*15 ^{th}
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 as^{7}

r = cz/H_{o} = v/H_{o}
(4)

where *H _{o}* 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

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-(v^{2}/c^{2})]} –
1 &nb