Calculating Blackbody Radiance V2
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On the Linkage Between Planck's Quantum and Maxwell's Equations
The Finnish Society for Natural Philosophy 25 years, K.V. Laurikainen Honorary Symposium, Helsinki 11.-12.11.2013 On the Linkage between Planck's Quantum and Maxwell's Equations Tuomo Suntola Physics Foundations Society, www.physicsfoundations.org Abstract The concept of quantum is one of the key elements of the foundations in modern physics. The term quantum is primarily identified as a discrete amount of something. In the early 20th century, the concept of quantum was needed to explain Max Planck’s blackbody radiation law which suggested that the elec- tromagnetic radiation emitted by atomic oscillators at the surfaces of a blackbody cavity appears as dis- crete packets with the energy proportional to the frequency of the radiation in the packet. The derivation of Planck’s equation from Maxwell’s equations shows quantizing as a property of the emission/absorption process rather than an intrinsic property of radiation; the Planck constant becomes linked to primary electrical constants allowing a unified expression of the energies of mass objects and electromagnetic radiation thereby offering a novel insight into the wave nature of matter. From discrete atoms to a quantum of radiation Continuity or discontinuity of matter has been seen as a fundamental question since antiquity. Aristotle saw perfection in continuity and opposed Democritus’s ideas of indivisible atoms. First evidences of atoms and molecules were obtained in chemistry as multiple proportions of elements in chemical reac- tions by the end of the 18th and in the early 19th centuries. For physicist, the idea of atoms emerged for more than half a century later, most concretely in statistical thermodynamics and kinetic gas theory that converted the mole-based considerations of chemists into molecule-based considerations based on con- servation laws and probabilities. -
Black Body Radiation and Radiometric Parameters
Black Body Radiation and Radiometric Parameters: All materials absorb and emit radiation to some extent. A blackbody is an idealization of how materials emit and absorb radiation. It can be used as a reference for real source properties. An ideal blackbody absorbs all incident radiation and does not reflect. This is true at all wavelengths and angles of incidence. Thermodynamic principals dictates that the BB must also radiate at all ’s and angles. The basic properties of a BB can be summarized as: 1. Perfect absorber/emitter at all ’s and angles of emission/incidence. Cavity BB 2. The total radiant energy emitted is only a function of the BB temperature. 3. Emits the maximum possible radiant energy from a body at a given temperature. 4. The BB radiation field does not depend on the shape of the cavity. The radiation field must be homogeneous and isotropic. T If the radiation going from a BB of one shape to another (both at the same T) were different it would cause a cooling or heating of one or the other cavity. This would violate the 1st Law of Thermodynamics. T T A B Radiometric Parameters: 1. Solid Angle dA d r 2 where dA is the surface area of a segment of a sphere surrounding a point. r d A r is the distance from the point on the source to the sphere. The solid angle looks like a cone with a spherical cap. z r d r r sind y r sin x An element of area of a sphere 2 dA rsin d d Therefore dd sin d The full solid angle surrounding a point source is: 2 dd sind 00 2cos 0 4 Or integrating to other angles < : 21cos The unit of solid angle is steradian. -
Guide for the Use of the International System of Units (SI)
Guide for the Use of the International System of Units (SI) m kg s cd SI mol K A NIST Special Publication 811 2008 Edition Ambler Thompson and Barry N. Taylor NIST Special Publication 811 2008 Edition Guide for the Use of the International System of Units (SI) Ambler Thompson Technology Services and Barry N. Taylor Physics Laboratory National Institute of Standards and Technology Gaithersburg, MD 20899 (Supersedes NIST Special Publication 811, 1995 Edition, April 1995) March 2008 U.S. Department of Commerce Carlos M. Gutierrez, Secretary National Institute of Standards and Technology James M. Turner, Acting Director National Institute of Standards and Technology Special Publication 811, 2008 Edition (Supersedes NIST Special Publication 811, April 1995 Edition) Natl. Inst. Stand. Technol. Spec. Publ. 811, 2008 Ed., 85 pages (March 2008; 2nd printing November 2008) CODEN: NSPUE3 Note on 2nd printing: This 2nd printing dated November 2008 of NIST SP811 corrects a number of minor typographical errors present in the 1st printing dated March 2008. Guide for the Use of the International System of Units (SI) Preface The International System of Units, universally abbreviated SI (from the French Le Système International d’Unités), is the modern metric system of measurement. Long the dominant measurement system used in science, the SI is becoming the dominant measurement system used in international commerce. The Omnibus Trade and Competitiveness Act of August 1988 [Public Law (PL) 100-418] changed the name of the National Bureau of Standards (NBS) to the National Institute of Standards and Technology (NIST) and gave to NIST the added task of helping U.S. -
Turbulence Examined in the Frequency-Wavenumber Domain*
Turbulence examined in the frequency-wavenumber domain∗ Andrew J. Morten Department of Physics University of Michigan Supported by funding from: National Science Foundation and Office of Naval Research ∗ Arbic et al. JPO 2012; Arbic et al. in review; Morten et al. papers in preparation Andrew J. Morten LOM 2013, Ann Arbor, MI Collaborators • University of Michigan Brian Arbic, Charlie Doering • MIT Glenn Flierl • University of Brest, and The University of Texas at Austin Robert Scott Andrew J. Morten LOM 2013, Ann Arbor, MI Outline of talk Part I{Motivation (research led by Brian Arbic) • Frequency-wavenumber analysis: {Idealized Quasi-geostrophic (QG) turbulence model. {High-resolution ocean general circulation model (HYCOM)∗: {AVISO gridded satellite altimeter data. ∗We used NLOM in Arbic et al. (2012) Part II-Research led by Andrew Morten • Derivation and interpretation of spectral transfers used above. • Frequency-domain analysis in two-dimensional turbulence. • Theoretical prediction for frequency spectra and spectral transfers due to the effects of \sweeping." {moving beyond a zeroth order approximation. Andrew J. Morten LOM 2013, Ann Arbor, MI Motivation: Intrinsic oceanic variability • Interested in quantifying the contributions of intrinsic nonlinearities in oceanic dynamics to oceanic frequency spectra. • Penduff et al. 2011: Interannual SSH variance in ocean models with interannual atmospheric forcing is comparable to variance in high resolution (eddying) ocean models with no interannual atmospheric forcing. • Might this eddy-driven low-frequency variability be connected to the well-known inverse cascade to low wavenumbers (e.g. Fjortoft 1953)? • A separate motivation is simply that transfers in mixed ! − k space provide a useful diagnostic. Andrew J. -
Variable Planck's Constant
Variable Planck’s Constant: Treated As A Dynamical Field And Path Integral Rand Dannenberg Ventura College, Physics and Astronomy Department, Ventura CA [email protected] [email protected] January 28, 2021 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. -
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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. -
The Principle of Relativity and the De Broglie Relation Abstract
The principle of relativity and the De Broglie relation Julio G¨u´emez∗ Department of Applied Physics, Faculty of Sciences, University of Cantabria, Av. de Los Castros, 39005 Santander, Spain Manuel Fiolhaisy Physics Department and CFisUC, University of Coimbra, 3004-516 Coimbra, Portugal Luis A. Fern´andezz Department of Mathematics, Statistics and Computation, Faculty of Sciences, University of Cantabria, Av. de Los Castros, 39005 Santander, Spain (Dated: February 5, 2016) Abstract The De Broglie relation is revisited in connection with an ab initio relativistic description of particles and waves, which was the same treatment that historically led to that famous relation. In the same context of the Minkowski four-vectors formalism, we also discuss the phase and the group velocity of a matter wave, explicitly showing that, under a Lorentz transformation, both transform as ordinary velocities. We show that such a transformation rule is a necessary condition for the covariance of the De Broglie relation, and stress the pedagogical value of the Einstein-Minkowski- Lorentz relativistic context in the presentation of the De Broglie relation. 1 I. INTRODUCTION The motivation for this paper is to emphasize the advantage of discussing the De Broglie relation in the framework of special relativity, formulated with Minkowski's four-vectors, as actually was done by De Broglie himself.1 The De Broglie relation, usually written as h λ = ; (1) p which introduces the concept of a wavelength λ, for a \material wave" associated with a massive particle (such as an electron), with linear momentum p and h being Planck's constant. Equation (1) is typically presented in the first or the second semester of a physics major, in a curricular unit of introduction to modern physics. -
ATMS 310 Rossby Waves Properties of Waves in the Atmosphere Waves
ATMS 310 Rossby Waves Properties of Waves in the Atmosphere Waves – Oscillations in field variables that propagate in space and time. There are several aspects of waves that we can use to characterize their nature: 1) Period – The amount of time it takes to complete one oscillation of the wave\ 2) Wavelength (λ) – Distance between two peaks of troughs 3) Amplitude – The distance between the peak and the trough of the wave 4) Phase – Where the wave is in a cycle of amplitude change For a 1-D wave moving in the x-direction, the phase is defined by: φ ),( = −υtkxtx − α (1) 2π where φ is the phase, k is the wave number = , υ = frequency of oscillation (s-1), and λ α = constant determined by the initial conditions. If the observer is moving at the phase υ speed of the wave ( c ≡ ), then the phase of the wave is constant. k For simplification purposes, we will only deal with linear sinusoidal wave motions. Dispersive vs. Non-dispersive Waves When describing the velocity of waves, a distinction must be made between the group velocity and the phase speed. The group velocity is the velocity at which the observable disturbance (energy of the wave) moves with time. The phase speed of the wave (as given above) is how fast the constant phase portion of the wave moves. A dispersive wave is one in which the pattern of the wave changes with time. In dispersive waves, the group velocity is usually different than the phase speed. A non- dispersive wave is one in which the patterns of the wave do not change with time as the wave propagates (“rigid” wave). -
The International System of Units (SI)
NAT'L INST. OF STAND & TECH NIST National Institute of Standards and Technology Technology Administration, U.S. Department of Commerce NIST Special Publication 330 2001 Edition The International System of Units (SI) 4. Barry N. Taylor, Editor r A o o L57 330 2oOI rhe National Institute of Standards and Technology was established in 1988 by Congress to "assist industry in the development of technology . needed to improve product quality, to modernize manufacturing processes, to ensure product reliability . and to facilitate rapid commercialization ... of products based on new scientific discoveries." NIST, originally founded as the National Bureau of Standards in 1901, works to strengthen U.S. industry's competitiveness; advance science and engineering; and improve public health, safety, and the environment. One of the agency's basic functions is to develop, maintain, and retain custody of the national standards of measurement, and provide the means and methods for comparing standards used in science, engineering, manufacturing, commerce, industry, and education with the standards adopted or recognized by the Federal Government. As an agency of the U.S. Commerce Department's Technology Administration, NIST conducts basic and applied research in the physical sciences and engineering, and develops measurement techniques, test methods, standards, and related services. The Institute does generic and precompetitive work on new and advanced technologies. NIST's research facilities are located at Gaithersburg, MD 20899, and at Boulder, CO 80303. -
Ikonos DN Value Conversion to Planetary Reflectance Values by David Fleming CRESS Project, UMCP Geography April 2001
Ikonos DN Value Conversion to Planetary Reflectance Values By David Fleming CRESS Project, UMCP Geography April 2001 This paper was produced by the CRESS Project at the University of Maryland. CRESS is sponsored by the Earth Science Enterprise Applications Directorate at NASA Stennis Space Center. The following formula from the Landsat 7 Science Data Users Handbook was used to convert Ikonos DN values to planetary reflectance values: ρp = planetary reflectance Lλ = spectral radiance at sensor’s aperture 2 ρp = π * Lλ * d ESUNλ = band dependent mean solar exoatmospheric irradiance ESUNλ * cos(θs) θs = solar zenith angle d = earth-sun distance, in astronomical units For Landsat 7, the spectral radiance Lλ = gain * DN + offset, which can also be expressed as Lλ = (LMAX – LMIN)/255 *DN + LMIN. The LMAX and LMIN values for each of the Landsat bands are given below in Table 1. These values may vary for each scene and the metadata contains image specific values. Table 1. ETM+ Spectral Radiance Range (W/m2 * sr * µm) Low Gain High Gain Band Number LMIN LMAX LMIN LMAX 1 -6.2 293.7 -6.2 191.6 2 -6.4 300.9 -6.4 196.5 3 -5.0 234.4 -5.0 152.9 4 -5.1 241.1 -5.1 157.4 5 -1.0 47.57 -1.0 31.06 6 0.0 17.04 3.2 12.65 7 -0.35 16.54 -0.35 10.80 8 -4.7 243.1 -4.7 158.3 (from Landsat 7 Science Data Users Handbook) The Ikonos spectral radiance, Lλ, can be calculated by using the formula given in the Space Imaging Document Number SE-REF-016: 2 Lλ (mW/cm * sr) = DN / CalCoefλ However, in order to use these values in the conversion formula, the values must be in units of 2 W/m * sr * µm. -
Radiometry of Light Emitting Diodes Table of Contents
TECHNICAL GUIDE THE RADIOMETRY OF LIGHT EMITTING DIODES TABLE OF CONTENTS 1.0 Introduction . .1 2.0 What is an LED? . .1 2.1 Device Physics and Package Design . .1 2.2 Electrical Properties . .3 2.2.1 Operation at Constant Current . .3 2.2.2 Modulated or Multiplexed Operation . .3 2.2.3 Single-Shot Operation . .3 3.0 Optical Characteristics of LEDs . .3 3.1 Spectral Properties of Light Emitting Diodes . .3 3.2 Comparison of Photometers and Spectroradiometers . .5 3.3 Color and Dominant Wavelength . .6 3.4 Influence of Temperature on Radiation . .6 4.0 Radiometric and Photopic Measurements . .7 4.1 Luminous and Radiant Intensity . .7 4.2 CIE 127 . .9 4.3 Spatial Distribution Characteristics . .10 4.4 Luminous Flux and Radiant Flux . .11 5.0 Terminology . .12 5.1 Radiometric Quantities . .12 5.2 Photometric Quantities . .12 6.0 References . .13 1.0 INTRODUCTION Almost everyone is familiar with light-emitting diodes (LEDs) from their use as indicator lights and numeric displays on consumer electronic devices. The low output and lack of color options of LEDs limited the technology to these uses for some time. New LED materials and improved production processes have produced bright LEDs in colors throughout the visible spectrum, including white light. With efficacies greater than incandescent (and approaching that of fluorescent lamps) along with their durability, small size, and light weight, LEDs are finding their way into many new applications within the lighting community. These new applications have placed increasingly stringent demands on the optical characterization of LEDs, which serves as the fundamental baseline for product quality and product design.