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The Photoelectric Effect Without Photons

Constantinos Ragazas

Published Feb 1, 2010• 7 citations
OpenAlex

Abstract

Using the same ideas and approach followed in our derivation of Planck's Law is an exact mathematical identity and our explanation of the double-slit experiment, we in this note provide an explanation of the Photoelectric Effect and derive equations that conform well with experimental data.

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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.

•Feb 1, 2010•0 citations
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.
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 recent articles by this author, [ S. Karp , Statistical properties of ensembles of classical wave packets, J. Opt. Soc. Am.65, 421 ( 1975); S. Karp , Test for the nonexistence of photons, J. Opt. Soc. Am.66, 1421 ( 1976)], a radiation model was proposed that could lead to the identification of certain classical properties of the field, based upon photoelectric counting experiments. Mandel [ L. Mandel , Photoelectric counting measurements as a test for the existence of photons, J. Opt. Soc. Am.67, 1101 ( 1977)] responded by asserting that “It follows that for any field for which a classical wave description exists, in the sense that the phase-space density ϕ({ν}), and therefore P(u), are non-negative it is impossible to distinguish between photons and light waves in photoelectric counting experiments.” This statement is based upon the derivation of similar photoelectron counting equations using quantum and classical techniques. It is the mathematically loose associations and subsequent rigid physical interpretation implied in relating the two equations that is under contention. It seems to us that the model-computation-effect approach to physics is still solvent. In particular, if we can model an effect as small as the radiation from an individual electron and produce a predictable effect, then the physics underlying the model must be seriously considered.
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.