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According to Mach, Newton's examples simply illustrate relative rotation of spheres and the bulk of the universe. [8] When, accordingly, we say that a body preserves unchanged its direction and velocity in space, our assertion is nothing more or less than an abbreviated reference to the entire universe. —Ernst Mach [9]
The universe is a four-dimensional spacetime, but within a universe that obeys the cosmological principle, there is a natural choice of three-dimensional spatial surface. These are the surfaces on which observers who are stationary in comoving coordinates agree on the age of the universe.
While the local geometry does not determine the global geometry completely, it does limit the possibilities, particularly a geometry of a constant curvature. The universe is often taken to be a geodesic manifold, free of topological defects; relaxing either of these complicates the analysis considerably. A global geometry is a local geometry ...
The physical universe is defined as all of space and time [a] (collectively referred to as spacetime) and their contents. [10] Such contents comprise all of energy in its various forms, including electromagnetic radiation and matter, and therefore planets, moons, stars, galaxies, and the contents of intergalactic space.
Currently, the standard space interval, called a standard meter or simply meter, is defined as the distance traveled by light in vacuum during a time interval of exactly 1/299,792,458 of a second. This definition coupled with present definition of the second is based on the special theory of relativity in which the speed of light plays the role ...
The local geometry of the universe is determined by whether the relative density Ω is less than, equal to or greater than 1. From top to bottom: a spherical universe with greater than critical density (Ω>1, k>0); a hyperbolic, underdense universe (Ω<1, k<0); and a flat universe with exactly the critical density (Ω=1, k=0). The spacetime of ...
On this usage, comoving and proper distances are numerically equal at the current age of the universe, but will differ in the past and in the future; if the comoving distance to a galaxy is denoted , the proper distance () at an arbitrary time is simply given by = where () is the scale factor (e.g. Davis & Lineweaver 2004). [2]
Anaximander's model set a precedent for succeeding theories, including Copernicus's system, with the major change being the shift away from the geocentric model and towards the heliocentric model of the universe. The explained model, although accredited to Anaximander, did necessarily take from ideas originated in foreign cultures, such as the ...