Formulation of a more realistic quantum equation for rectifying the hidden flaws in Planck's black body equation

2020 ◽  
Vol 33 (1) ◽  
pp. 27-30
Author(s):  
Suniti K. Ghoshal
Keyword(s):  
Spectral Power ◽  
Spectral Power Density ◽  
Black Body ◽  
Black Body Radiation ◽  
Spectral Energy ◽  
Quantum Oscillator ◽  
Spectral Energy Density ◽  
Simple Modification ◽  
Quantum Equation ◽  
Final Formula

A thorough investigation of the Planck's black-body radiation reveals several potential flaws. It is found that Planck's final formula suffers from a serious dimensional discrepancy. While it relates to the spectral energy density of the black body radiation, the measured experimental data correspond to the spectral power density. It is shown that Planck's final formula is better written, <mml:math display="inline"> <mml:mi>P</mml:mi> <mml:mo>=</mml:mo> <mml:mi>b</mml:mi> <mml:mi>ν</mml:mi> </mml:math> where <mml:math display="inline"> <mml:mi>P</mml:mi> </mml:math> is power with units <mml:math display="inline"> <mml:mfenced open="[" close="]" separators="|"> <mml:mrow> <mml:mrow> <mml:mrow> <mml:mi>J</mml:mi> </mml:mrow> <mml:mo>/</mml:mo> <mml:mrow> <mml:mi>s</mml:mi> </mml:mrow> </mml:mrow> </mml:mrow> </mml:mfenced> <mml:mo>,</mml:mo> <mml:mo> </mml:mo> <mml:mi>b</mml:mi> </mml:math> is the quantum of energy with units <mml:math display="inline"> <mml:mfenced open="[" close="]" separators="|"> <mml:mrow> <mml:mi>J</mml:mi> </mml:mrow> </mml:mfenced> </mml:math> (numerically equals to Planck's constant, <mml:math display="inline"> <mml:mi>h</mml:mi> </mml:math> ), and <mml:math display="inline"> <mml:mi>ν</mml:mi> </mml:math> is the frequency of the quantum oscillator with units <mml:math display="inline"> <mml:mfenced open="[" close="]" separators="|"> <mml:mrow> <mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> <mml:mo>/</mml:mo> <mml:mrow> <mml:mi>s</mml:mi> </mml:mrow> </mml:mrow> </mml:mrow> </mml:mfenced> </mml:math> . It is shown that a simple modification in the Planck's black-body radiation formula brought about by replacing “ <mml:math display="inline"> <mml:mi>h</mml:mi> </mml:math> ” by “ <mml:math display="inline"> <mml:mi>b</mml:mi> </mml:math> ” in it could make it absolutely free from any flaws and discrepancies.

The Physical World

2017 ◽  
Author(s):  
Nicholas Manton ◽  
Nicholas Mee
Keyword(s):  
Quantum Mechanics ◽  
Particle Physics ◽  
Variational Principles ◽  
Black Body ◽  
Black Body Radiation ◽  
Physical World ◽  
Atomic Scale ◽  
Solid State Physics ◽  
Least Action ◽  
Dimensional Spacetime

The book is an inspirational survey of fundamental physics, emphasizing the use of variational principles. Chapter 1 presents introductory ideas, including the principle of least action, vectors and partial differentiation. Chapter 2 covers Newtonian dynamics and the motion of mutually gravitating bodies. Chapter 3 is about electromagnetic fields as described by Maxwell’s equations. Chapter 4 is about special relativity, which unifies space and time into 4-dimensional spacetime. Chapter 5 introduces the mathematics of curved space, leading to Chapter 6 covering general relativity and its remarkable consequences, such as the existence of black holes. Chapters 7 and 8 present quantum mechanics, essential for understanding atomic-scale phenomena. Chapter 9 uses quantum mechanics to explain the fundamental principles of chemistry and solid state physics. Chapter 10 is about thermodynamics, which is built around the concepts of temperature and entropy. Various applications are discussed, including the analysis of black body radiation that led to the quantum revolution. Chapter 11 surveys the atomic nucleus, its properties and applications. Chapter 12 explores particle physics, the Standard Model and the Higgs mechanism, with a short introduction to quantum field theory. Chapter 13 is about the structure and evolution of stars and brings together material from many of the earlier chapters. Chapter 14 on cosmology describes the structure and evolution of the universe as a whole. Finally, Chapter 15 discusses remaining problems at the frontiers of physics, such as the interpretation of quantum mechanics, and the ultimate nature of particles. Some speculative ideas are explored, such as supersymmetry, solitons and string theory.

Constructing Quantum Mechanics

2019 ◽  
Author(s):  
Anthony Duncan ◽  
Michel Janssen
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Stark Effect ◽  
Zeeman Effect ◽  
Black Body ◽  
Black Body Radiation ◽  
Wave Mechanics ◽  
Specific Heats ◽  
Old Quantum Theory ◽  
Upper Level

This is the first of two volumes on the genesis of quantum mechanics. It covers the key developments in the period 1900–1923 that provided the scaffold on which the arch of modern quantum mechanics was built in the period 1923–1927 (covered in the second volume). After tracing the early contributions by Planck, Einstein, and Bohr to the theories of black‐body radiation, specific heats, and spectroscopy, all showing the need for drastic changes to the physics of their day, the book tackles the efforts by Sommerfeld and others to provide a new theory, now known as the old quantum theory. After some striking initial successes (explaining the fine structure of hydrogen, X‐ray spectra, and the Stark effect), the old quantum theory ran into serious difficulties (failing to provide consistent models for helium and the Zeeman effect) and eventually gave way to matrix and wave mechanics. Constructing Quantum Mechanics is based on the best and latest scholarship in the field, to which the authors have made significant contributions themselves. It breaks new ground, especially in its treatment of the work of Sommerfeld and his associates, but also offers new perspectives on classic papers by Planck, Einstein, and Bohr. Throughout the book, the authors provide detailed reconstructions (at the level of an upper‐level undergraduate physics course) of the cental arguments and derivations of the physicists involved. All in all, Constructing Quantum Mechanics promises to take the place of older books as the standard source on the genesis of quantum mechanics.

scholarly journals The Changes of Ergonomic Engine Vibroacoustic Response Regarding Their Development

Energies ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 4215
Author(s):  
Radosław Wróbel ◽  
Lech Sitnik ◽  
Monika Andrych-Zalewska ◽  
Łukasz Łoza ◽  
Radostin Dimitrov ◽  
...  
Keyword(s):  
Human Health ◽  
Power Density ◽  
High Speed ◽  
Internal Combustion Engines ◽  
Spectral Power ◽  
Spectral Power Density ◽  
Steering Wheel ◽  
Combustion Engines ◽  
Head Restraint ◽  
Vibroacoustic Response

The article presents the results of research on the vibroacoustic response of internal combustion engines mounted in a vehicle. The vehicles studied belong to popular models, which became available in successive versions. Each group included vehicles of the same model of an older generation (equipped with a naturally aspirated engine) and of a newer generation, including downsized (and turbocharged) engines. Tests in each group were carried out under repeatable conditions on a chassis-load dynamometer. The vibrations were measured using single-axis accelerometers mounted on the steering wheel, engine, and driver’s head restraint mounting. The primary purpose of the study was to verify whether the new generations of vehicles equipped with additional high-speed elements (compressors) generate additional harmonics (especially those within the range potentially affecting travel comfort and human health) and whether there are significant changes in the distribution of spectral power density in the new generations. As the study showed, new generations of vehicles are characterized by a different vibroacoustic response, and the trend of change is the same in each of the families studied.

scholarly journals Influence of Microlensing on Spectral Anomalies of the Lensed Objects

2011 ◽  
Vol 20 (3) ◽  
Author(s):  
S. Simić ◽  
L. Č. Popović ◽  
P. Jovanović
Keyword(s):  
Energy Distribution ◽  
Spectral Energy Distribution ◽  
Angular Size ◽  
Black Body ◽  
Spectral Energy

AbstractHere we consider the influence of microlensing on the spectrum of a lensed object with the angular size 5 μas accepting that the composite emission of this object originates from three different regions arranged around its center. We assume that the lensed object has three concentric regions with a black-body emission; the temperatures of these regions are 10 000 K, 7500 K and 5000 K. We investigate how the integral spectral energy distribution (SED) of such stratified source changes due to microlensing by a group of solarmass stars. We find that the SED and flux ratios in the photometric B, V and R passbands show considerable changes during a microlens event. This indicates that the flux anomaly observed in some lensed quasars may be caused by microlensing of a stratified object.

Electromagnetic fluctuations from energetic particles in plasmas

1988 ◽  
Vol 40 (3) ◽  
pp. 407-417 ◽  
Author(s):  
Cheng Chu ◽  
J. L. Sperling
Keyword(s):  
Distribution Function ◽  
Velocity Distribution ◽  
Charged Particles ◽  
Velocity Distribution Function ◽  
Black Body ◽  
Black Body Radiation ◽  
Specific Model ◽  
Magnetized Plasma ◽  
Plasma Power ◽  
Correlation Techniques

Electromagnetic fluctuations, induced by energetic charged particles, are calculated using correlation techniques for a uniform magnetized plasma. Power emission in the ion-cyclotron range of frequencies (ICRF) is calculated for a specific model of velocity distribution function. The emissive spectra are distinct from that of the black-body radiation and have features that are consistent with experimental observation.

DOES LIOUVILLE'S THEOREM IMPLY QUANTUM MECHANICS?

1999 ◽  
Vol 13 (02) ◽  
pp. 161-189
Author(s):  
C. SYROS
Keyword(s):  
Quantum Mechanics ◽  
Radiation Spectrum ◽  
Black Body ◽  
Boltzmann Distribution ◽  
Black Body Radiation ◽  
Planck Constant ◽  
Klein Gordon ◽  
Energy Variable ◽  
Liouville’S Theorem ◽  
Liouville’S Equation

The essentials of quantum mechanics are derived from Liouville's theorem in statistical mechanics. An elementary solution, g, of Liouville's equation helps to construct a differentiable N-particle distribution function (DF), F(g), satisfying the same equation. Reality and additivity of F(g): (i) quantize the time variable; (ii) quantize the energy variable; (iii) quantize the Maxwell–Boltzmann distribution; (iv) make F(g) observable through time-elimination; (v) produce the Planck constant; (vi) yield the black-body radiation spectrum; (vii) support chronotopology introduced axiomatically; (viii) the Schrödinger and the Klein–Gordon equations follow. Hence, quantum theory appears as a corollary of Liouville's theorem. An unknown connection is found allowing the better understanding of space-times and of these theories.

Effect of Surface Roughness on the Total Hemispherical and Specular Reflectance of Metallic Surfaces

1964 ◽  
Vol 86 (2) ◽  
pp. 193-199 ◽  
Author(s):  
R. C. Birkebak ◽  
E. M. Sparrow ◽  
E. R. G. Eckert ◽  
J. W. Ramsey
Keyword(s):  
Surface Roughness ◽  
Black Body ◽  
Black Body Radiation ◽  
The Other ◽  
Angle Of Incidence ◽  
Metallic Surfaces ◽  
Specular Reflectance ◽  
Other Hand ◽  
Hemispherical Reflectance ◽  
Effect Of Surface

Measurements have been made of the hemispherical and specular reflectance of metallic surfaces of controlled roughness. The surfaces, which were ground nickel rectangles, were irradiated at various angles of incidence by a beam of black-body radiation, the temperature of which was also varied. The instrumentation which was devised to perform the experiments is described. The measurements show that beyond a certain surface roughness, the hemispherical reflectance is virtually independent of further increases in roughness. On the other hand, the specular reflectance decreases steadily with increasing roughness. Additionally, the hemispherical reflectance is found to be quite insensitive to the angle of incidence, while the specular reflectance increases with angle of incidence for the rougher surfaces.

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