It is posited that the frequency of electromagnetic radiation may be quantised and two methods are derived which permit the calculation of the magnitude, delta, of the quantisation.
The work does not establish the existence of frequency quantisation and the two methods derived may be described by the oxymoron, systematically arbitrary.
Both methods rely upon the Fidler diagram.
The first method employs the superposition of a fractal path on the diagram and gives, delta = (V)/(sqrt 2)^(n-1), where n is a disposable odd integer, and (V) is the Planck circular frequency. The second method involves the tiling of the diagram by a succession of self-similar tiles which are progressively-reducing versions of the diagram itself. In this case, delta = (V)/ (sqrt 2)^(2(n-1)), where n is any integer.
Erratum: The relevant Planck quantities on p16 should read:
Planck length, (L) = 4.05134*10^-35 m.
Planck circular frequency, (V) = 7.399825*10^42 Hz.
Planck spectroscopic wave number, (Z) = 2.468316*10^34 m^-1.
Planck specific energy, (S) = 12.1026*10^43 J/m.
Planck specific energy intensity, (I) = 2.987308*10^78 J/m^2.
Planck specific energy density, (D) = 7.373629*10^112 J/m^3.
The work also shows that the Fidler diagram is the two-dimensional projection of a three-dimensional surface.
Table of Contents
1. Introduction
2. Quantisation of the frequency of electromagnetic radiation
3. A frequency-quantised Fidler diagram
4. The Fidler diagram as the two-dimensional projection of a three-dimensional surface
5. The extended Fidler diagram
Research Objectives and Themes
The primary objective of this work is to explore the theoretical possibility of frequency quantisation within the electromagnetic spectrum. By challenging the axiomatic assumption of continuity in electromagnetic radiation, the author derives mathematical methods to quantify potential discretisation, utilizing the Fidler diagram as a geometric foundation for calculating specific physical quantities related to photons.
- The philosophical and physical limitations of the continuity assumption in electromagnetic radiation.
- Development of methods to calculate the magnitude of frequency quantisation (Δ).
- Geometric modeling of the electromagnetic spectrum using the Fidler diagram and its projections.
- Theoretical derivation of photon-related quantities such as specific energy, intensity, and density.
- Application of fractal and self-similar tiling techniques to discretise coordinate axes.
Excerpt from the Book
Quantisation of the frequency of electromagnetic radiation
We posit that the frequency, ν, of electromagnetic radiation is given by the simple linear equation: γΔ = ν ------------------------- (1),
Where, γ is a pure number and Δ, which must have units of Hertz, is a non-zero increment of frequency. We call γ the frequency number. Further, it is posited that for the purpose of this work, Δ, is a constant, has the character of a finite difference, and hence, is very small.
If the spectrum of electromagnetic radiation is continuous then all γ are members of the set of real numbers. Conversely, if the frequency is quantised then all γ are members of the set of natural numbers.
In the case of a continuous spectrum of radiation there is, at bottom, no utility in equation (1) if used in other than the manner prescribed, for the combination of free choices for Δ in conjunction with any number in the range of real numbers renders the equation hyperbolic, and an infinite set of rectangular hyperbolae, with frequency ν as parameter may be generated, which, in the context of the present work, is devoid of any physical meaning.
Summary of Chapters
Introduction: This chapter challenges the axiom of continuity in electromagnetic radiation, drawing parallels to macroscopic views of discontinuous processes and proposing that frequency may be quantised.
Quantisation of the frequency of electromagnetic radiation: The author introduces a linear equation to represent frequency as a function of a constant increment (Δ) and a frequency number, arguing that quantisation distinguishes the nature of these numbers.
A frequency-quantised Fidler diagram: This section presents a discretised version of the Fidler diagram and devises two methods—utilizing fractal paths and self-similar tiles—to establish a measure for frequency quantisation.
The Fidler diagram as the two-dimensional projection of a three-dimensional surface: The author explores the geometric structure of the Fidler diagram, demonstrating that it represents a projection of a complex helical surface.
The extended Fidler diagram: This concluding chapter derives equations for specific energy, intensity, and density, showing that these variables can be extracted from the diagram without requiring additional complex plotting.
Keywords
Electromagnetic radiation, frequency quantisation, Fidler diagram, Planck constant, photon energy, continuity, discontinuity, radiation Strouhal number, discretisation, spectral analysis, quantum mechanics, fractal path, self-similar tiles, specific energy, wave number.
Frequently Asked Questions
What is the core focus of this research?
The research examines the possibility that the frequency of electromagnetic radiation is not continuous, as typically assumed, but rather quantised.
What are the primary themes discussed?
Key themes include the critique of the continuity axiom, the geometry of the Fidler diagram, methods for frequency discretisation, and the calculation of photon-related energy properties.
What is the main research question or objective?
The objective is to derive mathematical methods that allow for the calculation of the magnitude of frequency quantisation (Δ) to investigate whether such a phenomenon could exist.
Which scientific methods are employed?
The author uses a combination of geometric analysis—specifically the superposition of fractal paths and the tiling of the Fidler diagram with self-similar structures—to derive quantitative expressions.
What is covered in the main body of the text?
The text progresses from a theoretical critique of continuity to the construction of a quantised diagram, culminating in the derivation of formulas for specific energy, intensity, and density of photons.
Which keywords best characterize the work?
The work is characterized by terms such as frequency quantisation, electromagnetic radiation, Fidler diagram, and spectral discretisation.
How is the Fidler diagram utilized in this study?
The diagram serves as a foundational coordinate system that the author manipulates through tiling and fractal paths to extract specific values for frequency increments.
What is the significance of the "Planck point" mentioned in the text?
The Planck point, defined by coordinates (1,1) in the Fidler diagram, serves as a critical reference point for the author's mathematical constructions and discretisation methods.
Does the author claim to have proven frequency quantisation?
No, the author explicitly states that the work does not establish the existence of frequency quantisation and describes the derived methods as "systematically arbitrary."
- Citar trabajo
- William Fidler (Autor), 2019, On the quantisation of the frequency of electromagnetic radiation, Múnich, GRIN Verlag, https://www.grin.com/document/463095
