THE REDSHIFT AND THE ZERO POINT ENERGY

 

Barry Setterfield & Daniel Dzimano

15th December 2003.

 

Abstract

The history of the redshift is traced and a variety of problems listed in addition to two major anomalies. One of these anomalies is the quantized redshift, which was first noted by Tifft in 1976 and was again confirmed in 2003 by Bell. The second anomaly is the breakdown in the redshift/distance relationship, evidenced by the observations of distant Type Ia supernovae, that has revived interest in the action of the cosmological constant. These problems and anomalies admit a resolution if the energy density of the electromagnetic fields making up the vacuum Zero Point Energy (ZPE) is increasing with time. This approach predicts that light emitted from distant galaxies should have a basic redshift quantization of 2.671 km/s, which is in good agreement with Tifft’s basic quantum of 2.667 km/s. In addition, the standard redshift/distance relationship is shown to derive from known physical processes that produced the ZPE rather than the expansion of space-time or the motion of galaxies. The equations governing these processes readily allow an alternate explanation for the deviation from the standard formula at high redshifts without recourse to the action of a cosmological constant. 

 

Introduction

One of the key pieces of evidence that cosmologists use to indicate universal expansion is the redshift of light from distant galaxies. The redshift is an astronomical term that describes the shifting of the spectral lines of elements towards the red end of the spectrum when compared with a laboratory standard here on earth. The redshift, z, is then defined as the measured change in wavelength, when compared with the standard, divided by that laboratory standard wavelength. If the change in wavelength is given by ∆λ and the laboratory standard wavelength is λ, then the redshift is defined as 1 - 2

 

z  =  ∆λ/λ                                                                                                                           (1)

 

This is the quantity that is actually measured. Notice that z is a dimensionless number as the units of wavelength cancel out. One might reasonably ask how this dimensionless number came to represent the expansion of the universe.   

 

Historical Background

The historical development of the idea began with the work of Vesto Slipher and Francis Pease between 1912 and 1922 at the Lowell Observatory in Flagstaff, Arizona. They measured the redshift of forty-two galaxies.3  In 1919, Harlow Shapley noted that the vast majority of those redshifts were positive, with the only exceptions being those in our own galactic neighborhood. Then during the period 1923-24, Edwin Hubble discovered Cepheid variables in neighboring galaxies.4 These stars vary in light output in such a way that their intrinsic luminosity and the period of variability are linked.  Measuring the period of variability can thereby in principle establish their intrinsic luminosity and hence their distance. Hubble used these stars to measure the distances to all forty-two galaxies that Slipher and Pease had examined. In so doing, he discovered that the observed redshifts were proportional to distance. In 1929 he published the law of spectral displacements, which is now called Hubble’s Law.5 If astronomical distance is r and redshift is z, then in mathematical terms Hubble’s Law can be written as:

 

r = z/h                                                                                                                               (2)

 

where h is a constant of proportionality.

 

Essentially Hubble’s Law is a redshift/distance relationship, and as such simply notes that the redshift of galaxies is proportional to their distance. That is the hard core of data that astronomers and cosmologists have to deal with. Although cautious about the procedure until more data came in, Hubble suggested that z could be multiplied by the speed of light, c, thereby transforming the dimensionless number into a velocity. Hubble pointed out that this procedure then allowed the redshift to be interpreted as a Doppler effect of galactic recessional velocities, v.6  This was done by analogy with the effect heard when a police car passes you with its siren going.  As it pulls away from you, the pitch of the siren drops.  In a similar way, Hubble suggested that the redshift, which lengthened the wavelengths of light from distant galaxies, might indicate they are moving away from us also. On this approach to the redshift data, equation (1) was thereby interpreted to read

 

zc = v         or re-arranging        z = v/c            which suggested          v/c = ∆λ/λ            (3)

 

This then allowed equation (2) to be re-written as7

 

r = cz/Ho = v/Ho                                                                                                                 (4)

 

where Ho is the new constant of proportionality called the Hubble constant. This was the situation up until the 1960’s. By 1960, the highest value of z obtained was around 0.4.  From the interpretation of equation (3) this meant these galaxies were receding at two-fifths of the velocity of light, and an essentially linear relationship was being maintained on the Hubble graph of redshift/distance from (2) or (4). 8-9 

 

However, around a redshift of about 0.4, and post-1960, a departure from linearity began to be noted as galaxy ‘velocities’ became more relativistic.  Consequently, by the mid-1960’s, the relativistic Doppler formula was applied and, even with the advent of the Hubble Space Telescope, it was found to be a reasonably accurate approximation for objects even at the frontiers of the universe. Thus equation (3) came to be re-written as 10

 

z = {[1+(v/c)]/ √[1-(v2/c2)]} – 1                  &nb