# The Nature of Reality

## The underlying structure of the universe: a modern mystery

We humans have a great capacity to embrace a variety of philosophical paradoxes: infinity and nothingness in one breath without having truly experienced either one; belief without empirical evidence; empirical evidence without belief, simultaneous order and chaos, deterministic and random destinies, existential meaning and nihilism.

Blaise Pascal (1623 – 1662) was a French mathematician, physicist, inventor, writer and religious Christian philosopher. In his Pensées, he grappled with several philosophical paradoxes: faith and reason, soul and matter, death and eternal life, meaning and vain thinking. He ultimately arrived at no definitive conclusions but did put forward a wager, now called Pascal's Wager, which drew on probability theory for its justification.

Despite the uncertainty surrounding the absolute nature of things, there is an uncanny accuracy between mathematical theory and equations and the composition and behaviour of certain physical phenomena. This has been borne out by repeated and numerous experiments using scientific data over decades and even centuries in some cases.

A more modern stretch of the human imagination is the evasive answer to the questions:

- Can mathematics, precariously balanced on only five assumptions, the Peano Axioms, which form the formal foundations for the natural numbers, be in fact the language of the universe?
- Can the Platonic universal forms, as an idealized view of the world, be in fact the template for all geometric reality?

Roger Penrose, a 2020 Nobel Prize Laureate in Physics, discusses pure mathematics from Pythagoras, Plato and Euclid to Einstein and beyond. It all leads to the ultimate riddle: Is mathematics a human invention or the discovery of the language of the universe?

Roger Penrose – Is Mathematics Invented or Discovered? (Published on April 13, 2020 by Closer to Truth)

“Mathematics describes the real world of atoms and acorns, stars and stairs, with remarkable precision. So is mathematics invented by humans just like chisels and hammers and pieces of music? Or is mathematics discovered—always out there, somewhere, like mysterious islands waiting to be found? Whatever mathematics is will help define reality itself.“

## Changing perspectives: surfing the waves to catch a glimpse of the quantum nature of reality

There is an entire discipline of Physics called “Wave Theory.” There is an entire field of Mathematics called “String Theory.” Can these two theories, the former applied, the latter pure, meld to produce a unified theory to describe our entire universe? For centuries, mathematicians and physicists have probed into the complexity of our world,

from the microcosm (molecules to atoms to protons, neutrons, & electrons to quarks, leptons and bosons),

through to the macrocosm (from our solar system to the ort cloud to the Milky Way to other galaxies to the cosmic background radiation from the time of the Big Bang),

in order to probe the fundamental nature of reality.

The reality is that most of what we know about the Universe came through the ability to see Light. This included objects which could be visualized through the naked eye (as was done by the Ancient mariners of our planet by following the movement of the stars) or by means of man-made lenses – such as a telescope, a prism, or a microscope. In modern physics, understanding the nature of Light itself became central to a deeper understanding of the world around us. From the scientific point of view, Light appeared to have a dual nature, that of a stream of particles (known as photons) and that of a wave (defined as streams of vibrating energy).

What is now called the “double slit experiment” radically changed the way we understand reality in the quantum world (the smallest structures in the Universe). Prior to this experiment conducted initially by a medical student, Thomas Young, in 1801, and later in the nineteenth century by other scientists, there was a great debate as to whether lights rays were streams of particles (photons) or whether they were waves. Even though this may not have been important for most of earth’s inhabitants at the time, it was of the essence in understanding what the Universe was made of from a scientist’s perspective.

Double Slit Experiment Explained by Jim Al-Khalili (Published on February 1, 2013 by Physics Videos by The Royal Institution)

The perspective of the true nature of Light changed again a little later in the nineteenth century when James Maxwell proved and demonstrated that light was an electromagnetic wave. He proposed the theory that electricity, magnetism, and Light were different manifestations of the same phenomenon.

**Therefore, in some sense the true nature of our real world begins with travelling Wave formations.** There are two types of vibrating mathematical waves: the ** transverse wave formations** in which the propagation of the wave vibrates perpendicularly (up and down) to the flow of the energy and the

*in which the propagation of the wave vibrates in a parallel fashion (back and forth) to the energy flow.*

**longitudinal wave formations**Both of these types of waves may be represented mathematically as transformations of the trigonometric sine function. Amplitude (height), wavelength (length of one cycle), period (time frame to complete one cycle), frequency (number of cycles per unit of time), and phase shifts (translations left or right) are properties of this function.

Some other periodic or repetitive processes can be approximated by what is called a **Fourier Series**. A Fourier series is an expansion of a periodic function in terms of an infinite sum of sine and cosine functions. Fourier series make use of the orthogonality relationship between these functions which results in the cosine function being a phase shift by 90 degrees of the sine function. For more information on Fourier Series and the frequency of signals, see:

Fourier Transform, Fourier Series, and the Frequency Spectrum (Published on September 6, 2015 by Physics Videos by Eugene Khutoryansky)

❝ Therefore, all signals that we see in real life can be thought of as the combination of an infinite number of sine waves that have always been present since the beginning of time, and which will continue to exist through all eternity. ❞

Eugene Khutoryansky(above video [14:58 – 15:25 minutes])

Tour of the Electromagnetic Spectrum (EMS) 01 – Introduction (Published on May 6, 2010 by ScienceAtNASA)

Moreover, **Einstein’s Theory of Special Relativity** (E = mc^{2}) implies that our entire Universe is made up of mass and energy, kept in a constant ratio (that is, a state of equilibrium) by the speed of light squared. The Theory of Quantum Mechanics proposes that all particles are described by waves and these waves measure the probability (at any instant) of the location of the particle in question, subject to the **Heisenberg Uncertainty Principle** (defined as any of a variety of mathematical inequalities indicating that there is a fundamental limit to the accuracy with which the values for certain pairs of physical quantities of a particle, such as a positron and its momentum, can be predicted from initial conditions). This, of course, introduces Probability Theory into the nature of reality mix because, as we are slowly beginning to realize, absolutely nothing is 100% certain in our lives.

Information (quantum data, if you like) which we receive from our environment far enough away so as not to be felt by touch or smelt by odour or tested by tasting, are sensed through the eye and the ear.

Therefore to examine inaccessible places in our Cosmos, we rely on an entire spectrum of electromagnetic waves for our perceptions of these worlds beyond our immediate reach. This has been gradually achieved over centuries by various technologies which aid the human eye and ear to gather relevant information about those particular environments.

**One might even make the astonishing, almost egregious, statement that the depiction of reality begins with the Pure Mathematics of the Sine and Cosine Waves,** their multitudinous combinations and transformations of amplitude, periodicity and frequency, and their statistical probabilities of existence and location, subject to the Heisenberg Uncertainty Principle.

This has led to the relatively recent mathematical depiction of particles, not as 0-dimensional points in space, but as 1-dimensional vibrating strings of energy with amplitude, periodicity and frequency (quantum mini-waves, if you like). The differing frequencies of vibration distinguishes one particle from another. See the videos below for more details on String Theory and its application to the nature of our physical and quantum reality.

String Theory by Brian Greene (Published on August 9, 2013 by TED-Ed)

“Physicist Brian Greene explains superstring theory, the idea that minuscule strands of energy vibrating in 11 dimensions create every particle and force in the universe.”

String Theory Explained – What is the True Nature of Reality? (Published on March 1, 2018 by Kurtzgesagt – In a Nutshell)

Waves: Light, Sound, and the Nature of Reality (Published on May 3, 2015 by Physics Videos by Eugene Khutoryansky)

A course idea...

## PHYS 205: Physics for Scientists and Engineers II

The course covers the principles of electricity and magnetism and includes a hands-on laboratory component.

Updated November 18, 2021 by Student and Academic Web Services (sas@athabascau.ca)