5. The ZPE and the Redshift

5.1 ZPE Variations and the Atom
5.2 The Quantization of the Redshift
5.3 Redshift Periodicities
5.4 Redshifts Probably Do Not Indicate Cosmic Expansion
5.5 Redshifts and an Increasing ZPE
5.6 Wavelengths and Frequencies
5.7 Atomic Behavior Between Quantum Jumps

5.1 ZPE Variations and the Atom

Atomic orbit energies therefore seem to be sustained by the ZPE. But we can go further. The Bohr atom scales all orbit energies according to the ground state orbit. So, if the ground state orbit has an energy change, all other orbits will scale their energies proportionally. This means that wavelengths of emitted light will also be scaled in proportion to the energy of the ground state orbit of the atom. It follows that, if the ZPE strength varied cosmologically, then all atomic structures throughout the cosmos might be expected to adjust their orbit energies simultaneously. Now atomic orbit radii have remained constant during the time that such measurements have been possible. But, throughout that time, the strength of the ZPE has increased. Therefore, any increase in the energy density of the ZPE seems to require that a quantum threshold must be crossed before atomic orbits take up their new energy state.

For example, if the strength of the ZPE was lower in the past, then, as the ZPE increased, a series of quantum thresholds was reached, and atomic orbit energies would increase in a set of jumps. Between these jumps or quantum changes, atomic orbit energies would remain constant since atomic orbits could not access additional energy available from the vacuum until that energy had built up to the quantum threshold. The light emitted by atomic processes would then be bluer with each jump as we approach the present epoch, but would remain unchanged between jumps. So, as we look back in time, we should see the light from known atomic transitions getting redder in a series of jumps, since the red end of the spectrum is the low energy end. Before we formalize this concept for the atom, let us examine the redshift.
It is usually assumed that the redshift indicates universal expansion. If this were true, redshift measurements should show a smooth progression with distance. However, this is not supported by the data since Tifft [96-100] and others [101-111] note that quantization of galaxy redshifts is occurring. The analysis here suggests that this quantized redshift of light from distant galaxies may be evidence for the increase in the strength of the ZPE with time as atomic orbits took on higher energy values with time in quantum jumps. Bluer light will then be emitted for a given orbit as time goes forward, or redder light as we look back in time. If there is this time-dependency, the redshift will continue to be a measure of distance, since looking back in time astronomically is the same as looking further into the distant cosmos. Thus, the redshift as a measure of distance is not negated by the proposals being made here. The matter of why the redshift/distance function appears to follow a curve reminiscent of a relativistic Doppler formula will be addressed later. It will be shown that a very similar curve can be obtained by a consideration of processes related to the formation and build-up of the ZPE in a way which has nothing to do with velocities of galaxies or universal expansion. The fact that the redshift/distance relation approximated to the Doppler formula is thus fortuitous.

5.2 The Quantization of the Redshift

The redshift quantization becomes apparent when redshifts of pairs of galaxies are compared, or when galaxy redshifts have the genuine Doppler shift of our solar system motion removed [98, 112]. Recent data on redshift quantization appeared in two Abstracts in Astrophysics authored by Morley Bell on 5th and 7th May 2003. The second Abstract read in part: “[Galaxy] clusters studied by the Hubble Key Project may contain quantized intrinsic redshift components that are related to those reported by Tifft. Here we report the results of a similar analysis using 55 spiral … and 36 TypeIa supernovae galaxies. We find that even when more objects are included in the sample there is still clear evidence that the same quantized intrinsic redshifts are present…” This topic is discussed in detail by Setterfield and Dzimano [25]. But we must clarify what is meant, and what is not meant, by the quantization.

From 1976 onward, Tifft pointed out that redshift differences between galaxies, or pairs of galaxies, were not smooth, but went in jumps, or were quantized [96]. The Coma cluster of galaxies had bands of redshift running through the whole cluster [97]. In several instances, a quantum jump in redshift actually passed through some galaxies. The quantization he originally noted was 72.46 km/s [97], and up to 13 multiples of that figure were found. Later work established a more basic quantization at 36.2 km/s. This was supported by Guthrie & Napier who concluded a quantization at 37.6 km/s really did exist [102, 113]. Tifft’s most accurate studies indicate a basic redshift quantization of about 8/3 km/s, with all higher quantizations being multiples of this basic value [100]. Much of Tifft’s later data came from 21-cm observations at high signal-to-noise levels so random uncertainties were very small. Indeed, for Tifft’s basic quantization, Lewis has claimed accuracies in redshift measurements to better than 0.1 km/s [114]. The basic quantization is thus 26 times larger than the errors.

It should be emphasized that the model presented here still requires that redshift be a function of distance. This model suggests the redshift results from the increase in the ZPE strength with time affecting the orbit energy of atoms. Orbit energies increase with time in a way detailed below, so atoms emit light which becomes progressively bluer in jumps with time. Therefore, as we look back in time to progressively more distant objects, their light appears to become redder in jumps. Thus the redshift is still a measure of distance, no matter which model is used.  As is shown below, the fact that the redshift/distance formula approximates to the relativistic Doppler formula is probably fortuitous, since it deviates from that formula at high redshifts, but in a way which is readily understandable on this approach.

5.3 Redshift Periodicities

Now the Tifft quantizations must not be confused with another effect which has been noted with quasars and very distant galaxies. The quantizations show that redshifts increase in a series of steps, with constant redshifts between the steps. By contrast, distant quasars/galaxies show large-scale clustering at preferred redshifts. Quasar periodicities were first noted by the Burbidges in 1967, and given a formula by Karlsson from his observations in 1971, 1973 and 1977. Other astronomers generally agreed that “…if you looked at all quasars known, that preferred values of redshift were apparent” [115]. The Karlsson formula was not unique as Duari et al. produced an equally viable mathematical relationship for preferred quasar redshifts [116]. In these cases, the redshift periodicity was very large scale. For Duari et al., the periodicity peaked at 16,940 km/s. This is much greater than Tifft’s basic step of 8/3km/s.

It is important to distinguish between these two separate phenomena. The large scale periodicities simply represent large numbers of objects at nearly the same redshift and so reflect clustering of galaxies and quasars. By contrast, the Tifft quantizations are a small scale effect involving differences in redshift between galaxies in a cluster. It has nothing to do with numbers of galaxies at a given redshift.  Quantization has everything to do with discrete jumps in redshift and constant redshifts between jumps. This gives the appearance of bands of redshift going through a whole cluster with quantum jumps of redshift at the edge of each band. Because the redshift differences are small, it is hard to discern the Tifft quantizations at high redshifts where techniques are less sensitive. It should thus be noted that any negation of periodicities will not negate the Tifft quantizations as they are two separate effects.

5.4 Redshifts Probably Do Not Indicate Cosmic Expansion

If the redshift represents cosmic expansion, it is hard to explain how this occurs in jumps. This is one reason why redshifts cannot be the result of motion. Evidence from Tifft and Arp indicates that motion of galaxies actually destroys the quantization, so the real velocities of galaxies in clusters are very low [96, 117]. Only at the centers of clusters are high velocities expected. The Tucson conference on quantization in April 1996 noted that, in the innermost parts of the Virgo cluster, “deeper in the potential well, [galaxies] were moving fast enough to wash out the periodicity.” [39]. (Here, “periodicity” is the quantization by another name and shows the confusion that exists about the two separate phenomena). So any significant velocity smears out the quantization. This suggests that redshifts are not due to motion at all, but have another basic cause, with any real Doppler effects being secondary.

The third item of evidence was first noted in the Coma Cluster where some redshift jumps (or boundaries between redshift steps) were discerned within individual galaxies [96]. It is unlikely that a single galaxy has two different rates of cosmological expansion or velocities of recession since it would rapidly disrupt. This therefore indicates that galaxy motion is not responsible for the redshift. But the fourth item dramatically reduces possible explanations. Tifft notes many galaxies actually underwent a decrease in redshift by one basic quantum over a period of a decade or more [100]. These data have no explanation on the cosmological expansion model. The explanation consistent with all data is that the redshift is not an artefact of cosmological expansion. Rather, it is related to atomic emitters within galaxies themselves, and thus governed by the strength of the ZPE. So when the ZPE strength increases beyond a quantum threshold, atoms respond with higher orbit energies. The light these atoms emit then has a redshift which is lower by one basic quantum jump. The observed quantum drop in galaxy redshifts may thus be evidence for an increase in ZPE strength at the time that light left those objects. The reason for the size of the basic quantum jump now demands attention.

5.5 Redshifts shifts and an Increasing ZPE

In reference [25], and Appendix 5 here, the size of Tifft’s basic quantization is reproduced theoretically from Puthoff’s equations which describe the power transferred from the ZPE to atomic orbits. The utilizable power that is transferred to the atomic orbit is given by [92].

Pu = e23/(72π2εmoc3)                      (21)

If Eu is the utilizable energy that can be absorbed from the ZPE, then Eu is proportional to Pu. Thus, looking further back in time, if the power maintaining the electron in its orbit prior to the quantum jump is P1 and the power utilized after the jump is P2, then reference [25] shows

P1 = P2+zP2 = P2(1+z)                              (22)

Consequently, it follows that

1/(1+z) = P2/P1 = E2/E1 = U2/U1                     (23)

If this is so, the quantized redshift may be evidence for the increase in ZPE strength with time. Now the redshift is often discussed in terms of wavelength. In that case, let the ZPE energy density decrease going back in time. Let the energy of the first Bohr orbit be E1 when the ZPE energy density has a value of U1. As the energy density of the ZPE changes to a value U2, the energy of atomic orbits undergoes a proportional change from E1 before the jump to E2 after the jump. But the energy of a given orbit is equal to the energy of a photon of light emitted from that orbit when an electron makes a transition to that orbit from outside the atom. The wavelength of light emitted from that orbit before the jump will thus be λ1 which is related to E1 by the expression E1 = hc1. Similarly the wavelength of light emitted after the jump (further out in space) is λ2 in the expression E2 = hc2.  From (7), the product hc is invariant astronomically [63- 68]. So for all ZPE variations, we have for emitted wavelengths

 U2/U1 = E2/E1 =  λ12                            (24)

Now, wavelengths change at the quantum jump so that from (22), (23) and (24) we have

 λ2 =  λ1 + Δλ1                                 (25)

From (25) we obtain one definition of the redshift, namely that

 λ21 = 1 + Δλ11 = 1+z                  (26)

But in (26) we need λ12 to accord with (24). So taking the inverse of (26), we have

U2/U1 = E2/E1 =  λ12 = 1/(1+z)        (26A)

From (26A), the redshift factor (1 + z) is inversely proportional to the ZPE strength, so the equation describing the behavior of (1 + z) must be the inverse the equation for ZPE behavior. In addition, (22) shows the increase in P2 at the jump is given by the dimensionless fraction z. Thus z is a dimensionless component of (21). The redshift quantum nΔz when n = 1 is the dimensionless factor derived theoretically in reference [25], and Appendix 5, and is equal to

 Δz = 1/112215 = 8.91144x10-6                  (27)

It is usual to express (27) in terms of a velocity by multiplying by c so that (27)

 cΔz = c(8.91144x10-6) = 2.671  km/s                   (28)

This compares favorably with Tifft’s basic quantum jump of 8/3 = 2.667 km/s [100] with a measurement error which is 1/25th the size of the quantization [114]. Since the redshift goes in jumps of Δz, then any redshift quantity, z, may be considered to be made up of (nΔz) steps, where nis the number of redshift quantum jumps. Thus we can write:

z  =  n Δz                                          (29)

5.6 Wavelengths and Frequencies

We now note several points. First, the standard redshift/distance function given in (55) is a smooth curve. Since the ZPE, the vacuum permittivity and permeability, Planck’s constant and the speed of light are all smoothly varying, this smooth curve represents the behaviour of these quantities or their inverse. However, equation (29) shows the real redshift behaves in a step-wise fashion due to quantum increases in atomic orbit energy as the ZPE strength builds up. So the actual redshift curve has a step-like ripple which, on a larger scale, disappears so that the smooth function is an accurate description. Thus wavelengths of light emitted from galaxies over time will exhibit this step-like behavior in accord with the redshift curve. Equations describing atomic behavior that gives this redshift ripple will be examined shortly.

But the behavior of emitted frequencies at the quantum jump also needs a brief overview before atomic orbit equations are examined. Any change in the energy density of the ZPE is infinitesimally small at the actual moment of the change, so any change in lightspeed c is also infinitesimally small. This means that c1 before the jump essentially equals c2 after the jump. Therefore, it follows from equation (10) that f1λ1 = f2λ2. Thus the increase in wavelength at the jump means that there will be an inversely proportional decrease in frequency at the jump so that λ2/λ1 = f1/f2. Now the variation in lightspeed is smooth, and frequencies are smoothly changing in proportion. But, the quantum jump in atomic behaviour gives a discrete change in emitted frequencies on top of this smooth variation. So as we look back in time, the curve of emitted frequencies is like a rising saw-tooth function, with a small drop at the change.

The atomic changes giving the step-like character to the redshift have three components. First, there is the behavior of atomic masses and orbits between the jumps when the redshift has a constant value. Next are changes in atomic masses and orbits at the redshift quantum jump. Third is the derivation of the actual magnitude of the change at the quantum jump.

5.7 Atomic Behavior Between Quantum Jumps

Data in Table I, Figures 1 to 6 and reference [61] all imply the ZPE strength has increased over the last hundred years without any quantum change. Indeed, data from Figure 8 indicate that no quantum jump has occurred for millennia. Analysis of a century of data from some atomic constants reveals orbit energy is conserved as the ZPE increases [61]. The data indicate an increase in the ZPE strength gives an increase in atomic particle masses as in (16) or (16A). In applying this result to atomic behaviour in the interval between the quantum jumps the Bohr model is used since it allows a good approximation to the correct numerical results with computational ease [118]. Two basic Bohr equations must balance for equilibrium to be maintained in atomic orbits [119, 73]. The first describes orbital angular momentum such that

                                    mvr = nh/(2π) ~ U                                 (30)

where v is the velocity of the electron in its orbit, r is the orbit radius, m is the mass of the electron, h is Planck’s constant and n is the Bohr quantum number. The proportionality follows from the behaviour of h in (2) since n is unchanged. It also needs the term mvr on the left hand side of (30) be proportional to U, the ZPE energy density. Now m is proportional to U2 as in (16), so the second Bohr equation is needed to find the conditions for stability thus:

mv2r = e2/ε = constant                              (31)

the data from [63-68] and treatment in [19] show the ratio e2/ε is constant throughout the cosmos, except in strong gravitational fields. The right hand side of (31) agrees with this. Equations (30) and (31) show that orbit equilibrium can be maintained as the strength of the ZPE and atomic masses increase provided orbital velocities behave in the interval such that

 v ~ 1/U                                           (32)

Emitted frequencies of light from these atoms will then vary since they are proportional to the orbital velocity of the electrons as outlined at (17). In the interval, it follows from (17) that:

 f ~ v ~ 1/U                                 (33)

From (31) and (32) it follows, within the interval, that orbit radii and orbit kinetic energies remain fixed. Now the total orbit energy of an electron in orbit n of the Bohr atom is [119]:

 E = -[2π2me4/(ε2h2n2)] = -hcR∞/n2 = constant         (34)

The constancy of atomic orbit energies follows when (2), (7) and (16) are applied to the terms involved in (34). This results in the constancy of R∞ in Figure 5. The conclusion is that, as the ZPE strength changes between jumps, orbit energies will remain constant, so wavelengths of light emitted from those atoms will remain constant. Therefore, between redshift jumps, the redshift of wavelengths remains unchanged. Atomic changes at the jumps now need scrutiny.


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