Is the Universe Rotating? What Physics Tests Reveal
All current astronomical observations are consistent with zero global rotation of the universe. Solar-system data set a model-independent upper limit of roughly 10−7 radians per year on cosmic rotation (Clemence 1957), while cosmic microwave background analyses push that limit far tighter, to as low as 10−15 rad/yr under some model assumptions (Barrow, Juszkiewicz & Sonoda 1985). General relativity (GR) permits rotating cosmological solutions, such as the Gödel metric, but nothing observed supports one.
Table of Contents
Key Takeaways
- Solar-system observations bound global cosmic rotation to about 10−7 radians per year, a limit reported by Clemence in 1957.
- Cosmic microwave background (CMB) studies constrain rotation far more tightly, with limits ranging from around 10−9 rad/yr (Su & Chu, 2009) to around 10−15 rad/yr (Barrow, Juszkiewicz & Sonoda, 1985).
- The Gödel metric, one of the earliest exact solutions to Einstein’s field equations, describes a rotating universe and contains closed timelike curves.
- Solar-system tests reported by Bertotti, Iess & Tortora in 2003 using the Cassini spacecraft strongly constrain Brans-Dicke-type deviations from general relativity.
- A rotating universe would not require a center of rotation, since homogeneous rotation about parallel axes produces no coordinate-independent center.
Can We Tell Whether the Universe Is Rotating?
Mach’s principle holds that motion, including rotation, only has meaning relative to other matter in the universe. If Mach’s principle were strictly true, there would be no way to test empirically whether the universe as a whole is rotating, because there would be nothing external for it to rotate relative to.
General relativity (GR), the theory of gravity developed by Albert Einstein, is not strongly Machian. GR provides several local, observable tests that an observer inside a sealed laboratory could use to detect rotation without reference to anything outside. An observer can check the motion of a gyroscope, a spinning device that resists changes to its orientation, or measure whether the Sagnac effect, an interference pattern that shifts when light travels through a rotating frame, vanishes.
How Do Alternative Theories Like Brans-Dicke Treat Rotation?
Some alternative theories of gravity are more Machian than general relativity. Brans and Dicke proposed one such theory in 1961 (Brans & Dicke, Physical Review 124, 1961, p. 925). In theories of that type, there may be no meaningful sense in which the universe could rotate at all.
Solar-system tests using radio links with the Cassini spacecraft, reported by Bertotti, Iess & Tortora in Nature in 2003, strongly constrain deviations from general relativity of the Brans-Dicke type. Observationally, the universe therefore behaves as non-Machian as general relativity predicts, leaving little room for Brans-Dicke-style rotation.
What Is the Gödel Metric and What Does It Say About Rotation?
Within general relativity, it is possible to construct cosmological solutions in which the universe rotates. One of the earliest exact solutions of Einstein’s field equations exhibiting global rotation is the Gödel metric, and it contains closed timelike curves, paths through spacetime that loop back on themselves in time.
If the universe rotated in the manner of Gödel’s solution, that rotation would be expressed as an angular velocity, a rate of rotation, rather than as angular momentum. Angular velocity is the quantity that gyroscopes and the Sagnac effect actually measure. General relativity lacks a general, unambiguous definition of angular momentum for arbitrary cosmological spacetimes, which is why rotation studies focus on angular velocity instead.
Can a Rotating Universe Exist Without a Center?
A rotating universe need not have a center of rotation and can still be homogeneous, meaning uniform in density and properties throughout. Observers at different locations could each identify a preferred axis, for example a particular direction on the celestial sphere, and describe rotation about that axis.
Those lines of sight would be parallel to one another. There would be no coordinate-independent way to single out any one location as the unique center of rotation.
How Do Gyroscopes and the Solar System Test for Cosmic Rotation?
The most direct test in principle is comparing a local gyroscope’s orientation against the positions of distant galaxies. If a gyroscope precesses at angular velocity −ω relative to distant matter, then the universe is rotating at angular velocity ω. Currently available mechanical gyroscopes do not have sufficiently small random and systematic errors to place very tight limits on ω this way.
Instead, researchers use the entire solar system as a giant gyroscope. Solar-system observations give a model-independent upper limit of about 10−7 radians per year on any global cosmic rotation, a figure reported by Clemence in 1957. That bound is roughly an order of magnitude too weak to rule out extreme rotating solutions such as Gödel’s universe on its own.
What Do Cosmic Microwave Background Observations Show?
A rotating universe would imprint a preferred axis and a characteristic anisotropy pattern on the cosmic microwave background (CMB), the relic radiation left over from the early universe. CMB-based searches for a preferred direction provide tighter, though more model-dependent, limits on cosmic rotation than solar-system tests.
Published limits range from around 10−9 radians per year, reported by Su & Chu in 2009, down to around 10−15 radians per year in some analyses, reported by Barrow, Juszkiewicz & Sonoda in 1985. The wide spread between these figures depends heavily on the model assumptions and datasets used in each study.
Conclusion
All current observations are consistent with zero global rotation of the universe, so rotation does not play a prominent role in modern cosmological models. Centrifugal effects from any hypothetical rotation are negligible for cosmological expansion and have no bearing on ordinary everyday sensations.
Frequently Asked Questions
Could the universe be rotating without our knowledge?
Current observational limits make large-scale rotation extremely unlikely but do not rule it out completely. Solar-system data cap rotation at about 10−7 radians per year, while cosmic microwave background studies push that limit down to as little as 10−15 radians per year under certain models, so any real rotation would have to be exceedingly slow.
What is the Gödel metric?
The Gödel metric is one of the earliest exact solutions to Einstein’s field equations describing a rotating universe. It is notable for containing closed timelike curves, theoretical paths through spacetime that loop back on themselves, raising questions about causality that remain purely theoretical since no such rotation has been observed.
Does a rotating universe need a center point?
No. A rotating universe can be homogeneous, with no unique center of rotation, because observers at different locations can each define their own preferred rotation axis using parallel lines of sight. There is no coordinate-independent way to designate one location as the true center.
How do scientists measure cosmic rotation?
Scientists compare the orientation of gyroscopes, or the solar system treated as a giant gyroscope, against the positions of distant galaxies. They also search the cosmic microwave background for a preferred axis and anisotropy pattern that a rotating universe would be expected to imprint.
Why does Mach’s principle matter for this question?
Mach’s principle proposes that rotation only has meaning relative to other matter in the universe. If it were strictly true, there would be no way to test whether the universe as a whole rotates, since nothing would exist outside it to rotate relative to. General relativity does not fully follow this principle, which is why local tests for rotation are possible at all.
What limits does the Cassini spacecraft place on alternative gravity theories?
Radio link measurements from the Cassini spacecraft, reported by Bertotti, Iess & Tortora in Nature in 2003, strongly constrain deviations from general relativity of the Brans-Dicke type. These solar-system tests show that gravity in our solar system behaves very close to standard general relativity’s predictions.
This article was authored by several Physics Forums members with PhDs in physics or mathematics.
“Does rotation of four dimensional space result in hyperbolic expansion of three dimensional sub-space with increasing time?”
There can’t be any invariant answer to this, because there is no preferred way to split up spacetime into “space” and “time”, so there is no invariant definition of “three-dimensional sub-space”.
Does rotation of four dimensional space result in hyperbolic expansion of three dimensional sub-space with increasing time?
The Cosmic Background Radiation experiment (COBE 2006) data indicated that overall rotation of the universe was zero, which was within the limits of accuracy of the instrument.In 1949, Kurt Gödel proved the existence of solutions involving closed time-like curves, to Albert Einstein's field equations within the Theory of General Relativity. His solution required a rotating universe, which would allow time travel to the past and caused Einstein to have doubts about his own theory. His solutions are known as the Gödel metric. Hollywood time travel stories are very popular 'Star Trek IV' etc. However, time traveller's from the future are either very discrete or choose to come to our period (I don't blame them!). Or the universe does not rotate significantly, as indicated by COBE.