Fundamental Constants

Atomic mass measurements are essential for obtaining several of the fundamental constants. The most precise atomic mass measurements, at the 10 −10 level of precision or better, employ measurements of cyclotron frequencies of single ions in Penning traps. We discuss the relation of atomic masses to fundamental constants in the context of the revised SI. We then review experimental methods, and the current status of measurements of the masses of the electron, proton, neutron, deuteron, tritium, helium-3, helium-4, oxygen-16, silicon-28, rubidium-87, and cesium-133. We conclude with directions for future work.

We show how removing faith-based beliefs in current philosophies of classical and constructive mathematics admits formal, evidence-based, definitions of constructive mathematics; of a constructively well-defined logic of a formal mathematical language; and of a constructively well-defined model of such a language.

We argue that, from an evidence-based perspective, classical approaches which follow Hilbert's formal definitions of quantification can be labelled `theistic'; whilst constructive approaches based on Brouwer's philosophy of Intuitionism can be labelled `atheistic'.

We then adopt what may be labelled a finitary, evidence-based, `agnostic' perspective and argue that Brouwerian atheism is merely a restricted perspective within the finitary agnostic perspective, whilst Hilbertian theism contradicts the finitary agnostic perspective.

We then consider the argument that Tarski's classic definitions permit an intelligence---whether human or mechanistic---to admit finitary, evidence-based, definitions of the satisfaction and truth of the atomic formulas of the first-order Peano Arithmetic PA over the domain N of the natural numbers in two, hitherto unsuspected and essentially different, ways.

We show that the two definitions correspond to two distinctly different---not necessarily evidence-based but complementary---assignments of satisfaction and truth to the compound formulas of PA over N.

We further show that the PA axioms are true over N, and that the PA rules of inference preserve truth over N, under both the complementary interpretations; and conclude some unsuspected constructive consequences of such complementarity for the foundations of mathematics, logic, philosophy, and the physical sciences.

Quantum Queries explores a variety of issues involving some of the puzzles and prospects associated with important topics in physics such as: Constants, antimatter asymmetries, neutrinos, entanglement, Bohr-Einstein debates, quantum mechanics, the Higgs mechanism, Heisenberg uncertainty, superposition principle, the many-worlds perspective, vacuum energy, dimensionality, special relativity, particle physics, scientific methodology, grand unification models, and Supersymmetry. While the foregoing discussions are neither exhaustive nor definitive, nonetheless, the purpose of the critical reflections being alluded to above are directed toward addressing one basic question: To what extent do the foregoing ideas -- considered either singly or collectively -- help to resolve the reality problem with which all human beings are faced?

Table of Content of Vol I - Revision I (2017) of this Title
A vast program of axiomatization of physics in direct response to David Hilbert's 6th Problem with tangible and verifiable numeric results. A resolution of long-time search for theoretical derivation of the fundamental physical constants and origin of the primordial mathematical-physics symmetries subtending the quantum realm and the cosmological arena.

Research into ancient physical structures, some having been known as the seven wonders of the ancient world, inspired new developments in the early history of mathematics. At the other end of this spectrum of inquiry the research is concerned with the minimum of observations from physical data as exemplified by Eddington's Principle. Current discussions of the interplay between physics and mathematics revive some of this early history of mathematics and offer insight into the fine-structure constant. Arthur Eddington's work leads to a new calculation of the inverse fine-structure constant giving the same approximate value as ancient geometry combined with the golden ratio structure of the hydrogen atom. The hyperbolic function suggested by Alfred Landé leads to another result, involving the Laplace limit of Kepler's equation, with the same approximate value and related to the aforementioned results. The accuracy of these results are consistent with the standard reference. Relationships between the four fundamental coupling constants are also found.

Using a long-range polarization potential for HeH+, we can obtain an empirical value for the Boltzmann constant kB with an order of magnitude greater precision than the previous best experimental value based on the dipole polarizability of 4He. We find that relativistic and QED effects of order αFS in the fine structure constant are crucial in the quadrupole polarizability in order to fit the dipole polarizbility with this precision using the polarization potential. By calculating finite-mass corrections for 3He, we also present theoretical values for the dipole and quadrupole polarizabilities of 3He with 9 and 7 digits of precision respectively.

This academic paper is a collection of notes I created while taking an online Calculus course. To assist much of my self-taught knowledge, I wrote these notes in a handheld notebook. This notebook would serve as the foundation for what turned out to be a platform for many independent discoveries years later. I began to notice repetitive underlying patterns, sequences, and constants. This paper further investigates these discoveries as a way to discover a simpler execution. Disclaimer I am an architecture alumnus by way of educational training and a project manager by way of profession. I am not a mathematician so my findings may be rudimentary to some scholars with a higher degree of acumen in the related subjects. This was my way of trying to make sense of calculus. If anyone can point out any erroneous nature to my findings, please do so in a respectable and patient manner. I have attached images of my handwritten notes so one can see the thought process behind the execution. I am a visual learner so I have adopted tendencies in showcasing my work in a similar fashion, making it aesthetically pleasing to the eyes.

This paper will present some time dependent relations among fundamental constants which are presented as being novel. They are derived from the Expansion Field Equation which was presented in my paper entitled " Expansion Field Theory as a Foundation for a Unified Theory of Fields. " (EFT). Starting with the Gravitational Constant, time dependent relations are derived using EFT for the following Constants: The Elementary Charge (Q)*, The Electron Mass (Me),and The Bohr Radius, (a 0).

The vacuum catastrophe results from the disagreement between the theoretical value of the energy density of the vacuum in quantum field theory and the estimated one observed in cosmology. In a similar attempt in which the ultraviolet catastrophe was solved, we search for the value of the cosmological constant by brute-force through computation. We explore combinations of the fundamental constants in physics performing a dimensional analysis, in search of an equation resulting in the measured energy density of the vacuum or cosmological constant that is assumed to cause the accelerated expansion of the universe.

A new cosmological paradigm based upon global discrete scale invariance proposes a radical revision in our understanding of atomic scale dynamics.  The discrete fractal scaling of this paradigm predicts a very large and discrete scale-dependence for gravitational coupling factors.  The alternative gravitational scaling leads to revised values for the Planck mass, Planck length and Planck time, which appear to be more unified and physically comprehensible than is the case with the conventional Planck scale values.  The fundamental interrelationship of the revised Planck mass, the corrected gravitational constant for atomic scale systems, the reduced Planck’s constant and the velocity of light suggests a hidden meaning for Planck’s constant.  Within the context of the discrete fractal cosmological paradigm, Planck’s constant is revealed as the fundamental unit of gravitational action for atomic scale systems.  Implications for atomic scale dynamics are briefly outlined.

In my articles of 1992-1996 it was demonstrated that size of elements of matter (particles, DNA molecule...) are whole integer numbers since it is related with their wave nature. The size (curvature) is wave number. The wave number is number of waves in some resonator, it is measured in reversed meters, the same notion is "curvature" that is value of reversed radius. It is resonance condition of existence of elements of matter. So, we can present the speed of light value as whole number. It can be useful for accurate calculations in space projects.

We constrain the deviation of adiabatic evolution of the Universe using the data on the Cosmic Microwave Background (CMB) temperature anisotropies measured by the {\it Planck} satellite and a sample of 481 X-ray selected clusters with spectroscopically measured redshifts. To avoid antenna beam effects, we bring all the maps to the same resolution. We use a CMB template to subtract the cosmological signal while preserving the Thermal Sunyaev-Zeldovich (TSZ) anisotropies; next, we remove galactic foreground emissions around each cluster and we mask out all known point sources. If the CMB black-body temperature scales with redshift as $T(z)=T_0(1+z)^{1−\alpha}$, we constrain deviations of adiabatic evolution to be $\alpha=−0.007\pm0.013$, consistent with the temperature-redshift relation of the standard cosmological model. This result could suffer from a potential bias associated with the CMB template, that we quantify it to be less than −0.02, but is free from those biases associated with using TSZ selected clusters; it represents the best constraint to date of the temperature-redshift relation of the Big-Bang model, confirming previous results.

Robert Brandom holds that what we mean is best understood in terms of what inferences we are prepared to defend, and that such a defence is best understood in terms of rule-governed social interactions. This manages to explain quite a lot. However, for those who think that there is more to making correct/incorrect inferences than obeying/breaking accepted rules, Brandom’s account fails to adequately capture what it means to reason properly. Thus, in an effort to sketch an alternative that does not rely primarily on peer pressure, I draw on the work of C. S. Peirce. Peirce argued that, when we reason, we manipulate abstract diagrams in order to observe what results. Since some manipulations are barred by the self-same nature of the diagrams, I try to show that this qualitative incompatibility, which I dub “contrapiction,” is a good (non-social) reason to regard some reasoning as bad.

This paper presents work extracted from a more complete unified theory. It is abbreviated and introduces changes to fundamental properties as if they are curiosities.  The results are hoped to demonstrate that the changes must be more than curiosities. The idea presented in previous papers and used  here is that: Empirical evidence consists of changes in patterns of changes  of velocities of objects; and that: All properties inferred to exist from empirical evidence must be definable in the same terms as that evidence is expressed. The evidence is expressed in measures of distance and time. The special increment of time returns in this paper. The increment has the same magnitude as electric charge. It is the period of time required for light to travel the radius of the hydrogen atom.

This academic paper is a collection of notes I created while taking an online Calculus course. To assist much of my self-taught knowledge, I wrote these notes in a handheld notebook. This notebook would serve as the foundation for what turned out to be a platform for many independent discoveries years later. I began to notice repetitive underlying patterns, sequences, and constants. This paper further investigates these discoveries as a way to discover a simpler execution. Disclaimer I am an architecture alumnus by way of educational training and a project manager by way of profession. I am not a mathematician so my findings may be rudimentary to some scholars with a higher degree of acumen in the related subjects. This was my way of trying to make sense of calculus. If anyone can point out any erroneous nature to my findings, please do so in a respectable and patient manner. I have attached images of my handwritten notes so one can see the thought process behind the execution. I am a visual learner so I have adopted tendencies in showcasing my work in a similar fashion, making it aesthetically pleasing to the eyes.

Rather than attempting to fit gravitation into the quantum format, quanta are derived from gravitation, i.e. electron mass, m^3 = k^2 (H/G) (e/c)^4; light quark mass mass, m^3 = (H/G) (h/c)^2; relativity/quantum bridge, γ^2 = (n/2) (α sub-g)^-1; Strong force, Fg,1 = 0.021(c^17hH^2/G^5)^1/6; where H ≈ 6 x 10^-13 m/s^2, prediction for acceleration of the local galactic supercluster. Dark energy and "dark matter" as field are implicit, where the mass density about a galaxy, for instance, should fall off at ρ ≈ 0.002 r^-1 kg/m^3. Particles are seen as gravitational sinks instead of sources, avoiding renormalization and the overwhelming calculated mass of the quantum vacuum.

Atomic mass measurements are essential for obtaining several of the fundamental constants. The most precise atomic mass measurements, at the 10 −10 level of precision or better, employ measurements of cyclotron frequencies of single ions in Penning traps. We discuss the relation of atomic masses to fundamental constants in the context of the revised SI. We then review experimental methods, and the current status of measurements of the masses of the electron, proton, neutron, deuteron, tritium, helium-3, helium-4, oxygen-16, silicon-28, rubidium-87, and cesium-133. We conclude with directions for future work.

In 2018 the units of the International System are expected to be redefined by fixing the numerical values of seven constants. In addition to specifying units, these definitions will implicitly specify a set of metric conventions – namely, criteria for determining equality among quantity intervals – for many kinds of quantity. For these kinds of quantity, the determination of differences and ratios will become implicitly tied to the mathematical forms of accepted fundamental laws. This overlooked consequence of the redefinition generates a conceptual tension between the need for long-lasting unit definitions and the need for testable fundamental laws. While fundamental laws will remain testable through the same methods that have been employed for their testing prior to the redefinition, certain kinds of evidence that support challenges to fundamental theory will become unavailable under the ‘New SI’.

We propose an improved methodology to constrain spatial variations of the fine structure constant using clusters of galaxies. We use the Planck 2013 data to measure the thermal Sunyaev-Zeldovich effect at the location of 618 X-ray selected clusters. We then use a Monte Carlo Markov Chain algorithm to obtain the temperature of the Cosmic Microwave Background at the location of each galaxy cluster. When fitting three different phenomenological parameterizations allowing for monopole and dipole amplitudes in the value of the fine structure constant we improve the results of earlier analysis involving clusters and CMB power spectrum, and we also found that the best-fit direction of a hypothetical dipole is compatible with the direction of other known anomalies. Although the constraining power of our current datasets do not allow us to test the indications of a dipole obtained though high-resolution optical/UV spectroscopy, our results do highlight that clusters of galaxies will be a very powerful tool to probe fundamental physics at low redshift.