Measurement Quantization

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Measurement Quantization (MQ) is an approach to classical description whereby the existing nomenclature is extended so as to separate the fundamental reference measures - length, mass, and time - from counts of those measures. Historically, the notion of fundamental units of measure had been entertained, first by George Stoney as Stoney Units. and later by Planck as Planck Units. The physical significance of these unit systems had not until now been established nor were the expressions derived. By example, Planck's unit expressions were resolved by arranging the physical constants c, G, and ħ in such a way as to expose each of the three dimensions singularly.

A new paper entitled "Measurement Quantization" establishes their physical significance. For brevity, solutions found in the appendices of this MQ review paper will be denoted in advance of the citation. The paper is a summary review of prior research which advanced the MQ approach by demonstrating classical solutions to significant problems in modern physical theory. Early work in 2018 developed the initial concepts and offered physical support by way of measurements of the Planck momentum by Shwartz, et. al. In late 2018 new derivations of Einstein's expressions for special relativity were resolved from first principles, beginning with the Pythagorean theorem as a function of the discrete internal frame of reference for the universe. Discrete expressions were then derived describing the effects of relativity as a function of the initial derivation of discrete gravity. Notably, the latter expressions are not meant to replace Einstein's expressions, which approach the relativistic effects of the gravitational phenomenon as a function of field equations. Additional research in 2019 resolved classical descriptions of galactic rotation, also characterized as the dark matter phenomenon. Finally, a more comprehensive description of early universe events was resolved, which included the transition of the universe from an initial quantum epoch to its present expansionary epoch. This led to the discovery of a discrete definition for the fine structure constant, which then led to derivations of a majority of the physical constants from first principles.

The Measurement Quantization approach is advanced over prior methods with the discovery of a discrete description to gravitational curvature. With this and MQ expressions for the speed of light, escape velocity, and Heisenberg's uncertainty principle, defined relative to the internal and system frames of the universe, it is shown that there exists only one solution set to the measures of length n_L=1, time n_T=1, and mass n_M=1/2 (Appx. I, J). With this, the fundamental measures can then be derived.

Discrete Gravity

A discrete approach to describing gravitational curvature.

The MQ approach to a description of gravitational curvature is advanced over other discrete approaches, such as Loop Quantum Gravity (LQG), whereby three frames of reference are identified as physically significant (Appx. K). The reference frame is defined as the frame of the observer whereby the notions of fundamental length, mass, and time are assessed. The internal frame is assessed as a function of events and phenomena relatively within the expanding system frame of the universe. This expansion is better known as the metric expansion of space.

Therein, side a of a right-angled triangle is assigned the count value of 1, representing the reference frame of the observer. This value is constant - the same - for all considerations of distance. Side b is some count of the reference measure representative of the observed distance. And side c represents the more precise calculated count - a non-discrete result - as resolved using the Pythagorean theorem and those inputs assigned to sides a and b. Side c represents the non-discrete frame of the universe. These definitions align with respect to the previously resolved internal frame, which gives rise to the notions of measure. Whereas the system frame has no external reference, it is non-discrete. Describing the difference between these frames allows us to resolve expressions and values for the physical constants from first principles. We present the discrete solution to gravitational curvature (left) and set it equal to its classical description (right) in the expression that follows (Appx. C).

$\frac{Q_L{c}^3}{r{\theta }_{si}.}=\frac{G}{r^2}$

(Eq. 1)

Length Contraction with Respect to the Internal Frame

The most evident and immediate consequence of a discrete internal frame is length contraction as a function of distance. Specifically, where the count Q_L describes the fractional portion of the reference measure, and whereas the notion of a fractional reference has no physical significance, we find that Q_L is lost with each increment t_f in elapsed time. This loss is what leads to the phenomenon of gravitation. It also leads to a contraction of length which we can describe mathematically such that (Appx. D).

$\frac{Q_L^2}{2}+Q_L{n}_{Lr}=\frac{1}{2}$

(Eq. 2)

This length contraction effect - described as the Informativity differential - is recognized as 2Q_Ln_Lr and can be shown to have a macroscopic limit most easily shortened and described as,

$\underset{n_{Lr}\to \mathrm{\infty }}{\lim }{Q}_L{n}_{Lr}=\frac{1}{2}$

(Eq. 3)

Physical Support

Support for the physical significance of the fundamental measures as discrete references, an emergent property of the internal frame, is best approached directly, by measure of the effects of length contraction when measuring physical constants such as G and ħ. These measures are periodically carried out and published by the CODATA collaboration. We present the 2010, 2014, and 2018 publications in the first three rows of Table 1.

In the latter four rows, we use the more precise expressions of MQ - which include the effects of length contraction - to resolve the value's for each column measure as a function of either G at the electromagnetic demarcation (Appx. AB, AE, AN) (the count of l_f associated with a measure at the lower bound) or at the upper count limit. The expressions are:

$\hslash =\frac{{\theta }_{si}{l}_f}{Q_L{n}_{Lr}.}$

(Eq. 4)

$G=2Q_L{n}_{Lr}{c}^3\frac{t_f}{m_f}$

(Eq. 5)

With respect to an MQ nomenclature, upper limit measures of the physical constants are not italicized. All other measures are.

Table 1. Matching CODATA values for ħ, G and the Planck Units with MQ Calculated Values.

^a CODATA publications for 2010, 2014 and 2018.

^b Using precise G and ħ, we account for the Informativity differential at the blackbody demarcation n_Lr= 84.6005496647(07) (i.e., italicized), the upper count limit (i.e., lim_nLr→∞) (not italicized), or a mix of the two.

Therein, we find digit-for-digit correspondence with measurement. To distinguish these matches, we correlate results with calculation using differently dashed or solid lines in a given column. The changing value of G and the corresponding changes in ħ across the three publications are the result of different approaches to the measure of gravitation. Specifically, the fist row - the 2010 publication - describes a traditional measure of G, for instance that made with a pendulum. The second row describes that made using an electromagnetic field, for instance, an oil drop experiment. The third row we have highlighted in bold. This can also be calculated (Eqs. 22-27), the result of a misunderstanding of the effects of length contraction, whereby one uses Planck's expression for the ground state orbital of an atom to assess a value for the fundamental mass. One can then resolve a calculated value for G, which produces the result on line three. The remaining Planck unit values are then calculated, as noted in bold.

Importantly, these are significant discrepancies, differences in measure that have to date gone unexplained. An analysis of this measurement anomaly represents just one approach to physically assess the foundations of Measurement Quantization. While such predictions and measurements are unusual, the expressions provide a no free variable outcome supporting existing classical mechanics. Counterarguments would need to address the source expressions, either gravity, the speed of light, escape velocity or Heisenberg's uncertainty principle.

Advances Using MQ

Using the measurement quantization approach to classical expression has led to a better understanding of several difficult problems in modern physical theory. We present a list of problems addressed following. Notably, when we say addressed, this means that classical expressions are used to describe the phenomenon. The resultant calculations are then compared to the measurement data - often in a table like the table presented above - whereby digit-for-digit correspondence is demonstrated to the extent of our best measurements. Such physical correspondence is not unexpected with respect to classical expression.

1. With MQ we derive expressions from first principles for the physical constants along with resultant calculated values (Appx. L, M, W, AA, AM, AO, AP, AQ, BA). Notably, all derivations are a function of only the fundamental measures (Appx. W).
2. MQ offers a unifying description of the gravitational and electric constants (Appx. AT) (see also) therein describing a geometry that separates the phenomena of gravitation from electromagnetism. Notably, while the MQ approach achieves a physical understanding of this relation, this differs from the long-held goal of unification by means of field theory.
3. MQ defines and correlates the discrete internal frame of the universe with the non-discrete system frame of the universe (Appx. K). The difference between these frames is one significant advance over other discrete approaches such as Loop Quantum Gravity.
4. MQ provides a no free variable description of an early quantum epoch (Appx. BG) wherein mass accretes at a constant rate (Appx. BE). This period addresses the homogenous and isotropic properties of the CMB as it is observed today.
5. The size of the universe can be calculated as a function of its age to five significant digits (Appx. AZ).
6. MQ provides a single classical expression that describes galactic rotation (Appx. AK), thus providing a classical solution to the controversy known as dark matter. When calculations are plotted with respect to star velocity data provided by S. McGaugh, a standard deviation of 1.394 km/s is found.
7. MQ provides a description of the expanding universe - also characterized by the phenomenon known as dark energy - whereby the metric expansion of space is a geometric quality of the universe (Appx. AY, BA, BB, BD).
8. MQ provides clarity around the subject of multidimensional models, such that such models are inconsistent with the existing laws of classical mechanics (Appx. Appx. I, J). Fortunately, MQ offers a test for such models. Any dimension having a count of two or greater must carry with it the phenomenon of contraction (Appx. D), as demonstrated in Table 1.
9. MQ demonstrates that the Planck units are physically significant (Appx. I, J, X).
10. MQ presents a solution to the Hubble Tension, such that the difference between measures of universal expansion between studies using the CMB and studies using cepheids is a function of the geometry used in these physically different approaches.
11. MQ is used to derive new and existing expressions from first principles (Appx. AU, AV, AW) that describe those effects also described by Einstein, otherwise characterized as special and general relativity. Notably, the MQ approach to a description of the phenomenon of gravitation is not a field theory. MQ achieves a description as a function of motion (Appx. C), therein making both descriptions physically compatible.
12. MQ offers a derivation of the equivalence principle (Appx. AW).

Predictions

Use of the measurement quantization approach to physical description offers many opportunities to predict presently unknown measurements and later confirm those measurements. For one, MQ correlates the quantum with the macroscopic as well as the cosmological (Appx. AY), therein offering up to 13 digits of physical significance for calculated values such as the gravitational constant. MQ also makes a few surprise predictions regarding increasing mass in the universe and the order of events in the early evolution of our universe. We list the more notable predictions here.

1. MQ offers a calculated value for the gravitational constant with 13 digits of physical significance, 6.6740779428(56) 10^-11 m³ kg^-1 s^-2 (Appx. BM).
2. MQ offers a calculated value for half of the Planck momentum equal to 3.26239030392(48) kg m s^-1 (Appx. AD), a function of the measure of the fine structure constant
3. MQ uses physical support to predict a new form of length contraction associated with distance measurement (Appx. D).. This effect is unrelated to motion and gravitation, as described by Einstein
4. MQ presents that there was no inflationary period. (Appx. BF-BH). Such a period is neither predicted by the laws of classical mechanics nor physically supported by measures of the quantity, age, and present-day density and temperature of the CMB (Appx. BH)
5. The MQ approach to classical expression resolves that the mass of the universe is increasing at a steady rate (Appx. BE).
6. Where MQ demonstrates that the internal frame is physically significant (Appx. I, J), MQ recognizes that space is not curved. That is to say, the notion of length cannot possess a physically significant feature known as curvature, because fundamental length is a reference feature of the internal frame of the universe. Therein, MQ recognizes that space only appears curved, a function of the loss of the fractional count Q_L of l_f with each increment in elapsed time t_f. We confirm this interpretation as physically assessed in Table 1.
7. Where MQ demonstrates that the expansion of the universe is a geometric expansion of the fundamental expression (Appx. V). - a conserved relation describing length, mass, and time - we find that the universe must be flat (Appx. AY, BD)

Challenges to Measurement Quantization

Wherein the usually challenge of an advance in the foundations of physical theory must also satisfy all existing confirmation of classical investigation, MQ does not change or augment our existing understanding of classical mechanics. MQ is a physically significant expansion of the existing nomenclature, therein inheriting the physical support on which classical mechanics is built. This challenge to new ideas has often been cited as the largest impediment to any proposal that offers alternatives to the existing development of the Standard Model. Notably, C. Corda offers a unique constraining test which eliminates many competing theories, but not MQ.

An early phase challenge to MQ regards something known as a non-dimensional approach to classical expression. MQ escapes this challenge as well, as each count value is correlated with its corresponding dimensional measure. By example, we cannot freely mix, add or integrate a count of fundamental units of time with a count of fundamental units of length. All pitfalls to the use of dimensionless terms in classical expression are avoided.

References

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