Space, time, and velocity in cosmology (Q1356587)

The article proposes a cosmological special relativity in Hubble's expanding universe with a negligible gravity. The author gives space-velocity transformations for the cosmology under the assumption of the constancy of the expansion of the universe and under the assumption that the laws of physics are the same at all cosmic moments. (These assumptions are called the principle of the constancy of the expansion of the universe and the principle of cosmological relativity, correspondingly.) The transformations deduced from these principles are for one-dimensional motions; they connect space, time, velocity, Hubble's time similarly to the Lorentz transformations. The application of the principles of the constancy of the expansion of the universe and of the cosmic relativity to two cosmic observers at two cosmic frames of reference \(K(x,y,z,v)\), \(K'(x',y',z',v')\) gives \(x^2-\tau^2v^2= x^{\prime 2}-\tau^2v^{\prime 2}\) and gives the transformations of cosmological relativity. Here are used Hubble's variables of relative distances \(x\), \(x'\), \(y\), \(y'\), \(z\), \(z'\) of the cosmic frames \(K\), \(K'\) of reference; \(v\), \(v'\), \(t\), \(t'\) are their relative velocities and times; \(\tau\) is Hubble's constant -- the rate of the expansion of the universe. The article derives some consequences from the obtained transformations such as the length and velocity contractions, as well as consequences about redshifts and the observed high velocities of gas molecules and fast whirling galaxies.