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
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
A cold solid body does not produce any emissions, but with increasing temperature, it begins to become brighter and changes colour. A black body is a theoretical object, which absorbs 100% of the radiation that arrives on it. A black body heated to a sufficiently high temperature emits radiation. The study of the properties of black body radiation played a key role in the development of quantum physics. The history of the black body begins around 1860 when Kirchhoff defines what is meant by black body and formulates some general laws on its properties. Planck began to work on a cavity model where the walls were composed of resonators, that is, by electrically charged harmonic oscillators capable of exchanging energy with the electromagnetic radiation. In 1905, Einstein confirmed the idea of Planck explaining the photoelectric effect and showing that the radiation is not only emitted, but also absorbed in the form of packets or photons.
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.
Introduction The preceding chapters have focused on atomic transitions induced by applied radiation. That is, there is an optical field illuminating the atoms, and their response is calculated. It is implicitly assumed that an excited atom left alone will spontaneously return to the ground state, and conserve energy by emitting light that satisfies E 2 − E 1 = ħ ω 21 in accordance with the Planck and Bohr pictures. But this spontaneous emission process is not addressed quantitatively in these earlier chapters. Spontaneous emission is one of the most pervasive phenomena of atomic physics, and yet its origins remain among the least well-understood. The number of misconceptions is enormous, and they are to be found in textbooks, journal articles, and lecture notes. Because the natural decay of an excited atom adds energy to what is usually an empty mode of the electromagnetic field, the process is fundamentally quantum mechanical. Classical or even semi-classical descriptions cannot be assured to give correct answers. This is not to say that such discussion is to be avoided, but only that caution is needed in interpreting the results. Toward the end of the nineteenth century, many experimental results made it clear that classical mechanics needed to be supplemented by new theories. The first venture into the new physics was Planck's hypothesis that the energy of classical radiating oscillators like those discussed in Chap. 1 would have to be quantized into integer multiples of ħ ω. This notion led to his famous formula for the spectrum of thermal radiation from a non-reflective object (black body), and this formula describes a radiation field in thermodynamic equilibrium with its environment. The result of Planck's hypothesis in the context of thermal equilibrium plays a vital role in the discussion of spontaneous emission. Einstein A - and B -coefficients Soon after Bohr proposed a model of atomic structure consisting of discrete energy levels, connected by radiation whose energy satisfied Δ E = ħω when atoms made transition between them, Einstein published the first serious attempt to connect the absorption and emission processes. Absorption, he reasoned, could occur only in the presence of applied radiation, whereas spontaneous decay occurred without the application of any field.
Quantum Mechanics and its Interpretations Peter E. Hodgson (bio) Quantum Mechanics is an elegant and indeed beautiful formalism, and enables the results of many physical measurements to be calculated with great accuracy. But from the earliest days there has been intense debate about the interpretation of quantum mechanics, and it shows no signs of being settled; if anything, it is becoming more intense over the years. It should therefore be evident that the most that can be done here is to try to show where the real difficul-ties lie, and how the failure to recognize that quantum mechanics is an essentially statistical theory has led to a series of confusing quantum paradoxes. It is just these paradoxes that have often been used to support theological speculations. The Discovery of the Quantum The quantum nature of the physical world was discovered by Max Planck in the early years of the twentieth century. He was studying thermodynamics and his attention was drawn to the frequency distribution of black-body radiation. This radiation is emitted from a small hole in a heated enclosure with rough walls, which ensures [End Page 62] that the radiation reaches statistical equilibrium before emission. The frequency distribution is found to be independent of the material lining the walls of the oven, so Planck realized that it must be a fundamental characteristic of all matter. This frequency distribution had been measured by several experimentalists, and Planck resolved to try to see how it can be derived theoretically. Already Rayleigh and Jeans had used classical radiation theory to derive an expression that fitted the data well at low frequencies but tended to infinity at high energies, which was of course unacceptable. The physicist Wien had derived a formula that fitted the data at high frequencies but failed at low frequencies. Planck used an ingenious argument based on entropy to interpolate between these two formulae and obtained a formula, now known as the Planck distribution, that fitted the data perfectly. His next task was to understand the physics behind his formula. He used the familiar technique of assuming that the energy is emitted in small finite amounts, and then let their size tend to zero, so as to represent a continuous distribution. To his great surprise, the intermediate formula with discrete amounts of energy, called quanta, gave the Planck distribution, but the final result, with infinitely small quanta, did not. All his instincts as a physicist rebelled against this conclusion. Surely energy must be emitted continuously. He tried hard to find a way to avoid this unwelcome conclusion, but without success. He had to admit that it is a feature of the world. Soon it was confirmed by Einstein’s interpretation of the photoelectric effect. This story shows clearly that physicists do not impose their ideas on the world, but recognize and accept what they find, whether or not it agrees with their original ideas. The world is made by God in ways that often we cannot imagine. [End Page 63] The Old Quantum Theory A few years later Rutherford discovered that the atom has a small central nucleus containing most of its mass surrounded by a number of electrons. Bohr used the idea of the quantum to build his model of the atom. He assumed that the electrons go around the nucleus in discrete orbits, and that radiation is emitted when an electron falls from one orbit to a lower one. With this model, he was able to calculate to high accuracy the frequencies of the radiation emitted from an excited hydrogen atom. This was a great achievement, but to get his result he had to assume that the electrons stayed in their orbits, whereas classical theory predicted that they would continuously lose energy and rapidly spiral into the nucleus. Quantum Mechanics and its Interpretations These problems were solved by the development of quantum mechanics in the 1920s by Heisenberg, Schrodinger, Dirac, and others. This enabled what is called the wave function to be calculated for any physical system, and from the wave function the probabilities of occurrence of measurable quantities can be found. It is a beautiful theory, and is the indispensable means of calculation for atomic, nuclear...
In deriving his radiation law in 1900, Max Planck employed a simple harmonic oscillator to model the exchange of energy between radiation and matter. Traditionally the harmonic oscillator has been viewed as modelling an entity which is itself oscillating, although a suitable oscillating entity has not been forthcoming. (Opinion is divided between a material oscillator, an imaginary oscillator and a need to revise Planck"s derivation to apply to cavity modes of oscillation). We offer a novel, atomistic interpretation of Planck"s derivation wherein the harmonic oscillator models a transition between the internal quantum states of an atom|not a normal electronic atom characterised by possible energies 0 and hv , but an atom populated by subatomic bosons (such as pions) and characterised by multiple occupancy of quantum states and possible energies nhv ( n = 0;1;2; :::). We show how Planck"s derivation can be varied to accommodate electronic atoms. A corollary to the atomistic interpretation is that Planck"s derivation can no longer be construed as support for the postulate that material oscillating entities can have only those energies that are multiples of hv .
A historical overview is given on the basic results which appeared by the year 1926 concerning Einstein's fluctuation formula of black-body radiation, in the context of light-quanta and wave-particle duality. On the basis of the original publications – from Planck's derivation of the black-body spectrum and Einstein's introduction of the photons up to the results of Born, Heisenberg and Jordan on the quantization of a continuum – a comparative study is presented on the first lines of thoughts that led to the concept of quanta. The nature of the particle-like fluctuations and the wave-like fluctuations are analysed by using several approaches. With the help of classical probability theory, it is shown that the infinite divisibility of the Bose distribution leads to the new concept of classical "poissonian photo-multiplets" or to the "binary photo-multiplets" of fermionic character. As an application, Einstein's fluctuation formula is derived as a sum of fermion type fluctuations of the binary photo-multiplets.