Need Debunking: Foucault's Pendulum debunked through Mach's principle (the Earth is a static object in the center of the Universe)

[Pumpernickel]

Hello, I'm a first-time poster, so I hope I'll get everything right.

This claim is the result of an ongoing discussion with one of my family members that propose the Earth is stationary in space. Countering the argument, I presented the Foucault's Pendulum and the Coriolis effect as the best examples of evidence that the Earth is in motion around the Sun.

They have responded by saying these two pieces of evidence have been debunked by something called Mach's principle that in fact proved the opposite, and went on to say that General Relativity justified static Earth since Einstein incorporated Mach's Principle into General Relativity.

I asked for clarification and scientific backing of this idea, they brought up the 1821 article "On the Effect of Distant Rotating Masses in Einstein's Theory of Gravitation" by Hans Thirring:
https://www.geocentricity.com/bibastron/research/translations/thirring/thirring.pdf

With the article, they also provided a quote from a book by Charles Misner, Kip Thorne and John Wheeler "Gravitation". The quote supposedly is a citation of Albert Einstein acknowledging that Foulcault's Pendulum does not prove an Earth in motion: https://bit.ly/2JReksc

If one rotates the shell relative to the fixed stars about an axis going through its center, a Coriolis force arises in the interior of the shell, that is, the plane of a Foucault pendulum is dragged around.

.

Since I've never heard of Mach's Principle and never heard of any scientific findings disproving that the mentioned pendulum experiment and the Coriolis effect as evidence of an Earth in motion, I was of course extremely skeptical. When pressed, they proposed the idea of General and Special Relativity not being valid theories and they proclaimed that the idea of the luminiferous ether being a more valid theory. From what I gathered the theory of relativity aether which suggested that the aether did not exist and suggested that it was not needed.

They have gone on to link me a bunch of articles supposedly proving the aether theories and the Earth being a static object in the center of the Universe. I will not post hose articles here right now, since I feel it would be deviating too much from the main claim about the Foucault's Pendulum being debunked.

 

[JohnJones]

Foucault's Pendulum is one example of the Coriolis effect, which is one of the pieces of evidence that suggests that the Earth revolves around its own axis. It does not show that the Earth rotates around the Sun. Another piece of evidence is the fact that we see the stars go round us every 24 hours, which Flat Earthers counter by saying that the Earth is stationary and the stars rotate around us.

Mach's principle is a vaguely-stated hypothesis rather than a law. Mach was considering whether rotation is relative or absolute. Straight-line motion is thought to be relative: if you are moving with a certain velocity relative to me in a straight line, there is no experiment that will tell us whether it's really you or me that's moving. But rotation appears to be different -- if I spin round and round relative to the stars, I get dizzy; if I spin fast enough, my arms will be pulled out to the sides by centrifugal force, and so on. In Newtonian physics, this would be explained by saying that I am spinning with respect to absolute space. But in relativistic physics, there is no absolute frame of reference. So Mach's suggestion is that the frame of reference with respect to which I am rotating is determined by the motion of the large masses in the Universe.

Now we, and Mach, think that most of the mass in the Universe is to be found in the distant stars and galaxies. So the preferred frame of reference is the one in which the distant stars and galaxies are stationary and we rotate, rather than the one in which we are stationary and everything else rotates around us. I don't know if a Flat Earther would agree on this, possibly they would say that the Earth is much more massive than all the stars and galaxies put together.

From our point of view, Mach's principle is consistent with Foucault's experiment: the pendulum is on a frame rotating with respect to the distant stars, so it experiences Coriolis force and its plane of oscillation is displaced relative to the frame.

The 1921 [not 1821] article by Hans Thirring asks, "Is Einstein's Theory of General Relativity Consistent with Mach's Principle?" In this article, he imagines the Earth to be surrounded by a large rotating shell of matter, and solves Einstein's equations to show that objects on the Earth would experience a Coriolis force due to this rotating shell. So General Relativity is consistent with Mach's principle.

So Thirring's result, which is generally accepted as correct, says that according to General Relativity, Foucault's result is consistent with a rotating Earth, but is also consistent with a universe in which everything revolves around us.

So I would have to say that your family member is correct: the results of Foucault's experiment do not allow us to conclude that we are on a rotating Earth surrounded by stationary stars, they are also consistent with a stationary Earth around which all the stars rotate every 24 hours. Because the latter interpretation would require the stars to move faster than light, most physicists go with the former.

Having got this far, it's puzzling that your family member would then go on to say that General Relativity was invalid, since he's just used it as a critical part of his argument. But perhaps that's a topic for another post.

 

[Mendel]

The assignment of a moving Earth is at first one of convenience.
Historically, it stems from explaining the planetary motions as elliptical orbits focused on the sun, which makes them easy to understand.

Rotating Earth is suggested by the proposition that all of the stars move in approximate lockstep, but with great care we can see an indvidual parallax, so they're not affixed to a dome. We also see a precession of the axis of rotation, which we explain by Earth tumbling; I would expect the axis of a dome to be fixed in place.

The Earth's spin is also measured by the gyroscopic compass aboard every commercial seagoing vessel. It finds North after being turned on without the aid of a magnet, just from the physics of the spin. I have seen a series of believable youtube videos where an indivudual crafted a gyrocompass at home. While less immediately obvious that the pendulum, the gyrocompass has the advantage of daily use over a century on thousands of ships.

Now there are three ways this measured forces of spin can be explained:
a) easy: the Earth spins
b) hard: the universe spins (where is the heavy shell, how heavy is it, and how fast does it spin?) and induces a coriolis force via gravity
c) impossible: Earth stands still, gravity does not exist, and there is no physical explanation for the spin

a) Allows us to predict spin-based phenomena such as laser gyroscopes (fun fact: since a few decades ago, every airplane has been able to determine its latitude and orientation from a solid-state device that does not incorporate a magnet).
b) would allow it if we were willing to do unnecessarily complex calculations that deliver results distinguishable from method a) only when applied on astronomic scales
c) is no use to engineering whatsoever, but supports a belief in stationary Earth

a) and b) are compatible with each other, since a) can simply be considered a slightly less accurate version of b). Since a) and b) share a common cosmology and the same prediction on how the pendulum behaves, you can hardly say that one debunks the other. But even if it were so, we still lack evidence for c).

The interesting question here is, why does your family member defend the notion that Earth is stationary? Which need is fulfilled by this belief? And can this need be fulfilled in another way that is compatible with this specific belief changing? If you undestand and then address the force that clamps them to this belief, it becomes easier to get them to reconsider.

 

[Mick West]

So I would have to say that your family member is correct: the results of Foucault's experiment do not allow us to conclude that we are on a rotating Earth surrounded by stationary stars, they are also consistent with a stationary Earth around which all the stars rotate every 24 hours. Because the latter interpretation would require the stars to move faster than light, most physicists go with the former.

I think the last part bears emphasis. With relativity, SOME of the physics for things could work in any given frame of reference. For example, maybe my head is fixed in space. When I feel like I turn it, the rest of my body and the entire universe perhaps actually turns around my head. But for this to actually work would require a considerable amount of magic.

Now if I had the only apparent head in the universe then I might forgive myself this assumption (or at least the equivocation) but there's billions of other heads. Why would the universe revolve around mine?

Likewise, there are lots of other planets - several of which we can observe directly, a few of which we've sent robots too. We can do the math here and see the nice elliptical orbits of the planets around the sun, and the rotation of those planets around their axes, and we see that they are just like the Earth, that our planet (like my head) is nothing special.

Geocentrism is understandable when all you know is what you see around you and the stars and planets are just lights in the sky. But when you actually get the wider view, when I see other people turning their heads, or we see other planets moving as they do, then there's no support of it at all beyond an appeal to magic.

 

[Mendel]

Likewise, there are lots of other planets - several of which we can observe directly, a few of which we've sent robots too. We can do the math here and see the nice elliptical orbits of the planets around the sun, and the rotation of those planets around their axes, and we see that they are just like the Earth, that our planet (like my head) is nothing special.

I missed this when I read it the first time, so maybe it bears emphasizing. And this goes back to Galileo observing Jupiter and Venus through the telescope. Jupiter having moons strongly suggested a degree of similarity to Earth, and Jupiter could clearly be seen spinning. All of the planets do, and even the sun does it, as the sun spots attest.

The question turns to why Earth should be the only ball in the solar system that does not spin, when all available evidence does not contradict the notion that it does? Because even relativity theory doesn't require that.
Thirring's work shows that any spot in the universe could be considered stationary, if I understand him correctly? There's as much physical reason to assume Jupiter is stationary and unspinning as there is that we are. The belief that it is we who stand still can't come from proper observation of the outside world. It might be worth investigating where it does come from.

 

[Mick West]

Because the latter interpretation would require the stars to move faster than light

Not only stars, if all the planets are orbiting the sun once every 24 hours, then anything with an orbital radius over 2.6 billion miles would be traveling faster than the speed of light. So Uranus, Neptune, and Pluto.

This effort in trying to violently shoehorn contradictory observations into a belief reminds me of the Flat Earth, where ultimately (if they are being honest) they would have to accept that either the world is round, or it flat and the entirety of reality is distorted in a magical and inexplicable way so that it just looks round.

 

[Mendel]

[the world is] flat and the entirety of reality is distorted in a magical and inexplicable way so that it just looks round.

... and then some accuse everybody else of being brainwashed ;-)

 

[Z.W. Wolf]

The discovery of stellar aberration in 1727 by James Bradley was the decisive evidence for heliocentrism and the moving Earth.

There were steps between the Ptolemaic model and the modern heliocentric model.

-The Copernican heliocentric model placed all 5 known planets in circular orbits around the sun while retaining epicycles and deferents. [Still quite flawed.]
-The rival Tychonic system placed the earth at the center, with the sun and moon orbiting the earth and all 5 known planets orbiting the sun. The inferior planets were in small orbits that never circled the earth and the superior planets were in large orbits that did circle the earth but were not orbiting the earth. Retrograde motion was explained with no need for epicycles and deferents. Interesting.

Both retained the celestial sphere model.

Wikipedia

The Copernican explanation for the lack of parallax was that the stars were such a great distance from Earth that Earth's orbit was almost insignificant by comparison. However, Tycho noted that this explanation introduced another problem: Stars as seen by the naked eye appear small, but of some size, with more prominent stars such as Vega appearing larger than lesser stars such as Polaris, which in turn appear larger than many others. Tycho had determined that a typical star measured approximately a minute of arc in size, with more prominent ones being two or three times as large.

Astronomers in Tycho's time were doing naked eye observation, they didn't fully grasp atmospheric effects, or know much about optics of the human eye or optics in general. They swore they could see stars with shapes and sizes. (Many people still do and will draw stars confused as UFO's with complicated shapes.)

Tycho used basic geometry to show that, assuming a small parallax that just escaped detection, the distance to the stars in the Copernican system would have to be 700 times greater than the distance from the sun to Saturn. Moreover, the only way the stars could be so distant and still appear the sizes they do in the sky would be if even average stars were gigantic—at least as big as the orbit of the Earth, and of course vastly larger than the sun. (As a matter of fact, most stars visible to the naked eye are giants, supergiants, or large, bright main-sequence stars.) And, Tycho said, the more prominent stars would have to be even larger still. And what if the parallax was even smaller than anyone thought, so the stars were yet more distant? Then they would all have to be even larger still.[11] Tycho said

Deduce these things geometrically if you like, and you will see how many absurdities (not to mention others) accompany this assumption [of the motion of the earth] by inference.[12]

Copernicans offered a religious response to Tycho's geometry: titanic, distant stars might seem unreasonable, but they were not, for the Creator could make his creations that large if he wanted.[13] In fact, Rothmann responded to this argument of Tycho's by saying

[W]hat is so absurd about [an average star] having size equal to the whole [orbit of the Earth]? What of this is contrary to divine will, or is impossible by divine Nature, or is inadmissible by infinite Nature? These things must be entirely demonstrated by you, if you will wish to infer from here anything of the absurd. These things that vulgar sorts see as absurd at first glance are not easily charged with absurdity, for in fact divine Sapience and Majesty is far greater than they understand. Grant the vastness of the Universe and the sizes of the stars to be as great as you like—these will still bear no proportion to the infinite Creator. It reckons that the greater the king, so much greater and larger the palace befitting his majesty. So how great a palace do you reckon is fitting to GOD?

-Kepler refined the Copernican system with his first and second laws of planetary motion:The Law of Ellipses and The Equal-Areas Law.

The Tychonic system hung on for awhile in the 17th century but faded. I don't think there were many astronomers who believed in it much past 1650.

In the late 17th century, a number of physical astronomy theories drawing from Kepler's work—notably those of Giovanni Alfonso Borelli and Robert Hooke—began to incorporate attractive forces (though not the quasi-spiritual motive species postulated by Kepler) and the Cartesian concept of inertia.[87] This culminated in Isaac Newton's Principia Mathematica (1687), in which Newton derived Kepler's laws of planetary motion from a force-based theory of universal gravitation.[88]

By then the Tychonic system was a quaint footnote. Did anyone still find it relevant? I don't know. The last nail (if it was needed) wasn't the measurement of parallax in 1838. It was the discovery of stellar aberration in 1727 by James Bradley while he was searching for evidence of stellar parallax. By that time mainstream astronomy assumed parallax would someday be found with better instruments.


Source: https://youtu.be/N3RXa0GLeHI?t=485

 

[Mick West]

Phil Plait has an interesting article on this topic and makes the point that Earthquakes affect the rotation of the Earth.
https://www.discovermagazine.com/the-sciences/geocentrism-seriously#.UVEn7leiBpd

Geocentrists have to assume that all local phenomena are caused by cosmic motion. For example, the Coriolis effect, which makes hurricanes spin different ways in the northern and southern hemispheres, is relatively easy to explain if you assume a spheroidal rotating Earth. For a Geocentrist, you have to assume that the Universe itself is revolving around us, and affecting the weather here. Again, the math works out, but it's standing a pyramid on its tip: you have it precisely backwards. And with one poke the whole thing falls over.

We also know earthquakes can affect the rotation of the Earth. That makes sense since they shift the mass around on the surface, and that changes how the Earth spins. To a Geocentrist, though, that earthquake affects the entire Universe.

 

[Z.W. Wolf]

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

The Sagnac effect, also called Sagnac interference, named after French physicist Georges Sagnac, is a phenomenon encountered in interferometry that is elicited by rotation. The Sagnac effect manifests itself in a setup called a ring interferometer. A beam of light is split and the two beams are made to follow the same path but in opposite directions. On return to the point of entry the two light beams are allowed to exit the ring and undergo interference. The relative phases of the two exiting beams, and thus the position of the interference fringes, are shifted according to the angular velocity of the apparatus. In other words, when the interferometer is at rest with respect to a nonrotating frame, the light takes the same amount of time to traverse the ring in either direction. However, when the interferometer system is spun, one beam of light has a longer path to travel than the other in order to complete one circuit of the mechanical frame, and so takes longer, resulting in a phase difference between the two beams. This arrangement is also called a Sagnac interferometer. Georges Sagnac set up this experiment to prove the existence of the aether that Einstein's theory of special relativity had discarded.[1][2]

A gimbal mounted mechanical gyroscope remains pointing in the same direction after spinning up, and thus can be used as a rotational reference for an inertial navigation system. With the development of so-called laser gyroscopes and fiber optic gyroscopes based on the Sagnac effect, the bulky mechanical gyroscope is replaced by one having no moving parts in many modern inertial navigation systems. The principles behind the two devices are different, however. A conventional gyroscope relies on the principle of conservation of angular momentum whereas the sensitivity of the ring interferometer to rotation arises from the invariance of the speed of light for all inertial frames of reference.

Source: https://youtu.be/SrGgxAK9Z5A

 

[Mendel]

Rothmann responded to this argument of Tycho's by saying

[W]hat is so absurd about [an average star] having size equal to the whole [orbit of the Earth]? What of this is contrary to divine will, or is impossible by divine Nature, or is inadmissible by infinite Nature? These things must be entirely demonstrated by you, if you will wish to infer from here anything of the absurd. These things that vulgar sorts see as absurd at first glance are not easily charged with absurdity, for in fact divine Sapience and Majesty is far greater than they understand. Grant the vastness of the Universe and the sizes of the stars to be as great as you like—these will still bear no proportion to the infinite Creator. It reckons that the greater the king, so much greater and larger the palace befitting his majesty. So how great a palace do you reckon is fitting to GOD?

This is the perfect response to argument from incredulity. When another FEer claims that Earth can't possibly travel through space at humongous speeds in 3 directions at once, I'll just copy this.

 

[DavidB66]

Coincidentally, I've been thinking about writing a post (or several posts) about the question: are the Ptolemaic (geocentric) and Copernican (heliocentric) systems of the universe equally valid, in view of General Relativity? Short answer: no. Long answer: maybe later.

Einstein and other eminent authorities can be quoted in favour of the answer 'yes', but none of them discuss the issue in any detail, and I think the quotes are best taken as just a colourful way of expressing Mach's Principle.

Mach's Principle itself raises several issues:
a. what does it mean?
b. does General Relativity require it?
and
c. is it true?

On (a), numerous different interpretations of the Principle have been given, but for the present purpose I think the essential claim is that the effects of inertial motion of an object, such as the Coriolis and Eotvos Effects, are entirely due to the relative motion of the object with respect to the mass of other objects in the universe, including the distant galaxies. If this is true, then in principle one could not distinguish between the earth rotating relative to the rest of the universe, and the rest of the universe rotating relative to the earth.

On (b), I think the general consensus is that General Relativity is consistent with the Principle, but does not require it. There are solutions of the GR field equations in which it would be false.

On (c), I think it is an open question.

But either way, it can hardly be quoted in support of the geocentric (or flat earth) doctrine that the earth is static. The earth shows numerous physical phenomena (including Foucault's Pendulum) which are inconsistent with the traditional geocentric doctrine (or Tycho's hybrid theory). Either the earth is mobile, or the distinction between static and mobile, relative to the universe as a whole, is meaningless.

 

[DavidB66]

To add to my previous comment, there is a relevant discussion by Stephen Hawking in a somewhat obscure and unexpected place. The logician Kurt Gödel (incidentally a close friend of Einstein at Princeton) wrote a few papers on General Relativity. These are included in the OUP collected edition of Gödel's works, with an introductory note by Hawking. To quote the most relevant passage:

The possible rotation of the universe has a special significance in general relativity because one of the influences that led Einstein to the theory in 1915 was Mach's principle. The exact formulation of the principle is rather obscure, but it is generally interpreted as denying the existence of absolute space. In other words, matter has inertia only relative to other matter in the universe. The principle is generally taken to imply that the local inertial frame defined by gyroscopes should be non-rotating with respect to the frame defined by distant galaxies.
Gödel showed that it was possible to have solutions of the Einstein field equations in which the galaxies were rotating with respect to the local inertial frame. He therefore demonstrated that general relativity does not incorporate Mach's principle. Whether or not this is an argument against general relativity depends on your philosophical viewpoint, but most physicists nowadays would not accept Mach's Principle, because they feel that it makes an untenable distinction between the geometry of space-time, which represents the gravitational and inertial field, and other forms of fields and matter.

Source: Kurt Gödel: Collected Works, Volume II, Publications 1938-1974, ed. Solomon Feferman et al, Oxford University Press, 1990, page189.
Presumably Hawking's note was written around 1990. So far as I know there is no online source.

Incidentally, Gödel was not the first to question the connection between Mach's principle and GR. Already around 1920 de Sitter had shown that a solution exists in which a particle has inertia in otherwise empty space. Einstein himself fluctuated in his commitment to Mach's principle, and by the end of his life he remarked that 'As a matter of fact, one should no longer speak of Mach's principle at all'. The subject remains controversial. See the citations and discussion in the standard biography of Einstein by Abraham Pais: Subtle is the Lord: the Science and the Life of Albert Einstein, 1982, pp. 285-88.

 

[Mendel]

I asked for clarification and scientific backing of this idea, they brought up the 1821 article "On the Effect of Distant Rotating Masses in Einstein's Theory of Gravitation" by Hans Thirring:
https://www.geocentricity.com/bibastron/research/translations/thirring/thirring.pdf

Page 50 f.:

The third equation yields the surprising result that the centrifugal force possesses an axial component. [..]
The fact that in nature we only have been able to observe a radial, but never an axial component of the centrifugal force can be brought into agreement with the results obtained here by noting that the approximation of the heaven of fixed stars by means of an infinitesimally thin hollow sphere is certainly not physical. But [even] when we want to improve our approximation (possibly by means of mass distribution,) the method of approximation used here will never obtain a field that is completely equivalent to a real centrifugal field.

This means that, yes, the Mach effect can produce a centrifugal force, but it also produces another force that we don't see on Earth, and no, that's not what happens in reality. The Mach effect does not explain reality as we know it if we assume a stationary Earth.


I'd like to comment on the words that I italicized. The original German reads:
https://fedora.phaidra.univie.ac.at/fedora/get/o:137122/bdef:Book/view#

Daß wir in der Natur bloß eine radiale, aber nie eine axiale Komponente der Zentrifugalkraft kennengelernt haben, ließe sich mit den hier gefundenen Resultaten nun etwa dadurch in Einklang bringen, dass wir sagen: Die Approximation des Fixsternhimmels durch eine unendlich dünner Hohlkugel ist eben einen unrichtige. Aber selbst wenn wir unsere Approximation (etwa durch eine räumliche Massenverteilung) verbessern wollten, erhielten wir bei der hier verwendeten Integrationsmethode niemals ein Feld, das dem wirklichen Zentrifugalfelde vollkommen äquivalent ist.

The english "not physical" is the German "unrichtig", which simply means "incorrect" or "false".
The second use of "approximation" in "method of approximation" is "Integrationsmethode" in German. While the former suggests that somehow the approximation is not accurate enough, the true intention is to say that this kind of mathematical analysis must result in this axial force. The English translation reflects that by calling the "hollow shell" approximation not just incorrect, but "not physical": there can be no physical model of it (even if you tweak the mass distribution) that results in that force not being present.

(Thirring then continues his analysis by assuming that the body inside the hollow shell also rotates, and there are a huge number of fixed stars outside the hollow shell that are at rest, and at that point we have firmly left flat Earth cosmology behind.)

 

[AmberRobot]

So, if the rest of the Universe spins around the Earth, making it seem like the Earth has a rotation rate, I guess it would just have to be simply coincidence that anomalies in the Earth's rotation rate can be correlated with large earthquakes.

 

[Hevach]

There's an interesting hole in relativity: Absent some accepted "stationary" frame of reference (like the ground you're standing on or the planet you're orbiting) you can't technically be certain whether the bullet is rushing towards you or you are rushing towards the bullet. And because no frame of reference is truly stationary, even with it you can't be sure that you and the planet aren't *both* rushing towards the bullet.

All of the universe (not just the objects but the space itself, which would also mean objects in it would not be moving faster than light because) pivoting around the Earth would look exactly like Earth spinning in its place within it.

You can apply occam's razor, though. When we look in space, we see a lot of spheroid objects, and what do they all do? The sun spins in place. All the major and minor planets spin in their orbits. It's not easy to measure, but we've proven that other stars spin. We've even shown that black holes spin.

That frame of reference hole in relativity means that, strictly speaking, yes, the universe might be swiveling around one of these objects as it sits stationary and we can never tell the difference. But we also can't tell *which* one it's swiveling around. It might be Earth, but it's just as likely to be the Sun or Mars or Hovering Squid World 97A.

When it comes to things that science can't see and which don't actually matter anyway, science doesn't really care.

 

[Mauro]

There's an interesting hole in relativity: Absent some accepted "stationary" frame of reference (like the ground you're standing on or the planet you're orbiting) you can't technically be certain whether the bullet is rushing towards you or you are rushing towards the bullet. And because no frame of reference is truly stationary, even with it you can't be sure that you and the planet aren't *both* rushing towards the bullet.

All of the universe (not just the objects but the space itself, which would also mean objects in it would not be moving faster than light because) pivoting around the Earth would look exactly like Earth spinning in its place within it.

You can apply occam's razor, though. When we look in space, we see a lot of spheroid objects, and what do they all do? The sun spins in place. All the major and minor planets spin in their orbits. It's not easy to measure, but we've proven that other stars spin. We've even shown that black holes spin.

That frame of reference hole in relativity means that, strictly speaking, yes, the universe might be swiveling around one of these objects as it sits stationary and we can never tell the difference. But we also can't tell *which* one it's swiveling around. It might be Earth, but it's just as likely to be the Sun or Mars or Hovering Squid World 97A.

When it comes to things that science can't see and which don't actually matter anyway, science doesn't really care.

I find it hard to understand why the absence of an absolute frame of reference should be a 'hole' in special relativity. It's been since Galileo's time that we know there is no such thing as an absolute frame of reference, as anybody who ever boarded a train can easily tell. What Einstein did was to extend this basic concept to the (experimentally verified) fact that the speed of light is constant in any frame of reference. Then, with general relativity, he extended this concept further, assuming that an uniformly accelerating frame of reference is undistinguishable from a gravitational field.
And this has no bearing on a rotating body: it's a totally different beast from a frame of reference moving at a costant speed (vs. some other frame of reference) of even from an uniformly accelerating one, because a rotating body is not accelerating uniformly, its acceleration varies continuosly, not necessarily in magnitude but surely in direction. This give rise to effects, such as Coriolis 'force', which are not present with rectilinear motion (accelerating or not).