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In physical cosmology, the Copernican principle, named after Nicolaus Copernicus, is a philosophical assumption that the Earth is not in a central, specially favored position. More recently, the principle has been generalized to the relativistic concept that humans are not privileged observers of the universe. In this sense, it is equivalent to the mediocrity principle, with important implications for the philosophy of science.

Since the 1990s the term has been used (interchangeably with "the Copernicus method") for J. Richard Gott's Bayesian-inference-based prediction of duration of ongoing events, a generalized version of the Doomsday argument.

Recent observations such as "the axis of evil", a signal embedded in the anisotropy of the CMB which is aligned to the ecliptic and the equinoxes, challenge the Copernican Principle.

Origin and implications
Michael Rowan-Robinson emphasizes the importance of the Copernican principle: "It is evident that in the post-Copernican era of human history, no well-informed and rational person can imagine that the Earth occupies a unique position in the universe."

Hermann Bondi named the principle after Copernicus in the mid-20th century, although the principle itself dates back to the 16th-17th century paradigm shift away from the Ptolemaic system, which placed Earth at the center of the Universe. Copernicus demonstrated the motion of the planets can be explained without the assumption that Earth is centrally located and stationary. He argued that the apparent retrograde motion of the planets is an illusion caused by Earth's movement around the Sun, which the Copernican model placed at the centre of the Universe. Copernicus himself was mainly motivated by technical dissatisfaction with the earlier system and not by support for any mediocrity principle. In fact, although the Copernican heliocentric model is often described as "demoting" Earth from its central role it had in the Ptolemaic geocentric model, neither Copernicus nor other 15th- and 16th-century scientists and philosophers viewed it as such.

In cosmology, if one assumes the Copernican principle and observes that the universe appears isotropic from our vantage-point on Earth, then one can prove that the Universe is generally homogeneous (at any given time) and is also isotropic about any given point. These two conditions comprise the cosmological principle.

In practice, astronomers observe that the Universe has heterogeneous structures up to the scale of galactic superclusters, filaments and great voids, but becomes more and more homogeneous and isotropic when observed on larger and larger scales, with little detectable structure on scales of more than about 200 million parsecs. However, on scales comparable to the radius of the observable universe, we see systematic changes with distance from the Earth. For instance, galaxies contain more young stars and are less clustered, and quasars appear more numerous. While this might suggest that the Earth is at the center of the Universe, the Copernican principle requires us to interpret it as evidence for the evolution of the Universe with time: this distant light has taken most of the age of the Universe to reach and shows us the Universe when it was young. The most distant light of all, cosmic microwave background radiation, is isotropic to at least one part in a thousand.

Modern mathematical cosmology is based on the assumption that the Cosmological principle is almost, but not exactly, true on the largest scales. The Copernican principle represents the irreducible philosophical assumption needed to justify this, when combined with the observations. Due to recent measurements of redshift in super novas, faster than light expansion is being implied. This has led some astronomers to consider a prefered directions and local void theories, where earth is considered occupying a space in a local void. These are a non-homogeneous theories, and lead to invalidation of the Copernican Principle.

Bondi and Thomas Gold used the Copernican principle to argue for the perfect cosmological principle which maintains that the universe is also homogeneous in time, and is the basis for the steady-state cosmology. However, this strongly conflicts with the evidence for cosmological evolution mentioned earlier: the Universe has progressed from extremely different conditions at the Big Bang, and will continue to progress toward extremely different conditions, particularly under the rising influence of dark energy, apparently toward the Big Freeze or Big Rip.

Confirmation or Demise?
Measurements of the effects of the cosmic microwave background radiation in the dynamics of distant astrophysical systems in 2000 are claimed to prove the Copernican principle on a cosmological scale. The radiation that pervades the universe was demonstrably warmer at earlier times. Uniform cooling of the cosmic microwave background over billions of years is explainable only if the universe is experiencing a metric expansion.

Anisotropies in the CMB, deconvolved into spherical harmonics in COBE, WMAP, both indicate an axis (aligned with the ecliptic and equinoxes). Recently Planck confirmed that the anistropies are present and were not due to COBE or WMAP measurement errors. The CMB according to the Copernican Principle via the standard model should have no bias towards the earth or any position in space the earth. Planck was launched to confirm or deny the axis, and did in fact confirm its existence. This is a clear questioning of the Copernican Principal.

Ecliptic alignment of cosmic microwave background anisotropy
Results from Wilkinson Microwave Anisotropy Probe (WMAP) appear to run counter to Copernican expectations. The motion of the solar system, and the orientation of the plane of the [ecliptic] are aligned with features of the microwave sky, which on conventional thinking are caused by structure at the edge of the observable universe

Lawrence Krauss is quoted as follows in the referenced Edge.org article:

"But when you look at [the cosmic microwave background] map, you also see that the structure that is observed, is in fact, in a weird way, correlated with the plane of the earth around the sun. Is this Copernicus coming back to haunt us? That's crazy. We're looking out at the whole universe. There's no way there should be a correlation of structure with our motion of the earth around the sun — the plane of the earth around the sun — the ecliptic. That would say we are truly the center of the universe."

It would be somewhat surprising if the WMAP alignments were a complete coincidence, but the anti-Copernican implications suggested by Krauss are far more surprising, now that they are confirmed to be true by Planck. Other possibilities that were considered are (i) that residual instrumental errors in WMAP cause the effect (ii) that unexpected microwave emission from within the solar system is contaminating the maps. The Planck announcement of March 21st, 2013, dashed this last hope for the Copernican Principle, as it has confrmed the WMAP and COBE results[8].

Modern tests
From the PhysicsWorld.org news article "New tests of the Copernican Principle proposed," "Robert Caldwell from Dartmouth College and Albert Stebbins from Fermi National Laboratory in the US explain how the Cosmic Microwave Background (CMB) radiation spectrum — an all pervasive sea of microwave radiation originating just 380 000 years after the Big Bang — could be used to test whether the Copernican Principle stands."

"In a separate paper, Jean-Philippe Uzan from the Pierre and Marie Curie University in France along with Chris Clarkson and George Ellis from the University of Cape Town in South Africa suggest another way to test the Copernican Principle. Their scheme involves measuring the red-shift of galaxies — the shift in wavelength of light to longer wavelengths due to a speedup — very precisely over time to see if there are changes. The team argues that this red-shift data can be combined with measurements of the distance of the galaxies to infer if the universe is spatially homogeneous — which is a tenet of the Copernican Principle."