Pioneer anomalous
acceleration – responding to Ned Wright’s similar page
Hd=4.234 Gyr
correction started July 30, 2001
The Other Possible Cause of Red-shift
Aladar Stolmar
ABSTRACT
Two possible causes of the nebular red-shift were listed by its discoverer, Edwin Hubble. He even warned the astronomers that “the possibility that the red-shift may be due to some other cause, connected with the long time or distance involved in the passage of light from the nebula to observer, should not be prematurely neglected”. [1] A continuation of the investigation of the other than recession cause of red-shift was performed on the large scale. As a result of theoretical investigations a correlation was found to represent the Cosmic Microwave Background Radiation as caused by the Hubble discovered distance dependant red-shift of the originated in very distant regions of the Universe stellar radiation. The conclusion suggested by this investigation that the Universe shows stability and uniformity to immense distances, does not expand and available for investigation up to about 100 billion light years.
The Nature of the Problem
I. Introduction
“Thus the observable region at present is a sphere, centered on the observer, with a radius of about five hundred million light years. Throughout this sphere about a hundred million nebulae are scattered, each a stellar system comparable to our own system of the Milky Way. The study of this observable region as a sample of the Universe has led to the recognition of two large-scale features. The first feature is homogeneity. … the observable region appears to be very much the same, in all directions and at all distances. The second characteristic is the fact that the light-waves from distant nebulae seem to grow longer in proportion to the distance they have traveled.” … “it seems likely that red-shifts may not be due to an expanding Universe, and much of the speculation on the structure of the universe may require re-examination.” [5] Hubble lectured in 1947. “the photons emitted by a nebula lose energy on their journey to the observer by some unknown effect, which is linear with distance and which leads to a decrease in frequency without appreciable transverse deflection and, in particular, without any decrease in rate of arrival at the observer” [1] The provided evidence by the Pioneer 10 Doppler data proves that this effect is not linear, but exponential. Hubble and Tolman gave a remark that “if the red-shift is not due to recessional motion, its explanation will probably involve some quite new physical principles” [1] and there are some “quite new physical principles” resulting in that the Hubble discovered red-shift distance relation could be seen as a new fundamental property of matter: there is a half-life of photons.
II. Plan of Treatment
The purpose of this article to give
detailed consideration of the Hubble discovered red-shift distance relationship
on large scale. It is assumed therefore that the Universe is uniform and
populated with nebulae or galaxies as seen in our neighborhood to immense
distances. The same Hubble red-shift versus distance law is valid and even
about the same half-life of photons applies everywhere. The spectrum of
electromagnetic radiation is continuous and the change of the frequency due to
the distance traveled is the effect of the half-life of photons only. Using the
relationship between the red-shift of observed photon’s wavelength to the
distance of emitter we introduce the coefficient Hd or Hubble
wavelength doubling distance constant, half-life of photon what we will use
with z red-shift being the ratio of the difference of frequencies (dn) of original emission (n0) and observed (n) to the observed frequency. 
and 
. Photons’ half-life: 
. The location of an emitting stellar object as radial
distance R is found directly from the ratio of observed and emitted wavelengths
or frequencies as
(1)
The meaning of Hd Hubble distance constant is seen from this equation (1): Hubble distance constant equals to the distance or equivalent time of progression for which the wavelength of a photon doubles or the frequency drops to the half of the original. At large distances the resolution of individual objects is lost, the observation of view angles is possible only with a multitude of sources in each line of site at the same time. Also the relative uniformity of the subject of our investigation, the so called Cosmic Microwave Background Radiation makes it possible to use the entire sphere as the global calculation’s subject avoiding the task of investigation of local fluctuations, which are indeed natural, represent the clusters and super-clusters of galaxies and will be observed with the increase of resolution of observations. If the so called CMBR Planck curve could be reproduced from common stellar radiation with large red-shift arriving to our position and the Dipole is already associated with the Earth motion [3] as a Doppler effect superimposed on the position of the peak, it shell be viewed as proof of the pure distance cause of Hubble red-shift. We are enclosed in spheres, centered on us with increasing radii the larger radius enclosing the smaller ones. The radiation coming to us from farther away sphere increases as the number of stars increases with the third power of radius, shifted to the red as per Hubble’s law, half-life of photons and the area of each individual star is viewed smaller – and the number of photons arriving to us is proportional to this view angle - as per the square of radius, from
[steradians] (2)
view angle determination. The resulting effect is the CMBR so called Planck curve – as will be shown later.
III. The Theoretical Formulae
For theoretical treatment of the sources of radiation we select the individual stars themselves. In order to approximate the arriving to us and detected radiation in the microwave wavelength range first we limit the observed range from 1 to 600 GHz. The object is to show that the origin of the observed CMB radiation is distant stellar radiation. To be able to calculate the intensity arriving to us we should select an average radiation intensity characteristic and viewed size of the surface radiating as well as density of such stars in the volumes of distant regions of the Universe. For first approximation our Sun could be selected with its A area and about 5750 K black body radiation, which is represented by Planck law. We will calculate the number of stars in the volumes of spherical shells located near radiuses R by multiplying the volume by the average volumetric star density r and will place the combined area of stellar surfaces on 2/3 of the thickness of shell radius R to calculate the combined view angle as per (2) radiating to us from that radius as the number of stars in the volume multiplied by the A area of the Sun. The resulting view angle of all the stars in a spherical shell R+ > R-, around R average in steradians is:
[steradians] (3)
As we move away from our position we preserve the stellar surfaces viewed in the inner radiuses as covered view angles and we assume that the portion of new stellar view angles at the more distant radii are covered according to the portion of the total 4p angle, which is already covered. Replacing A * r with CCONST input parameter we can perform a series of sensitivity studies. The observation is performed at discrete frequencies, which further enhanced in the theoretical treatment by assuming that the observations are performed at every GHz frequency with a band of 1 GHz (represented as steps J in the program). For each n observed a range of n0 emitted frequency and corresponding star locations with R radial distances from us serve as source of radiation.
Considering the Hubble red-shift and the black body Planck luminosity curve we can calculate the emitted by the (1) equation represented star surfaces energy at the corresponding to the observed frequency and reduced by the division by the red-shift (z +1) as:
ENER(J) = ENER(J) + 2 * Omega(I) * Z2 ^ 4 / LA ^ 5 * CSP ^ 2 * HPL / (EXP(CSP * HPL * Z2 / KBO / LA / TOLB) - 1) / J (4)
Where J represents the observed frequency in GHz, I is the range of radius of the calculated shell, Z2 is the z+1, calculated from the radius and Hd=4.234 Gyr photon half-life red-shift value; LA is the wavelength, corresponding to the J observed frequency; LA / Z2 the emitted wavelength; CSP speed of light, HPL Planck quanta h, KBO Boltzmann constant, k and TOLB is the assumed average star black body temperature input parameter.
Remembering that 1 GHz <= n <= 600 GHz is the range of observations and that the possible value of Hd is 4.234 bly the subject volume extends to somewhere between 80 bly to 150 bly. Using the now available computer technology the determination of volumes on such a large scale, the calculation of the number of stars and the view angles of stars radiating and blocking the farther away regions of the Universe is possible but requires some simplifications. The extent of calculation Rmax and the r star density times the radiating area of a star, the average effective black body temperature of the radiating stars are inputs. Varying the input values – in the first approximation the interstellar material is omitted and the range of calculation is used to find a match to the shape of the so called CMBR Planck curve, and to get the calculated location of the peak right at the observed location. The CMB intensity is calculated by the same equation as the contributed by the shells radiation, just for a cavity with 2.723 K wall temperature, with no consideration of red-shift.
CMB(J) = 8 * PI / LA ^ 5 * CSP ^ 2 * HPL / (EXP(CSP * HPL / KBO / LA / 2.723) - 1) / J (5)
A second approximation was developed to represent the interstellar material – dust, gases, comets and asteroids and even the planets around stars – screening-blocking and scattering properties. The extent of calculation is expected to lose its influence on the results, a completely closed sky should develop before 150 billion light years radius. The blocking effect was represented as an assigned to each star blocking area, prorated to the star’s area with an input multiplication factor. There is a possibility that the relative amount of scattering dark matter should be significantly increased – based on dedicated results of observations.
IV.
Results of Calculations of Stellar Origin
Cosmic Microwave Background Radiation
The results of the quantitative evaluation are seen on the graphs: the shape of the calculated stellar origin Microwave Background Radiation intensity curve, resulting from a uniform infinite Universe with distance caused exponential Hubble red-shift law fits perfectly to the observed so called CMBR Planck curve on the left of the peak. The higher calculated values on the right from the peak require closer examination of the reported processing of CMBR data.
Figure 1 The above three graphs are calculated for Hd=8.468 Gyr value, with dark matter
Ned Wright referred to these graphs above. The fit to the observed data is significantly better with the new, correct value of the
Hd, as seen below in first approximation.
Figure 2 The figures are generated controlling the effect of dark matter by the radius of calculated volume Hd=4.234 Gyr
The value of Hd = 4-5 bly from the Pioneer 10 observation was corrected from the nuclear size calculation and Hd = 4.234 billion years was accepted.
V. Conclusion
Applying the Hubble red-shift versus distance law to very large distances in an assumed infinite and uniform Universe resulted in the so-called CMBR Planck curve. The cause for the red-shift may not be recession, but the distance itself– as predicted by Hubble and Tolman.
References
1.
Two methods of
investigating the nature of nebular red-shift – Edwin Hubble and Richard C.
Tolman, Bibcode: 1935ApJ....82..302H
2. H0: The incredible shrinking constant, 1925-1975 – Virginia Trimble Bibcode: 1996PASP..108.1073T
3. Dipole Anisotropy in the COBE Differential Microwave Radiometers First-Year Sky Maps Kogut. A. at al. Bibcode: 1993ApJ...419....1K
4. Effects of Red Shifts on the Distribution of Nebulae Hubble Edwin Bibcode: 1936ApJ....84..517H
5. The 200-inch telescope and some problems it may solve Edwin Hubble Bibcode: 1947PASP...59..153H