—————————— read pre-print on research gate (new window) ——————————

• θ_si can be measured as the polarization angle of quantum entangled X-rays at the degenerate frequency of a maximal Bell state. As an angle θ_si=3.26239 rad ± 2 μrad; as a momentum θ_si=3.26239030392(48) kg m s^-1 and with respect to the Target Frame, θ_si has no units. The relation of angle and mass is mathematically demonstrated, as well, by No-Ping Chen, et. al.
• n_Lc describes the count of l_f representative of a change in position of light measured with respect to the observer’s frame of reference.

• A_ee is the dilated age of the universe as measured from the current expansionary epoch. Its value is a function of expansion with respect to the total elapsed time representing the quantum epoch.
• A_qe is the non-dilated age of the universe corresponding to the quantum epoch.
• A_U is the age of the universe.
• R_U is the radius of the universe.
• l_f, m_f and t_f are the fundamental measures, more precise expressions for Planck’s units – length, mass, and time – that consider the effects of length contraction associated with discrete measure.
• n_L, n_M and n_T are physically significant discrete counts of l_f, m_f and t_f respectively.
• n_Tl is the count of t_f as measured in the local frame of reference.
• n_To is the count of t_f that is observed.

A study of temperature measurements of the CMB literature was published by D.J. Fixsen in November of 2009.¹ He found that the best measure of temperature corresponded to a value of 2.72548 +/- 0.00057 K. The study supports the Informativity expressions to four significant digits.

D.J. Fixsen, The Temperature of the Cosmic Microwave Background, (2009), arXiv: 0911.1955, http://dx.doi.org/10.1088/0004-637X/707/2/916.

We refer the reader to the prior article on the quantum epoch for a discussion of the earliest period of the universe. This epoch is characterized by a rate of expansion that is quantum in nature lasting from R_U<l_f to R_U=3l_f. Using principles of Measurement Quantization (MQ) - a physically significant description of classical expressions - we find that this epoch lasts 363,312 years before reaching the prerequisite size necessary for external referencing. Thereafter, the quantum epoch ends and the expansionary epoch begins. Knowing the fixed rate of universal mass accretion, we can then determine the associated mass/energy accumulated during the quantum epoch that is today observed as a Cosmic Microwave Background (CMB). Calculations match measurements to digit-for-digit to the same precision afforded by measurement, five digits.

Without a firm understanding of the Measurement Quantization approach, the concepts and calculations required to describe this period are not possible. As a brief overview, we note that MQ is a nomenclature predicated on observations regarding a discrete description of gravity and discrete expressions for the Heisenberg uncertainty principle, escape velocity and the speed of light. Using this approach, it is shown that measure has three properties: discreteness, countability and in reference to three frames of reference.

We refer the reader to articles such as that regarding the uncertainty principle, the fundamental measures, discrete gravity and the Shwartz and Harris quantum entanglement experiments for a discussion of the foundations of MQ. We also refer the reader to those articles on the contraction and dilation of measure with respect to an inertial frame, and the equivalence of inertial and gravitational frames for MQ specific solutions to the phenomenon also described by relativity.

With this foundation, we approach time dilation between epochs. That is, where the initial expansion was constrained by an inability to reference points outside of the quantum bubble, elapsed time is dilated with respect to that of the expansionary period.

This is important as we cannot calculate how much mass has accreted without knowing the dilation between epochs. And that relation is resolved as a function of the radial rate of expansion, as described by a scaling of the fundamental expression H_U=2θ_si.

With this, we resolve the age of the CMB relative to the internal frame of the quantum epoch to be 363,312 years. Relative to an internal frame of the expansionary epoch, this is dilated, appearing as 678,894 years.

Applied to the remaining calculations to resolve quantity, we resolve the present-day density and temperature of the CMB and this is resolved in MQ form having the same form as Einstein's SR expression for time dilation.