Improving the Accuracy of the Numerical Values of the Estimates Some Fundamental Physical Constants

Total Page:16

File Type:pdf, Size:1020Kb

Improving the Accuracy of the Numerical Values of the Estimates Some Fundamental Physical Constants Improving the accuracy of the numerical values of the estimates some fundamental physical constants. Valery Timkov, Serg Timkov, Vladimir Zhukov, Konstantin Afanasiev To cite this version: Valery Timkov, Serg Timkov, Vladimir Zhukov, Konstantin Afanasiev. Improving the accuracy of the numerical values of the estimates some fundamental physical constants.. Digital Technologies, Odessa National Academy of Telecommunications, 2019, 25, pp.23 - 39. hal-02117148 HAL Id: hal-02117148 https://hal.archives-ouvertes.fr/hal-02117148 Submitted on 2 May 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Improving the accuracy of the numerical values of the estimates some fundamental physical constants. Valery F. Timkov1*, Serg V. Timkov2, Vladimir A. Zhukov2, Konstantin E. Afanasiev2 1Institute of Telecommunications and Global Geoinformation Space of the National Academy of Sciences of Ukraine, Senior Researcher, Ukraine. 2Research and Production Enterprise «TZHK», Researcher, Ukraine. *Email: [email protected] The list of designations in the text: l p - the length of the Planck; mp - the mass of the Planck; t p - the time of the Planck; mp - the mass of the Planck, which determined through the characteristics of muon; l p - the length of the Planck, which determined through the characteristics of muon; t p - the time of the Planck, which determined through the characteristics of muon; c - the speed of light in a vacuum; qp - the Planck charge; e - the elementary electric charge; - the fine structure constant; h - the Planck constant over 2pi; G - the gravitational constant; ap - the Planck acceleration; a p - the Planck acceleration, which is determined based on the characteristics of the muon; Fp - the Planck force; Fp - the Planck force, which is determined based on the characteristics of the muon; Ep - the Planck energy; E p - the Planck energy, which is determined based on the characteristics of the muon; Pp - the Planck power; Pp - the Planck power, which is determined based on the characteristics of the muon; Tp - the Planck temperature; Tp - the Planck temperature, which is determined based on the characteristics of the muon; k - the Boltzmann constant; Sp - the total of energy luminosity of a hypothetical Planck particle; S p - the total of energy luminosity of a hypothetical Planck particle, which is determined based on the characteristics of the muon; - the constant of Stephen – Boltzmann; I p - the current of Planck; I p - the current of Planck, which is determined based on the characteristics of the muon; Vp - the voltage of Planck; Vp - the voltage of Planck, which is determined based on the characteristics of the muon; Z p - the impedance of Planck; Z p - the impedance of Planck, which is determined based on the characteristics of the muon; Z0 - the characteristic impedance of vacuum; C p - the electric capacitance of Planck; C p - the electric capacitance of Planck, which is determined based on the characteristics of the muon; Lp - the inductance of Planck; L p - the inductance of Planck, which is determined based on the characteristics of the muon; Bp - the module of the magnetic induction of Planck; Bp - the module of the magnetic induction of Planck, which is determined based on the characteristics of the muon; H p - the module of the magnetic field strength of Planck; - the module of the magnetic field strength of Planck, which is determined based on the characteristics of the muon; 0 - the magnetic constant; R - the Rydberg constant; Ry - the Rydberg constant times hc in J; Rc - the Rydberg constant times c in Hz; p DC - the proton Compton wavelength over 2 pi; n0 DC - the neutron Compton wavelength over 2 pi; e DC - the electron Compton wavelength over 2 pi; DC - the muon Compton wavelength over 2 pi; a0 - the Bohr radius; me - the electron mass; m - the proton mass; p m - the neutron mas; n0 m - the muon mass; ke - the electric force constant; RK - the von Klitzing constant; KJ - the Josephson constant; Eh - the constant Hartree energy; pl - the estimate of the value of the linear density of the Planck mass, which determined through the characteristics of muon; ps - the estimate of the value of the surface density of the Planck mass, which determined through the characteristics of muon; pv - the estimate of the value of the density of the Planck mass, which determined through the characteristics of muon. Abstract. At the 26th General Conference on Measures and Weights, it was decided to switch from natural standards in the international system of SI units to standards that are based on fundamental physical constants. This solution raises the requirement for the accuracy of the numerical values of the fundamental physical constants. A technique is proposed for improving the accuracy of numerical values of the estimates: of Planck's constant over 2pi, of gravitational constant, of electric charge, of Planck temperature, of Planck acceleration, of Planck force, of Planck energy, of electron mass, of proton mass, of neutron mass, of Rydberg constant times hc in J, of Rydberg constant times c in Hz, of von Klitzing constant, of constant Hartree energy, of Josephson constant based on their representation through Planck's constants: of length, of mass, of time. Increasing of the accuracy numerical values of Planck’s length’s and the Planck’s mass is based on the fractal similarity of the golden algebraic fractals of the main characteristics of the hypothetical Planck particle and muon. Also, to improve the accuracy of the numerical values of the fundamental physical constants, the following physical laws are applied: the ratio of the Bohr radius to the Compton electron wavelength over 2pi is equal to the fine structure constant. The moment of the mass of any elementary particle, defined through its Compton wavelength over 2pi, is equal to the moment of Planck’s mass. The fine structure constant can be determined through the Bohr radius and the Rydberg constant. Keywords: Planck's constant; fundamental physical constants; fractals; the accuracy units of measure. 1. Introduction. Some fundamental physical constants can be expressed in terms of Planck's constants: of the length lp , of the mass mp , of the time tp. According to CODATA [1], their numerical values have the following values: qp 35 8 44 lp 1.616 229(38) 10m ; mpp 2.176 470(51) 10 kg ; t 5.391 16(13) 10 s . (1) 6 From (1) it follows that the accuracy of the numerical values l p and mp is 10 , and the accuracy of the numerical 5 valueh t p is 10 . The speed of light in vacuum c , taking into account (1): lp сs299 792 438 m11 . (2) tp The speed of light in a vacuum according to CODATA-2014 [1]: сs 299 792 458 m11 . (3) The Planck charge : e qC 1.875 5459 018 ,1 (4) p where: e the elementary electric charge according to CODATA-2014 [1]: e 1.602 176 6208(98) 1019 C , (5) the fine structure constant according to CODATA-2014 [1]: 7.297 352 5664 1033 (0.000 000 0017 10 ). (6) It is known [2] that: 2 7 36 2 qp10 m p l p 3.517 673 932 10 C , kgm ; (7) 2 7 38 2 e10 mpp l 2.566 970 689 10 C , kgm . (8) The Planck constant over 2pi with (1,3,5,6,8): 2 mppl h 1.054 572 0440 1034 Js , (9) t p or: 34 h mpp l c 1.054 572 1144 10Js , (10) or: ec2 h 1.054 571 8001 1034 Js . (11) 107 The Planck constant over 2pi according to CODATA-2014 [1]: h 1.054 571 800 1034 Js.(13) (12) The gravitational constant taking into account (1,3,5,6,12): 3 lp 11 3 1 2 (13) G2 6.674 082 298 10 m kg s , mtpp or: 2 lcp G 6.674 083 188 1011 m 3 kg 1 s 2 , (14) mp or: hc 11 3 1 2 (15) G2 6.674 081 199 10 m kg s , mp or: 23 lcp G 6.674 085 179 1011 m 3 kg 1 s 2 , (16) h or: 25 tcp G 6.674 086 069 1011 m 3 kg 1 s 2 , (17) h or: 22 lcp G107 6.674 085 177 10 11 m 3 kg 1 s 2 . (18) e2 Theh Gravitational constant according to CODATA-2014 [1]: 11 3 1 2 G G6.674 08(31) 10 m kg s . (19) The Planck acceleration ap : lp 51 1 2 (20) amp 2 5.560 815 075 10 s , tp Fp or: c am 5.560 815 4460 1051 1 s 2 . (21) p t Ep p The Planck force : mlpp 44 1 1 2 (22) Fp m p a p 2 1.210 294 719 10 kg m s , tp or: mcp 44 1 1 2 Fp m p a p 1.210 294 799 10 kg m s . (23) tp The Planck energy : 29 Epp m c 1.956 113 684 10 J , (24) or: 2 mlpp 9 (25) Ep F p l p 2 1.956 113 423 10 J , t p or: mpp cl 9 Ep F p l p 1.956 113 553 10 J , (26) t p or: h 9 EJp 1.956 112 970 10 , (27) tp or: 2 ec 9 (28) EJp 7 1.956 112 970 10 .
Recommended publications
  • Quantum Theory of the Hydrogen Atom
    Quantum Theory of the Hydrogen Atom Chemistry 35 Fall 2000 Balmer and the Hydrogen Spectrum n 1885: Johann Balmer, a Swiss schoolteacher, empirically deduced a formula which predicted the wavelengths of emission for Hydrogen: l (in Å) = 3645.6 x n2 for n = 3, 4, 5, 6 n2 -4 •Predicts the wavelengths of the 4 visible emission lines from Hydrogen (which are called the Balmer Series) •Implies that there is some underlying order in the atom that results in this deceptively simple equation. 2 1 The Bohr Atom n 1913: Niels Bohr uses quantum theory to explain the origin of the line spectrum of hydrogen 1. The electron in a hydrogen atom can exist only in discrete orbits 2. The orbits are circular paths about the nucleus at varying radii 3. Each orbit corresponds to a particular energy 4. Orbit energies increase with increasing radii 5. The lowest energy orbit is called the ground state 6. After absorbing energy, the e- jumps to a higher energy orbit (an excited state) 7. When the e- drops down to a lower energy orbit, the energy lost can be given off as a quantum of light 8. The energy of the photon emitted is equal to the difference in energies of the two orbits involved 3 Mohr Bohr n Mathematically, Bohr equated the two forces acting on the orbiting electron: coulombic attraction = centrifugal accelleration 2 2 2 -(Z/4peo)(e /r ) = m(v /r) n Rearranging and making the wild assumption: mvr = n(h/2p) n e- angular momentum can only have certain quantified values in whole multiples of h/2p 4 2 Hydrogen Energy Levels n Based on this model, Bohr arrived at a simple equation to calculate the electron energy levels in hydrogen: 2 En = -RH(1/n ) for n = 1, 2, 3, 4, .
    [Show full text]
  • An Atomic Physics Perspective on the New Kilogram Defined by Planck's Constant
    An atomic physics perspective on the new kilogram defined by Planck’s constant (Wolfgang Ketterle and Alan O. Jamison, MIT) (Manuscript submitted to Physics Today) On May 20, the kilogram will no longer be defined by the artefact in Paris, but through the definition1 of Planck’s constant h=6.626 070 15*10-34 kg m2/s. This is the result of advances in metrology: The best two measurements of h, the Watt balance and the silicon spheres, have now reached an accuracy similar to the mass drift of the ur-kilogram in Paris over 130 years. At this point, the General Conference on Weights and Measures decided to use the precisely measured numerical value of h as the definition of h, which then defines the unit of the kilogram. But how can we now explain in simple terms what exactly one kilogram is? How do fixed numerical values of h, the speed of light c and the Cs hyperfine frequency νCs define the kilogram? In this article we give a simple conceptual picture of the new kilogram and relate it to the practical realizations of the kilogram. A similar change occurred in 1983 for the definition of the meter when the speed of light was defined to be 299 792 458 m/s. Since the second was the time required for 9 192 631 770 oscillations of hyperfine radiation from a cesium atom, defining the speed of light defined the meter as the distance travelled by light in 1/9192631770 of a second, or equivalently, as 9192631770/299792458 times the wavelength of the cesium hyperfine radiation.
    [Show full text]
  • Units and Magnitudes (Lecture Notes)
    physics 8.701 topic 2 Frank Wilczek Units and Magnitudes (lecture notes) This lecture has two parts. The first part is mainly a practical guide to the measurement units that dominate the particle physics literature, and culture. The second part is a quasi-philosophical discussion of deep issues around unit systems, including a comparison of atomic, particle ("strong") and Planck units. For a more extended, profound treatment of the second part issues, see arxiv.org/pdf/0708.4361v1.pdf . Because special relativity and quantum mechanics permeate modern particle physics, it is useful to employ units so that c = ħ = 1. In other words, we report velocities as multiples the speed of light c, and actions (or equivalently angular momenta) as multiples of the rationalized Planck's constant ħ, which is the original Planck constant h divided by 2π. 27 August 2013 physics 8.701 topic 2 Frank Wilczek In classical physics one usually keeps separate units for mass, length and time. I invite you to think about why! (I'll give you my take on it later.) To bring out the "dimensional" features of particle physics units without excess baggage, it is helpful to keep track of powers of mass M, length L, and time T without regard to magnitudes, in the form When these are both set equal to 1, the M, L, T system collapses to just one independent dimension. So we can - and usually do - consider everything as having the units of some power of mass. Thus for energy we have while for momentum 27 August 2013 physics 8.701 topic 2 Frank Wilczek and for length so that energy and momentum have the units of mass, while length has the units of inverse mass.
    [Show full text]
  • Rydberg Constant and Emission Spectra of Gases
    Page 1 of 10 Rydberg constant and emission spectra of gases ONE WEIGHT RECOMMENDED READINGS 1. R. Harris. Modern Physics, 2nd Ed. (2008). Sections 4.6, 7.3, 8.9. 2. Atomic Spectra line database https://physics.nist.gov/PhysRefData/ASD/lines_form.html OBJECTIVE - Calibrating a prism spectrometer to convert the scale readings in wavelengths of the emission spectral lines. - Identifying an "unknown" gas by measuring its spectral lines wavelengths. - Calculating the Rydberg constant RH. - Finding a separation of spectral lines in the yellow doublet of the sodium lamp spectrum. INSTRUCTOR’S EXPECTATIONS In the lab report it is expected to find the following parts: - Brief overview of the Bohr’s theory of hydrogen atom and main restrictions on its application. - Description of the setup including its main parts and their functions. - Description of the experiment procedure. - Table with readings of the vernier scale of the spectrometer and corresponding wavelengths of spectral lines of hydrogen and helium. - Calibration line for the function “wavelength vs reading” with explanation of the fitting procedure and values of the parameters of the fit with their uncertainties. - Calculated Rydberg constant with its uncertainty. - Description of the procedure of identification of the unknown gas and statement about the gas. - Calculating resolution of the spectrometer with the yellow doublet of sodium spectrum. INTRODUCTION In this experiment, linear emission spectra of discharge tubes are studied. The discharge tube is an evacuated glass tube filled with a gas or a vapor. There are two conductors – anode and cathode - soldered in the ends of the tube and connected to a high-voltage power source outside the tube.
    [Show full text]
  • Estimation of Forest Aboveground Biomass and Uncertainties By
    Urbazaev et al. Carbon Balance Manage (2018) 13:5 https://doi.org/10.1186/s13021-018-0093-5 RESEARCH Open Access Estimation of forest aboveground biomass and uncertainties by integration of feld measurements, airborne LiDAR, and SAR and optical satellite data in Mexico Mikhail Urbazaev1,2* , Christian Thiel1, Felix Cremer1, Ralph Dubayah3, Mirco Migliavacca4, Markus Reichstein4 and Christiane Schmullius1 Abstract Background: Information on the spatial distribution of aboveground biomass (AGB) over large areas is needed for understanding and managing processes involved in the carbon cycle and supporting international policies for climate change mitigation and adaption. Furthermore, these products provide important baseline data for the development of sustainable management strategies to local stakeholders. The use of remote sensing data can provide spatially explicit information of AGB from local to global scales. In this study, we mapped national Mexican forest AGB using satellite remote sensing data and a machine learning approach. We modelled AGB using two scenarios: (1) extensive national forest inventory (NFI), and (2) airborne Light Detection and Ranging (LiDAR) as reference data. Finally, we propagated uncertainties from feld measurements to LiDAR-derived AGB and to the national wall-to-wall forest AGB map. Results: The estimated AGB maps (NFI- and LiDAR-calibrated) showed similar goodness-of-ft statistics (R­ 2, Root Mean Square Error (RMSE)) at three diferent scales compared to the independent validation data set. We observed diferent spatial patterns of AGB in tropical dense forests, where no or limited number of NFI data were available, with higher AGB values in the LiDAR-calibrated map. We estimated much higher uncertainties in the AGB maps based on two-stage up-scaling method (i.e., from feld measurements to LiDAR and from LiDAR-based estimates to satel- lite imagery) compared to the traditional feld to satellite up-scaling.
    [Show full text]
  • Package 'Constants'
    Package ‘constants’ February 25, 2021 Type Package Title Reference on Constants, Units and Uncertainty Version 1.0.1 Description CODATA internationally recommended values of the fundamental physical constants, provided as symbols for direct use within the R language. Optionally, the values with uncertainties and/or units are also provided if the 'errors', 'units' and/or 'quantities' packages are installed. The Committee on Data for Science and Technology (CODATA) is an interdisciplinary committee of the International Council for Science which periodically provides the internationally accepted set of values of the fundamental physical constants. This package contains the ``2018 CODATA'' version, published on May 2019: Eite Tiesinga, Peter J. Mohr, David B. Newell, and Barry N. Taylor (2020) <https://physics.nist.gov/cuu/Constants/>. License MIT + file LICENSE Encoding UTF-8 LazyData true URL https://github.com/r-quantities/constants BugReports https://github.com/r-quantities/constants/issues Depends R (>= 3.5.0) Suggests errors (>= 0.3.6), units, quantities, testthat ByteCompile yes RoxygenNote 7.1.1 NeedsCompilation no Author Iñaki Ucar [aut, cph, cre] (<https://orcid.org/0000-0001-6403-5550>) Maintainer Iñaki Ucar <[email protected]> Repository CRAN Date/Publication 2021-02-25 13:20:05 UTC 1 2 codata R topics documented: constants-package . .2 codata . .2 lookup . .3 syms.............................................4 Index 6 constants-package constants: Reference on Constants, Units and Uncertainty Description This package provides the 2018 version of the CODATA internationally recommended values of the fundamental physical constants for their use within the R language. Author(s) Iñaki Ucar References Eite Tiesinga, Peter J. Mohr, David B.
    [Show full text]
  • Certain Investigations Regarding Variable Physical Constants
    IJRRAS 6 (1) ● January 2011 www.arpapress.com/Volumes/Vol6Issue1/IJRRAS_6_1_03.pdf CERTAIN INVESTIGATIONS REGARDING VARIABLE PHYSICAL CONSTANTS 1 2 3 Amritbir Singh , R. K. Mishra & Sukhjit Singh 1 Department of Mathematics, BBSB Engineering College, Fatehgarh Sahib, Punjab, India 2 & 3 Department of Mathematics, SLIET Deemed University, Longowal, Sangrur, Punjab, India. ABSTRACT In this paper, we have investigated details regarding variable physical & cosmological constants mainly G, c, h, α, NA, e & Λ. It is easy to see that the constancy of G & c is consistent, provided that all actual variations from experiment to experiment, or method to method, are due to some truncation or inherent error. It has also been noticed that physical constants may fluctuate, within limits, around average values which themselves remain fairly constant. Several attempts have been made to look for changes in Plank‟s constant by studying the light from quasars and stars assumed to be very distant on the basis of the red shift in their spectra. Detail Comparison of concerned research done has been done in the present paper. Keywords: Fundamental physical constants, Cosmological constant. A.M.S. Subject Classification Number: 83F05 1. INTRODUCTION We all are very much familiar with the importance of the 'physical constants‟, now in these days they are being used in all the scientific calculations. As the name implies, the so-called physical constants are supposed to be changeless. It is assumed that these constants are reflecting an underlying constancy of nature. Recent observations suggest that these fundamental Physical Constants of nature may actually be varying. There is a debate among cosmologists & physicists, whether the observations are correct but, if confirmed, many of our ideas may have to be rethought.
    [Show full text]
  • Chapter 09584
    Author's personal copy Excitons in Magnetic Fields Kankan Cong, G Timothy Noe II, and Junichiro Kono, Rice University, Houston, TX, United States r 2018 Elsevier Ltd. All rights reserved. Introduction When a photon of energy greater than the band gap is absorbed by a semiconductor, a negatively charged electron is excited from the valence band into the conduction band, leaving behind a positively charged hole. The electron can be attracted to the hole via the Coulomb interaction, lowering the energy of the electron-hole (e-h) pair by a characteristic binding energy, Eb. The bound e-h pair is referred to as an exciton, and it is analogous to the hydrogen atom, but with a larger Bohr radius and a smaller binding energy, ranging from 1 to 100 meV, due to the small reduced mass of the exciton and screening of the Coulomb interaction by the dielectric environment. Like the hydrogen atom, there exists a series of excitonic bound states, which modify the near-band-edge optical response of semiconductors, especially when the binding energy is greater than the thermal energy and any relevant scattering rates. When the e-h pair has an energy greater than the binding energy, the electron and hole are no longer bound to one another (ionized), although they are still correlated. The nature of the optical transitions for both excitons and unbound e-h pairs depends on the dimensionality of the e-h system. Furthermore, an exciton is a composite boson having integer spin that obeys Bose-Einstein statistics rather than fermions that obey Fermi-Dirac statistics as in the case of either the electrons or holes by themselves.
    [Show full text]
  • 1. Physical Constants 1 1
    1. Physical constants 1 1. PHYSICAL CONSTANTS Table 1.1. Reviewed 1998 by B.N. Taylor (NIST). Based mainly on the “1986 Adjustment of the Fundamental Physical Constants” by E.R. Cohen and B.N. Taylor, Rev. Mod. Phys. 59, 1121 (1987). The last group of constants (beginning with the Fermi coupling constant) comes from the Particle Data Group. The figures in parentheses after the values give the 1-standard- deviation uncertainties in the last digits; the corresponding uncertainties in parts per million (ppm) are given in the last column. This set of constants (aside from the last group) is recommended for international use by CODATA (the Committee on Data for Science and Technology). Since the 1986 adjustment, new experiments have yielded improved values for a number of constants, including the Rydberg constant R∞, the Planck constant h, the fine- structure constant α, and the molar gas constant R,and hence also for constants directly derived from these, such as the Boltzmann constant k and Stefan-Boltzmann constant σ. The new results and their impact on the 1986 recommended values are discussed extensively in “Recommended Values of the Fundamental Physical Constants: A Status Report,” B.N. Taylor and E.R. Cohen, J. Res. Natl. Inst. Stand. Technol. 95, 497 (1990); see also E.R. Cohen and B.N. Taylor, “The Fundamental Physical Constants,” Phys. Today, August 1997 Part 2, BG7. In general, the new results give uncertainties for the affected constants that are 5 to 7 times smaller than the 1986 uncertainties, but the changes in the values themselves are smaller than twice the 1986 uncertainties.
    [Show full text]
  • Download Full-Text
    International Journal of Theoretical and Mathematical Physics 2021, 11(1): 29-59 DOI: 10.5923/j.ijtmp.20211101.03 Measurement Quantization Describes the Physical Constants Jody A. Geiger 1Department of Research, Informativity Institute, Chicago, IL, USA Abstract It has been a long-standing goal in physics to present a physical model that may be used to describe and correlate the physical constants. We demonstrate, this is achieved by describing phenomena in terms of Planck Units and introducing a new concept, counts of Planck Units. Thus, we express the existing laws of classical mechanics in terms of units and counts of units to demonstrate that the physical constants may be expressed using only these terms. But this is not just a nomenclature substitution. With this approach we demonstrate that the constants and the laws of nature may be described with just the count terms or just the dimensional unit terms. Moreover, we demonstrate that there are three frames of reference important to observation. And with these principles we resolve the relation of the physical constants. And we resolve the SI values for the physical constants. Notably, we resolve the relation between gravitation and electromagnetism. Keywords Measurement Quantization, Physical Constants, Unification, Fine Structure Constant, Electric Constant, Magnetic Constant, Planck’s Constant, Gravitational Constant, Elementary Charge ground state orbital a0 and mass of an electron me – both 1. Introduction measures from the 2018 CODATA – we resolve fundamental length l . And we continue with the resolution of We present expressions, their calculation and the f the gravitational constant G, Planck’s reduced constant ħ corresponding CODATA [1,2] values in Table 1.
    [Show full text]
  • Rational Dimensia
    Rational Dimensia R. Hanush Physics Phor Phun, Paso Robles, CA 93446∗ (Received) Rational Dimensia is a comprehensive examination of three questions: What is a dimension? Does direction necessarily imply dimension? Can all physical law be derived from geometric principles? A dimension is any physical quantity that can be measured. If space is considered as a single dimension with a plurality of directions, then the spatial dimension forms the second of three axes in a Dimensional Coordinate System (DCS); geometric units normalize unit vectors of time, space, and mass. In the DCS all orders n of any type of motion are subject to geometric analysis in the space- time plane. An nth-order distance formula can be derived from geometric and physical principles using only algebra, geometry, and trigonometry; the concept of the derivative is invoked but not relied upon. Special relativity, general relativity, and perihelion precession are shown to be geometric functions of velocity, acceleration, and jerk (first-, second-, and third-order Lorentz transformations) with v2 coefficients of n! = 1, 2, and 6, respectively. An nth-order Lorentz transformation is extrapolated. An exponential scaling of all DCS coordinate axes results in an ordered Periodic Table of Dimensions, a periodic table of elements for physics. Over 1600 measurement units are fitted to 72 elements; a complete catalog is available online at EPAPS. All physical law can be derived from geometric principles considering only a single direction in space, and direction is unique to the physical quantity of space, so direction does not imply dimension. I. INTRODUCTION analysis can be applied to all.
    [Show full text]
  • Variable Planck's Constant
    Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 29 January 2021 doi:10.20944/preprints202101.0612.v1 Variable Planck’s Constant: Treated As A Dynamical Field And Path Integral Rand Dannenberg Ventura College, Physics and Astronomy Department, Ventura CA [email protected] Abstract. The constant ħ is elevated to a dynamical field, coupling to other fields, and itself, through the Lagrangian density derivative terms. The spatial and temporal dependence of ħ falls directly out of the field equations themselves. Three solutions are found: a free field with a tadpole term; a standing-wave non-propagating mode; a non-oscillating non-propagating mode. The first two could be quantized. The third corresponds to a zero-momentum classical field that naturally decays spatially to a constant with no ad-hoc terms added to the Lagrangian. An attempt is made to calibrate the constants in the third solution based on experimental data. The three fields are referred to as actons. It is tentatively concluded that the acton origin coincides with a massive body, or point of infinite density, though is not mass dependent. An expression for the positional dependence of Planck’s constant is derived from a field theory in this work that matches in functional form that of one derived from considerations of Local Position Invariance violation in GR in another paper by this author. Astrophysical and Cosmological interpretations are provided. A derivation is shown for how the integrand in the path integral exponent becomes Lc/ħ(r), where Lc is the classical action. The path that makes stationary the integral in the exponent is termed the “dominant” path, and deviates from the classical path systematically due to the position dependence of ħ.
    [Show full text]