Lorentz transform of black-body radiation temperature

Nakamura, Takenobu

doi:10.1209/0295-5075/88/20004

Cited by 22 publications

(22 citation statements)

References 19 publications

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“…Disputes have arisen supporting three published Lorentz group transformations: Temperature Deflation [6], [7] and Temperature Inflation [12], [13], [14] (which can be operationally quantified with a relativistic Carnot cycle [15], [16], [17]), and Temperature Invariance [18], [19], [20], [21]. (2) where h is Planck's constant, c is the speed of light, kB is Boltzmann's constant, To is the rest frame absolute temperature, ν is the frequency, and λ is the wavelength.…”

Section: The Application Of Inverse Temperature To the Blackbody Specmentioning

confidence: 99%

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The relativistic blackbody spectrum in inertial and non-inertial reference frames

Lee

Cleaver

2017

New Astronomy

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By invoking inverse temperature as a van Kampen-Israel future-directed timelike 4-vector, this paper derives the Relativistic Blackbody Spectrum, the Relativistic Wien's Displacement Law, and the Relativistic Stefan-Boltzmann Law in inertial and non-inertial reference frames. 2 Significant misperceptions have arisen concerning temperature in relativistic thermodynamics due in part to the confusion surrounding the respective differences between empirical and absolute temperatures. The empirical temperature is a Lorentz invariant, relativistic scalar that considers the radiation rest frame and the observer frame to be in thermal equilibrium [22]. This ensues from the Zeroth Law of Thermodynamics, and correlates directly to the absolute temperature in the radiation (source) frame. The Zeroth Law's validity is required without making use of any thermodynamic property (including entropy and energy) [23].The absolute temperature of a thermodynamic system is a consequence of the Second Law of Thermodynamics. It is the product of the Lorentz factor and the absolute temperature in the radiation frame, and contains no angular dependence. Even though the difference between empirical and absolute temperatures may be observable in nonrelativistic thermodynamics, it becomes persuasively illuminated in relativistic thermodynamics.The Planck distribution describes a solid angular photon number density, and defines a directional (or effective) temperature. However, this results from solely mathematical manipulations, and its thermodynamic relevance is, at best, questionable. Alternatively, temperature transformations can be accomplished by treating inverse temperature as a van Kampen-Israel future-directed timelike 4-vector. Although Przanowski and Tosiek [24] i , and Lee and Cleaver [4] ii have demonstrated temperature inflation without making use of inverse temperature, angular dependence is required for the relativistic blackbody spectrum. Derivation of the Relativistic Spectral RadianceThe relativistic blackbody spectrum can be obtained by considering the blackbody spectrum of a stationary radiation source, and including temperature inflation (in terms of inverse temperature), Doppler shifting, and relativistic beaming. The inertial and non-inertial frames cases are each examined. In the non-inertial case, the Unruh Effect is not considered because it is many orders of magnitude smaller than the effect presented here. Inertial FramesThe radiation (source) frame photon energy density ε in frequency and wavelength spaces of a Planckian distribution are:

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Section: The Application Of Inverse Temperature To the Blackbody Specmentioning

confidence: 99%

“…(11) and (12) clearly reveal that, in terms of the radiation frame temperature, the Bose-Einstein distribution for spectral radiance is retained in a relativistic inertial reference frame (as shown in Figure 1). Regardless, inverse temperature remains a valid thermodynamic quantity [2].…”

Section: The Application Of Inverse Temperature To the Blackbody Specmentioning

confidence: 99%

The relativistic blackbody spectrum in inertial and non-inertial reference frames

Lee

Cleaver

2017

New Astronomy

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“…Although completely solved, the problem still stimulates scientific production [3]. It is the purpose of the present paper to show how the relation between inertial observers can be obtained from the basic principles of Relativisic Quantum Mechanics.…”

Section: Introductionmentioning

confidence: 95%

Boosted Statistical Mechanics

Testa

2015

Int J Theor Phys

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“…However, this result lately was challenged by Ott [15] and Arzeli [16] who reached exactly the opposite conclusion, i.e., T = γ T , while Landsberg et al [17][18][19] claimed that T = T and an universal Lorentz transformation of temperature can't exist. Presently, the last opinion is dominant but controversy is still going on [20,21]. Thus, we don't regard T as the temperature in the moving frame s but only an effective temperature.…”

Section: Particular Expressionsmentioning

confidence: 99%

Radiation Laws of a Kerr Nonlinear Blackbody in a Moving Frame of Reference

2011

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A Kerr nonlinear blackbody (KNB) is a new kind of blackbody in which bare photons with opposite wave vectors and helicities are bound into pairs and unpaired photons are transformed into nonpolaritons. In the present paper, the radiation of a KNB is considered from the viewpoint of an observer in arbitrary uniform motion with respect to a rest frame of reference of the radiation. It is found that the radiation laws, which include the distribution of nonpolaritons and so forth, are modified due to the motion. Moreover, under a special condition, we notice that the only effect of the motion is to introduce an angledependent directional temperature, which replaces the rest-frame temperature of the cavity. Besides, we try to extend the model of a KNB to the whole Universe and apply the modified radiation laws to the question of 2.7 K cosmic microwave background radiation (CMBR).

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Lorentz transform of black-body radiation temperature

Cited by 22 publications

References 19 publications

The relativistic blackbody spectrum in inertial and non-inertial reference frames

The relativistic blackbody spectrum in inertial and non-inertial reference frames

Boosted Statistical Mechanics

Radiation Laws of a Kerr Nonlinear Blackbody in a Moving Frame of Reference

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