Georgi Stankov, May 16, 2017
The equation of the Hubble’s Law as presented in the previous publication on cosmology shows that this cosmological law is an application of the Universal Law and assesses one-dimensional space-time according to the definition of the new Axiomatics:
dv = dl/dt = Hol = [1d-space-time]
As the Hubble constant Ho is a natural constant, the law assesses the constant space-time of the visible universe as the maximal particular system of All-That-Is that is accessible to human senses and material instruments:
dv = dl/dt = Holmax = [1d-space-time]
The proof is fairly simple. According to Hubble’s law, the maximal escape velocity dv which a galaxy reaches before it emits a light signal to the observer is the speed of light dv→c. As Hubble’s law claims universal validity, it also holds for escape velocities that are greater than c. In this case, the light emitted by galaxies with dv > c will not reach the observer because the speed of light is smaller than their opposite escape velocity. The resultant speed (space-time) of the emitted photons is negative with respect to the observer, that is, such photons will never reach the observer but they still exist and should be considered in cosmology.
As our information on any material celestial object in the universe is transmitted through photon space-time, galaxies with a higher escape velocity than the speed of light are no longer visible to the observer. This means that there is an event horizon of the visible universe, beyond which Hubble’s law still holds true, but can no longer be observed. The validity of Hubble’s law beyond the event horizon also follows from the fact that it is an application of the Universal Law of space-time, while the visible universe is a particular system thereof.
The event horizon determines the boundaries of the visible universe with respect to human cognition. The boundaries of the visible universe are determined by the magnitude of c because photon space-time is the ultimate level of space-time which we can perceive at present. As all levels of space-time are U-subsets and contain themselves as an element, we cannot exclude the possibility that there are further levels beyond photon space-time with a higher velocity than c. If we gain access to them, we shall enlarge our event horizon of the visible universe.
As we see, the event horizon assesses the space of the visible universe with respect to our senses and present level of technological development. This cosmological system can be expressed as [1d-space]-quantity, for instance, as radius RU (open straight line), circumference SU (closed line), or KS = SP(A)[2d-space] = spherical area = charge, in geometry (method of definition = method of measurement).
As in all other systems, these quantities are constant: they assess the constant space of the visible universe with the constant time of Ho. We conclude:
Hubble’s law assesses the constant space-time of the visible universe:
dv = dl/dt = Holmax = Ho RU →c = [1d-space-time]vis= constant
The maximal distance from the observer lmax is defined as the radius of the visible universe: lmax = RU . In cosmology, one usually speaks of the “universe“. Whenever we use this term from now on, we shall mean the “visible universe“, which is a system of space-time and is thus not identical with the primary term.
From the radius of the universe, we can easily obtain the event horizon of this basic cosmological system as KS (the surface area of the visible universe as a sphere) within geometry:
Event horizon = KS = SP(A)[2d-space] = 4πRU2 = constant
This quantity is constant for any observer in space-time. This practical equivalence is an aspect of the cosmological principle. In this case, the cosmological principle is a U-subset of the principle of last equivalence for the system “visible universe“ – it is an application of the principle of circular argument and is thus not identical with the primary axiom. This clarification is essential for the subsequent refutation of the standard model of cosmology as hot expanding hypothesis.