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A Time-dependent Local Representation of Energy

Constantinos Ragazas

Published Feb 1, 2010• 1 citation
OpenAlex

Abstract

Whereas globally energy propagates continuously as a wave, in this note we consider that energy can be represented locally by an exponential of time. Using such representation we are able to show that Planck's Formula for blackbody radiation is an exact mathematical identity. We are also able to explain the photoelectric effect without the photon hypothesis and derive an equation relating the photoelectric current to the intensity and frequency of radiation. This equation conforms well with graphical characteristics of the actual experimental data. Moreover, this representation of energy explains the quantum hypothesis, provides a simple intuitive explanation of the double-slit experiment and permits a definition of the temperature of radiation. It also explains the physical meaning of Planck's constant h and why it exists.

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arXiv:1701.06867•Jan 24, 2017•1 citation
Whereas globally energy propagates continuously as a wave, in this note we consider that energy can be represented locally by an exponential of time. Using such representation we are able to show that Planck's Formula for blackbody radiation is an exact mathematical identity. We are also able to explain the photoelectric effect without the photon hypothesis and derive an equation relating the photoelectric current to the intensity and frequency of radiation. This equation conforms well with graphical characteristics of the actual experimental data. Moreover, this representation of energy explains the quantum hypothesis, provides a simple intuitive explanation of the double-slit experiment and permits a definition of the temperature of radiation. It also explains the physical meaning of Planck's constant h and why it exists.
In our derivation of Planck's Law (showing that this Formula is an exact mathematical identity that describes the interaction of measurement) the 'accumulation of energy' locally at time t was a key variable. By starting with this as the primary variable and defining energy, momentum and force in terms of it we are able to mathematically derive such basic laws of Physics as Conservation of Energy and Momentum, and Newton's Second Law of Motion. Following the same approach we demonstrate in this short note how Schrodinger's Equation relates to this formulation. This leads to a physical meaning of the wave-function ψ and a plausible explanation of the double-slit experiment.
This chapter deals with the important experimental studies on black-body radiation, Wein’s law, Rayleigh–Jeans law, Planck’s distribution law, etc. The black-body radiation studies reveal that the maximum wavelength of radiation 1 is inversely proportional to temperature T . The expression for Wein’s law has been deduced on the basis of thermodynamic considerations. The law gives a clue to understand that it holds true only at low temperatures and short wavelengths. The Rayleigh–Jeans law is based on the general theorem of elasticity and is in excellent quantitative agreement with experimental observations for large wavelengths and high temperatures, leading to ultraviolet ‘catastrophe’. Actually, Max Planck enunciated the correct form of the temperature–radiation law based on some assumptions and finally proposed Planck’s quantum theory. This chapter also explains the photoelectric effect and important conclusions drawn on the basis of experimental facts. Einstein applied the quantum theory to explain the photoelectric effect and to define threshold frequency. On the basis of plot of frequency of radiation versus voltage applied, a linear graph was obtained, which enabled finding the value of Planck’s constant h. The Compton effect has also been written in a lucid manner involving the mathematical formulation from which the Compton shift can easily be obtained. This chapter also details the atomic hydrogen spectrum including Bohr’s model of an atom, energy of electron revolving around the nucleus, radius of an orbit and expression for velocity of electron. It also mentions the drawbacks of Bohr’s theory. References, problems, and questions on this concept are provided at the end of the chapter.
The current physical view of the Universe (the Metaphysics of Physics) is one that just does not make sense and is counter-intuitive to our Experience. It begins with the Quantization of Energy Hypothesis used by Planck to derive his blackbody radiation formula and by Einstein to explain the photoelectric effect, which later evolved into Quantum Mechanics. By examining these conceptual foundations of Modern Physics we are able to show that the same experimental facts that lead to Quantum Physics can be differently explained without using energy quanta, continuously and not discretely. We are able to derive Planck's Law without using quanta and explain the photoelectric effect without needing photons. We summarize in this paper results presented in a series of papers that show with mathematical reasoning and rigor how this is possible. The main purpose of this endeavor is to create a view of the Universe that 'makes sense', that agrees with our Experience and provides physical meaning to our Understanding of it.
We tried to introduce the idea of quantization in Chapter 9 as a completion of a one semester course. However, we skipped over some really interesting events in the history of Science between 1900 and 1913 when Bohr derived the quantized energy of the H atom. First we want to carry out the 1901 Planck derivation of the formula for blackbody radiation [1]. Many texts just show the curve, write e¼ hn, and move on. As a student, this author found that limited explanation very frustrating since energy quantization is a fundamental concept. Even among graduate texts in quantum mechanics, we are aware of only one that does the complete treatment which we will draw upon for the mathematics [2] but supplement with a narrative that we have found helpful to students over the years. Then in 1905, Albert Einstein (1879-1955), one of the most influential scientists of all time, gave an explanation of the photoelectric effect [3] for which he received the Nobel Prize in 1921. Even reducing our list to essential topics, we need to discuss the Davisson-Germer experiment [4]. The photoelectric effect introduces the idea that light waves can act as particles while the Davisson-Germer experiment showed that particles can act like waves and confirmed the De Broglie equation [5]. However, you can be assured that it will not be as difficult as you might have anticipated and if you can absorb the meaning of just these three key experiments you should be able to begin thinking in terms of quantum mechanics! Despite our slow historical development, this is 2010 and we have to get to the twenty-first century somehow!
In the year 1900 Max Planck was led by experimental observations to propose a strange formula for the intensity as a function of frequency for light emitted by a cavity. It relied on peculiar properties to be obeyed by the emitters and absorbers in the cavity. I highlight the mathematically suggestive nature of the formula, accessible even to a high school student, that could have provided a clue to the physical reasoning of Planck. In 1905, Einstein made the bold photon hypothesis and was able to predict the formula for the photoelectric effect which was not fully explored then. The first part of this article concerns the period 1905 to 1923 with a possible explanation for the difficulties in acceptance of the new concept. In the second part of the article I present how S. N. Bose's 1924 paper provided a systematic derivation of Planck formula by consistently adopting the conception of photons within Boltzmann's framework. In conclusion we discuss the implications of Quantum Mechanics that eventually emerged, showing that the seeds of some of its uncanny conceptual content were already foreshadowed in Einstein's proposal.