The old quantum theory of black body radiation was manifestly logically inconsistent. It required the energies of electric resonators to be both quantized and continuous. To show that this manifest inconsistency was inessential to the theory's recovery of the Planck distribution law, I extract a subtheory free of this manifest inconsistency but from which Planck's law still follows.
The old quantum theory of black body radiation was manifestly logically inconsistent. It required the energies of electric resonators to be both quantized and continuous. To show that this manifest inconsistency was inessential to the theory's recovery of the Planck distribution law, I extract a subtheory free of this manifest inconsistency but from which Planck's law still follows.
Planck, Einstein and Bose all had to introduce statistics, and thus counting, in order to successfully derive an equation for the energy distribution within the black-body radiation spectrum, and what we now call Bose-Einstein statistics. Some of the details involved in the counting procedure vary while still giving the same result. However, the interpretation of what we count may differ dramatically from one another (as, for example, between Planck and Bose), without impacting the final, mathematical result. We demonstrate here a further alternative, which varies both, in the details of the counting, as well as in the interpretation, while still producing the same well known statistics. This approach puts the "quantumness" back into the radiation emission/absorption process, possibly dispensing with the requirement of quantized light, at least in the context of black-body radiation.
Background/Objective: To demonstrate that the formula for Energy distribution of radiation emitted from the cavity of a black-body, derived by German physicist Max Planck in the year 1900, has an alternative explanation independent of probability. Method: Energy released by radiations emitted from the cavity of a black-body, is compared with the energy released from an incandescent electric bulb. Electrical energy added to the bulb is envisaged to transform into energy-sphere that breaks-up into small packets of energy akin to radioactive decay of matter, and generates electromagnetic radiations causing brightness. Finding: Conjoining the quantization of energy and the technique of radioactive decay, a formula is derived for the brilliance of the incandescent bulb. The formula, thus derived, is found to be identical to the formula derived by Max Planck. This finding leads us to a unique outcome that the assumption of oscillators inside the cavity of black-body is not a requisite for deriving the formula as suggested by Max Planck, and believed till date. Elimination of oscillators also makes Boltzmann’s statistical method, which was utilized by Max Planck in his derivation, irrelevant to the formula, thereby making it independent of probability. Use of probability in physics leads to uncertainties and weirdness which is evident in quantum physics. This technique eliminates the probability from this basic formula of quantum physics and introduces a distinctive mode of generation of electromagnetic radiations from energy-spheres. Application/Improvements: This technique can further be explored and applied in ascertaining the behavior of electrons and other sub-atomic particles without the usage of probability. Keywords: Black-body, Probability, Quantization, Quantum Physics, Radiation
Abstract Planck’s law for black-body radiation marks the origin of quantum theory and is discussed in all introductory (or advanced) courses on this subject. However, the question whether Planck really implied quantisation is debated among historians of physics. We present a simplified account of this debate which also sheds light on the issue of indistinguishability and Einstein’s light quantum hypothesis. We suggest that the teaching of quantum mechanics could benefit from including this material beyond the question of historical accuracy.
The experimental foundations of quantum theory are presented in some detail in this chapter: on the one hand, the investigation of black-body radiation, which helps in developing an interdisciplinary view of physics, besides having historical interest; on the other hand, the energy and linear momentum of photons, atomic spectra, discrete energy levels, wave-like properties of electrons, interference phenomena and uncertainty relations. Black-body radiation Black-body radiation is not just a topic of historical interest. From a pedagogical point of view, it helps in developing an interdisciplinary view of physics, since it involves, among the other, branches of physics such as electrodynamics and thermodynamics, as well as a new constant of nature, the Planck constant, which is peculiar to quantum theory and quantum statistics. Moreover, looking at modern developments, the radiation that pervades the whole universe (Gamow 1946, Penzias and Wilson 1965, Smoot et al . 1992, Spergel et al . 2003) is a black-body radiation, and the expected emission of particles from black holes (space–time regions where gravity is so strong that no light ray can escape to infinity, and all nearby matter gets eaten up) is also (approximately) a black-body radiation (Hawking 1974, 1975). In this section, relying in part on Born (1969), we are aiming to derive the law of heat radiation, following Planck's method. We think of a box for which the walls are heated to a definite temperature T .
Abstract There are two rather different phenomena that furthered the development of quantum theory: blackbody radiation and atomic spectra. In fact quantum theory began in 1900 with Planck’s radiation law and his introduction of the quantum of action h (Episode 7). His derivation of the law was by no means stringent. He assumed the existence of many resonators (atoms or molecules) of different but fixed frequencies ν, which could emit or absorb radiation only in quanta of energy E = hν. Einstein, in his light-quantum hypothesis of 1905, postulated that the energy quantization is a property of the radiation field itself and not due to the material resonators. He found a similarity between a cavity filled with radiation consisting of quanta and a vessel filled with gas consisting of atoms. However, he could not obtain Planck’s law but only Wien’s (Episode 10).