated/synchronized in a

particular manner'. This counts as well for measuring rods, the

calibration of these being chosen such that distances can be

defined on the basis of the distance a light signal advances in a

certain time. Hence, `position', like `time', is defined by the

choice of a certain measurement procedure.

The upshot of this is that SRT describes so-called events (x,t),

for instance light flashes occurring at the position of a digit on

a certain measuring rod and at the time indicated by a stationary

clock being at that position. Confusion is lurking when you try to

attribute to SRT more meaning (like e.g. Lorentz contraction) than

just this. SRT does not tell you anything about the physical

behaviour of measuring rods (such rods not even existing for

measuring cosmic distances).

The null result of the MMX indicates that the time taken for light to traverse one arm of the instrument is the same as the time taken to traverse the other arm. The fact that the result remains null regardless of the rotation and orbital motion of the Earth then imposes a certain constraint on physical models of the propagation of light.

A simple Galilean aether, which was what Michelson and Morley were anticipating of course, is incompatible with that result (although it could match at one particular time of day and time of year if the lab happened to be at rest in the aether at that moment).

Special relativity complies with that constraint, as can a suitably constructed Lorentzian Aether theory. Both of those models include length contraction although the manner in which they explain it is significantly different. Your question then becomes whether any alternative theory could be constructed which would meet the constraint required by the experiment but not include length contraction. I don't believe any is known but it's hard to prove a negative so it would appear the possibility could exist.

TDM: A null result can only prove something if the entire physical context of an experiment is known.

The same is true of positive results of course. The aim of any good experimenter is to ensure that the environment is sufficiently well understood  that unknown effects on the results are well characterised. Michelson and Morley were proficient experimenters in that sense and their results, refined over many years, have with stood a great deal of scrutiny.

Many thanks Thierry and George

TDM  “How could a null result like the Michelson & Morley experiment (MMX) possibly prove anything?”

Any experiment validates some ideas and invalidates some ideas. M&M experiment is not an exception. It showed, within a moving platform, time intervals for round trips of light at two equal perpendicular paths are equal. We should then see what ideas are validated by this experiment and what ideas can be rejected.  

What I have tried to show is that the experiment rejects the idea of length contraction. Those who tried to put forward this idea in the first place ignored the movement of the half-silver mirror in their analysis of the experiment, which is not allowed in science.

I put section three in the article to show why length contraction is necessary in special relativity if:

1.      The constancy of the speed of light is accepted

2.      Moving-source only affects the direction of light

The prime application of these two ideas is the light clock which is the hinge pin of SR.

Clearly, M&M consists of two perpendicular light clocks. The null result thus similarly rejects time dilation and constancy of the speed of light in SR.

TDM “Conclusion: neither MMX, nor special relativity … is proven at all.

MMX is an experiment and does not need proving. It might be argued that it was not done in the intended conditions, say vacuum, and thus be rejected as a reliable experiment. But SR is a theory that needs proving. I have not said SR can be proven or rejected. I simply said M&M experiment does not validate length contraction, time dilation and constancy of the speed of light.

TDM: That is true, but a positive result gives information, null doesn't in this case.

You seem to be confusing an experiment that fails to give a result with one that gives an accurate result which happens to be zero. The null result gives precisely as much information as a positive (or negative) number. The nonsense in your claim is obvious when we phrase the question as follows:

• If the propagation time for one arm is t, what is the propagation time for the other arm?

The answer is t ± Δt so the MMX then gives a positive result.

TDM: A positive result would in that case at least give a physical information.

A positive result in this case would tell us the anisotropy in the propagation times, the null result tells us that there is none. What matters is the accuracy of the determination. Michelson and Morley and later Morley and Miller improved that over the years to give a result with an uncertainty of better than 4km/s.

TDM: By example, a propagation of light in a medium at zero speed at the Earth's surface gives the same null result.

Similarly a constant positive result could arise from a partially dragged aether so again the fact that the result is a null is irrelevant.

A dragged aether is ruled out by other experiments, what we learn from the MMX is specifically that the propagation times are equal.

Sorry Ziaedin, I haven't had time to read your paper yet but the normal analysis does take account of the motion of the mirror so I'm not sure where you've gone wrong.

You really need to start learning some basics Thierry.

The zero result of the MMX Experiment only shows that all kinds of effects related to the propagation of light are isotropic. Any specific conclusions related to separate effects like length contraction, time dilatation, and speed of light in vacuum or in any media are not supported.

They are supported but not proven Wolfgang, that is the subtle difference.

Statements about properties of the combination of all effects related to light propagation are supported, but statements about specific effects are not supported. That is the subtle difference. You cannot exclude cancelling out of different specific effects.

Not quite. The statements are supported because the results match what the theory predicts. Each theory may predict a number of individual effects but it is the theory as a whole that is tested. In other words, the effects only exist in combination.

SR says the propagation times should be equal so is supported.

Lorentz-style aether says the propagation times should be equal so is supported.

Basic Galilean aether says the propagation times should be different so is falsified.

WK: You cannot exclude cancelling out of different specific effects.

That depends on the details. The experiments of Michelson and Morley allowed cancellation of some terms so could be explained by length contraction alone or a combination of that with time dilation. The asymmetrical design of Kennedy and Thorndike removed the cancellation and required both effects further constraining compatible theories.

Agreed, in combination with additional information the MMx experiment allows conclusions about specific effects like propagation time dilatation or length contraction. 

Dear Ziaedin Shafiei,

Your problem has been encountered by anyone trying to understand

the meaning of Einstein's relativity theory, in general due to

unclear or even mistaken formulations in early papers and even

textbooks. In particular Lorentz contraction is an issue: is this

contraction real or only apparent?

In order to be able to answer this question you should carefully

consider what Einstein actually did in 1905. He did define `time'

in such a way that the speed of light is the same for each observer

(he had to do so in order to be able to encompass the Maxwell equations

in his newly to be developed theory, c being in this theory a

scalar property of the medium in which light propagates). For this

reason he calibrated clocks in such a way that this condition is

satisfied. It turned out that this requirement is fulfilled

precisely if the Lorentz transformations are fulfilled.

You should now be aware that this definition of `time' is only

fulfilled on the basis of a certain calibration procedure of

clocks. You could use other calibration procedures (for instance

Newton's one). But then you would be unable to use Maxwell's

classical theory of electromagnetism, which seems to be

unattractive.

Using Einstein's procedure you, hence, should be aware that `time'

is not some abstract property but just something corresponding to

the `pointers of clocks that have been calibrated/synchronized in a

particular manner'. This counts as well for measuring rods, the

calibration of these being chosen such that distances can be

defined on the basis of the distance a light signal advances in a

certain time. Hence, `position', like `time', is defined by the

choice of a certain measurement procedure.

The upshot of this is that SRT describes so-called events (x,t),

for instance light flashes occurring at the position of a digit on

a certain measuring rod and at the time indicated by a stationary

clock being at that position. Confusion is lurking when you try to

attribute to SRT more meaning (like e.g. Lorentz contraction) than

just this. SRT does not tell you anything about the physical

behaviour of measuring rods (such rods not even existing for

measuring cosmic distances).

There is no "time dilation" and "length contraction", therefore the ME cannot prove their existence. While, the velocity of light is constant in any frame of reference, and this constancy does not required "time dilation" and "length contraction".

Dear Shukri

As I did not know why you mentioned your first sentence I read your article, The Doppler Effect and the three… which is uploaded in this site.

With all due respect, Eq. 6 in your paper is not a “general solution of the ME with Eq. 5” but it is an incorrect attempt to force all three Ts to be equal with no reason at all. In fact, it has been tried to force the two longitudinal intervals to be equal, as it suits the outcome, Eq 8. This might be the pretext for claiming there is no time dilation, etc as already all three Ts are maintained to be equal.   

Please let me know if I am mistaken and there are reasons for Eq. 6. If it cannot be explained as a short answer I would appreciate it if you could provide me with a paper in which this is proven.

Dear George

I know everyone is busy and might not be able to read the article. That is why I tried to simplify my argument in figures 12 and 13. I also did not repeat the derivation of the equations, which I am sure everyone is familiar with. I very much appreciate it if you have a look and see why I claim the movement of the half-silvered mirror is ignored in length contraction.

Dear Ziaedin, one of many explanations for eq. 6, you can find at Fig. 3a. 

Many thanks Shukri

Fig. 3a does not prove anything. It all depends on the speed of light, c. If the magnitude and direction of light is affected by the speed of its source then you are right. But if magnitude of c is constant, which I think you accept, then this is what special relativity tries to tell us that these three time intervals in Eq. 6 are not equal any more.

Dear Ziaedin, you must care about the velocity of light and relative velocity between light and its source. They are two different things. As wee can see in eq. 6 (but not only) the velocity of source affects the relative velocity, therefore we take different velocity for different directions, while the velocity of light remains c. Not only you, but Einstein and all relativists make the same carelessness about the difference between velocity of light and relative velocity between light and its source.

Dear Shukri

We only accept an argument in science if there is an experiment or evidence for it. So far, the only evidence for your argument is Fig. 3a in your paper. Surely a figure is not an evidence by itself. In fact, the same figure is shown in almost all relativity books. They use it as evidence for special relativity as put forward by Einstein but backing it up with added assumptions, logic and mathematical derivations. Can you please direct me to the detailed proof of your claim?

It should be added that in sec 6 of my article it is written "The experiment in fact suggests that both magnitude and direction of light is affected by the speed of the source similar to the wagon and ball case in classical mechanics." That is, the argument is based on MM experiment. Hence, I do not understand how MME can be combined with your argument "the velocity of light is constant in any frame of reference".

Dear  Ziaedin,

“…problem has been encountered by anyone trying to understand the meaning of Einstein's relativity theory, in general due to unclear or even mistaken formulations in early papers and even textbooks…”

The understanding of the meaning of Einstein's relativity theory relates, first of all, not to some “unclear” formulations in early papers – the formulations are quite clear. And so yet from these formulations, first of all from the postulate that in the objective reality there is no of the absolute Matter’s spacetime and so all in inertial reference frames are totally and completely equivalent, quite clearly   immediately any number of evidently absurd consequences immediately, directly and non-ambiguously follow.

I.e. the result of understanding of this theory, even after an analysis of the first Einstein’s papers is evident: the theory is principally incorrect since Matter’s spacetime must be absolute.

Nonetheless indeed further the Minkowski’s, i.e. recent, version of the SR appeared, where Minkowski postulated, additionally to Einstein’s version, that the Lorentz transformations describe real transformations of the real Matter’s spacetime in different [inertial] reference frames, just so the “fundamental properties of the space/time/spacetime” and the “relativistic effects”, i.e. the “space contraction”, the “time dilation” in whole spacetime, etc., were “discovered”; when, because of that the spacetime is absolute and so fundamentally physically and logically cannot  be transformed, are nothing more then some wrong suggestions that have no relation to the reality. That is a next result of the indeed understanding of the SR.

Including in SR there it is postulated that the contraction of lengths of moving bodies is the result of the space contraction, when this “contracted space” contracts everything inside, including the lengths of the bodies; what seems evidently questionable also – by what mystic ways some reference frame impacts on the spacetime to contract/dilate, etc. the spacetime’s components? And by what mystic way this transformed spacetime impacts on real concrete material objects?

The answer again is: the postulated in the SR “relativistic effects” don’t exist in the reality, however changes of the motions’ spatial [in the 3D space] speeds of concrete bodies at concrete bodies interactions indeed result in that their spatial lengths  differ [i.e. are lesser then] from the lengths that the objects have, if they are at the absolute 3D rest.

At the bodies’ motions nothing, of course, happens with the space/time/spacetime, including there cannot be any “time dilation”, however indeed, the rate of changes of internal states of moving bodies indeed    differ [i.e. is lesser then] from the rates that the objects have if they are at the absolute 3D rest.

For that above the fact of “the constancy of the speed of light” has no relations, the light and the speed of light aren’t, seems quite evidently, some magic phenomena that cause the lengths contractions and slowing down of the internal processes rates of/in the moving bodies; the photons are rather banal particles and practically all what differ photons from any material object that has some non-zero “rest mass” is that they are created by purely spatial impacts/ momentums and so move in the 3D space only, when the having rest mass objects is always move in full 4D sub-spacetime of Matter’s spacetime with 4D speeds. At that all these 4D speed have identical absolute values that are equal to the standard speed of light value; just because of that all having rest mass objects have always non-zero temporal component, their spatial speeds always are lesser then the speed of light, as that Pythagoras prescribes in this case.

Besides the changing of ratios “Vt:Vs”, where Vt, Vs are temporal and spatial components of the 4D speeds above, Vt2+ Vs2=c2, since every particle is some gyroscope it, and every bodies since they consist of the particles, are always oriented in the 4D sub-spacetime relating to their 4D motion directions,  thus the having rest mass bodies rotate in the 4D sub-spacetime after usually spatial interactions/impacts. Just therefore moving bodies really have different spatial 3D projections that are “contracted” comparing with the “own”  bodies’ lengths at the absolute rest.

This effect exists, of course, only at concrete objects motions; when some equivalent of this  effect is the postulated in  the SR as the rotation of the whole Matter’s spacetime . The spacetime fundamentally cannot be rotated by anything, however Matter’s laws are so symmetrical, that the Lorentz transformation work well and, since the Minkowski formalism is nothing more then a correct re-formulation of these transformations, the using of the transformations and the formalism result in  many cases in physical inferences that are well adequate to the reality. However that is true not always.

More, including what is the physical sense of the Lorentz transformations, when and why  the  transformations are adequate to the objective reality; why and in what cases  the measured speed of light value is equal to c, etc. see https://www.researchgate.net/publication/273777630_The_Informational_Conception_and_Basic_Physics , https://www.researchgate.net/publication/317067896_The_notion_speed_and_the_Lorentz_transformations , https://www.researchgate.net/publication/317620440_About_some_conventions_in_mechanics

And, again, don’t attempt rationally to understand what are the “space/length contraction”, the “time dilation”, etc. That simply is impossible, since these [and all other] “relativistic effects” are irrational.

Cheers

Article The Informational Conception and Basic Physics

Working Paper The notion " speed " and the Lorentz transformations

Article About some conventions in mechanics

Dear Sergey

SS “And, again, don’t attempt rationally to understand what are the “space/length contraction”, the “time dilation”, etc. That simply is impossible, since these [and all other] “relativistic effects” are irrational.”

Even if SR is not rational and realistic we need to assess it rationally with the helping hand of experiments. There is no other alternative, whatsoever. I agree that SR initially used thought experiment rather than real experiment and it is in my humble opinion a major weakness but still we must either accept or reject it with real experiment.

What I tried to do in the article is to examine M&M experiment. I tried to say it does not validate length contraction based on examining the movement of the half-silvered mirror in the experiment. I expected that some physicists, like yourself in this forum, to tell me if this analysis is right. If it is right then there is a rational argument against length contraction, etc. If wrong then we should accept it as a possible consequence of M&M experiment.

I am doubtful of my analysis as I have not seen it mentioned before and it is such an obvious issue to be noticed by great scientists such as Lorentz and other physicists later on. So please look at Figures 12 and 13 of my article and let me know if all is fine. I really appreciate your kind favour.

for me there are just two possible tenable positions yet.

One is special relativity, that the speed of light is the same in every inertial frame, ie.

independent of the motion of a reference frame that has a constant velocity. From this one should believe in length contraction. It is tenable due to transformations between frames primed and unprimed. There is no specific medium in space.

The other point of view is that as soon as the light leaves the source, it is in a medium,

which in turn has the property whereby the speed of light must have the value it has and none other. No frame transformation is needed. Length contraction not necessary.

Unfortunately for this last viewpoint I believe there is some evidence for time dilation

and other consequences predicted from SR. However it might be yet possible to assume further properties for the medium so as to at least match the predictive property of SR

Your argument is hopelessly confused, so looking for an explicit error is impossible. On the other hand, one must agree that the MM experiment does not prove Lorentz transformation. As shown by Robertson and Mansouri-Sexl, the MM experiment is compatible with a broad range of other theories. To eliminate them, we should consider

1) experiments contradicting emission theories

2) aberration experiments showing that ether cannot be entrained by the earth

3) The Kennedy-Thorndike experiment showing that the MM effect cannot be explained using lateral dilation

4) The Ives-Stilwell experiment to display time dilation.

With these, and a large number of other experiments, which you might find rewarding to study, SRT has been fairly well established.

Dear F. Leyvraz

Thanks for trying to read my article and I am sorry if you found it confusing.

What I am not clear about though is why looking into the movement of half-silvered mirror is hopelessly confusing to you. Can you please clarify?

Prof Leyvraz said it is your argument that is confused, not the person reading it.

I'll try to get a look soon, I've been far too busy recently. My approach is to work through anything that is valid but stop at the first problem I see, anything thereafter may be dependent on that first problem so clarifying each point before continuing is most efficient.

Dear George  

Thanks for your remark. I think I meant the same. My apologies to Prof Leyvraz if my answer was not written properly.

I simply want to know where my argument is hopelessly confused. I simply have looked at the movement of the half-silver mirror and argued that it does not support length contraction. The argument is summarised in two figures. Figure 12 shows why length contraction was proposed and Figure 13 shows why it is not an acceptable idea.

I appreciate all your advices, and I really mean it, but please note that I have not examined say Ives-Stilwell experiment in the article. I tried to examine only M&M. The existence of other experiments does not mean we are not allowed to re-examine M&M experiment.

ZS: .. please note that I have not examined say Ives-Stilwell experiment in the article. I tried to examine only M&M. The existence of other experiments does not mean we are not allowed to re-examine M&M experiment.

The Ives-Stilwell experiment relates specifically to time dilation. The more general conversation about falsification of theories is based on combining results from many experiments, you are quite right that the analyses of each should be self-consistent, but they can and usually will depend on results from other experiments. Some care is then needed to make sure that arguments don't become circular.

Thanks George,

You are right that all experiments related to one subject should be collectively considered but again if an experiment is not analysed correctly it can lead us to countless misleading ideas. 

Hi Ziaedin,

I finally got the chance to have a brief look at your paper. I've ignored everything up to Fig. 10 for the moment as it is not needed yet.

Figures 10 and 11 are fine, note that the light from the source is moving in the same direction as velocity vector v.

In 12 and 13, you have switched the source and observer so the light from the source is now perpendicular to v. However, as the observer and source can be swapped, that is a minor cosmetic point.

The light path from the source should not bend at the mirror, the path from source to mirror should be slanted and the source moves with the mirror so should appear twice. That is also true if you switch observer and source so is again a minor point, not a problem.

However, in figure 12, your value of LT/2 is wrong, you need to use Pythagoras Theorem to calculate the path length. That is crucial, it will change your equations and in particular the time taken. That may also affect fig 13, I'll leave you to go over the consequences and update both diagrams before I review any more as I said previously. That correction may solve it all.

The attached link shows the standard calculation which should save you some time.

https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment#Observer_resting_in_the_aether

The MM experiment couldn't prove the existence of aether, which is not synomymous with : the MM experiment proved the non existence of aether !

The MM experiment didn't show what Michelson and Morley expected. Then a theory was developped on the basis that aether doesn't exist. This theory was able to explain many phenomena, now we are expecting a new theory which may explain more. I think that the asumption of an existence of aether will come again in the future, despite we can explain many things without it. Anyway, how can the reason accept that matter would not be based on a substance, but only on a geometric transformation of space-time ? Can physic phenomena be based on a geometric locus where only geometric tranformations occur ? Between this model and what it describes, there is still a huge gap to be reduced.

Dear George

Many thanks for your comments.

T0 is defined as the proper time interval in the beginning of section 3 which is the unit of time for a round trip of light from either bottom or top of the mirror, e.g. T0=2L/c. The reason for this is given in Tuning Einstein’s light clock in which the details of calculations are also given.

In the text on the top of Figure 12,  LT is defined as transverse round trips of light but the bottom right figure does not clearly identify it whereas its close-up does.

The end result is correct and ties up with the Wiki page. Following your comments, I will clean up the figures and maybe I should add the detailed calculation in a revised version.

ZS: On the top of Figure 12,  LT is defined as transverse round trips of light but the bottom right figure does not clearly identify it whereas its close-up does.

In figure 11, LT/2 is the distance between the point where the ray passes through the beam splitter and the top mirror, let's call that LM so LM=2LT. There is no transverse length contraction so in figure 12, the distance between the mirror and splitter is still LM but the path length of the light is now given by Pythagoras so (LT/2)2 = LM2 + (vT0/2)2.

Dear George

  (LT/2)2 = LM2 + (vT0/2)2 should be   (LT/2)2 = LM2 + (vTT/2)2

Where TT  is the transverse time interval according to SR. In this formula we should replace

LT/2 = cTT/2

LM = cT0/2

To get  

(cTT/2)2  = (cT0/2)2  +  (vTT/2)2   

(cTT)2  -  (vTT)2   = (cT0)2  

TT2  (c2 - v2 ) = (cT0)2

TT2  = (cT0)2 / (c2 - v2 )

TT  = cT0 / (c2 - v2 )1/2

TT  = T0 / (1 - v2 /c2 )1/2 = T0𝛾

then LT  = c TT = cT0 𝛾

This is written under the green arrow in figure 12. 

dear Ziaedin, if Michelson and Moreley would travel very fast, maybe they become shorter, or thinner; thin asa 2 sheets :))

Dear Paul

You are right and this is a well known issue. Apparently, if even a muon passes earth by, earth involuntarily is flattened and if the muon slows down or stops, earth expands again. In pages 15-19 of Twins Paradox_ZS.pdf, uploaded to https://www.researchgate.net/project/special-relativity, I have briefly discussed this possibility in SR. SR shows, based on Mount Washington Observatory experiment, that this is a real effect and not an illusion such as the shrinking of a jumbo jet flying away from us. Not to mention that we also get smaller and quickly disappear if observed by anyone in the plane.

Dear Ziaedin,

“…if even a muon passes earth by, earth involuntarily is flattened and if the muon slows down or stops, earth expands again…SR shows, based on Mount Washington Observatory experiment, that this is a real effect and not an illusion… this is a real effect and not an illusion such as the shrinking of a jumbo jet flying away from us. Not to mention that we also get smaller and quickly disappear if observed by anyone in the plane.”

- yeah, indeed famous muons, near 100 years already, from the times when they were mu-mesons, in numerous SR publications “confirm the special relativity” “contracting/flattening” the space and “dilating the time” in Matter’s spacetime; “proving” that that are the “real effects” and not an illusions; at that you didn’t point the once more relativistic effect, though: from the SR postulate that there is no the absolute Matter’s spacetime and all inertial reference frames are totally and completely equivalent, then if there are, say, two relatively moving with a speed V frames, then in every frame its observer must believe that (s)he is at rest when the vis-à-vis moves this speed; and both speeds are totally real.

So, for example, when a next muon appears in Earth atmosphere with a near speed of light speed, then, according to theSR, really Earth, Sun, etc., i.e. all Matter as a whole, including humans on Earth start to move with the same [opposite to the muon’s speed] speed; and after the muon in micro/milliseconds disappears, all Matter, including humans, immediately stop its motion. It is evident that at that all Matter makes that with some unbelievable accelerations.

Moreover, since in Earth atmosphere every second seems millions of fast particles are born, which move in 4π different directions, from that follows that every object in Matter is flattened in 4π different directions and its time is simultaneously dilated by millions ways, etc. Again, that are direct, evident and unambiguous consequences from the SR.

All that above is evident absurd, and so all that above indeed isn’t an illusion by at least two reasons: (i)- since that simply don’t exist/don’t happen in the objective reality, and (ii) - because of some illusion appears in some human when (s)he observes something and further erroneously interpretes that something. When till now there weren’t any normal humans who observed even their own “flattening”, that (s)he becomes to age in millions time slower then usually, that it is necessary to have always some safety belts to compensate huge accelerations, etc., etc., etc…

Again, if you indeed want to understand what happens in Matter in the reality – see the SS post and linked in the post papers above in this thread.

Cheers

Dear Thierry,

“…Dear Sergey, it is indeed true that never, ever, an observational evidence has been given that the magnetic field that emanates from a moving electron beam, has a different value, depending on the velocity of the observer…”

I didn’t write about electrodynamics in the post above, when, as to me [and not only], that isn’t so; including

“there is no observational evidence for the alleged Lorentz invariance.”

isn’t so also.

The electrodynamics, and the Lorentz invariance as well, work well in rigidly enough interacted systems, with which observers usually meet in practice. It doesn’t work completely in free systems [and just because of this fact it is possible to observe the bodies motions in the absolute frame that is at rest in the absolute Matter’s space, see https://www.researchgate.net/publication/259463954_Measurement_of_the_absolute_speed_is_possible], but, again, in practice usually all studied interacting objects interacted before experiments a long time enough already, and the systems are “rigid”.

What is indeed written in the SS post above is that the “fundamental relativistic effects”,

i.e. transformations of the Matter’s spacetime that are postulated in the SR/GR /claimed in numerous SR/GR publications as objectively really existent, including in Ziaedin’s famous example, when fast muons, which appear the Earth atmosphere, really “contract the space” and “dilate time”, “confirming so” the SR already near 100 years, are nothing more then some fantastic declarations, which don’t exist in the reality, since they principally cannot exist, as that is evident for anybody who indeed understands what the space/time/spacetime are [the explanations what they are see https://www.researchgate.net/publication/260930711_the_Information_as_Absolute ]. Matter’s spacetime is simply “absolute” [5]4D empty container, and emptiness cannot be “contracted”, “dilated”, “bended”, etc.; and besides these ""effects" from the SR/GR postulate that there is no the absolute Matter’s spacetime any number of evidently absurd consequences follow.

Cheers

Dear Prof Leyvraz

Michelson and Morley experiment supports nothing: that light speed is considered constant is an axiom; as primary notions axioms need no demonstration.

More: wonder how they could measure the speed of light in an empty space, because nobody could ever ignore that: if one puts light into the vacuity, the voidage isn’t empty anymore.

Can anyone tell me does have the special theory of relativity the analytical pathway of explanation of MMX?

Dear Thierry

Please do not mix theory with experiment. Any experiment in this universe is inevitably universal unless you find another universe with another set of rules. Einstein’s correct interpretation of M&M dismissed the theory of ether but due to a simple mistake by some scientists such as FitzGerald and Lorentz length contraction was introduced. I simply tried to show where the mistake is done and challenge the science built on it.

I would like to add what Henri Poincaré said about ether in "La Science et l'hypothèse" :

« Peu nous importe que l'éther existe réellement, c'est l'affaire des métaphysiciens ; l'essentiel pour nous c'est que tout se passe comme s'il existait et que cette hypothèse est commode pour l'explication des phénomènes. Après tout, avons-nous d'autre raison de croire à l'existence des objets matériels ? Ce n'est là aussi qu'une hypothèse commode ; seulement elle ne cessera jamais de l'être, tandis qu'un jour viendra sans doute où l'éther sera rejeté comme inutile. »

We could also mention the intrinsic relative observations and measurements that one condemned to make in physics. By refereing to the principle of relativity, Henri Poincaré will also say that :

« Il semble que cette impossibilité de démontrer le mouvement absolu soit une loi générale de la nature. »

It seems like the question of the existence of an ether will stay an epistmologic question, rather than a question which a physicist could answer by any experience.

Dear Shukri,

“…Can anyone tell me does have the special theory of relativity the analytical pathway of explanation of MMX?…”

- the SR explanation of the MM experiment is known from 1908 year and is as: when some inertial reference frame [Earth is rather good example] moves in the space, then in this frame the space is “contracted” [along the motion’s direction] and the time is “dilated” in whole Matter’s spacetime in accordance with the Lorentz transformations.

However the SR there is no any explanation – how/by what way/means… the frame so impact on the Matter’s spacetime, besides, correspondingly, possible some unknown or even magic forces. Further this “contracted” space, using again some unknown/magic forces, contracts all material objects inside the space, including the MM interferometer’s arm, which is directed along the Earth motion around Sun.

In spite of the magic above, this rather strange explanation is in every textbook with the SR.

In the reality there is no magic, the absolute Matter’s 3D space of Matter’s absolute [5]4D spacetime cannot be and isn’t, of course, contracted depending of a motion of a frame, i.e. of a set of clocks and rules.

However real material bodies, after they are impacted by real forces so that they become to move in the space, indeed become be shorter in the space in accordance with the transformation.

That happens because of the bodies rotate in the (X, cτ) plain of the 4D sun-spacetime [where “τ” is the “coordinate time” of this sub-spacetime]so, that its projection on the motion direction becomes be shorter in the Lorentz factor in accordance with the Pythagoras theorem. Including the arm above does that.

At that the “own” arm’s length remains be the same as it was at rest or when is directed transversely to the motion direction, and at a rotation of the interferometer on 90o, it return in this state.

However when it is directed along the motion, it indeed exists in the space in the contracted state, and, since photons move in the space only, they move on this shortened distance – as that the experiment had shown.

More see at least first 6 pages in https://www.researchgate.net/publication/259463954_Measurement_of_the_absolute_speed_is_possible DOI 10.5281/zenodo.48709

It would be useful to read also https://www.researchgate.net/publication/317620440_About_some_conventions_in_mechanics DOI 10.5281/zenodo.1142628

Cheers

Dear Willem

"... In particular Lorentz contraction is an issue: is this contraction real or only apparent?"

When we realize that Lorentz contraction was based on false analysis then it is neither real nor apparent. It is simply wrong. We can go back to "real" v "apparent" debate only if Lorentz was correct. That is why I asked the question and requested feedback. So far no one has argued that Lorentz was in fact correct and my analysis is false (pages 8 and 9). May I ask if you agree with me on this point?

Dear George D

Many thanks for providing some comments related to Figures 12 and 13 about 7 month ago. I finally managed to make them more clear and also added an appendix to provide the necessary calculations for the same figures. The new version of the article "Michelson and Morley Experiment Does not Validate Length Contraction-ZS-1p2.pdf" is attached to the question.

Dear Shukri

SK “Can anyone tell me does have the special theory of relativity the analytical pathway of explanation of MMX?”

Your above quoted question was asked about three months ago. My question was asked 8 months ago. I am sure you know that coming up with a new theory or explanation for this complex subject is not an easy task at all. That is why there has been no response from the proponent of SR. As you also know, the fact is that everyone is busy and unless this subject is in the list of one’s current obligations it is hard to divert resources to work on this issue.

However, there is one more possibility. There is always resistance towards any idea that tries to change status quo. No one jumps with joy that what was considered to be a ground-breaking science is just an obvious mistake because no one bothered to analyse M&M experiment thoroughly.

That is why some want to put you down or pretend as if nothing important has been said.

That is why the most I expected from the physics community was mere recognition that there might be an issue here, nothing more.

My hope is that everyone now has looked at figures 12 and 13 of my article. The falsehood of length contraction and time dilation cannot be shown any clearer. But, unfortunately, if one does not want to accept an undeniable evidence then how much more one can do.

if so, LT should be a contracting operator versus fixed-point theorem...? good question! I`ll aaalyse that!

In response to a comment in another thread, I'll point out your errors based on your improved diagrams, they make it much easier.

Both figures 12 and 13 are wrong, the correct answer for the top left box is trivially:

xL = v T

where v is the speed of the mirror, T is the time between the light passing through the plane of the splitter on the outbound and return legs, and xL is the distance the splitter moves in that time.

Starting from your definition of LT and LL in figure 11, the indication of LT/2 in both right hand diagrams of figure 12, is wrong, the transverse path length from Pythagoras should be:

LT2 + (xL / 2)2 = (c T / 2)2

For the bottom left the correct equations would be:

L1 = LL / ɣ + xL / 2

L2 = LL / ɣ - xL / 2

and obviously:

c T = L1 + L2 = 2 (LL / ɣ)

Putting those together, you can solve for ɣ. Your Appendix A needs to be revised accordingly.

In section 7, you write "If we accept the constancy of 𝑐 then ..." but you should note that the assumption in the above is only that c is isotropic, that it has the same value in the longitudinal and transverse directions. That follows from Maxwell's Equations where:

c = 1 / √(ϵ0 μ0)

and both ϵ0 and μ0 are the usual scalar constants.

P.S. Note also that Michelson and Morley used monochromatic light for setting up the equipment to ensure LL= LT and then white light for the measurements for best resolution, that will make solving the equations simpler.

[ E & O E ]

Dear George

I responded to your comments last year, made the Figures clearer and pointed out your mistakes and then I did not hear anymore from you. The calculations are not mine. That is why I referred you to Wikipedia to check them, as you might not have access to a book in which these calculations are done such as A.P. French, Special Relativity. You usually tell me to go and read an elementary SR book to understand the issue but I am really surprised that you have not checked these simple calculations in any reference and repeated the same mistakes.

Here is the repeat of my comments:

“T0 is defined as the proper time interval in the beginning of section 3 which is the unit of time for a round trip of light from either bottom or top of the mirror, e.g. T0=2L/c.”

Definition of LT and LL in figure 11 is given in the top of page 8. “the initial longitudinal, LL , and transverse, LT , round trips of light …”. This is due to the fact that going and coming travel lengths are not equal but for transverse leg. Figure 11 also shows speed arrow which means that LT is not completely vertical due to the v. The two part of LL are also not equal due to the same fact. For clarification, the exaggerated movements are depicted in Figure 12 and 13.

The calculation is done in the appendix of the article, Wikipedia and A.P. French, Special Relativity. Please recheck.

Dear Ziaedin,

ZS: ... then I did not hear anymore from you

Yes, RG seems to have stopped giving me notifications on about half the threads I'm following, I don't know why. Sorry I missed your update.

ZS: T0 is defined as the proper time interval

OK, that means it's the coordinate time in figure 11 but not in figures 12 and 13. I was using T as the latter. I'm just going out now so I'll re-examine later.

I looked at the Wikipedia version, I'm sure the explanation by French will be similar.

This section is the equivalent of your diagram 11:

https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment#Observer_comoving_with_the_interferometer

In that frame, the transverse speed is reduced to sqrt(c2 - v2), your value for T0 does not take that into account.

This section is the equivalent of your diagrams 12 and 13:

https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment#Observer_resting_in_the_aether

I've corrected a misleading comment in the Wikipedia description, in this frame, the aether is not moving so the speed is c at all times, it is the path length that is affected, not the speed.

The analysis is slightly different from mine in that it calculates the expected fringe shift while I calculated the length contraction necessary to give none.

If you think there's an error in the Wikipedia version where does it lie?

Dear George

T0 is defined as proper time. It is the time duration for a round trip of light in either arms if the frame is stationary or in SR it is the round trip of the light measured in the apparatus frame. It can be calculated as

T0 = 2L/c

There is no difference between the calculation in the article in comparison to Wiki as shown in the attached figure.

Dear Ziaedin,

ZS: T0 is defined as proper time.

The definition of "proper time" means that it is always exactly zero for light, you're using the term in an unusual manner.

ZS: It is the time duration for a round trip of light in either arms if the frame is stationary ...

What does "frame is stationary" mean, usually we talk of objects being stationary relative to a frame, meaning they are at rest, or we can call one frame the "stationary frame" just to identify it.

I'm not saying you're wrong with any of that, just pointing out that your terms are unusual.

ZS: .. or in SR it is the round trip of the light measured in the apparatus frame. It can be calculated as

T0 = 2L/c

OK, I have no problem with that but the analysis that I gave and in Wikipedia is not for SR, it is for a Galilean aether which is what Michelson and Morley were assuming. If you want to calculate the predicted fringe shift, that's what you need to be using.

In SR, the whole thing is trivial, in the lab frame, the arms are of equal length and the speed of the light is c in any direction so there is obviously no fringe shift. From any other frame, length contraction and the Pythagorean increase in the transverse path cancel the effect of the 1/(c+v)+1/(c-v) factor to give the same result.

I'm not following you yet and you didn't answer my question, where do you see any error in the Wikipedia calculation?

Many thanks George

GD “I'm not following you yet and you didn't answer my question, where do you see any error in the Wikipedia calculation?”

May I answer your last question first to clarify my main point.

So far, I have tried to show the calculations are well known. They are in textbooks for everyone to check and I did not say that they are wrong. In fact, in the first version of the article I did not bother to recreate them. In the current version they are in appendix.

I claim that Lorentz and Fitzgerald proposed the idea of length contraction (LC) only based on their analysis of the movement of light in M&M experiment. After the null result from the experiment, all physicists were mesmerized that there was no expected fringe shift when the whole frame was turned by any amount. Therefore, the concentration was on the movement of light. Hence, when LC was proposed to tie up the movement of light with the result of the experiment nobody thought they need to check the idea further. I tried to summarize this analysis in Figure 12.

What I have done is to check if the idea resolves any other movement within the experiment. The obvious candidate is the movement of the half-silvered-mirror (HSM). Unfortunately, we realize that the idea of LC does not fix that movement. I tried to summarize this analysis in Figure 13.

In that case, we have an idea which applies to one movement but not the second one. Scientifically, we have no option but to forget that idea.

Please let me know if you agree with me so far. Also let us consider your other questions one by one.

Dear all,

Lenghts of objects don't change because of the propagation of a wave.

A wave does not change time neither.

MME can be predicted by using a wave theory approach based on phase shifts and frequency shifts.

We can predict the null result of MME without any lenght contraction and without any time dilation.

It is very naive to beleive that time can be changed because of a wave.

Voigt changed the variables x and t in the phase of a wave phi=kx+wt in his paper about Doppler's principle in 1887. Unfortunately, Lorentz and followers did two errors: they naively considered that x and t are really changing and they multiplied Voigt's transformation with the gamma factor (they did it from a mathematical perspective, to form a group, not from a physical perspective).

In 2019, we work with k, wave number, and w, angular frequency. That's all.

Best regards

please see here:

https://www.researchgate.net/publication/331320142_Michelson-Morley_experiment_general_Doppler's_principle_Maxwell's_equations_particle_accelerators_and_Mossbauer_experiment

Dear Ziaedin,

GD “I'm not following you yet and you didn't answer my question, where do you see any error in the Wikipedia calculation?”

ZS: May I answer your last question first to clarify my main point.

Good idea.

ZS: So far, I have tried to show the calculations are well known. They are in textbooks for everyone to check and I did not say that they are wrong. In fact, in the first version of the article I did not bother to recreate them. In the current version they are in appendix.

One source of confusion is that the calculations in Wikipedia are for the aether theory that M&M were using while your seem to be for SR so they don't match.

ZS: Hence, when LC was proposed to tie up the movement of light with the result of the experiment nobody thought they need to check the idea further. I tried to summarize this analysis in Figure 12. What I have done is to check if the idea resolves any other movement within the experiment. The obvious candidate is the movement of the half-silvered-mirror (HSM). Unfortunately, we realize that the idea of LC does not fix that movement. I tried to summarize this analysis in Figure 13.

I have several problems with those.

1) The distance moved by the mirror is simply vT but T has to be as measured in the frame of figures 12 and 13. You seem to have used T=T0ɣ where T0 is the time in figure but that is just adding complexity and assumes time dilation when you are only commenting on length contraction. You should work with the times as measured in the frame of figures 12 and 13.

2) The length of the transverse path is not as shown, you've forgotten Pythagoras Theorem. That's the same error Michelson made in his 1881 analysis which was pointed out by Poitier. I suspect that's the real cause of your discrepancy.

3) The fringe shift depends on the travel times, not the lengths so you should calculate and compare the times for the two legs. Calculate TT and TL and you should find they are only equal if the length is reduced to LL/ɣ.

ZS: Please let me know if you agree with me so far. Also let us consider your other questions one by one.

As you can see, there are several points of disagreement. I think these probably summarise or repeat my earlier questions.

Dear Halim,

HB: Lenghts of objects don't change because of the propagation of a wave.

SR says that the length doesn't change at all, it only has different numerical values depending on your choice of coordinate system.

Dear George

• GD “One source of confusion is that the calculations in Wikipedia are for the aether theory that M&M were using while your seem to be for SR so they don't match.”

The fact is that Lorentz transformation equations (LT) are introduced based on Lorentz’s analysis of M&M experiment well before SR. LT were later adopted by SR. In the first part of the article I have tried to show why SR and aether theory ended up using the same mathematics. More on that later after you accept the correctness of the formulas in the article.

• GD “You seem to have used T=T0ɣ where T0 is the time in figure …”

Please refer to the comparison between my results and Wiki in my previous answer. To make my point clearly illustrated I only tried to show the formulas in concise forms. For example, I simply replaced 1/(1-v2/c2) ½ in the Wiki formula with 𝛾 which is well known practice. Also, as I mentioned before, I replaced 2L/c with T0.

• GD “you've forgotten Pythagoras Theorem. That's the same error Michelson made in his 1881 analysis which was pointed out by Poitier. I suspect that's the real cause of your discrepancy.”

The mistake by Michelson was corrected well before M&M experiment and physicists used correct formulas afterwards. Again, please note the formulas in the Figures match the correct version in Wiki.

• GD “The fringe shift depends on the travel times, not the lengths so you should calculate and compare the times for the two legs. Calculate TT and TL and you should find they are only equal if the length is reduced to LL/ɣ.”

In response to the first part, you are right but time and distance can be exchanged in this experiment. For example, one can fine-tune the adjusting/moving mirror in M&M experiment and see fringe shift. Also, Lorentz tried to explain away the null result by length contraction.

Please note TT and TL are in fact calculated but, in the Appendix, they are referred to as Tv. in both cases. Many thanks to pointing out this to me. I will fix this confusing naming in the next version.

To conclude, the calculations are all correct. The only point is that we must consider the movement of the half-silvered-mirror as a check for the idea of length contraction.

Dear Ziaedin,

Your calculation is correct.

Either you consider

1- relative speeds with constant lenghts (in moving frame) or

2- constant spend c with relative lengths (in Ether frame),

the results are the same for t1 and t2.

t1 and t2 are different, but this is not the end of the story. If we calculate the phases of the wave there is no difference.

The same phenomenon exists in Fabry-Perot cavity at resonance. There are time delays between successively transmitted rays, which are due to multiple reflections inside the cavity. But these time delays do not matter at resonance, where all rays are in phase, simply because a sin wave does not have a beginning and does not have a end.

Best regards

Dear George

I uploaded the new version of the article. Many thanks for pointing out the use of different labels in the appendix and the main content.

Dear Halim

Many thanks for reading the article and your comments.

Thanks to George, it is more clear/less confusing now.

Dear Ziaedin,

GD: “The fringe shift depends on the travel times, not the lengths so you should calculate and compare the times for the two legs. Calculate TT and TL and you should find they are only equal if the length is reduced to LL/ɣ.”

ZS: Also, Lorentz tried to explain away the null result by length contraction.

That's also the solution in SR but it is missing from your calculations. In the appendix you have two lines:

𝐿AB − 𝑥AB = 𝐿

𝐿BA + 𝑥BA = 𝐿

To take account of length contraction, those should be:

𝐿AB − 𝑥AB = 𝐿 / 𝛾

𝐿BA + 𝑥BA = 𝐿 / 𝛾

You then get:

𝒗 TL = 𝒗 T0 𝛾

which is the same as the transverse calculation.

Dear George

It does not work like that. We cannot have length contraction for only one side of the equation and only one length and do not consider it for all other lengths which are in the direction of movement.

If it is mathematically allowed, then we should apply length contraction to any length which is not perpendicular to the direction of movements. This must also apply to formulas in the transverse case. Of course, the effect depends on the angle. Please try it and see the results.

Dear Ziaedin,

ZS: If it is mathematically allowed, then we should apply length contraction to any length which is not perpendicular to the direction of movements.

That's right, you apply the contraction to the extent in that direction, and it is not just "allowed", it is the hypothesis you are testing so you must apply it. In your diagrams, the longitudinal arm is exactly aligned in the direction of motion so gets the full effect, hence shortens to LL/ɣ, but the transverse arm is exactly perpendicular so is not affected at all and remains LT.

Dear George and James

Suppose we have two lengths A=11 m and B=1 m. Their difference is A-B=C. C is 10 m but it does not matter in what unit this difference is measured. The difference can be in mm, cm or m. However, during mathematical manipulation we are not allowed to change the measurement unit only in one side. The results become strange and incorrect.

Now, if we accept length contraction, suppose this two length are moving at close to the speed of light so that 𝛾=1000. Then if we only multiply the right hand side by 1/𝛾 then we end up with strange results too.

11-1=10/1000=0.01

The correct formula is

(A-B)/ 𝛾=C/ 𝛾 or

A-B=C.

Dear Ziaedin,

What you say is true but there is no subtraction involved. Suppose in figure 11, both arms are 10m, they have been carefully adjusted to be exactly equal. In figures 12 and 13, the transverse arm is not altered, it is still 10m, but the longitudinal arm has the length (10/𝛾)m because it extends in the direction of motion (the transverse arm would be narrower by that factor, the width of the longitudinal arm is unaffected).

The distance moved by the mirror is already calculated in the right frame in figures 12 and 13 so is not subject to contraction. In figure 11, it doesn't move at all.

Dear George

your last comment, if one accepts length contraction, is correct. But your mathematical derivation for the movement of light along the longitudinal arm, in your earlier comments, is not as you tried to divide only one side of the equation by 𝛾. This is not allowed in mathematics.

GD "𝐿AB − 𝑥AB = 𝐿 / 𝛾 and 𝐿BA + 𝑥BA = 𝐿 / 𝛾"

Please check the veracity of the formulas in the article against any text books if you have still any doubt.

Transverse arm is perpendicular to the movement but the movement of light is not, according to both figure 12 and the similar one in Wiki. Actually, I have tried to question this in the beginning of the article. But I should leave it for now.

Dear Ziaedin,

ZS: your last comment, if one accepts length contraction, is correct.

Thank you, keep that in mind.

GD: 𝐿AB − 𝑥AB = 𝐿 / 𝛾 and 𝐿BA + 𝑥BA = 𝐿 / 𝛾

ZS: Please check the veracity of the formulas ..

What I wrote is correct. The value L is the arm length measured in the instrument frame shown in figure 11. Mathematically, you are not allowed to mix numbers from different frames, so the first thing you have to do is convert that length in the instrument frame to the aether frame shown in figures 12 and 13 by dividing by 𝛾, so the length in that frame is L/𝛾. Once you have done that, you can add or subtract the 𝑥 terms because those are already in the aether frame.

ZS: you tried to divide only one side of the equation by 𝛾. This is not allowed in mathematics.

You have to apply the laws of algebra but you apply them to (L/𝛾) which is the length in the frame.

Ziaedin, mixing values from values different frames as you have done here is one of the most common mistakes people make when learning SR, you've slipped up that way and you just need to fix that error.

Mathematically, the Lorentz Transforms are a subset of the Poincaré Group and as such it is mathematically impossible to get a contradiction. Any time one appears, you know you have missed something somewhere.

https://en.wikipedia.org/wiki/Poincar%C3%A9_group

ZS: Transverse arm is perpendicular to the movement but the movement of light is not, ...

Right, but your calculation requires the length of the arm and since that is exactly perpendicular, it is only translating sideways, it isn't shortened at all.

P.S. You attached the graphic from Wikipedia but that is calculating the time difference in the absence of length contraction, that is what Michelson was trying to measure. Your version is looking as consistency with length contraction hence they are different.

Dear George

Am I right to say that you think the formulas for transverse arm are fine but for longitudinal are not? The reason is that 𝐿AB − 𝑥AB = 𝐿 and 𝐿BA + 𝑥BA = 𝐿 are not correct and they should be

𝐿AB − 𝑥AB = 𝐿 / 𝛾 and 𝐿BA + 𝑥BA = 𝐿 / 𝛾.

Dear Ziaedin,

The formulas that you present and which you found in wikipedia are correct.

Tl and Tt are different.

Tt=2L/sqrt(c^2-v^2)=2L/(c sqrt(1-(v/c)^2))=gamma x 2L/c

and

Tl=2Lc/(c^2-v^2)=2L/(c (1-(v/c)^2)) =gamma^2 x 2L/c

I don't understand what is your point.

Best regards

Thanks Halim

George thinks they are not correct for longitudinal arm. I just wanted him to confirm where the errors are made. I am sure he has checked the end result with those in Wiki and maybe a text book but he still is not convinced.

Dear Ziaedin. I have sent to you private message, best regards

Dear Ziaedin,

ZS: Am I right to say that you think the formulas for transverse arm are fine but for longitudinal are not? The reason is that 𝐿AB − 𝑥AB = 𝐿 and 𝐿BA + 𝑥BA = 𝐿 are not correct ...

That is what I am saying, you have not taken length contraction into account at all in those equations.

ZS: ... and they should be 𝐿AB − 𝑥AB = 𝐿 / 𝛾 and 𝐿BA + 𝑥BA = 𝐿 / 𝛾.

Your definitions have been a bit unclear but I think that is correct, or possibly

(𝐿AB / 𝛾) − 𝑥AB = (𝐿 / 𝛾) and (𝐿BA / 𝛾) + 𝑥BA = (𝐿 / 𝛾).

depending on in which frame LAB and LBA are defined. What you mustn't do is divide 𝛾 into the 𝑥 terms.

Dear George

We are talking about the correct analysis of M&M experiment. You cannot say that both of the two below sets of equations are right. How you can mathematically justify it?

𝐿AB − 𝑥AB = 𝐿 / 𝛾 and 𝐿BA + 𝑥BA = 𝐿 / 𝛾

(𝐿AB / 𝛾) − 𝑥AB = (𝐿 / 𝛾) and (𝐿BA / 𝛾) + 𝑥BA = (𝐿 / 𝛾).

Why x term should not be divided by 𝛾? Is it not in the direction of movement?

You have checked that the end result of my calculations is exactly the same as what is written in Wiki. In that case, do you think the result given by Wiki is also wrong?

Dear Ziaedin,

ZS: You cannot say that both of the two below sets of equations are right.

I'm not saying both are right, I'm saying the length of the physical arm is 𝐿 in the instrument frame so becomes (𝐿/𝛾) in the aether frame, what I wasn't sure about was the frame in which you were defining 𝐿AB and 𝐿BA. Looking at your paper again, I think the second version is correct and I misread your diagram the first time.

ZS: Why x term should not be divided by 𝛾? Is it not in the direction of movement?

The rule is that you divide by 𝛾 when you convert a measurement in that direction from one frame to the other. 𝑥 is already measured in the aether frame, you don't change frame so there is no ambiguity about that, you definitely don't divide it.

The bottom line again, is that the equations are part of a group so mathematically MUST be consistent, regardless of any physics. This is just a homework problem for you to figure out where you've gone wrong. I've tried to help you as much as I can, I've pointed out where your error lies but the details depend on the definition of your variables.

Dear George

In that case you also think Wiki and text books are not correct. Can you please confirm.

No, Wikipedia and the text books are correct, they show the Galilean calculation.

You are trying to show the SR calculation and you've got that wrong because you didn't include length contraction. There is no length contraction in the Galilean calculation.

Dear George

You are definitely wrong as my calculations are exactly as Wikipedia and the text books. Please check again. If not convinced I will copy and paste them for you when I have time. In fact I already showed that the end results are the same in one of my past comments.

ZS: .. my calculations are exactly as Wikipedia ..

How often do I have to repeat this, you have copied the equation but the Wikipedia is not calculating the SR prediction, it is calculating the Galilean phase shift that Michelson was expecting.

Wikipedia is correct for the Galilean theory, my calculation is correct for SR, and you have got half of each which creates the apparent conflict.

Dear George

I also did not calculate "the SR prediction". If the results are the same where is the difference?

ZS: I also did not calculate "the SR prediction".

If you were trying to use the Galilean transforms then there should be no gamma factors anywhere and you should get a time difference (hence a difference in the mirror movement) overall because the path lengths differ.

I think you need to decide which theory you are trying to check.

Dear George

There is gamma in Wiki too. I do not think you and I are reading from the same page. Please show me the Wiki calculations which you think is different from mine.

Good point, there is more than one analysis on the page.

The Galilean analysis with no length contraction is specifically this section:

https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment#Observer_resting_in_the_aether

Note that the conclusion is that with Michelson's equipment, there would be a shift of 0.44 fringes.

The same Galilean analysis but in the lab frame is here and gives the same result:

https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment#Observer_comoving_with_the_interferometer

There is no Lorentzian gamma factor in either of the above.

On the other hand, the analysis with length contraction is here:

https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment#Observer_comoving_with_the_interferometer

The gamma factor is included in the set of transforms at the end of that section.

In this case, there is no time difference so the two calculated distances for the movement of the mirror should be the same.

You have elements of both and they are incompatible so it would help if you made it clear which of those you are trying to replicate.

Dear George

GD “There is no Lorentzian gamma factor in either of the above.”

The first formula under Observer resting in aether in Wiki is attached.

The last term is 𝛾2 as I showed it before in my earlier comments.

Sorry George I do not think you are serious in these exchanges and I prefer we stop here.

Dear Ziaedin,

The last term has the same form as 𝛾2 but it comes from the Pythagorean increase in the path length if you look carefully at the diagram. It shouldn't be a surprise as that is how gamma is derived but don't mistake it for the gamma used in SR.

ZS: Sorry George I do not think you are serious in these exchanges and I prefer if we stop here.

You are welcome to do that of course, but I am quite serious, I have been teaching people SR for almost 30 years and you are making a very common mistake. I can try to help you see it or leave you to your own efforts, that's your choice.

The bottom line remains that the Lorentz Transforms are part of the Poincare Group and are therefore mathematically incapable of producing a contradiction such as you suggest.