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


New Member
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:

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:

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.


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.


Active Member
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

Staff member
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.


Active Member
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

Staff member
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.
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Z.W. Wolf

Senior Member
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.

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.)

-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.

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.

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Mick West

Staff member
Phil Plait has an interesting article on this topic and makes the point that Earthquakes affect the rotation of the Earth.

Z.W. Wolf

Senior Member


Active Member
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.


Active Member
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?
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.


Active Member
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.


Active Member
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:
Page 50 f.:
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:
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.)


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