From the Chalkboard

Topic # 02

"An Accelerating Universe?"

Truth:Finally Explained

{Posted October 2001, re-visited June 2014}

We shall apply to our visible universe the concept of the logical addition of velocities, namely Galilean Transformations of Velocities. Refer to Appendix IV of the Book, Ref 1,2, the principal axiom of moving light sources, where the rule of Galilean transformations of velocities are applied in Euclidean Space Geometry.

Let us assume now we have a vast universe containing such an enormous, but countless numbers of point light sources of matter, stars and galaxies with a uniformity such that an observer in our frame of reference would be unable to find significant deviations in the physical characteristics of our universe simply by looking out into the celestial sphere in ALL directions.  A preferred spatial direction to point our telescopes to view our universe would be for all practical purposes completely absent. That is to say that the density distribution of our physical universe containing the many, many light emitting objects would appear to have no preferred direction.

Assume that in our vast universe among the countless numbers of light emitting stellar objects and galaxies, there are a certain number objects out there that are doomed to suffer a quick extinction, i.e., there are some stellar systems that will end up in a violent super novae. The probability, however, for such an event to occur among the many light emitting objects being viewed by the Earth based observers would be very, very small. One will have to wait for a very long time to be able to witness such an event occurring in our tiny speck of the universe visible to us given the current technical means available to us now.

As  a Gedankenexperiment (English: Thought Experiment) let us gaze up into the heavens looking through our imaginary cone that narrows our view of the visible universe. Sphere of Visible Universe

Let the vertex of this cone be located at our point of observation on the Earth. Let the height of this cone extend into the far reaches of our universe as is dictated by the current level of technical means available to us. Let this cone define a given solid angle of Ω Steradians that cuts a tiny section out of the sphere enclosing our observable universe. This section has an area that is equal to r2, where r = L, the length or the height of this cone and where r is the radius of the sphere that encloses our observable universe. Recall that this sphere has a solid angle of 4π Steradians and a surface area of 4πr2. Let us chose cone with a small solid angle of Ω = 1 Steradian for simplicity. For analytical purposes, let this solid angle Ω remain constant for our Thought Experiment. An observer with advance technical means would note only those events that occur within the solid angle defined by this cone that narrows our view of observation. But, as our observational techniques improve the length L of our cone will also increase. Assume that the Hubble constant is valid and that the distant objects we observe recede from us with a velocity v that is directly proportional to the distance L of the object being observed. The Earth based observer would now note an increase in the number of supper novae events with increasing occurrence as our technical means of astronomical observations improve. The observer would simple multiply his results obtained from the cone by 4π in order to obtain a number of supper novae events for the entire sphere for the whole universe where a practically uniformed universe may be assumed.

We Shall Examine Two (2) Distinct Schools of Thought

 1) Assume we have a universe in Euclidean Space Geometry that is governed by Galilean Transformations of  Velocities. Here, a universe void of secondary sources of emission will permit primary photons of light to propagate undisturbed though the vast regions of space strictly obeying Galilean Transformations of Velocities. As the observational distances L increase the receding velocities c-v also decrease relative to our frame of reference. A rise in the observed number of supper novae events should continue to occur and 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 increase in the transit time L/(c-v) would occur due to the reduced propagation velocity c-v of the signals that bring information to our observers.  The Earth based observer is therefore required to wait much longer in order to witness more distant events due to the increased transit times as a consequence of Galilean Transformations of Velocities. 2) On the other hand assume a constancy of the velocity of light in all frames of reference. Here, in such a universe one would have assume an effective acceleration of the more distance light emitting objects, reaching much greater distances of Lacc faster in order to force the observation of an apparently increase in transit times, Lacc/c, namely, the time that would be required for light coming from the light emitting objects effectively accelerating to vast astronomical distances. This delayed light will reach our telescopes assuming the validity of a constancy of the velocity of light in all frames of reference.

BOTTOM  LINE

A modeling of the universe in Euclidean Space Geometry would not require the flawed assumptions of a accelerating universe.

References

 1) "Extinction Shift Principle: A Pure Classical Alternative to General and Special Relativity", Dowdye, Jr., E.H.,  Physics Essays, Volume 20, 56 (2007) (11 pages); DOI: 10.4006/1.3073809 2) "Discourses & Mathematical Illustrations pertaining to the Extinction Shift Principle under the Electrodynamics of Galilean Transformations", Third Edition 2012 (Online: Amazon.com, Barnes and Noble, Create Space)