The Harmonies of the Universe
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Table of contents :
Chapter 1: A Geometrical Framework Designed by Using Prime Numbers
Chapter 2: The Inverse Square Law
Chapter 3: Elements and Atomic Structure
Chapter 4: Theory of the Origin of the Universe
Chapter 5: Visible Light
Chapter 6: The Harmonies of the Universe
Chapter 7: Each Element Has Its Own Pitch

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The Harmonies of the Universe Quantum Mechanics and Music

Gerald W. Scanlon

ALSO BY GERALD W. SCANLON God’s Particle and Elements: Core of the Universe. A Theory of Everything Higgs Field Unveiled. God’s Field at Creation God’s Atomic Model Unveiled. A New Proposal Fundamental Forces at Creation Fundamental Particles at Creation The Expanding Ten-Dimensional Universe Waves at Creation A Theory of Everything The First Second of the Universe. A String Theory Approach Revelations of the Quantum Scrolls. The End of Time The Creation of Spacetime and Higgs Field A Geometrical Framework for Understanding the Universe

Understanding the Universe via the Inverse Square Law Quantum Gravity, Light, and Sound Towards the Holy Grail of Physics Found: The Pattern in the Distribution of Prime Numbers. Hidden at the Core of the Universe

Copyright © 2020 Gerald W. Scanlon All rights reserved. No part of this publication may be reproduced, distributed, or transmitted in any form or by any means, including photocopying, recording, or other electronic or mechanical methods, without the prior written permission of the publisher, except in the case of brief quotations embodied in critical reviews and certain other noncommercial uses permitted by copyright law. Email: [email protected]

Contents Chapter 1: A Geometrical Framework Designed by Using Prime Numbers Chapter 2: The Inverse Square Law Chapter 3: Elements and Atomic Structure Chapter 4: Theory of the Origin of the Universe Chapter 5: Visible Light Chapter 6: The Harmonies of the Universe Chapter 7: Each Element Has Its Own Pitch

Chapter 1: A Geometrical Framework Designed by Using Prime Numbers

More than 2500 years ago, according to ancient sources, Pythagoras applied his discoveries in music theory to the behavior of the celestial objects. Pluck a string, and the pitch of the note it produces is related to the length of the string. When the lengths of two strings are a simple ratio, e.g., 1/2, 2/3, etc., the notes together sound harmonious. Pythagoras believed that the universe itself hummed with its own harmony—beautiful, divine, and inaudible to human ears. He characterized the intervals between successive orbits, such as those of Mercury and Venus, as either tones or half-tones (the smallest intervals in the musical scale), adding up to seven whole tones that form a perfectly harmonious natural order. An ultimate theory of the universe is one that would not only be able to explain the harmonies of the universe, but also be able to explain all other phenomena of the universe. I believe that an ultimate theory has to be linked to the beginning of time and space or an alpha point (A). I also believe that an ultimate theory has to be simple enough so it could be understood by a person with an average knowledge of science and mathematics. Finally, I believe there is one simple fundamental structure or geometrical framework, which would be able to unlock all the mysteries of the universe, and would lead us to the ultimate theory. In this book, I will first design a geometrical framework by using prime numbers. I will then link the geometrical framework to the inverse

square law, atomic structure, origin of the universe, and light before revealing the connection between quantum mechanics and music. Prime numbers are whole numbers greater than 1, that have only two factors: 1 and the number itself. The first 25 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.

All primes, with the exception of 2, are odd numbers and they can be distributed as shown in the following image.

In the distribution of the odd primes, number 9 is the first number to break its symmetry.

Let’s take that symmetry breaking as our first cue from the primes and use it to help design the geometrical framework. Therefore, numbers 18, located on the number line before symmetry was broken will be used for the geometrical framework.

We can get a closer look at the numbers by “blowing them up” or squaring them. The following image shows the figures of the odd numbers 1, 3, 5, and 7 after they have been squared.

The following image shows a geometrical figure that can be formed by the odd numbered squared figures. They appear to be rotating around a central point.

The following image shows the figures of the even numbers 2, 4, 6, and 8 after they have been squared.

The following image shows a geometrical figure that can be formed by the even numbered squared figures. They appear to be rotating around a central point.

So, here are the eight squared figures to be used in designing the geometrical framework.

They can be placed diagonally in space as shown in the following image.

The following image shows a geometrical figure that can be formed by the eight squared figures. They appear to be rotating around a central point.

Chapter 2: The Inverse Square Law

Light waves, sound waves, and gravity obey the inverse square law. Therefore, a geometrical framework designed with prime numbers that reflect the inverse square law will also show the presence of light, sound, and gravity. The inverse square law states that a specified physical quantity or intensity is inversely proportional to the square of the distance from the source of that physical quantity. The fundamental cause for this can be understood as a geometric dilution corresponding to a point source radiation into three-dimensional space as shown in the following image.

Notice, the squared figures that are being used to design the geometrical framework are the same as the figures used to show the inverse

square law. Therefore, the geometrical framework that is being designed for the ultimate theory will demonstrate the presence of light waves, sound waves, and gravity.

The geometrical framework now needs a point source to shine light onto the squared figures. To find such a point source of light, let’s turn

again to the prime numbers to help us find it. This time, let’s look at prime number 11, which is the prime that follows the pattern after symmetry was broken.

The value of 112 is equal to 121. Are the primes providing us with information with the number 121? What can be gleaned from the number 121? How about if we look at the building blocks of the universe? The building blocks of the universe are the 118 known elements. Simple math shows 121-118=3 so we still need to find 3 more elements to get to the value of 121. The following image shows a point has 0 dimensions, a line as 1 dimension, a square has 2 dimensions, and a cube has 3 dimensions.

Let’s incorporate those figures into the geometrical framework. In addition to adding a point and line to it, let’s add another point to show the

beginning of the universe and call it the alpha point (A). We now have 121 elements in the geometrical framework: (A), point, line, and 118 elements.

Now, let’s number the figures of the geometrical framework and start the numbering with the alpha point (A). Since many would see the alpha point as the place where science meets religion at the beginning of the universe, it seems appropriate to assign it a value of “absolute 1”. Science would likely accept such a value and everyone who believes in a supreme being would not object that quantum theory led us to the “Absolute One”. The next question is how to number the rest of the figures in the geometrical framework. At this point, let’s assume the geometrical framework can be interpreted in such a way that it reveals some of the wonders and mysteries of life itself. Reproduction is one of the marvels of life and it starts with a sperm and an egg.

The point and line of the geometrical framework can be thought of as a sperm and an egg. The square figure can be seen as the moment of conception, when the sperm and egg come together. Cell division and growth of the embryo can be seen with the rest of the figures. Since life doesn’t begin until conception, a negative value of -1 can be assigned to the sperm (point) and a value of 0 to the egg (line). Conception (square) has both those values together inside it. Cell division and growth of the embryo is shown in the rest of the figures of the geometrical framework.

Consecutive numbering (1-118) of the remaining even numbered squared figures is continued as shown in the following image.

Consecutive numbering (1-86) of the odd numbered squared figures is done in the same way as shown in the following image.

Chapter 3: Elements and Atomic Structure

An element is a substance that is made entirely from one type of atom. For example, the element hydrogen is made from atoms containing a single proton and a single electron. If you change the number of protons an atom has, you change the type of element it is. The atomic structure of an element refers to the constitution of its nucleus and the arrangement of the electrons around it. Primarily, the atomic structure of matter is made up of protons, electrons and neutrons. The protons and neutrons make up the nucleus of the atom, which is surrounded by the electrons belonging to the atom. The atomic number of an element describes the total number of protons in its nucleus. The geometrical framework can be linked to elements and atomic structure. The atomic number of the 118 known elements can be placed inside the even numbered squared figures as shown in the following image.

The odd numbered squared figures have 86 of the known elements placed inside of them as shown in the following image.

The noble gases are the chemical elements in group 18 of the periodic table. They are the most stable due to having the maximum number of valence electrons their outer shell can hold. Notice that each of the squared figures of the geometrical framework has a noble gas in its center.

The squared figures can be placed in space diagonally as shown in the following image on the geometrical framework.

The following image of the geometrical framework is quite impressive as it gives us a look back at time and we can view the 118 elements as they emerged from the alpha point (A) at the beginning of spacetime.

Around 450 B.C., the Greek philosopher Democritus introduced the idea of the atom. However, the idea was essentially forgotten for more than 2000 years. In 1800, John Dalton reintroduced the atom. He provided evidence for atoms and developed atomic theory. The Bohr model of the atom was proposed by Neil Bohr in 1915. Even though it has been replaced by the present day electron cloud model; it’s still quite handy for explaining chemical bonding and the reactivity of some groups of elements at a simple level. It is a system consisting of a small, dense nucleus surrounded by orbiting electrons—similar to the structure of the Solar System. The Bohr model of the atom can be displayed on the geometrical framework showing 118 electrons orbiting the nucleus in well-defined orbits.

Chapter 4: Theory of the Origin of the Universe

Since the Big Bang, 13.7 billion years ago, the universe has passed through many different phases or epochs. Due to the extreme conditions and the violence of its very early stages, it arguably saw more activity and change during the first second than in all the billions of years since. In this chapter, the geometrical framework will be used to show what may have happened during the all-important first second. Let’s begin with the fundamental forces. The four fundamental forces that govern the universe are gravitational, electromagnetic, strong nuclear, and weak nuclear. Gravity is the force of attraction that acts between masses. Electromagnetic is the force that acts between electrically charged particles and produces electricity, magnetism, and light. The strong nuclear force is responsible for holding together the atom’s nucleus while the weak nuclear force is involved in radioactive decay. Numbers 1-8 will be used to help explain the origin of our universe. They are divided into sets of 2 and each set is associated with one of the fundamental forces.

It is believed the fundamental forces were together at the beginning of the universe. (A), point, and line show when the fundamental forces were together.

The following image shows the force associated with the squared figures of the geometrical framework.

In the previous chapter, we linked the 118 elements to the origin of the universe. A force can now be associated with them as they emerged from the alpha point (A).

The squared figures can be placed diagonally in space as shown in the following figure.

A timeline for the first second of the universe can be added to the geometrical framework. Since detailed information of the first second is needed, the time segment from 0 seconds to 1 second is divided into 44 segments. It is divided into 44 segments because the smallest usable time difference is the Planck time or roughly 10-44 seconds.

Scientists divide the first second of the universe into different epochs. The epochs are Planck, Grand Unification, Inflationary, Electroweak, Quark, and Hadron. The next image shows them and the time span each one covers, as well as the force associated with them. For example, the Inflationary Epoch covers the time span from 10-36 seconds to 10-32 seconds and is associated with the strong force.

Let’s view, step by step, how spacetime emerged from the alpha point (A) during the first second of the universe during each of the epochs.

Chapter 5: Visible Light

The electromagnetic (EM) spectrum is the range of all types of EM radiation. Radiation is energy that travels and spreads out as it goes. Visible light that comes from a lamp in your house and the radio waves that come from a radio station are two types of electromagnetic radiation. The EM spectrum is generally divided into seven regions, in order of decreasing wavelength and increasing energy and frequency. The common designations are radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays.

Visible light waves are the only EM waves we can see. We see these waves as the colors of the rainbow. Each color has a different wavelength. Red has the longest wavelength and violet has the shortest wavelength. When all the waves are seen together, they make white light.

The geometrical framework can be used to show the colors of visible light.

Visible light and the 118 known elements can trace their roots to the beginning of the universe.

Visible light emerged during the first second of the universe as the four fundamental forces were separating from each other.

Chapter 6: The Harmonies of the Universe

A harmony is when multiple notes are stacked on top of each other to create a unique sound. Harmonies have two or more sounds played simultaneously, and the result should be sonically pleasing, and the sounds should complement one another. Mathematical patterns underlie the musical scales and intervals which provide the most pleasing harmonies to our ears, and describe the probability waves at the heart of quantum theory. Pythagoras believed that the universe itself hummed with its own harmony—beautiful, divine, and inaudible to human ears. The physics behind musical instruments is beautifully simple. The sounds made by musical instruments are possible because of standing waves, which come from the constructive interference between waves traveling in both directions along a string or a tube. In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the reception of such waves and their perception by the brain. Only acoustic waves that have frequencies lying between about 20 Hz and 20 kHz, the audio frequency range, elicit an auditory percept in humans.

Sound can be of different types—soft, loud, pleasant, unpleasant, musical, audible, inaudible, etc. Some sounds may fall into more than one category. For instance, the sound produced when an airplane takes off is both loud and unpleasant. Musical sound is a pleasant, continuous and uniform sound produced by regular and periodic vibrations, e.g., sound produced by a piano, violin, flute, tuning fork, etc. C major (or the key of C) is a major scale based on C, with the pitches C, D, E, F, G, A, and B. C major is one of the most common key signatures used in western music. Its key signature has no flats and no sharps. There is a connection between music and quantum mechanics. The geometrical framework can be used to show how they are connected. The eights notes used to play the C major scale can be placed inside the eight squared figures of the geometrical framework.

The eight squared figures can be placed at the alpha point (A) on the geometrical framework. With a bit of imagination, you can almost hear the C major scale being played, as music emerges at the beginning of the universe.

The eight pitches of the C major scale are formed by a set of eight waves. The periodic table can be used to unveil the set of eight waves. A typical periodic table places the 118 elements in seven different periods. Each element is displayed with its symbol and atomic number. For example, the element hydrogen has a symbol of H and an atomic number of 1. The atomic number is the number of protons in the nucleus and the number of electrons orbiting the nucleus.

Two additional elements, a point (-1) and a line (0), can be added to the periodic table. We now have a table of atomic numbers with eight periods.

The table can be divided into four sections with two periods in each of them. The table has a length of 32.

The length of the table can be doubled to 64. The table now shows four waves extending across it.

The number of waves that pass a fixed point in a given amount of time is wave frequency. Wave frequency can be measured by counting the number of crests or compressions that pass the point in 1 second or other

time period. The higher the number is, the greater is the frequency of the wave. The following table shows the frequency of the four waves. The waves at the top of the table have a higher frequency and lower amplitude than those at the bottom.

So far, we have unveiled four waves embedded in the periodic table. The waves are formed with the set of even squared figures 2, 4, 6, and 8.

The set of odd squared figures 1, 3, 5, and 7 form four additional waves. The following image shows the eight waves which form the eight pitches of the C major scale.

The frequency of the eight waves can be seen on the following table. The waves at the top of the table have a higher frequency and lower amplitude than those at the bottom.

The set of eight waves, which form the eight pitches of the C major scale, can be placed at the alpha point (A) on the geometrical framework.

Chapter 7: Each Element Has Its Own Pitch

Frequency is the speed of the vibration of a wave and determines the pitch of a sound. It is only useful or meaningful for musical sounds where there is a strong regular waveform. For example, when you press a key on the piano it causes a small hammer inside the piano to hit a string. Each key is connected to its own hammer which hits a specific string. When the hammer hits a string, it vibrates and makes a sound that is tuned to a specific note. The keys on the piano are placed according to their frequency. The keys on the left of the keyboard produce a pitch with a lower frequency than those on the right.

Almost every piano has 52 white keys and 36 black keys, totaling 88 keys. Since there are 88 elements (point (-1), line (0), and 86 elements) in the set of odd squared figures and 88 keys on a piano keyboard, each element can be given its own key on a piano keyboard. Therefore, each element is able to produce its own pitch.

When one of the 52 white keys on the piano keyboard is hit, a specific note is produced by vibrating strings inside the piano.

As mentioned earlier, each element corresponds to a specific key on the piano keyboard. The following image shows the piano keys and musical notes which correspond to hydrogen, helium, lithium, beryllium, boron, carbon, nitrogen, and oxygen.

A wave pattern is formed by the vibrating strings inside a piano after the piano keys are hit.

The wave pattern, formed with the elements having atomic numbers 1-8, can be placed at the alpha point (A) on the geometrical framework.

Now, let’s look at the wave pattern formed with iron. Iron is a chemical element with symbol Fe and atomic number 26. It is by mass the most common element on Earth, right in front of oxygen (32.1% and 30.1%, respectively), forming much of Earth's outer and inner core. The piano key for iron is located at the center of the 52 white keys on a piano keyboard. It is the 26th piano key.

The wave pattern, formed with the elements having atomic numbers 1-26, can be placed at the alpha point (A) on the geometrical framework.

As you look at this final image, remember what I said at the beginning of the book, “I believe there is one simple fundamental structure or geometrical framework, which would be able to unlock all the mysteries of the universe, and would lead us to the ultimate theory.”

About the Author

Gerald W. Scanlon was born in Saginaw, Michigan and moved to Mexico when he was 21 years old. He had a fulfilling career as a teacher and is now enjoying his golden years of retirement. He has always had a love for math and still dreams of coming up with a perfect betting system for playing blackjack. It was actually while trying to develop a betting system that he was led to the elements on the periodic table. He saw a relationship with the way elements fill their orbitals and the patterns of wins and losses that occur while gambling. This insight led him to the amazing world of quantum mechanics where the secrets of the universe were waiting for him to unveil.