Is the Universe Rotating? Evidence, Tests & Limits
Table of Contents
Can we tell whether the universe is rotating?
If you believe wholeheartedly in Mach’s principle, there is no way to test empirically for the rotation of the universe as a whole, since there would be nothing else for it to rotate relative to. General relativity (GR), however, is not very Machian: GR provides several local, observable tests that an observer inside a sealed laboratory could use to detect rotation. For example, an observer can check the motion of a gyroscope or measure whether the Sagnac effect vanishes.
Mach’s principle, alternative theories, and Brans–Dicke
There are alternative theories of gravity that are more Machian than GR. Brans and Dicke proposed one such theory (Brans & Dicke 1961), and in theories of that type there may be no meaningful sense in which the universe could rotate. However, solar-system tests (Bertotti et al. 2003) strongly constrain deviations from GR of the Brans–Dicke type, so observationally the universe appears as non-Machian as GR predicts.
Rotating cosmologies and the Gödel metric
Within GR it is possible to construct cosmological solutions in which the universe is rotating. Historically, one of the earliest exact solutions of Einstein’s field equations exhibiting global rotation is the Gödel metric; it rotates and contains closed timelike curves. If the universe rotated like Gödel’s example, the rotation rate would be expressed as an angular velocity, not as angular momentum. Angular velocity is what gyroscopes and the Sagnac effect measure, and GR lacks a general, unambiguous definition of angular momentum for arbitrary cosmological spacetimes.
Rotation without a center
A rotating universe need not have a center of rotation and can be homogeneous. Observers at different locations could each identify a preferred axis (for example, a direction on the celestial sphere) and describe rotation about that axis. Those lines of sight would be parallel, and there would be no coordinate-independent way to single out one as the unique center of rotation.
How to test for cosmic rotation locally: gyroscopes and the solar system
In principle the most direct test is to compare a local gyroscope’s orientation with the distant galaxies. If a gyroscope precesses at angular velocity −ω relative to the distant matter, then the universe is rotating at angular velocity ω. In practice, we currently lack mechanical gyroscopes with sufficiently small random and systematic errors to place very tight limits on ω.
Instead, we can 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 rotation (Clemence 1957). That bound is roughly an order of magnitude too weak to rule out extreme rotating solutions such as Gödel’s on that basis alone.
Cosmic microwave background (CMB) limits
A rotating universe would imprint a preferred axis and a characteristic anisotropy pattern on the cosmic microwave background. CMB-based searches for a preferred direction therefore provide tighter, though model-dependent, limits on cosmic rotation. Published limits range from order 10−9 rad/yr (Su & Chu 2009) down to order 10−15 rad/yr in some analyses (Barrow, Juszkiewicz & Sonoda 1985), depending on the model assumptions and data used.
Conclusion
All current observations are consistent with zero global rotation, so rotation does not play a prominent role in modern cosmology. Centrifugal effects are negligible for cosmological expansion and are irrelevant for ordinary everyday sensations (for example, how you feel after a hangover).
References
- Brans, C. & Dicke, R. H., “Mach’s principle and a relativistic theory of gravitation,” Phys. Rev. 124 (1961) 925. http://loyno.edu/~brans/ST-history/
- Bertotti, B., Iess, L. & Tortora, P., “A test of general relativity using radio links with the Cassini spacecraft,” Nature 425 (2003) 374.
- Clemence, G. M., “Astronomical time,” Rev. Mod. Phys. Vol. 29 (1957) 2.
- Collins, C. B. & Hawking, S. W., “The rotation and distortion of the universe,” Mon. Not. R. Astr. Soc. 162 (1973) 307.
- Hawking, S. W., “On the rotation of the universe,” Mon. Not. R. Astr. Soc. 142 (1969) 529.
- Barrow, J. D., Juszkiewicz, R. & Sonoda, D. H., “Universal rotation: how large can it be?,” Mon. Not. R. Astr. Soc. 213 (1985) 917. http://adsabs.harvard.edu/full/1985MNRAS.213..917B
- Su, S.-F. & Chu, M.-C., “Is the universe rotating?,” 2009. http://arxiv.org/abs/0902.4575
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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.