Absolute rotation
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physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
, the concept of absolute rotation— rotation independent of any external reference—is a topic of debate about relativity,
cosmology Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe. The term ''cosmology'' was first used in English in 1656 in Thomas Blount's ''Glossographia'', and in 1731 taken up in Latin by German philosopher ...
, and the nature of
physical law Scientific laws or laws of science are statements, based on repeated experiments or observations, that describe or predict a range of natural phenomena. The term ''law'' has diverse usage in many cases (approximate, accurate, broad, or narrow) ...
s. For the concept of absolute rotation to be scientifically meaningful, it must be measurable. In other words, can an observer distinguish between the rotation of an observed object and their own rotation? Newton suggested two experiments to resolve this problem. One is the effects of
centrifugal force In Newtonian mechanics, the centrifugal force is an inertial force (also called a "fictitious" or "pseudo" force) that appears to act on all objects when viewed in a rotating frame of reference. It is directed away from an axis which is parall ...
upon the shape of the surface of water rotating in a
bucket A bucket is typically a watertight, vertical cylinder or truncated cone or square, with an open top and a flat bottom, attached to a semicircular carrying handle called the ''bail''. A bucket is usually an open-top container. In contrast, a ...
, equivalent to the phenomenon of
rotational gravity Artificial gravity is the creation of an inertial force that mimics the effects of a gravitational force, usually by rotation. Artificial gravity, or rotational gravity, is thus the appearance of a centrifugal force in a rotating frame of r ...
used in proposals for human spaceflight. The second is the effect of centrifugal force upon the tension in a string joining two spheres rotating about their center of mass.


Classical mechanics


Newton's bucket argument

Newton suggested the shape of the surface of the water indicates the presence or absence of absolute rotation relative to
absolute space Absolute may refer to: Companies * Absolute Entertainment, a video game publisher * Absolute Radio, (formerly Virgin Radio), independent national radio station in the UK * Absolute Software Corporation, specializes in security and data risk manage ...
: rotating water has a curved surface, still water has a flat surface. Because rotating water has a concave surface, if the surface you see is concave, and the water does not seem to you to be rotating, then ''you'' are rotating with the water. Centrifugal force is needed to explain the concavity of the water in a co-rotating frame of reference (one that rotates with the water) because the water appears stationary in this frame, and so should have a flat surface. Thus, observers looking at the stationary water need the centrifugal force to explain why the water surface is concave and not flat. The centrifugal force pushes the water toward the sides of the bucket, where it piles up deeper and deeper, Pile-up is arrested when any further climb costs as much work against gravity as is the energy gained from the centrifugal force, which is greater at larger radius. If you need a centrifugal force to explain what you see, then you are rotating. Newton's conclusion was that rotation is absolute. Other thinkers suggest that pure logic implies only relative rotation makes sense. For example,
Bishop Berkeley George Berkeley (; 12 March 168514 January 1753) – known as Bishop Berkeley (Bishop of Cloyne of the Anglican Church of Ireland) – was an Anglo-Irish philosopher whose primary achievement was the advancement of a theory he called "immateri ...
and Ernst Mach (among others) suggested that it is relative rotation with respect to the fixed stars that matters, and rotation of the fixed stars relative to an object has the same effect as rotation of the object with respect to the fixed stars. Newton's arguments do not settle this issue; his arguments may be viewed, however, as establishing centrifugal force as a basis for an
operational definition An operational definition specifies concrete, replicable procedures designed to represent a construct. In the words of American psychologist S.S. Stevens (1935), "An operation is the performance which we execute in order to make known a concept." F ...
of what we actually mean by absolute rotation. Rather than justifying a causal link between rotation and centrifugal effects, Newton's arguments may be viewed as ''defining'' "absolute rotation" by stating a ''procedure'' for its detection and measurement involving centrifugal force. See


Rotating spheres

Newton also proposed another experiment to measure one's rate of rotation: using the tension in a cord joining two spheres rotating about their center of mass. Non-zero tension in the string indicates rotation of the spheres, whether or not the observer thinks they are rotating. This experiment is simpler than the bucket experiment in principle, because it need not involve gravity. Beyond a simple "yes or no" answer to rotation, one may actually calculate one's rotation. To do that, one takes one's measured rate of rotation of the spheres and computes the tension appropriate to this observed rate. This calculated tension then is compared to the measured tension. If the two agree, one is in a stationary (non-rotating) frame. If the two do ''not'' agree, to obtain agreement, one must include a centrifugal force in the tension calculation; for example, if the spheres appear to be stationary, but the tension is non-zero, the entire tension is due to centrifugal force. From the necessary centrifugal force, one can determine one's speed of rotation; for example, if the calculated tension is greater than measured, one is rotating in the sense opposite to the spheres, and the larger the discrepancy the faster this rotation. The tension in the wire is the required centripetal force to sustain the rotation. What is experienced by the physically rotating observer is the centripetal force and the physical effect arising from his own inertia. The effect arising from inertia is referred to as reactive centrifugal force. Whether or not the effects from inertia are attributed to a fictitious centrifugal force is a matter of choice.


Rotating elastic sphere

In a similar fashion, if we did not know the Earth rotates about its axis, we could infer this rotation from the centrifugal force needed to account for the bulging observed at its equator. In his ''Principia'', Newton proposed the shape of the rotating Earth was that of a homogeneous ellipsoid formed by an equilibrium between the gravitational force holding it together and the centrifugal force pulling it apart. This effect is more easily seen with the planet Saturn which has a radius 8.5 to 9.5 times that of Earth but has a rotational period of only 10.57 hours. The ratios of Saturn's diameters is approximately 11 to 10.
Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a " natural philosopher"), widely recognised as one of the grea ...
explained this in his ''
Principia Mathematica The ''Principia Mathematica'' (often abbreviated ''PM'') is a three-volume work on the foundations of mathematics written by mathematician–philosophers Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913. ...
'' (1687) in which he outlined his theory and calculations on the shape of the Earth. Newton theorized correctly that the Earth was not precisely a sphere but had an oblate ellipsoidal shape, slightly flattened at the poles due to the
centrifugal force In Newtonian mechanics, the centrifugal force is an inertial force (also called a "fictitious" or "pseudo" force) that appears to act on all objects when viewed in a rotating frame of reference. It is directed away from an axis which is parall ...
of its rotation. Since the surface of the Earth is closer to its center at the poles than at the equator, gravity is stronger there. Using geometric calculations, he gave a concrete argument as to the hypothetical ellipsoid shape of the Earth. A modern measurement of the Earth's oblateness leads to an equatorial radius of 6378.14 km and a polar radius of 6356.77 km, about 0.1% less oblate than Newton's estimate. This error is the difference in the estimated ratio of diameters. However, a more demanding measure of oblateness is the ''
flattening Flattening is a measure of the compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution ( spheroid) respectively. Other terms used are ellipticity, or oblateness. The usual notation for flattening i ...
'', defined as ''f = (a−b)/a'' where ''a'' and ''b'' are the semimajor and semiminor axes. Using the cited numbers, the flattening of Newton's prediction differs by 23% from that of modern estimates.
A theoretical determination of the precise extent of oblateness in response to a centrifugal force requires an understanding of the make-up of the planet, not only today but during its formation. In 1672
Jean Richer Jean Richer (1630–1696) was a French astronomer and assistant (''élève astronome'') at the French Academy of Sciences, under the direction of Giovanni Domenico Cassini. Between 1671 and 1673 he performed experiments and carried out celestial ...
found the first evidence that gravity was not constant over the Earth (as it would be if the Earth were a sphere); he took a
pendulum clock A pendulum clock is a clock that uses a pendulum, a swinging weight, as its timekeeping element. The advantage of a pendulum for timekeeping is that it is a harmonic oscillator: It swings back and forth in a precise time interval dependent on i ...
to Cayenne,
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and found that it lost minutes per day compared to its rate at Paris. This indicated the acceleration of gravity was less at Cayenne than at Paris. Pendulum gravimeters began to be taken on voyages to remote parts of the world, and it was slowly discovered that gravity increases smoothly with increasing latitude, gravitational acceleration being about 0.5% greater at the poles than at the equator. It was only in 1743 that
Alexis Clairaut Alexis Claude Clairaut (; 13 May 1713 – 17 May 1765) was a French mathematician, astronomer, and geophysicist. He was a prominent Newtonian whose work helped to establish the validity of the principles and results that Sir Isaac Newton had ou ...
, in ''Théorie de la figure de la terre'', was able to show that Newton's theory that the Earth was ellipsoidal was correct. Clairaut showed how Newton's equations were incorrect, and did not prove an ellipsoid shape to the Earth. However, he corrected problems with the theory, that in effect would prove Newton's theory correct. Clairaut believed that Newton had reasons for choosing the shape that he did, but he did not support it in '' Principia.'' Clairaut's article did not provide a valid equation to back up his argument as well. This created much controversy in the scientific community.


Special relativity

French physicist
Georges Sagnac Georges Sagnac (14 October 1869 – 26 February 1928) was a French physicist who lent his name to the Sagnac effect, a phenomenon which is at the basis of interferometers and ring laser gyroscopes developed since the 1970s. Life and work Sagna ...
in 1913 conducted an experiment that was similar to the
Michelson–Morley experiment The Michelson–Morley experiment was an attempt to detect the existence of the luminiferous aether, a supposed medium permeating space that was thought to be the carrier of light waves. The experiment was performed between April and July 188 ...
, which was intended to observe the effects of rotation. Sagnac set up this experiment to prove the existence of the
luminiferous aether Luminiferous aether or ether ("luminiferous", meaning "light-bearing") was the postulated medium for the propagation of light. It was invoked to explain the ability of the apparently wave-based light to propagate through empty space (a vacuum), so ...
that Einstein's 1905
theory of special relativity In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates: # The laws ...
had discarded. The Sagnac experiment and later similar experiments showed that a stationary object on the surface of the Earth will rotate once every rotation of the Earth when using stars as a stationary reference point. Rotation was thus concluded to be absolute rather than relative.


General relativity

Mach's principle In theoretical physics, particularly in discussions of gravitation theories, Mach's principle (or Mach's conjecture) is the name given by Einstein to an imprecise hypothesis often credited to the physicist and philosopher Ernst Mach. The hypothe ...
is the name given by Einstein to a hypothesis often credited to the
physicist A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate cau ...
and philosopher Ernst Mach. The idea is that the local motion of a
rotating reference frame A rotating frame of reference is a special case of a non-inertial reference frame that is rotating relative to an inertial reference frame. An everyday example of a rotating reference frame is the surface of the Earth. (This article considers onl ...
is determined by the large-scale distribution of matter in the universe. Mach's principle says that there is a physical law that relates the motion of the distant stars to the local inertial frame. If you see all the stars whirling around you, Mach suggests that there is some physical law which would make it so you would feel a
centrifugal force In Newtonian mechanics, the centrifugal force is an inertial force (also called a "fictitious" or "pseudo" force) that appears to act on all objects when viewed in a rotating frame of reference. It is directed away from an axis which is parall ...
. The principle is often stated in vague ways, like "
mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different eleme ...
out there influences
inertia Inertia is the idea that an object will continue its current motion until some force causes its speed or direction to change. The term is properly understood as shorthand for "the principle of inertia" as described by Newton in his first law ...
here". The example considered by Einstein was the rotating elastic sphere. Like a rotating planet bulging at the equator, a rotating sphere deforms into an oblate (squashed)
spheroid A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters. A spheroid has ...
depending on its rotation. In classical mechanics, an explanation of this deformation requires external causes in a frame of reference in which the spheroid is not rotating, and these external causes may be taken as "absolute rotation" in classical physics and special relativity. In
general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
, no external causes are invoked. The rotation is relative to the local
geodesics In geometry, a geodesic () is a curve representing in some sense the shortest path ( arc) between two points in a surface, or more generally in a Riemannian manifold. The term also has meaning in any differentiable manifold with a connection. ...
, and since the local geodesics eventually channel information from the distant stars, there appears to be absolute rotation relative to these stars.


See also

* Absolute time and space *
Mach's principle In theoretical physics, particularly in discussions of gravitation theories, Mach's principle (or Mach's conjecture) is the name given by Einstein to an imprecise hypothesis often credited to the physicist and philosopher Ernst Mach. The hypothe ...
*
Foucault pendulum The Foucault pendulum or Foucault's pendulum is a simple device named after French physicist Léon Foucault, conceived as an experiment to demonstrate the Earth's rotation. A long and heavy pendulum suspended from the high roof above a circular ...


References

{{DEFAULTSORT:Absolute Rotation Force Rotation Theory of relativity