Yes, but what you need here is at least one theory compatible with Airy, Sagnac, Michelson&Morley, and Michelson&Gale.

That's wrong. E.g. the Michelson&Gale experiment falsifies Special Relativity by falsifying the postulate that the speed of light does not depend on the movement of the observer.

Relativity is at least one theory compatible with those experiments. I know there's some misinformation and out there about Michelson-Gale-Pearson, but MGP is relatively  easily explained with Lorentz transforms, so it's compatible with SR. The MGP paper itself says MGP is compatible with SR or with a stationary ether.

No. The reason is: Airy, Sagnac, Michelson&Morley, and Michelson&Gale. These experiments together falsify all Copernicanism and confirm what every child sees before it is fooled at school.

Sungenis has a co-author of his "Galileo was wrong" books who is an academic physicist. What do you find curious?

OK. What about a rock and the moon. Is the view that the rock accelerates toward the moon equally valid as the view that the moon accelerates toward the rock ? Why or why not? Is there something "Copernican" about that?
I'm asking you about Popov's papers. Look carefully at the formulas for potentials. First, to make this work one of them has to have a different form than the others. That means the same rules don't apply everywhere. You'll probably say that's OK.
But second - and this is what jumped out for me -  one of the formulas includes the mass of the sun squared. How do you interpret that one?

But whatever they wrote there, fact is, that the second postulate of Special Relativity states that the speed of light c is a constant. Now if the speed of light c indeed was a constant, Michelson et al. would have measured a zero displacement in fringes, indicating that both light beams had travelled at one and the same speed c.

But if the loop is rotating, the Lorentz transform is different for light going in different directions, and the difference gives the fringe pattern.

See also: https://www.mathpages.com/rr/s2-07/2-07.htm
"This analysis is perfectly valid in both the classical and the relativistic contexts."

Mass of the sun yes, but not squared.

If Newton's formula has the mass of the sun, then Popov's too: Popov "postulates the existence of vector and scalar potentials caused by the simultaneous motion of the masses in the Universe, including the distant stars." These potentials are designed to produce forces which make the objects move in the same way Newton saw them. Nothing to worry about the mass of the sun.

Look at equation 4.5 in "Newton-Machian analysis of Neo-tychonian model of planetary motions".
https://arxiv.org/abs/1301.6045

I know that these relativists are magicians who will write meters of text to fool you.

This magician uses terms c - v and c + v for the light in his formula and then says "This analysis is perfectly valid in both the classical and the relativistic contexts." Well, sorry, it isnt. The second postulate of Special Relativity says that the speed of light is constant c. Terms c - v or c + v contradict Special Relativity as soon as v has a non-zero value, which is the case in the experiment.

The math works with Lorentz transforms.

You have referred to https://www.mathpages.com/rr/ before, for aberration at least.
Lengthy quote from https://www.mathpages.com/rr/s2-07/2-07.htm

... For realistic values of v (i.e., very small compared with c), the phase difference reduces to the well-known result  4Aw/c2. It's worth noting that nothing in this derivation is unique to special relativity, because the Sagnac effect is a purely "classical" effect. The apparatus is set up as a differential device, so the relativistic effects apply equally in both directions, and hence the higher-order corrections of special relativity cancel out of the phase difference.

Despite the ease and clarity with which special relativity accounts for the Sagnac effect, one occasionally sees claims that this effect entails a conflict with the principles of special relativity. The usual claim is that the Sagnac effect somehow falsifies the invariance of light speed with respect to all inertial coordinate systems. Of course, it does no such thing, as is obvious from the fact that the simple description of an arbitrary Sagnac device given above is based on isotropic light speed with respect to one particular system of inertial coordinates, and all other inertial coordinate systems are related to this one by Lorentz transformations, which are defined as the transformations that preserve light speed. Hence no description of a Sagnac device in terms of any system of inertial coordinates can possibly entail non-isotropic light speed, nor can any such description yield physically observable results different from those derived above (which are known to agree with experiment).

Nevertheless, it remains a seminal tenet of anti-relativityism (for lack of a better term) that the trivial Sagnac effect somehow "disproves relativity". Those who espouse this view sometimes claim that the expressions "c+v" and "c-v" appearing in the derivation of the phase shift are prima facie proof that the speed of light is not c with respect to some inertial coordinate system. 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-relativityists are undaunted, and merely proceed to construct progressively more convoluted and specious "objections".

Sorry Stanley, but according to Special Relativity there is no object which moves faster than c with respect to whichever inertial system, and light always moves at speed c with respect to whichever inertial system.

And light is still moving at c in the analysis on that page.

Classically speaking, light starts in both directions from the same point. As the loop rotates, light takes longer to get back to the starting point going one way than the opposite.

With Lorentz transforms. the time dilation works in different directions, giving the same result as the classical analysis.

For v = 30 km/s and c = 300,000 km/s, the Lorentz factor (1-(v/c)^2)^.5 = .999999995 or so. So if relativity DID make a difference and you're expecting .5 fringe shifts classically, you might expect .499999998 fringes with relativity. That's the same to more than 8 significant digits. You couldn't visually distinguish classical and relativistic results.

In the Fizeau experiment with water, the difference between classical and relativistic analysis is about a factor of 2. Even somewhat sloppy experimenters can distinguish that.

One does not need any calculations to grasp the situation: Special Relativity was designed to explain the fact that Michelson & Morley experiments yield a null-result while assuming that the earth is orbiting around the sun. As a matter of course, Special Relativity would explain the Sagnac and the Michelson & Gale experiments in the same way, if and only if they'd yield a null-result, too. But they don't. Consequently Special Relativity is falsified by both of them.

But the distances taken by the counter-rotating beams are not the same.

I'm going to use a circular path so I don't have to try typesetting vector integrals.
R is the radius of a circular sagnac device. The speed of light is c.
T is the time it takes for a pulse to return to the starting point.
w is the angular rotation.

But what is T+?  T+ = D+ / c.
So the equation is D+ = 2 pi R + w R D+ / c
Solve that for D+ = 2 pi R / (1 - w R /c).
But w R = v, giving  D+ = 2 pi R / (1 - v /c).
Therefore T+ = D+ / c = 2 pi R / (c - v)
Thus T+ - T- = 2 pi R ( 1/(c-v) - 1/(c+v) )

This is the formula above.

Exactly.

This is of course a classical analysis, not special relativity.

Now you contradict the mathpages-author, who says "This analysis is perfectly valid in both the classical and the relativistic contexts."

Do you now agree, that he is fooling us? That in Special Relativity nothing moves faster than c (not 2c as he says)?

In SR you would need to apply a transform to account for time dilation.

You said so in your last post. But you won't be able to do that in any reasonable sense. In the experiments, we have a single observer. The Lorentz-transform would have to be used to transform events as seen by a different observer, who is moved relative to the first one. But that's of no use here, since the experiment is done with only one observer.

Stanley, could you please ask yourself and then explain to us how Special Relativity can account for a null-result in the Michelson&Morley experiment, and at the same time for a non-null-result in the Michelson&Gale experiment? How could Michelson detect and measure the relative movement of the earth with respect to the skies, but not the relative movement of the earth with respect to the sun?

How could Special Relativity, designed to confirm the null-result in the Michelson&Morley experiment, at the same time confirm the non-null-result in the Michelson&Gale experiment?

So you see the equation is NOT distance/velocity as if the velocity of light was c-v and c+v?
The equation comes about because the end point is moving.
It's a general analysis of Sagnac devices.

In some situations, the observer is moving with respect to the device, sometimes not. But even with SR adjustment the formula is essentially the same, and the numerical results the same to several significant digits. So yes, the analysis is valid in both contexts.

And as far as the statement about 2c, it's not really material to the issue if you recognize that using c+v in the expression is not implying that light is going at c+v.

The terms c - v and c + v express the fact that something is going at c - v with respect to something and that something is going at c + v with respect to something.

In the classical view on the experiment, the two light beams are going at c - v and c + v with respect to the observer, while they're going both at c with respect to the aether.

The formula contradicts Special Relativity, since in Special Relativity both beams would have to go at c with respect to the observer as well as go at c with respect to the imagined reference system of the classical aether. In Special Relativity light beams go at c with respect to any and all objects and reference frames.


The magomatician authoring the article on mathpages.com says:

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 [...]

That's an error, since in Special Relativity you cannot simply write c - v or c + v to denote the speed of light with respect to a given object, where c and v are the speeds of light and of the object with respect to the same inertial system. Rather, you have to use a special Velocity-addition formula (see Wikipedia). Velocities u and v are added using (v + u) / (1 + (vu)/c^2). Here we have u := c and thus the relativistic sums are:

 (v + c) / (1 + (vc)/c^2) = c (v + c) / (c + (vc^2)/c^2) = c (v + c) / (c + v) = c
  (v - c) / (1 - (vc)/c^2) = c (v - c) / (c - (vc^2)/c^2) = c (v - c) / (c - v) = c

The result does not surprise, since in Special Relativity the light beams have to move at c with respect to any objects.

Consequently the equation

 

is correct for the classical case and wrong in the context of Special Relativity, since the used additions of speeds c - v and c + v are classical additions and not relativistic ones. As shown above, relativistically the sum c plus v yields c and the difference c minus v yields c, too. Using relativistic additions, the resulting displacement in fringes Δt is zero, since both beams go at c.

Conclusion: the Sagnac experiment falsifies Special Relativity.




Albert Einstein Zur Elektrodynamik bewegter Körper. In: Annalen der Physik und Chemie, 1905




Sagnac, Georges: L’éther lumineux démontré par l’effet du vent relatif d’éther dans un interféromètre en rotation uniforme. In: Comptes Rendus., 1913

...is correct for the classical case and wrong in the context of Special Relativity, since the used additions of speeds c - v and c + v are classical additions and not relativistic ones. As shown above, relativistically the sum c plus v yields c and the difference c minus v yields c, too. Using relativistic additions, the resulting displacement in fringes Δt is zero, since both beams go at c.

Conclusion: the Sagnac experiment falsifies Special Relativity.

NO. NO. NO.
Look at my derivation in https://www.cathinfo.com/fighting-errors-in-the-modern-world/new-sungenis-film-the-fool-on-the-hill/msg660786/#msg660786
Light moves at speed c.
The time difference arises because the distance taken is different in the opposing directions.
The expressions c+v and c-v come out of expressing the difference in the times due to different distances.
There is nothing SR about that, per se.

But the result doesn't really change if you add in length contraction and time dilation. (Depending on the observer I think in some cases the SR corrections cancel out so that it is exactly the same formula, but let's not get stuck in such details.)

You need to recognize that c+v and c-v are just expressions in the math. They do not need relativistic velocity addition. Until you can get past that there's no point discussing other aspects of MGP.