QUANTUM THEORY
Amplitude-Frequency Duality
An investigation into the true nature of light and energy quantization
The nature of light was debated about for hundreds of years before it was finally decided, in the early 1860s, that light is an “electromagnetic wave”.
This verdict was thanks to the efforts of Scottish physicist James Clerk Maxwell, whose work on the mathematics of electromagnetism uncovered a ‘wave equation’ where the calculated speed of the wave was the same as the known ‘speed of light’. Maxwell’s work was credible evidence that light was not only a ‘wave’, but a subset of a larger “spectrum of electromagnetic radiation”.
[Note: The existence of this larger spectrum of radiation was confirmed in 1887, when German physicist Heinrich Hertz managed to successfully generate and detect radio waves.]
Things however took a bit of a turn towards the end of the 19th Century, when the concept of electric light started to become big business.
Electric lights are based on the common understanding that “hot things glow”. Thus by passing an electric current through a very thin wire, the wire heats up and gives off light. This emitted light is known in physics as “Thermal Radiation”.
As competition between the various new electric companies grew, these pioneering businesses were desperate to get a handle on how to generate the most amount of light with the least amount of electric current. Unfortunately, scientists were having a real problem trying to explain the physics behind thermal radiation — because their theories just did not fit the data.
But then something strange happened.
In January 1901 German physicist Max Planck published a paper titled: “On the Law of Distribution of Energy in the Normal Spectrum”. In this work Planck showed how to successfully derive the mathematics of thermal radiation, but to do so he had to employ a ‘mathematical trick’ that involved the “quantization” of energy.
This mathematical work turned out to be “revolutionary” for it seemed to imply that the EMISSION of energy (from a hot body) could only occur in DISCRETE chunks of energy (ε=hf) — where (h) was a newly discovered constant of nature, and (f) was the frequency of the light.
Five years later German patent clerk Albert Einstein showed that not only was light emitted in chunks of (hf), but it must also TRAVEL in packets of (hf), implying that light itself must be quantized.
But all this beggared the question:
What exactly is the SOURCE of “energy quantization”?
And the short answer appeared to be that: “Energy is quantized because Planck’s Constant (h) acts to LIMIT how small a quantity of energy of a given frequency can be — through the formula (ε=hf).” Thus the source of all energy quantization was considered to be the newly discovered universal constant (h). And this is how things stand to this very day.
But are we sure that this “well-established” narrative is correct?
We believe it is NOT.
In this paper we will attempt to show how: On the surface Planck’s 1901 paper appears to present Planck’s Constant (h) as being the source of energy quantization. But in truth this understanding is really the direct result of an apparently innocuous, but baseless, assumption that Planck employed in his paper. Strip away this baseless assumption however (and its resulting contextual narrative), and what we find is that the true source of energy quantization is not Planck’s Constant (h) but the radiation frequency (f).
In this paper we will present the case that:
- Although energy is ‘quantiz-able’ by (f), that does NOT mean that energy itself must be a fundamentally quantized quantity.
- The wave energy of light, and all radiation, is quantizable by (f) because for radiation, the frequency of an energy oscillation and the amplitude of an energy oscillation are actually one and the same thing.
In this paper we will be presenting the case for declaring that: the defining characteristic of light (and all electromagnetic radiation) is that it has an Amplitude-Frequency Duality.
PART 1— THE ENTROPY OF RADIATION
The Prevailing Narrative
Back before Planck’s so-called “quantum revolution”, energy was believed to be continuous — meaning it could exist in ANY amount or magnitude. But Planck’s work in the winter of 1900–1901 seemed to suggest that, at the most fundamental level of reality, there is no such thing as a “differential of energy”.
A differential of energy (dE) is the mathematical way of describing a change in energy that is so infinitesimally small that it is equivalent to almost no change at all; and thus a differential of energy (dE) is the mathematical way of describing “continuous energy” (i.e. energy that changes in a continuously smooth non-jumpy fashion) …
Planck’s work ushered in a whole new paradigm in physics in which reality seemed to make no sense at all. In this new paradigm changes in energy can only occur in “quantum jumps” of (ε=hf), which means that in this new reality only certain discrete energy values are allowed! But WHY should this be the case?
Well as things stand today, the prevailing narrative (surrounding energy quantization) is that:
Planck’s Constant (h) is a “Quantum of Action”, which although a very very small quantity, is NOT a “differential of action” (i.e. not a zero-like quantity); which means the quantity of energy (ε=hf) cannot be reduced to a differential of energy, and this ultimately LIMITS how small an incremental change in energy (ΔE) can be.
Thus, according to this ‘well-established’ narrative, for any given frequency of radiation there exists a minimum allowable amplitude of (ε=hf); and changes in this energy amplitude can only occur in incremental chunks of (ε).
We believe however that this well-established narrative is wrong.
In our previous paper we argued that, despite Planck’s obvious success in mathematically deriving the correct formula for thermal radiation, there is a serious flaw in his 1901 paper that successive generations of physicists have failed to recognize.
And this flaw does not relate to Planck’s mathematics; the flaw relates to Planck’s accompanying contextual narrative.
In presenting his work Planck explains what he believes is the real ‘physics’ behind his mathematics, but this contextual narrative is actually based on an IMPLICIT ASSUMPTION — an assumption that is baseless; but was at the time, and still is now, universally accepted as being true.
Unfortunately for us, this baseless assumption has turned out to be very detrimental to our understanding of the physics of the quantum world.
A Baseless Assumption
In his paper of 1901, Max Planck put forward a narrative that essentially described his model as being set up to model a ‘distribution of amplitudes’ available to a SINGLE-FREQUENCY oscillator.
But this narrative was manufactured on the back of an innocent but baseless assumption — an assumption that has gone completely unnoticed for well over a century now for it seems that it has never occurred to anyone to think otherwise.
The assumption we speak of is that: Radiation oscillates in exactly the same way that material objects do!
But this assumption is unreliable for there is no evidence to support it. Moreover, it is made even less credible by the fact that even today contemporary physics still cannot explain HOW exactly these radiation oscillations move through empty space (i.e. can move without a supporting medium) — for according to the prevailing narrative: they just simply DO!
[Note: to be absolutely precise, the prevailing narrative states that light moves as an ‘excitation’ through an invisible, but omnipresent, “electromagnetic field” …]
On the back of this baseless assumption Planck then went on to argue (due to thermal equilibrium between the radiation and the hot body) that it was possible to model the distribution of amplitudes of thermal radiation for a given frequency with a system of single-frequency material resonators in the hot body.
We argue however that on the back of Planck’s unsubstantiated assumption (employed at the very dawn of quantum theory) our understanding of the reality of quantum physics has been corrupted; and with it the true nature of light, and energy quantization.
We will argue here that the removal of Planck’s baseless assumption (about the classical nature of radiation oscillations), and his resultant contextual narrative (about modelling individual frequencies of radiation with single-frequency material resonators) leads to a radical review of what Planck’s mathematics is actually modelling.
The Entropy of Radiation
We believe that with his contextual narrative Planck managed to confuse himself, and in so doing managed to misrepresent what his own model is modelling.
According to Planck, he was modelling quantized energy distribution among ten material oscillators, ALL of which have the same frequency.
But, according to the bare mathematics of his model, the underlying methodology was simply to share (in quantized form) the total available energy among a DISCRETE number of oscillators that made up his mathematical system. And as it turns out, this methodology works equally well whether one is dealing with a system of single-frequency oscillators, or a system of UNRESTRICTED oscillators.
And so, we would argue, that while on the surface Planck’s revolutionary paper might appear to be equating the distribution of thermal radiation with a quantized treatment of “atomic entropy”; what he is ACTUALLY doing (when we strip away his misleading commentary) is modelling the distribution of thermal radiation with a discrete treatment of “radiation entropy”.
So our argument is that, thanks solely to Planck’s contextual narrative, it might seem as if (h) emerges as a result of the quantization of energy (available to a system of single-frequency oscillators), but in the absence of his misleading narrative it becomes clear that: (h) actually emerges as a result of equating the quantization of energy with a spectrum of radiation amplitudes.
Consequently, we would argue, Planck’s model DOES indeed model a ‘distribution of amplitudes’, just NOT a distribution of amplitudes FOR A SINGLE FREQUENCY!
Moreover, Planck’s mathematical model of thermal radiation uncovered not only (h) but also a second universal constant (k). And given that (k) turned out to be a ‘scaling’ factor in thermodynamics, we would argue that both constants emerged from the mathematics because both constants represent ‘universal scaling constants’ — with (k) being the scaling constant that scales macroscopic temperature down to the average energy of microscopic particles, and (h) being the scaling constant that scales macroscopic radiation down to the behaviour of some form of fundamental ‘radiation oscillator’.
So now a question arises: what might be the form of this radiation oscillator?
Form of the Radiation Oscillator
A clue to answering this question resides in the universal significance of (h).
Although history records the importance of Planck’s work as being his use of the so-called “quantum hypothesis”; for Planck himself, the true significance of his work was the discovery of (h) and its implication for the existence of the so-called “Planck Scale”.
Now, on the back of our postulating that (h) is a scaling factor for radiation, it seems reasonable to posit that the concept of the Planck Scale could be taken one step further.
Since the Planck Scale appears to represent the fundamental scale of reality, it seems reasonable to suggest that maybe
Planck’s Constant reveals the ‘size’ of the radiation oscillators.
And THIS, we believe, is the true significance of the discovery of Planck’s Constant (h).
Planck’s discovery of this universal constant was, we believe, the discovery of a signpost to the nature and form of the radiation oscillator. In the paper “The amplitude IS the frequency”, we used this alternative understanding of the significance of (h) to put forward a conjecture.
The Conjecture is
Space is Quantized, and these individual elements of space can oscillate about their own 3-dimensional equilibrium.
But, to justify the concept of an oscillating 3-dimensional volume, we will need to interrogate the concept of “CURL”.
PART 2 — THE NATURE OF LIGHT
The Concept of Curl
The concept of “Curl” was introduced by Scottish Physicist James Clerk Maxwell to explain “Circular Fields”. Maxwell referred to circular electric and magnetic fields as “Electric Curl” and “Magnetic Curl”.
In his 1861 paper titled “On Physical Lines of Force”, Maxwell wrote down the mathematical laws governing electrodynamics of “circulating” electric and magnetic fields.
In his next paper titled “A Dynamical Theory of the Electromagnetic Field” (written in 1864, and published in 1865) Maxwell was able to show that these mathematical laws could be used to generate two “Wave Equations” — one for the Electric Field, and one for the Magnetic Field. And in both equations the SPEED of the wave turned out to be a known speed — the known “Speed of Light” (c).
Motivated by this discovery, Maxwell proposed that light (and ALL other forms of electromagnetic radiation) must be undulations in the same fields that support electric and magnetic phenomena.
Today, when Maxwell’s contribution to the study of light is discussed, the main focus tends to be on the fact that he not only derived wave equations for electric and magnetic fields, but that he also discovered the speed of light hidden within these equations.
However, there is another very interesting fact about Maxwell’s wave equations that has been consistently overlooked in the story of physics; and that is the fact that BOTH sides of BOTH wave equations are different ways of representing the “Rate of Change of CURL” …
Quantized Space
Now Maxwell described Curl as being “a circulation, per unit area, over an infinitesimal path, around a point in space”. And a ‘point’ in physics is perceived to be a “zero-dimensional” quantity.
But what if there is no such thing as a “zero-dimensional point” in space? What if space is actually “quantized” into tiny “Infinitesimal Volumes”?
If this were in fact to be the case then the concept of curl would have to relate, NOT to a zero-dimensional point in Space but, to an infinitesimal three-dimensional “Element of Space” !
And, in this scenario Maxwell’s description of curl as being a “Circulation PER UNIT AREA”, would equate to the “twisting” of a two-dimensional “cross-sectional area” of an infinitesimal-volume about its remaining third dimension.
Moreover, these theoretical volumes could theoretically come in all shapes and sizes but, given that there would be a truly enormous number of infinitesimal volumes within a molecule of sand, it is reasonable to suggest that the “average” volume could be treated as if it were a “perfect three-dimensional cube”, (of an average quantum size). And this statistical averaging brings to the fore a simple geometric restriction.
Since it is impossible to flatten a three-dimensional volume beyond two-dimensional space, this means that the cross-sectional area of an average 3D cubic volume of space cannot be twisted beyond 90 degrees.
And we can use this concept of a “maximum amount of spatial twist” to render an alternative version of the famous Planck Energy-Frequency Relation.
An Alternative Version of (ε = hf)
So what follows is all built on one simple conjecture:
- Three-dimensional Space is “quantized” into infinitesimal “atoms of space”, and these individual elements of space can be disturbed from, and oscillate about, their “equilibrium” 3D state.
To start we will want to express our geometric restriction (on quantized space) in mathematical form.
Equation (1.1) ______ θₘₐₓ = (π/2) radians
Now, associated with any ‘amount of twist’ is a ‘turning-circle of twist’; and the greater the amount of twist, the ‘tighter’ is its turning-circle.
This means that for a “maximum amount of spatial curl” (θ-max) there must be a minimum turning circle with a “minimum radius of spatial curl” (r-min). So let’s also write this down in mathematical form.
Equation (1.2) ______ (S) = (θₘₐₓ)(rₘᵢₙ)
Now in geometry this product, of the angle of turn (measured in radians) times the radius of the turn (measured in meters), is known as the “arc-length” of the turn (also measured in meters). So (S) can essentially be thought of as being the “arc-length of twist” or the “arc-length of curl”.
Moreover, since the amount of curl and the radius of curl are inverse quantities, (S) must be a constant; which means that we can write this arc-length of curl in a more generalized form
Equation (1.3) ______ (S) = (θ)(r)
Next, by equating equations (1.2) and (1.3) we can generate an equation for the radius of curl (for an average infinitesimal volume).
Equation (1.4) ______ (r) = (θₘₐₓ/θ)(rₘᵢₙ)
This equation reflects the fact that as the amount of curl (θ) goes up, the radius of curl (r) goes down, and so the minimum radius of curl (r-min) occurs when theta equal theta-max (θ = θ-max).
Now, in our macroscopic world, an initial displacement from equilibrium is often the starting point for an “oscillation”; and it is reasonable to assume that the same physics applies in the quantum world.
Thus, in quantized space, an initial twisting displacement (θ) of a quantum volume can act as the “Angular-Amplitude” for an angular oscillation (wherein the volume twists back and forth about its equilibrium’s state).
Now many years ago the Italian astronomer physicist and engineer Galileo Galilei figured out something very interesting. He figured out that angular-speeds and angular-frequencies are one and the same thing.
So, given that there is a maximum speed in the universe (i.e. the speed of light (c)), there must also exist a maximum angular-frequency, such that
Equation (1.5) ______ (ωₘₐₓ) = (c)/(rₘᵢₙ)
So now if we combine equation (1.4) with equation (1.5), and rearrange, we get
Equation (1.6) ______ (c) = (ωₘₐₓ)(r)(θ/θₘₐₓ)
And by dividing both sides by (r) we get
Equation (1.7) ______ (c/r) = (ωₘₐₓ)(θ/θₘₐₓ)
And this equation reduces to a generalized equation for angular-frequency
Equation (1.8) ______ (ω) = (ωₘₐₓ)(θ/θₘₐₓ)
Next, we can convert this angular-frequency of oscillation into a “cycle-frequency” of oscillation, by dividing both sides by two-pi. And this gives us
Equation (1.9) ______ (f) = (fₘₐₓ)(θ/θₘₐₓ)
So, given that both (f-max) and (θ-max) are constants, we now have the oscillation frequency of our quantum volume expressed solely in terms of the “Amplitude of Oscillating Curl” (θ).
Lastly, if we multiply both sides of equation (1.9) by the Planck Constant (h) we get
Equation (1.10a) ______ ε = (hfₘₐₓ) (θ/θₘₐₓ)
Equation (1.10b) ______ ε = (εₘₐₓ) (θ/θₘₐₓ)
So here we have equations for the energy contained in an oscillation of three-dimensional quantum space. And, as we can see, there is a direct relationship between the energy (ε) and the angular-amplitude of the oscillating curl (θ). Moreover since theta is restricted to only having values less than or equal to theta-max, this means that we can NEVER have a single quantum of energy greater than (ε-max).
Thus, having started with a simple geometric restriction as expressed in equation (1.1), we have ultimately derived the existence of four constants (r-min), (ω-max), (f-max) and (ε-max), and we would like to know their values.
Here we are going to have to rely on a guess. Our hunch is that (ε-max) equates to the “Planck Energy”, which would mean that (f-max) equates to the “Planck Frequency”, and (r-min) equates to the “Planck Length”. Thus the values of the four constants are as follows.
(rₘᵢₙ) = (0.1616255) (10⁻³⁴) meters
(ωₘₐₓ) = (1.85492) (10⁴³) radians per second
(fₘₐₓ) = (2.9522) (10⁴²) cycles per second
(εₘₐₓ) = (1.9561) (10⁹) Joules
[Note: The existence of a maximum amount of energy (εₘₐₓ) that a single quantum/energy-element can have will ultimately prove to be very important when we get to our unification of quantum mechanics with general relativity.]
The Amplitude IS the Frequency
Now, an alternative way to view the relationship between energy (ε) and the amplitude of curl (θ) is to multiply both sides of equation (1.8) by the Reduced Planck Constant (ħ). This gives us
Equation (1.11) ______ ε = (ħωₘₐₓ)(θ/θₘₐₓ)
And given that omega-max equals (2π) times (f-max), and theta-max equals (π/2 radians), we can rewrite equation (1.11) as follows
Equation (1.12) ______ ε = (4ħfₘₐₓ)(θ)
This equation makes more explicit the direct relationship between the energy of a quantum (ε) and its amplitude of curl (θ). Essentially, equation (1.12) is telling us that, at the fundamental level, a quantity of energy is nothing more than a Measure of the Amplitude of Oscillating Curl.
And so by building on our initial restriction for a maximum amount of spatial curl, we have found that:
for spatial oscillations, amplitude and frequency are essentially one and the same thing.
This idea can be expressed more explicitly by rearranging equation (1.9) and incorporating within it equation (1.1).
(f) = (2/π)(fₘₐₓ)(θ)
The idea that for radiation “the amplitude and the frequency are one and the same thing” is, we would argue, the single most important thing to understand about the nature of the quantum realm.
It is THE thing that differentiates the microscopic realm of quantum physics, from our macroscopic world of classical physics (where in classical wave mechanics, amplitude and frequency are always independent of each other).
It is, we would argue, also the single most important thing about quantum theory that the entire physics community has failed to comprehend from day-one of this far-reaching theory (of radiation and the sub-atomic world).
And the primary reason that the physics community has failed to recognize this characteristic feature of radiation is largely down to the narrative outlined in the paper that first introduced the idea of “quantized energy” to an unprepared world.
In the classical world of mechanical waves, amplitude and frequency were always independent of each other. Thus when physicists (weaned on classical waves) started to explore this relatively new arena of radiation/energy waves, they were obviously simply not capable of recognizing this new, and paradigm-shifting, type of wave: a wave that exhibits AMPLITUDE-FREQUENCY DUALITY.
PART 3 — THE NATURE OF ENERGY QUANTIZATION
An Alternative Model
So, by doing some surgery on Planck’s narrative, we are led to an alternative understanding of the significance of (h); and from there to the conjecture that “space is quantized”. And on the back of this conjecture, Planck’s mathematical model takes on a completely different meaning.
Instead of the available energy being shared among 10 material oscillators (of the same frequency), now the available energy can be understood as being shared among 10 units of space (which have no restrictions on frequency or amplitude).
And the result of this change in perspective is that Planck’s mathematical work now seems to point to the following conclusions:
- What we know as “radiation” are really just oscillations in quantized space.
- For any given temperature of a hot body, there exists a signature distribution of ‘amplitudes’ associated with its thermal radiation.
- For radiation/spatial oscillations, the amplitude and the frequency are one and the same thing.
And so by building on one simple conjecture (about the ‘atomic’ nature of 3-dimensional space) we have come to the conclusion that all observable frequencies of radiation are simply different amplitudes of said radiation.
And this means that any change in amplitude (no matter how small) is simply a change in frequency.
A Differential of Energy
Our alternative version of the Planck Relation (as expressed in equation 1.12) tells us that the energy of a quantum is directly proportional to the amplitude of curl (θ), and the constant of proportionality is the quantity (4ħfₘₐₓ).
And this means that any CHANGE in this amplitude of curl will represent both a change in frequency and a change in energy. And so we can use this idea to rewrite equation 1.12 as follows
Equation (3.01) ______ Δε = (4ħfₘₐₓ)(Δθ)
So, given that in our new narrative spatial oscillators are NOT restricted to a single frequency, this means we can assume that, for ANY spatial oscillator, the quantity (Δε) can theoretically be made infinitesimally small by reducing the change in amplitude of curl (Δθ) to an infinitesimally small quantity.
Thus, as the change in the amplitude of curl (Δθ) tends towards zero, it becomes a “DIFFERENTIAL OF THE AMPLITUDE OF CURL” (dθ), which means that the quantity (Δε) effectively becomes a “differential of energy” — which is representative of smooth and CONTINUOUS change.
Mathematically this ‘differential of energy’ can be represented as follows:
Equation (3.02) ______ dε = (4ħfₘₐₓ)(dθ)
This equation is telling us that:
A “differential of energy” is proportional to the “differential in the amplitude of curl”.
Moreover, given that the quantity (4ħfₘₐₓθ) equates to the quantity (hf), this means that we can rewrite equation (3.02) as follows:
Equation (3.03) ______ dε = h(df)
And this equation is telling us that:
A “differential of energy” is proportional to the “differential of amplitude/frequency”, and that the constant of proportionality is Planck’s Constant (h).
This equation, in a sense, signals a return to the continuous energy of classical physics, for it shows that (h) is NOT in any way limiting how small an increment of energy can be. Planck’s Constant (h) in this equation acts simply as a constant of proportionality — a scaling factor between the macroscopic and microscopic worlds. So, in their different ways, both equation (3.02) and equation (3.03) essentially tell us that:
Energy is NOT fundamentally quantum in nature. (Energy is a continuous quantity even in the quantum realm).
Thus, in defiance of 122 years of physics teaching otherwise, we believe that: energy is, and has always been, a continuous quantity — EVEN in the quantum realm.
The Source of Energy Quantization
The ultimate consequence of our revision of Planck’s narrative points to the fact that energy REMAINS a continuous quantity, even in the quantum realm. But the fact that energy is fundamentally a continuous quantity does not mean that this continuous quantity is not ‘quantizable’.
And since quantized energy is clearly a known feature of the “quantum realm”, the question now arises that: if energy is not a fundamentally quantized quantity, then
What exactly is causing energy to be quantizable?
To answer that question, we must recognize that just as a differential of energy (dε) is proportional to a differential of amplitude (df), so too a ‘quantity of energy’ (ε) is proportional to a ‘quantity of amplitude’ (f). This relationship is expressed mathematically as the familiar Planck Relation (ε=hf).
And so the answer, we believe, is that:
Energy is quantizable into packets of (hf) because (f) represents the amplitude (or packet size) of a ‘SINGLE CYCLE’ of spatial oscillation.
And this means that while the intensity of any given photon is determined by its amplitude of curl, the intensity of a beam of light of any given frequency is determined by the number of packets/photons of the given frequency. This idea can be expressed mathematically in the same form as Planck’s original “quantum hypothesis”
Equation (3.04) ______ E = n(ε)
And it means that just as a continuous quantity like money is quantizable into a bunch of $5 bills, so too radiation energy is a continuous quantity that is quantizable into a number of packets of a given frequency.
CONCLUSIONS
The argument we have presented in this paper is clearly in direct conflict with the well-established teaching of Quantum Theory. But, as is well known, the well-established version of quantum theory is very confusing, and full of logical inconsistences.
We suggest the reason for all this confusion originated with the original paper of quantum theory, in which Max Planck employed a baseless assumption leading to a misleading contextual narrative (which unfortunately poisoned all the physics that came after).
As things stand today, physics believes that energy quantization occurs because Planck’s quantum of action (although a very very small quantity) is NOT a differential of action; and consequently this non-differential value of (h) is acting on any given frequency to LIMIT both: how small the ‘minimum amplitude’ can be; and how small the smallest ‘incremental change in amplitude’ can be.
In this paper, we have clearly argued against this well-established narrative. We have argued that the belief that “(h) is acting to restrict energy amplitudes to certain discrete values” is simply a direct result of Planck’s original belief that his model was modelling a distribution of amplitudes FOR A SINGLE FREQUENCY.
In contrast, our belief is that there exists a minimum amplitude for every frequency of radiation simply because for any given frequency there is only one possible amplitude . In other words, there exists a minimum amplitude for every frequency of radiation because for radiation the amplitude IS the frequency.
This simple tweak in understanding (about the nature of electromagnetic waves) allows us to suggest that (h) has NO inhibiting effect on the continuous nature of energy — that it is merely acting as a constant of proportionality in the direct relationship between energy and frequency.
Our analysis of Planck’s 1901 paper, stripped of its assumption and contextual narrative leads us to the conclusion that energy is NOT fundamentally quantized. In fact:
Radiation Energy comes in a CONTINUOUS range of amplitudes; and this continuous range of amplitudes are what we observe as frequencies.
In other words:
For radiation, frequency and amplitude are one and the same thing.
And this means that
The vibrational energy of any given frequency is not quantized by minimum increments of amplitude; this vibrational energy is quantized by the amplitude itself.
In other words:
Energy quanta are NOT increments of amplitude; they ARE the amplitude.
Consequently we would argue that:
The TRUE SOURCE of the quantization of energy is not the constant of proportionality (h) but the amplitude of the cycle (f).
And thus
The TRUE NATURE of energy quantization is that Energy (of any given frequency) comes in discrete quanta because a single periodic oscillation (with a set amplitude) is a single discrete thing!
So In Summary: We believe that although (h) is the source of many things in quantum theory it is NOT the source of energy quantization. Energy is not quantized by (h), but by individual packets of wave amplitude (f). And consequently the intensity of any given frequency/amplitude of energy will depend on the NUMBER (n) of its quantized packets of energy amplitude (ε=hf) — mathematically this equates to Planck’s ‘Quantum Hypothesis’ (E=nε).
And so just like how money is a continuous quantity that is often quantized into different denominations of dollar bills, so too:
The energy of radiation is NOT a fundamentally quantized quantity, but it is “QUANTIZABLE” into a packet of energy of a given amplitude/frequency.
Moreover, the fact that energy is quantizable by frequency is a direct result of the Amplitude-Frequency Duality of light. And this duality of amplitude and frequency is, we would argue, THE SIGNATURE FEATURE of the subatomic world
Amplitude-Frequency Duality is what differentiates electromagnetic waves from ordinary mechanical waves; and as such it is the singular most important thing about what characterizes all behaviour in the subatomic world.
Amplitude-Frequency Duality is also, we would argue, THE thing about the subatomic world that the physics community has, to this day, consistently failed to recognize.
And this failure to recognize the signature feature of the subatomic world has meant that physicists have effectively been stumbling around in the dark from the very dawn of the so-called “quantum revolution”. It has meant that, despite all the advancements in quantum theory throughout the 20th Century, quantum physicists still do not truly see what differentiates quantum physics from all the physics that came before.
We believe that Amplitude-Frequency Duality is the thing that differentiates the microscopic quantum realm from our macroscopic classical world. We believe that:
Amplitude-Frequency Duality is the Fundamental Essence of Light, and the Nature of Energy Quantization in the Quantum Realm.
In fact, we would go so far as to say that:
Amplitude-Frequency Duality is the Fundamental Essence of Quantum Theory, and the Quintessential Essence of all things in the Quantum Realm.
REFERENCE
Max Planck, 1901, On the Law of Distribution of Energy in the Normal Spectrum. Annalen der Physik, vol. 4, p. 553
© Kieran D. Kelly
This is Post #7 in the series on NeoClassical Quantum Theory
