**Topic010:The Cosmological Correction, Curvature In Time, Bill Tifft, 8/15/15**

The late 1970s through early 1990s marked a period when much progress was made defining basic properties of redshift quantization and its implications. The period included recognition of the global nature of quantized redshifts, both locally (galactocentric) and cosmically (cosmocentric), recognition that the redshift was variable and rapidly evolving, that it contained both a precise quantum structure and a continuous lookback distortion, and that both of these patterns could be precisely specified. Correction for the lookback distortion is the subject of this topic, but requires that I discuss some properties of the emerging QTC cosmology first. As I discuss each of the above mentioned subjects, now writing in retrospect, I will often use information out of historical perspective to show effects. For example, Topic008 introduced the subject of galocentric global quantization. Global periodicities related to the original 72.45 km/s period were shown to be present including a period of 24.15 km/s related to narrow profile 21-cm data associated with dwarf galaxies. This was illustrated in Figure 5 of the ASP paper. The lower left frame of Figure 5 illustrates the confirmation of galactocentric quantization using an independent Guthrie-Napier study published in 1991 plotted at a very precise period not known to me before 1993. As data and understanding improved such advance information is used in retrospect to precisely illustrate findings. The real learning process is more chaotic but the end product is clear. Topic009 which introduced redshift variability also used advance knowledge of redshift periodicities and morphological (profile width categories) to show continuity of redshift deviations between the oldest (Roberts) data and more recent (Fisher-Tully) data in the lower frames of ASP Figure 6.

Topic009 further demonstrated that the 24.15 km/s period was in fact a composite transformation stage of finer periodic structure which led to the recognition of basic shorter periods of 5.3313 and 2.6657 km/s. These very short periods demonstrate the precision with which 21 cm data can define periodicities and show the total absence of any significant dynamical blurring effects within composite redshift patterns of sets of completely independent galaxies. We were now faced directly by the issue of what actually is the underlying structure which defines the large scale quantum pattern. The short periods provided the ideal tool needed to begin a study of the structure. We had determined that we could detect relatively long global redshift periods locally, within about 1000 km/s, for galaxies with the narrowest and widest 21-cm profiles. The situation was complex at intermediate widths and could not be extended to higher redshifts globally, specifically to the Virgo cluster. Differentially relatively long period quantization was present at higher redshifts hence some z dependent phase shifting within periodic patterns appeared to be present to obscure periodicity over longer intervals of z. Differential quantization and orientation effects ruled out ordinary dynamical dilation effects, hence an alternative source of nonlinearity in phasing of the redshift itself with lookback time was required. Such a phase shift would be difficult to detect using long periods. A small cumulative correction to z for long periods would produce only a small phase shift in a period, but at short periods the cumulative shift in the phase of a period with increasing z should be readily detectable. The lower left frame of Figure 7 of the ASP paper (figure 2.38 in my book) readily shows the phase drift using no z dependent correction when phase calculated for the 2.6657 km/s period was plotted against redshift for the narrow profile dwarf galaxies. (For book information or acquisition see Post001 and Post002.) Since 1984 we had used a possible theoretical correction suggested by my colleague John Cocke. Figure 2.39 in my book shows the effect of that adjustment which over corrected for periodicity drift with redshift. We had clearly detected the z dependent drift affecting periodic phasing of quantum intervals which appear as the dipole redshift quantum interval embedded in galaxy nuclei. The issue was now to understand and correct for the distortion in order to extend studies to higher redshift.

As an alternative to his original model of z dependence of a quantized redshift periodic interval, John suggested that the intervals could be related to the square root of the Hubble constant H(t). This relationship is relatively easy to understand dimensionally in the current model of QTC which is represented as a 3-dimensional sphere of time within which particles of space, where matter resides, are outflowing on timelines diverging from a near singularity at to. The temporal nuclear dipole in galaxies, which drives galaxy evolution, is seen as evolving in quantum steps (the redshift periods), as a one dimensional interval of energy or its reciprocal time, t. The temporal volume of the universe at any instant is proportional to t cubed. The rate of change of this volume goes as t squared (the volume of a sphere grows as the square of its radius, or more generally cosmologically as the square of its scalefactor). In terms of the expansion of the universe this rate of growth is the Hubble constant, hence the dipole 1-d interval (dt) should depend upon the square root of H(t).

In any expanding evolving cosmology, based on continuous or quantum physics, the geometry of the universal medium is `curved’ and photons follow curved paths defined by the geometry. In classical cosmology curvature is induced gravitationally, relates to the deceleration status of the expansion, and is denoted as qo. Classically the curvature is seen locally as the deflection of light passing close to the sun. On the cosmological scale whether the expansion will stop and fall back (closed form), continue to expand without limit (open form) or just coast to a stop as time approaches infinity (called a flat form) depends upon the net gravitational restraint determined by the mean density (called Omega). In normalized cosmic units at a scale of 1 (now) the status depends upon whether Omega is greater or less than 1 (which defines the flat state). In fact Omega appears to be essentially equal to 1, which corresponds to qo = 1/2. This situation is referred to as the `flatness’ problem. Why should H(t) be precisely at this balance point at this moment in the history of a dynamically controlled expanding universe? In QTC there is no deceleration or acceleration, the structure is a steadily expanding sphere of time. In a dynamical formulation where qo is defined, QTC is always at the`flat’ balance point between unlimited expansion or fallback. Observed in such a dynamical formulation qo is a constant 1/2 and there is no flatness problem. It has already been shown in prior topics that gravitation does not apply between objects on the large scale in QTC. Forces do not transmit through time.

H(t) can be represented dynamically as a function of z and qo. John’s form of his H(z,qo) relationship was utilized two ways. Initially to verify that qo actually was 1/2 John proposed a study of redshift intervals seen within Lyman Alpha forests of quasars at high z (in the range z = 1.89 to 3.74). The Lyman Alpha forest redshift structure was considered to possibly be caused by dwarf galaxies, or something equivalent, in a quasar’s foreground. As such the patterns should show or include 24 km/s intervals after correction for interval distortion of redshift pairs within forests. The study does show a distinct period of 24.2 km/s, significant above the 99% level, confirming qo = 1/2. For a detailed discussion, beyond the scope of this blog, see Cocke and Tifft, Astrophysical Journal, November 15, 1989.

With the verification that qo was apparently indistinguishable from 1/2 John’s interval for the differential z interval was integrated in a Taylor series about qo = 1/2 to derive a direct relationship between an observed, z(obs), and corrected, z(corr), value for individual redshifts. That expansion yields a zero order term and higher order terms in (qo – 1/2). For qo exactly 1/2 the zero order term provides the complete correction. This is shown for the dwarf galaxy set in the upper left frame of Figure 7 of the ASP paper (figure 2.40 in my book). No phase drift with z is detectable. The formulation of the correction is shown in the lead figure of this blog, the zero order transformation is shown in both directions along with the form including the first order correction. Tests using these relationships, which have been published, are discussed in my book and find no detectable deviation from qo = 1/2. Further discussion of the correction and its relationship to the underlying quantized redshift require further information about periodicities and a transformation to a more fundamental cosmological framework which are discussed in my book and presented in following topics. With these final steps the simple zero order correction to observed redshifts, due to curvature of time in the QTC model, opened the door to studies of quantization within the large scale of the universe.

As I prepared this topic a news note just released from the 2015 General Assembly of the IAU (International Astronomical Union), currently meeting in Hawaii, indicated that the GAMA project has shown that the energy production of the universe is steadily and rather rapidly decreasing with time. The universe is in a one-way decline, which is consistent with the QTC model of an expanding decaying sphere (actually a `now’ shell in QTC) of time. Since the rate of the shell expansion in QTC is c, to the extent that the age of the universe is known the actual scale of our now shell, bounded by the past and future which reside behind dark shields, can be determined. QTC will also differ in what the nature of the energy structure actually is, but that is a different related issue for future consideration.

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