Copernican principle

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Figure 'M' (for Latin Mundus) from Johannes Kepler's 1617–1621 Epitome Astronomiae Copernicanae, showing the Earth as belonging to just one of any number of similar stars.

 

In physical cosmology, the Copernican principle states that humans, on the Earth or in the Solar System, are not privileged observers of the universe.

Named for Copernican heliocentrism, it is a working assumption that arises from a modified cosmological extension of Copernicus's argument of a moving Earth. In some sense, it is equivalent to the mediocrity principle.

Origin and implications

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 proposed that the motion of the planets can be explained by reference to an assumption that the Sun and not 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, it was successors to Copernicus, notably the 16th century Giordano Bruno, who adopted this new perspective. The Earth's central position had been interpreted as being in the "lowest and filthiest parts". Instead, as Galileo said, the Earth is part of the "dance of the stars" rather than the "sump where the universe's filth and ephemera collect". In the late 20th Century, Carl Sagan asked, "Who are we? We find that we live on an insignificant planet of a humdrum star lost in a galaxy tucked away in some forgotten corner of a universe in which there are far more galaxies than people."

In cosmology, if one assumes the Copernican principle and observes that the universe appears isotropic or the same in all directions from the vantage point of Earth, then one can infer that the universe is generally homogeneous or the same everywhere (at any given time) and is also isotropic about any given point. These two conditions make up the cosmological principle. In practice, astronomers observe that the universe has heterogeneous or non-uniform structures up to the scale of galactic superclusters, filaments and great voids. It 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 Earth. For instance, galaxies contain more young stars and are less clustered, and quasars appear more numerous. While this might suggest that 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 Earth and shows 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. 

Michael Rowan-Robinson emphasizes the Copernican principle as the threshold test for modern thought, asserting that: "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."

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. 

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.

Derived equations

Copernicus was able to derive the lengths of superior and inferior planet's orbits, based on the lengths of their sidereal orbits.

Where for superior planets,

${\displaystyle {\frac {1}{P}}+{\frac {1}{S}}={\frac {1}{E}}}$

with P is the sidereal period of the superior planet, S the synodic period of the planet, and E the period of the planet that measurements are based on, in most cases the Earth.

The Formula for inferior planets is 

${\displaystyle {\frac {1}{P}}-{\frac {1}{S}}={\frac {1}{E}}}$

Tests of the principle

The Copernican principle has never been proven, and in the most general sense cannot be proven, but it is implicit in many modern theories of physics. Cosmological models are often derived with reference to the Cosmological principle, slightly more general than the Copernican principle, and many tests of these models can be considered tests of the Copernican principle.

Historical

Before the term Copernican principle was even coined, Earth was repeatedly shown not to have any special location in the universe. The Copernican Revolution dethroned Earth to just one of many planets orbiting the Sun. Proper motion was mentioned by Halley. William Herschel found that the Solar System is moving through space within our disk-shaped Milky Way galaxy. Edwin Hubble showed that the Milky Way galaxy is just one of many galaxies in the universe. Examination of the galaxy's position and motion in the universe led to the Big Bang theory and the whole of modern cosmology.

Modern tests

Recent and planned tests relevant to the cosmological and Copernican principles include

• time drift of cosmological redshifts;
• modelling the local gravitational potential using reflection of cosmic microwave background (CMB) photons;
• the redshift dependence of the luminosity of supernovae;
• the kinetic Sunyaev-Zel’dovich effect in relation to dark energy;
• cosmic neutrino background;
• the integrated Sachs-Wolfe effect;
• testing the isotropy and homogeneity of the CMB.

Physics without the principle

The standard model of cosmology, the Lambda-CDM model, assumes the Copernican principle and the more general Cosmological principle and observations are largely consistent but there are always unsolved problems. Some cosmologists and theoretical physicists design models lacking the Cosmological or Copernican principles, to constrain the valid values of observational results, to address specific known issues, and to propose tests to distinguish between current models and other possible models. 

A prominent example in this context is the observed accelerating universe and the cosmological constant issue. An alternative proposal to dark energy is that the universe is much more inhomogeneous than currently assumed, and specifically that we are in an extremely large low-density void. To match observations we would have to be very close to the centre of this void, immediately contradicting the Copernican principle.