From the Chalkboard

This is topic # 02,  "An Accelerating Universe?"

{Posted October 2001}

We shall perform an additional Gedankenexperiment now, this time applying to our visible universe, logical addition of velocities and the emission theory.  Those who have the book may refer to Appendix IV, the principal axiom of moving light sources, the Galilean transformation of velocities in Euclidean Space.

Let us assume now we have a universe of such vastness, containing such an enormous number of point light sources, and also a uniformity such that any observer in our frame of reference would be unable to find any significant deviations of the characteristics of the universe by looking out towards the celestial sphere in any direction.  Thus, any preferred spatial direction would be, for all practical purposes, absent and the density distribution of the light sources would appear to be practically a function of only the distance from our point of observation.

Let us also assume that in our vast universe a certain number of point sources are doomed to suffer a quick extinction, i.e.,  a super novae occurrence. The probability, however, for such a fate for any one of the many light sources, we may assume, is very small.  Hence, one must wait a very long time to be able to witness such an event occurring in our tiny region of the universe that was only visible to us decades before the advent of modern astronomy! 

We shall now open up into the heavens an imaginary cone of observation.  Let the vertex of this cone be located at our own point of observation from Earth.  Let the height of this cone extends into the far reaches of the universe as is dictated by our current level of technical means.  The cone shall define a given solid angle of our observation.  For analytical purposes, let this solid angle remain constant.

The observer would note only those events that occur within the volume of this cone of observation.  With improved technical means, the height of the cone increases.  If we assume the validity of the Hubble constant, the velocity of these distant sources would increase as one observes more and more distant light sources.  As our technical means improve, the distances and also the velocities of these light sources would also increase.  The Earth based observer would note an increase in the number of supper novae occurrences as the time goes on towards the more advancement in the techniques of astronomical observations.

But, however, assuming a universe in Euclidean Space Geometry and vast regions of the universe void of secondary sources of emission, thereby permitting primary photons of light to past "undisturbed" vast regions of space, strictly obeying the rules of Galilean transformations and the logical addition of velocities, the rise in the observed number of supper novae events should at some point start to level off.  As the velocity v of the receding light sources increases, the velocity c-v relative to our point of observation decreases.  Hence, an increased transit time would be required due to the reduced velocity of  c-v.  The Earth based observer is therefore required to wait longer to witness distant events due to the increase in transit times for the signaling as a consequence of Galilean transformations.

If, on the other hand, one assumes a constancy of the velocity of light in all frames of reference, one would have to accelerate the distant light sources of the universe to even much greater distances in order to force the observation of the apparent increased transit times to agree with any theory!

A modeling of the universe using Galilean transformations and the logical addition of velocities with the emission theory would not require any kind of an accelerating universe by any means! The same increase in transit times of signals from any sources accelerated to greater distances can also be understood from simply a decrease in its velocity of propagation c-v, an intuitive reasoning as a consequence of Galilean transformations in Euclidian Space Geometry!