When the classical interpretation of electromagnetic waves started to fail observed experimental measurements of black body radiation, the solution was found by the realisation that the wave was quantised into discrete energy packets. This resolution led to the development of the Planck constant, which is at the foundation of quantum theory. Yet the exact reason for this value is still a complete mystery. In this article, we explain the fundamental error in calculation, which resolves the mystery of the quantisation of electromagnetic waves from a perspective of musical harmonics.
At the beginning of the 1800s, Thomas Young conducted the double slit experiment, proving the wavelike nature of light. As the century progressed, this led to some remarkable advances in science. The discovery of electricity, which started to transform the whole world. The electromagnetic spectrum, discovered by Maxwell, lead to the unification of magnetism, electrical energy, and the root of all visible light as different wavelengths and frequencies which travelled as the speed of light (c). It seemed like science had finally cracked the underlying nature of reality.
However, it soon became clear that something was fundamentally missing from our scientific understanding of the universe. When black body experiments began to disagree with the laws of classical electromagnetism, the solution was found by Max Planck, when he suggested the light can only exhibit specific energy levels, and rewrote the equations with the addition of a fixed quantity, now known as the Planck constant (h). Whilst this resolved the correlation between the mathematics of science and experimental observation, the reason as to why the Planck Constant (h) held its particular value remains a mystery.
In this article, we re-examine the mathematical calculations performed by Reyliegh and Jeans in their original calculations of the Black Body experiment, from the perspective of musical theory. In doing so, we finally unravel the mystery of the Planck constant, with astonishing consequences for modern quantum theory.
The ultra violet Catastrophy
The realisation that reality is quantised into discreet packets originates with what scientist term the Ultraviolet Catastrophe. When an object is heated up, it will begin to glow red. As it gets hotter, so it will change colour turning yellow (white), and at extreme temperatures blue. Quite clearly, this colour order is directly related to the visible spectrum of light. The hotter an object gets, the higher the frequency of light that is emitted. However, if we try to calculate the exact relationship between temperature and light using classical electromagnetic theory, we find that the correlation does not meet with experimental result. As this is much more pronounced at the ultraviolet level, the term Ultraviolet Catastrophe was used to express this anomaly.
When an object is heated, so the wavelength of light emitted gets smaller, and the colour changes from red up to blue. In the graph above, the calculation of Rayleigh and Jeans shows a curvature that tends towards infinity, as the object gets hotter. This would mean that the whole universe should be filled with ultraviolet light. Yet, quite obviously, this is not the case. Instead, we find that the amount of emitted radiation has a specific peak, after which it tapers off to zero. Max Plank was able to emulate this curvature for all the various temperatures by the introduction of a mathematical constant (h). This suggested that energy could only take on discrete values.
Originally, Planck thought that this constant would eventually be resolved somehow. But instead it was adopted, and became the revolution known as quantum mechanics. Today, the Planck constant is so fundamental to modern science that the whole modern interpretation of the SI unit measurement system is based upon its precise value. However, the reason for its existence still remains unexplained.
Black Body Radiation
To begin unravelling the mystery of the Planck constant, we first need to understand the experimental background of the ultraviolet catastrophe. It is well understood that a white object will tend to reflect energy, whereas a black object will tend to absorb it. Therefore, a black body is a theoretical object that will absorb all frequencies of light. Scientists can emulate such an object by creating a box with a small hole in it. Light entering the hole will be unlikely to escape it, which is why the hole looks black. If the box is heated, then the interior will start to glow, just like an oven. Light will then be emitted, which can be measured.
As the temperature rises, so the colour changes from red to white to blue. In this way, temperature can be mapped to different frequencies of light. This is called the Black Body Radiation, which produces a specific curvature when plotted on a graph. It is important to realise that an object will emit a variety of different frequencies, which is termed its spectral radiance. However, each specific temperature creates a unique curvature that peaks in a particular point on the electromagnetic spectrum.
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Through these Black Body experiments, scientist were able to gather a vast amount of data regrading the spectral emissions of different objects at different temperatures. However, what was missing were the mathematics that would emulate these results. Whilst the relationship between spectral radiance had already been successfully produced by Wilhelm Wien in 1893, these calculations were based in the field of thermodynamics, not electromagnetism. What was needed was a mathematic interpretation that would unify the experimental results with classic wave theory.
It was Rayleigh and Jeans that took on the challenge. The mathematics they used are quite complicated, involving lots of trigonometry, which for most people is beyond their scope of understanding. This video offers a detailed explanation, of the complete mathematical solution.
If the above video seems a little complicated, that is because it is. However, we can massively simplify the maths by understanding the basics of how waves work. A wave is expressed on a line which represents its direction of travel. A half arc forms the first part of the wave, which inverts in the second part. Together, they create a single wave, which then repeats. The distance between two peeks is called the ‘wavelength’, and the number of times the wave produces its peaks is called its frequency. The shorter the wavelength, the higher the frequency.
The wavelength and frequency of an electromagnetic wave is unified by the speed of light. When the frequency is multiplied by the wavelength, then it always produces the speed of light (c). It is interesting to note that wavelengths are ‘spacial’ whereas frequency is temporal. This means that all waveforms have both a space and a time component.
When Reyliegh and Jeans calculated the spectral radiance of the black body experiment, they used whole number integers of wavelength, which produce standing waves between the two sides of the box. A standing wave is formed of half wavelengths numbers. This is called the harmonic series, and is a natural phenomenon found in nature. For example, a wavelength of 1/2 produces what is called the fundamental of that particular key. The second harmonic is formed of a wave length that is exactly half the first. Then the third harmonic creates the musical 5th, and the forth harmonic the musical 4th.
The above image shows the first six steps of the harmonic series. Notice that as the wave gets divided into smaller and smaller parts, so the wave length get exponentially shorter. This in turn creates a logarithmic curvature similar to the Rayleigh-Jeans expression. As no limitation was placed on the number of times the wave can be divided, so the wave will curve towards infinity. This simple expression helps us to understand the fundamental problem with the Ultraviolet Catastrophe.
A string under tension when struck will produce a particular frequency based on its length, and width. In the example of a guitar, each string is the same length, but the tension and width of the string produces different tones. Each note needs to be tuned correctly, otherwise the music produced becomes discordant. Only when the frequencies fall into a specific ratio is the instrument tuned.
As noted previously, a string that is halved produces the octave, the 2nd in the harmonic series. When the string is quartered, it forms the musical 4th, and when divided into three, the musical 5th is produced. From the difference between the musical 4th and 5th, the tone is created. In between the tone, we find the semitone, which is often found st the black note in between two white notes on a piano keyboard. The octave is formed of 12 semitones, from which 7 notes are selected to form a musical scale. There are 7 types of musical scales, called modes, which are Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian and Locrian.
Music is based on a specific key, which is expressed by the first harmonic of the scale. In modern music we employ the tempered scale which dispenses of the need for musical exactness, by slightly detuning the note. This is how instruments such as the piano can avoid being retuned each time the musical key is transposed. However, it means that instruments that are tuned to the tempered scale are never perfectly in tune. This atonality is small enough to be discounted. You can find out more about this in our new theory of Harmonic Chemistry, that unifies these musical concepts into the structure of the periodic table. This short video explains why a piano can never be tuned to a perfect pitch
When we consider the problem of musical tuning, that moves toward discordance as the number of divisions increases, we can begin to recognise the similarity between this and the concept of quantised electromagnetic waves. In the harmonic series, the 7th harmonic seems to be where the problem of musical tuning first arises. By way of example, we can consider the idea of musical cents. This concept divides the octave into 1200 tiny lengths. Notice that the numbers 1, 2, 3 and 4, that form the first 4 harmonics, will all divide perfectly into the number 12. The 5th harmonic creates the first problem, as when divided by 1200 it should be found at the 240 cents, which should be the Major third. However, in music, this is not the case. Instead, it is the ratio 4:5 creates the major third. This is where the problems begin. The number 6, although it can be divided perfectly into 12, does not create the Pythagorean minor 2nd, or whole tone, which is found by the ratio 8:9 or 3³:2². Instead of the equal tempered 200 cents, this equates to a slight difference value 203.91 cents. Between the tone, we find the semitone. You might think this should be the 7th harmonic at 171.42. However, the perfect semitone is actually found to be made of the ratio 25:24 which is only 70.67, which is over 100 cents out.
What we see is that the division of a line, (string), creates drastically different results from equal temperament made of a single unit of equal spacing. Just like the error in the Rayleigh-Jeans calculations, at smaller wavelength the calculations fall into catastrophe.
This concept is most clearly demonstrated by examining the construction of the piano. Notice that the keys all fall in a straight line, whereas the internal strings form a curvature that is not uniform. The diagram on the left shows the difference between the sting divided (red line) and the equal division of a line (blue).
This notion of infinitely smaller division is covered in great detail in our new solution to the Continuum hypothesis, which resolves the Russell Paradox, offering new insight into the true structure of numbers, and the nature of infinity. When considering our new mathematical discovery of Aleph 05, bear in mind the concept of a standing wave is incremented by half wavelength steps.
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The geometry of Music
The structure of music is derived from the Circle of Fourths and Circle of Fithes, which in turn is derived from the division of a string into two and three. Previously, we saw that the first four in the harmonic series seems to correlate nicely with the 12 notes found in the chromatic scale. Based on the 1st harmonic, the fundamental, the octave arises perfectly by dividing the string into two. Then, the division of a string into 4 (4th harmonic) creates the musical 4th. By resetting the forth as the fundamental, the next set of notes in the circle of fourths is defined. Then the process is repeated until all 12 notes completes the circle. The same can be said of the division of the sting into three, which forms the circle of 5ths. The difference between the 4th and the 5th creates the tone.
It is a curious fact that both the circle of fourths and fifths can be placed on a single circle, which will express the intervals for each, read in either a clockwise or anticlockwise direction. There is a slight different in that some of the notes are expressed as a sharp (#) and others as flats. This relates to the nature of seven different musical modes, which differ slightly in their exact tuning, and are removed from the tempered scale. This means that the structure of music is derived from these two types of simple division.
It is an amazing fact that this concept can also be found in the simple exploration of fractal geometry. A fractal creates a self similar pattern at different scales. The triangle and the square are the two simplest 2D shapes that can be constructed. By dividing each side length into two, a smaller version of each shape can be constructed to fit perfectly inside. The inner triangle becomes rotated 180°, whereas the inner square is only rotated 45°. If the process is repeated, we find that both shapes take on the original orientation of the first after 3 steps.
Notice that the square divides the line into three sections, forming the musical 5th. After which the second iteration create the octave. However, the triangle immediately creates the octave, which on the second iteration becomes the music 4th. The unification of all musical structure is therefore contained within the fractal geometry of these two basic shapes. As the internal area of the triangle is much less than that of the square, the rate at which each circle diminishes is also greater. The second point of interest is that in both cases, we only need to progress through three iterations before the internal shape takes on the same orientation as the first. Clearly, this process could be continued into infinity. However, after three steps, the process is complete. This is why we often say, “There are only three steps to infinity”. The musical 5th of the square is unique, as the two circles overlap in perfect proportion. This is called the Vesica Piscis.
What this demonstrates is that the two types of division that create the musical 4th and 5th, are based in different types of geometry. The triangle only divides space through an even number series, whereas the square can divide the line into 3. When we add the numbers 3 and 4 we get seven, which is the number of notes comprising the musical scale. Furthermore, if you count the number of circles in total it equals 12 which is the number of notes in the chromatic scale. Five are derived from the square and seven from the triangle, which is exactly the same ratio as the number of white and black notes on the musical keyboard.
It seems to be quite amazing that outside of our new geometric theory of the universe, this notion has never been clearly expressed. The square and triangle are also unique, as they are the only regular shapes that can fill a 2D plain perfectly using just two colours. Also, we find that the 90° angle of the square is also found within the very structure of electromagnetic waves. Without recognising this fundamental nature, it seems that the comprehension of how light functions becomes quite difficult to comprehend. Yet, with this background in place, we can now begin to understand why Newton originally proposed there were seven colours in the rainbow, and in doing so finally begin to unveil the mystery of how the visible light spectrum actually works.
The structure of Light
The importance of the musical third and fourth when considering the nature of light cannot be underestimated. The visible colours of light are constructed from two types of wave. Whilst you may have been told that the light comprises only three prime colours (RGB), there is strong evidence that this is not the case. The Yellow-Blue wave is divided into two parts, just like the octave of a string. The second is the Red-Green wave that is divided into 3.
This theory of visible light is derived from the nature of ‘impossible colours‘. Certain colours, such as red and blue, can be mixed, whereas other colour, such as red and green, cannot. As we can see from the above image, this leads us to the conclusion that the visible spectrum of light is formed of two distinct types of ‘colour wave’. This explains why Yellow and Cyan occupy such a small portion of the visible light spectrum, compared to red, green, and blue, which is why they are often considered to be prime colours of light. Whereas those who paint are aware that red, yellow, and blue are considered prime, as green is produced from mixing yellow with blue. In the case of light, colour is subtractive, which means the wave lengths cancel out. More information on the nature of light can be found on our theory of Geo-optics.
Outside the discipline of human optics, this interpretation of electromagnetic light is never referred to. However, from this view, we can immediately begin to see an interesting correlation to the musical 4th and 5th. Red peaks in two places, at both the bottom and top end of the frequency spectrum. The mid-section of the wave contains green. The second wave starts with yellow at the bottom end of the spectrum, which increases in intensity up to the midpoint before receding and turning blue, just like a musical octave.
This nature of the visible spectrum begins to resolve why the Rayleigh-Jean Law fails to predict observed phenomena, as their calculations were based on the harmonic series, found by the successive addition of frequencies to the 1st harmonic. These are counted as whole numbers into infinity. The result is a premature curvature of the plot on the graph, that also tends toward infinity, without limit.
However, musical harmony is derived from the ratio of waves, which is based on the relationship of the fundamental, divided into two and then three. After which these go on to create the circle of 4ths and 5ths. If the fundamental changes, then so does the ratio of 4th and 5th. This limits the tuning of the wave. This is exactly what the Planck Constant does. It only provides for a certain limitation of light at specific temperatures. In terms of the spectral radiance, the fundamental is the peak of the radiant energy. The frequencies either side of the peak show where the harmonic series dissipates into incoherence. We can examine this nature by plotting the wavelength peaks for different temperatures.
Here we can see the spectral radiance is calculated for a wavelength 1, divided into quarters and thirds. Notice that the peak rises dramatically between the 0.5 and 0.25 region (top right). Whilst not as prominent, there is also a sharp upwards turn between the two thirds and third wavelength values (bottom right). When superimposed, the two graphs form a curvature that seems to match the spectral radiance found at the quarter wavelength of temperature.
Unlike music, the fundamentals of light (peak of spectral radiance) does not only fall into smaller wavelengths, as there is no physical string. Instead, it descends away from the peak towards both the higher and lower frequency range. The fact that the rate of the slope is slightly longer towards the lower frequencies is due to the fact of the increased wavelength of light.
In terms of music, is it the distinction of the musical 4th and 5th, that defines the 12 notes of the chromatic scale, which in turn limits the tunings of the musical scale. What we are beginning to show it that it is the same principle that is responsible for the ‘quantisation’ of the electromagnetic wave.
In essence, what this means is that the idea that light is quantised into discrete energy packets is not the correct description of the Planck constant. Moreover, it is the structure of harmonic ratio that is the root cause of the phenomena. This actually makes perfect sense, as spherical harmonics are at the heart of quantised phenomena of modern quantum theory. The notion of quantisation is quite simply a consequence of ratio, which divides a line, rather than the harmonic series which adds successive frequencies in equal measure, which is akin to the idea that light is produced in tiny wave packets, or photons. Whilst the wavelike nature of the photon cannot be discarded, the idea that is it a particle can. You can find out more about this in our post on the photoelectric effect. Armed with this knowledge we are now able for the first time to glean a simple understanding of light, based on music theory, which is powerful enough to decode the exact nature of the Planck Constant.
The Planck Constant
The resolution of the Ultraviolet Catastrophe was discovered by the mathematician Max Planck, who found that, by adding a specific value into the calculations for of classical wave mechanics, he was able to produce a result that exactly matched experimental observations. Whilst the equation worked, it was a complete mystery as to why this particular value should exist. This later became known as the Planck Constant (h), which is now recognised as a foundational constant of quantum physics. It is important to remember that this constant is so important that the whole modern interpretation of the SI unit system of science has been adjusted to exactly match its experimental value. Yet over 120 year on, scientist still have no idea as to why the value should even exist.
In our new system of Dimensionless Science, we have translated of 40 scientific constants into simple geometric ratio, by setting the speed of light to an integer, 3. Based on this, we are able to examine various scientific equations to produce exact values for other constants to an infinite degree of accuracy. In Dimensionless Science, the Planck constant (h) is defined by the formula:
(√33÷√43 x π² ) x 10-34
This gives the exact value of the Planck as being 6.4104, which can now be calculated to an infinity degree. Whilst this value deviates from the accepted value of h, (6.626 x 10-34), by 0.215, this is due to the fact that traditionally light is ascribed the value of 299 792 458 m/s, instead of 300 000 000 m/s. To explain why the Planck constant has this particular value, we can start by considering a cube of space.
To begin, we notice that the above expression of h contains the value π². The equation that transforms the radius of a circle into its surface area is π x r². By setting the radius to 1, the resultant surface now becomes π. As electromagnetism expresses two waves that are offset by 90°, we need to create another circle of the same dimension. This sets up a single standing wave in a cube that has a side length of 2. The expression π² simply represent the surface area of an electromagnetic wave, as a ‘musical’ fundamental.
Now that we have our standing wave, the next step is to examine the remaining part of the equation √(33/43). To explain this, we can begin by noting that there are only 8 notes in a musical octave. The number 1 is divided into 8. The second important point is that our cube with a side length of 2, (as the circle radius is only 1), will measure √3 from its centre to its corner point. Finally, we can take the value of a single note (1/8) and multiply it three times by the value √3. The result is √(33/43), which, when multiplied by the surface area of π², results in the value for the Planck constant.
Here we can see another expression for the value √(33/43), which is just a standing electromatic wave, that expands from diameter 1 to diameter 3. The value (3√3)/8. Notice that the cube expands through three stages, from a side length of 2, then 4, and finally 6. The reason for this is that a spherical light wave expands up to the speed of light, details of which can be found in a new geometric interpretation of the speed of light (c). Notice that the sphere expands in three stages. In the same way, our example of fractal geometry that forms the musical 4th and 5th in the triangle and square, goes through three iterations to form all the required musical ratios. Just as the value 3 appears for the speed of light in the system of dimensionless science, so that same value limits the formation of all musical harmony.
So does this mean that the energy is not quantised? Not exactly. The fact that the speed of light is limited to an expansion of three is due to the hyper-cubic nature of space. The energy in the vacuum is believed to be teaming with tiny virtual particles, a Quantum Foam, which pervades the whole universe. In our new theory of the 4D Aether, we explain how this mysterious substance functions from the perspective of 4D geometry.
In our post that explains the reason for the photoelectric effect, we find that it is the nature of space that causes the apparent quantisation of an electromagnetic wave. Not the concept of a photon as a particle. Similarly, we find that in our explanation of the Planck constant above, there are three types of cube that expand from a radius of 1 to 3. The speed of light. These three cubes act in 4D space as a hypercube, which is why electromagnetic waves are off-set by 90°. However, what we have explained in this article is that energy, a wave, is not quantised in the manner that is traditionally believed. Moreover, it is the disharmony of the harmonic series that limits the infinite nature of reality.
Why did Classical law of electromagnetism fail experimental perdictions?
The reason for the Ultraviolet Catastrophe are not that light energy is quantised into packets, moreover, Rayleigh and Jeans did not employ the notion of musical ratio in their calculation. Instead, they tried to explain the phenomena using the infinite harmonic series. Just as this produces discordance in music, once transposed through higher (or lower) scales, so the same is seen from the predicted outcomes. The Planck constant, that resolves this inequality, does not imply that light is quantised into discrete energy units. Moreover, that light is structured through the integration of the musical 4th and 5th. Whereas the Harmonic series adds equal quantities to a particular frequency, musical ratios are derived from the division of a sting. This creates a logarithmic curvature that can explain the error found in the Ultraviolet Catastrophe.
What does this mean for modern science?
This is the first time that any theory has been able to express a logical explanation as to why the Planck constant (h) exists. As h is considered by quantum mechanics as one of the most important constants in science, an explanation for its appearance provides us with clarification as to why spherical harmonics are suggested to form the various types of orbital shell (S, P, D and F). As the concept of the photon was also derived from the notion of wave packet particles of light, the resolution of h begins to shed a large shadow of doubt on the validity of this claim.
Carry On Learning
This article is part of our new theory on the 4D AETHER. browse more interesting post from the list below
The concept of the photon is based on our present solution to the photoelectric effect. However, this solution cannot be true, as the speed at which electrons are released into the circuit is much faster than the interactions between a photon and an electron. Our new 4D solution shows that it is the geometry of light and space that are actually responsible for this effect, ushering in a new theory of energy generation, extracted from the vacuum of space.
YOUR QUESTIONS ANSWERED
Got a Question? Then leave a comment below.
If light is made of four colours, then why do RGB monitors work?
There is no such colour as a reddy green, or a greeny red. Therefore, when these colours are mixed, these frequencies will cancel out both, leaving only yellow. Similarly, we do not see green coloured stars. For example, the spectral radiance of our sun peaks at cyan. However, it also includes a lot of green and red, which cancel out each other out. For this reason, objects will glow red, then yellow, but green does not appear as the existing red light removes it from the spectrum. Instead, the light turns to from yellow to blue as the red-green wave is no longer perceptible.
If the Planck constant can be defined with 3√3 / 8 then why define it as √(33/43)?
The term √(33/43) refers to a square root of a cube side length 3, divided by a cube side length 4. This interpretation is used when we examine the 4th dimensional nature of the constant. However, in terms of musical ratio, 3√3/8 can also be used. In the same way that the square and the triangle define geometric ratios in music, which is also a spherical wave in space. Whilst we can adopt a different perspective, such as a wave that expands across a line in time, the 3D perspective of music can utilise a similar mathematics.