Quantum Mechanics: Wave-Particle Duality and Uncertainty

Following the intellectual bread crumbs of Albert Einstein, let’s try to understand how his revolutionary ideas and theories of universal gravitation, the notion of spacetime, the establishment of the equivalence of mass and energy, the necessary condition of the existence of a “frame of reference” as a fundamental aspect of Physics, along with the revolutionary idea of the eternally fixed nature of the speed of light under all measurement conditions formed the basis, ironically, of perhaps the most influential and revolutionary theory in modern Physics – namely Quantum Theory, sometimes referred to as Quantum Mechanics primarily to distinguish it from Classical Mechanics which obeys an entirely different set of rules and laws as it turns out.

Quantum Theory is the term used to describe the stochastic (i.e. probabilistic) mathematical models that were developed in the early part of the 20^th century to describe the “behavior”, really the measurement of specific “qualities” or “characteristics” for lack of a better description, of so-called “sub-atomic” particles, what were initially referred to as corpuscles in the early Quantum Mechanics  academic literature.  Quantum Theory has effectively turned the field of physics on its head for the last century or so as its underlying theories and equations have proved to be accurate and have tremendous predictive power over and over again through various experiments throughout the 20^th century. 

Despite its predictive power however, the basic underlying principles, assumptions and tenets of Quantum Mechanics – mathematical models and equations which are fundamentally a) “probabilistic” and b) depend upon an “act of observation” for the derivation of a specific measurement – fly directly and squarely in the face, and essentially completely contradict, the basic causal, materialistic and deterministic assumptions upon which both Classical Mechanics and Relativity Theory rest.  These underlying contradictions and paradoxes have driven most if not all of the work in the field of Theoretical Physics since its inception in the middle of the 20^th century as researchers and mathematicians alike have struggled in vain to come up with some sort of “unified” theory that bridges the conceptual and theoretical gap between the two models and their inherent contradictory assumptions.

What is even more interesting, and quite pertinent and relevant to this work in fact despite its primarily theo-philosophical bent, is that these theories have much to say – individually as well as holistically despite their inherent incompatibilities – about what can be concluded about the nature of reality itself, the bounds of physics as a discipline and field of study as it were, as well as potentially how “reality”, however we choose to define it, came into existence.  Furthermore, we shall find that in fact that our definition of reality ultimately depends upon not just on the “physical scale” that we are looking at, but also (in somewhat of a circular logistical fashion) upon what characteristic and qualities of this “reality” that we are actually measuring which in turn to a large extent define the boundaries and assumptions of the “reality” that we are looking to describe and explain, and “predict” which is what Physics is ultimately designed to do.  In this respect, and perhaps unintentionally, 20^th century Physics has contributed greatly, even if inconclusively, to the resurgence of metaphysics, i.e. first philosophy.

To begin, Classical Mechanics is based upon Atomic Theory, a conceptual framework established by Niels Bohr in the early part of the 20^th century which posited that atoms, the fundamental component of the physical universe, were actually composed of a central, relatively massive nucleus, surrounded and encircled by much less massive particles called electrons which orbited this nucleus.  This theory to a large extent forms the intellectual basis for virtually our entire materialist modern-day view of “physical reality”, i.e. the model which underlies all of physics – Classical as well as Quantum.  Atomic Theory in its most basic and elementary form posits that all matter, all substance or physical reality, is composed of these composite “things”, “elements” or “objects” which are referred to as atoms.  According to the theory, at least in its initial form, atoms represent the fundamental building blocks of the entire physical universe and are, conceptually at least, indivisible in nature. 

Atomic Theory from this basic perspective can be traced back to ancient Hellenic philosophy in fact, as put forth by some of the Pre-Socratic philosophers such as Democritus, Leucippus, and the Epicurean school from the 6th and 5th centuries BCE.  The word “atom” in fact comes from the Greek word atomos which means “indivisible”.  In its earliest form as understood and articulated by these Pre-Socratic philosophers, specifically the Epicurean school, the world consisted of indivisible atoms that moved through a universal substratum of physical existence, i.e. the void or “ether”, which was effectively defined as the basic substratum of space through which these indivisible atoms moved.  It was believed that atoms joined together in various combinations which was the explanation for the existence of the variety of things or substances that existed in nature, animate and inanimate objects included.  It is important to point out and recognize however that these atoms are primarily conceptual constructs – powerful and meaningful conceptual constructs no doubt but still conceptual constructs.  For what we call atoms have been proven to consist primarily of empty space even if they in toto are measurable constructs that have quantifiable “mass” and “energy” and can be more or less distinguished from one another.  In one of the most illustrative and powerful analogies that describe the amount of empty space that exists in an atom, it is said that if an atom were the size of a football stadium, the nucleus would be the size of a pea at the center and the electrons would be circling and whizzing around the outside of the stadium itself, everything in between would be “empty”, i.e. not contain any elements or particles of mass or velocity. 

It wasn’t until the end of the 18th century however, more than two millennia after the initial basic tenets of Atomic Theory were put forth by the Ancient Greek philosophers, that physicists were able to expand upon this theory and provide a more empirical and mathematical basis for these essential building blocks of nature, building blocks which were eventually determined to be divisible in fact, and consisted of electrons, protons and other even further divisible structures that are the basis of much study and debate in modern particle physics.  The first of these developments was the law of conservation of mass, formulated by Antoine Lavoisier in 1789, which states that the total mass in a chemical reaction remains constant, and the second was the law of definite proportions, first proven by the French chemist Joseph Louis Proust in 1799 which states that if a compound is broken down into its constituent elements, then the masses of the constituents will always have the same proportions regardless of the quantity or source of the original substance.  Then, with the publication by James Maxwell in the work entitled Treatise on Electricity and Magnetism in 1873, it was shown that the interactions of both positive and negative charges that had been previously thought of as two separate forces, i.e. electricity and magnetism, could actually be viewed as just one force, what was subsequently referred to as electromagnetism.  This force which he “discovered” which was described in detail by a series of complex mathematical equations, i.e. Maxwell’s Equations, can be viewed as the synthesis of four basic laws or principles which describe the force itself.  These are; 1) electric charges attract or repel one another with a force inversely proportional to the square of the distance between them: unlike charges attract, like ones repel, 2) magnetic poles, or states of polarization at individual points, attract or repel one another in a similar way and always come in pairs: every “north” pole is yoked or conjoined to an opposite counterpart or a “south” pole, 3) an electric current in a wire creates a circular magnetic field around the wire, where its direction, clockwise or counter-clockwise, depends on the direction of the current, and 4) a current is induced in a loop of wire when it is moved towards or away from a magnetic field.

Then in 1897, J.J. Thompson discovered a particle, or corpuscle as he called it, that was some 1000 times smaller than the atom as it had been estimated at the time.  Thompson didn’t know it then but this corpuscle that he had discovered was actually the electron.  Thompson’s discovery was followed closely thereafter by the discovery of a positively charged constituent of mass that rested in the center of the atom by Ernest Rutherford in 1909, a student of Thompson.  Rutherford, building on the work of his teacher, discovered that most of the mass and positive charge of an atom was concentrated in a very small fraction of its volume, which he presumed to be its center, what later came to be known as the nucleus of the atom.  This result led Rutherford to propose a planetary model of the atom where electrons of negative charge orbited around a positively charged nucleus that again consisted of the vast majority of the mass contained in an atom.  Shortly after Rutherford’s discovery, one of his students, Niels Bohr, landed on a more broad and well defined model for the structure of the atom that leveraged findings in Quantum Mechanics (although the field wasn’t called that quite yet) and specifically some of Planck’s work on quantization to further describe and model the picture of the atom.  By studying the hydrogen atom, Bohr theorized that an electron orbited the nucleus of an atom in very specifically quantifiable and particular, i.e. discrete, circular orbits with fixed angular momentum and energy, with the electron’s orbital “distance” from the nucleus being a function of its energy level. 

Bohr’s theory clarified and shored up some of the basic shortcomings of the planetary model of the atom proposed by Rutherford because it explained how atoms could achieve stable states, a shortcoming of the prior work by Rutherford.  He further theorized, in one of the defining discoveries of 20^th century and modern Physics, that atoms could only make quantized leaps of energy states, and furthermore, when this change of states occurred, light or energy was emitted or absorbed from or into the atom itself with a frequency proportional to the change in energy state, explaining another phenomenon that was lacking in Rutherford’s planetary model of the atom and at the same time introducing, albeit unintentionally, the basic building blocks of the Quantum Theory.  Essentially what Bohr discovered and contributed to Quantum Theory, leveraging Plank’s models in the quantized nature of radiation emission, was that electrons orbit neutrons in the outer part of the atom corresponding to definite, discrete and fixed energy levels, and that when an electron jumps from one discrete state to another, it gives rise to the emission or absorption of electromagnetic radiation at a specific characteristic wavelength.[1] 

Atomic Theory as it stands today was later refined through works of many physicists in the fields of electromagnetism and radioactivity, developments which further divided atomic structure and gave rise to the term elementary particles, which refers to the subatomic particles we are most familiar with today, namely electrons, protons and neutrons.  But the story doesn’t end here.  Models in the world of Theoretical Physics start to get complicated pretty quickly over the next few decades after this wave (no pun intended) of discoveries in the early twentieth century.  And as the theories became more complex, and the experimental results that they predicted become more expansive, comprehensive and verified, some very interesting and revealing questions are posed about the fundamental nature of reality and the basic theoretical assumptions that govern said reality that have still yet to be answered, a problem that Einstein himself spent the majority of the end of his life trying to solve, unsuccessfully as it turns out.

 

Quantum Mechanics is the branch of Physics that deals with the behavior or particles and matter in the atomic and subatomic realms, or quantum realm so called given the quantized nature of “things” at this scale.  So you have some sense of scale, an atom is 10^-8 cm across give or take, and the nucleus, or center of an atom, which is made up of what we now call protons and neutrons, is approximately 10^-12 cm across.  An electron, or a photon for that matter, cannot truly be measured from a size perspective in terms of Classical Mechanics for many of the reasons we’ll get into below as we explore the boundaries of the quantum world, but suffice it to say at present our best guess at the estimate of the size of an electron are in the range of 10^-18 cm or so.[2] 

Whether or not electrons, or photons (particles of light) for that matter, really exist as particles whose physical size, and/or momentum can be actually “measured” is not as straightforward a question as it might appear and gets at some level to the heart of the problem we encounter when we attempt to apply the principles of existence or reality to the subatomic realm, or quantum realm, within the context of the semantic and intellectual framework established in Classical Mechanics that has evolved over the last three hundred years or so; namely as defined by independently existing, deterministic and quantifiable measurements of size, location, momentum, mass or velocity.  The word “quantum” comes from the Latin quantus, meaning “how much” and it is used in this context to identify the behavior of subatomic things that move from and between discrete states rather than a continuum of values or states as is assumed and fundamental to Classical Mechanics.  The term itself had taken on meanings in several contexts within a broad range of scientific disciplines in the 19^th and early 20^th centuries, but was formalized and refined as a specific field of study as Quantum Mechanics by Max Planck at the turn of the 20^th century and quantization arguably represents the prevailing and distinguishing characteristic of reality at this scale.

Newtonian Mechanics, or even the extension of Newtonian Mechanics as put forth by Einstein with Relativity Theory in the beginning of the twentieth century (a theory whose accuracy is well established via experimentation at this point), assumes that particles, things made up of mass, energy and momentum exist independent of the observer or their instruments of observation, and are presumed to exist in continuous form, moving along specific trajectories and whose properties (mass, velocity, etc.) can only be changed by the action of some force upon which these things or objects are affected.  This is the essence of Newtonian Mechanics upon which the majority of modern day physics, or at least the laws of physics that affect us here at a “human” or “cosmic” scale, is defined.  Theories and models of reality which as we have pointed out rest upon, whether explicitly called out or not, the fundamentally philosophical assumptions that are best described as objective realism and determinism.

The only caveat to this view that was put forth by Einstein is that these measurements themselves, of speed or even mass or energy content of a specific object, can only be said to be universally defined according to these physical laws within the specific frame of reference of an observer.  Their underlying reality is not questioned – these things clearly exist independent of observation or measurement, clearly (or so it seems) – but the values, or the properties of these things is relative to a frame of reference of the observer change depending upon your frame of reference.  This is what Relativity tells us.  So the velocity of a massive body, and even the measurement of time itself which is a function of distance and speed, is a function of the relative speed and position of the observer who is performing said measurement. 

For the most part, the effects of Relativity can be ignored when we are referring to objects on Earth that are moving at speeds that are minimal with respect to the speed of light and are less massive than say black holes.  As we measure things at the cosmic scale, where distances are measured in terms of light years and black holes and other massive phenomena exist which bend spacetime (aka singularities) the effects of Relativity cannot be ignored however.[3]  Leaving aside the field of cosmogony for the moment and getting back to the history of the development of Quantum Mechanics, at the end of the 19^th century Planck was commissioned by electric companies to create light bulbs that used less energy, and in this context was trying to understand how the intensity of electromagnetic radiation emitted by a black body (an object that absorbs all electromagnetic radiation regardless of frequency or angle of incidence) depended on the frequency of the radiation, i.e. the color of the light.  In his work, and after several iterations of hypotheses that failed to have predictive value, he fell upon the theory that energy is only absorbed or released in quantized form, i.e. in discrete packets of energy he referred to as bundles or energy elements, the so-called “Planck postulate”.  And so the field of Quantum Mechanics was born.[4] 

Despite the fact that Einstein is best known for his mathematical models and theories for the description of the forces of gravity and light at a cosmic scale, his work was also instrumental in the advancement of Quantum Mechanics as well.   For example, in his work in the effect of radiation on metallic matter and non-metallic solids and liquids, he discovered that electrons are emitted from matter as a consequence of their absorption of energy from electromagnetic radiation of a very short wavelength, such as visible or ultraviolet radiation.  Einstein termed this behavior the photoelectric effect, and in fact it was for this discovery that he won his one and only Nobel Prize in Physics in 1921  Furthermore, Einstein established that under certain conditions and in certain experiments, light appeared to behave like a stream of tiny particles, not just as a wave, lending credence and authority to the particle theories which had begun to be established to describe the subatomic realm, i.e. quantum realm.  As a result of these experiments, he hypothesized the existence of light quanta, or photons, laying the groundwork for subsequent wave-particle duality discoveries and reinforcing the discoveries of Planck with respect to black body radiation and its quantized behavior.

Prior to the establishment of light’s properties as waves, and then in turn the establishment of wave like characteristics of subatomic elements like photons and electrons by Louis de Broglie in the 1920s, it had been fairly well established that these subatomic particles, or electrons or photons as they were later called, behaved like particles.  However, the debate and study of the nature of light and subatomic matter went all the way back to the 17^th century where competing theories of the nature of light were proposed by Isaac Newton, who viewed light as a system of particles, and Christiaan Huygens who postulated that light behaved like a wave. 

It was not until the work of Einstein, Planck, de Broglie and other physicists of the twentieth century that the nature of these subatomic particles, both photons and electrons, were proven to behave both like particles and waves, the result depending upon the experiment and the context of the system which being observed.  This paradoxical principle came to be known as wave-particle duality and it is one of the intellectual cornerstones, and in fact underlying mysteries, of the nature of the sub-atomic world and in turn one has become one of the fundamental properties that underlie Quantum Theory  and distinguish it from Classical Mechanics.

As part of the discoveries of subatomic particle wave-like behavior, what Planck discovered in his study of black body radiation, and Einstein as well within the context of his study of light and photons, was that the measurements or states of a given particle such as a photon or an electron had to take on values that were multiples of very small and discrete quantities, i.e. were non-continuous, the relation of which was represented by a constant value known as the Planck constant[5]. 

In the quantum realm then, there was not a continuum of values and states of matter as had been the assumption upon which Classical Mechanics had been constructed, in the sub-atomic realm there existed not a continuum of “physical existence”, but instead bursts of energies and changes of state that were discrete, i.e. had fixed amplitudes or values, which of course implied that certain states or amplitudes could in fact not exist, representing a dramatic departure from the way physicists, and the rest of us mortals, think about movement and change in the “real world”, and most certainly represented a significant departure from Newtonian Mechanics upon which Relativity was based where the idea of continuous motion, in fact continuous existence, is a fundamental proposition upon which these models are predicated. 

The classic demonstration of light’s behavior as a wave, and perhaps one of the most astonishing and influential physical experiments in the history of science, is illustrated in what is called the “double-slit experiment”.  In the basic version of this experiment, a light source such as a laser beam is shone at a thin plate that that is pierced by two parallel slits.  The light in turn passes through each of the slits and displays on a screen behind the plate.  The image that is displayed on the screen behind the plate as it turns out is not one of a constant band of light that passes through each one of the slits as you might expect if the light were simply a particle or sets of particles, the light displayed on the screen behind the double-slitted slate is one of light and dark bands, indicating that the light is behaving like a wave and is subject to interference, the strength of the light on the screen cancelling itself out or becoming stronger depending upon how the individual waves interfere with each other.  This behavior is exactly akin to what we consider fundamental wavelike behavior, for example like the nature of waves in water where the waves have greater strength if they synchronize correctly (peaks of waves) and cancel each other out (trough of waves) if not.

Classical illustration of the famous “double slit” experiment.[6]

 

What is even more interesting however, and was most certainly unexpected, is that once equipment was developed that could reliably send a single particle, an electron or photon for example, through a double-slitted slate, the individual particles did indeed end up at a single location on the screen after passing through just one of the slits as was expected, but however – and here was the kicker – the location on the screen that the particle ended up at, as well as which slit the particle appeared to pass through (in later versions of the experiment which slit “it” passed through could in fact be detected) was not consistent and followed seemingly random and erratic behavior.  What researchers found as more and more of these subatomic particles were sent through the slate one at a time, was that the same wavelike interference pattern emerged that showed up when the experiment was run with a full beam of light as was done by Young some 100 years prior.[7]

Arguably this experiment illustrates the very essence of the mystery behind much of Quantum Mechanics, showing that our basic understanding of nature or physical reality was not in fact what it appeared to be.  In other words, the ground or substratum of the physical world could be seen as “objective” or “wavelike”, depending upon how one looks at it.  While this seems confusing at first, and no doubt is one of the most influential discoveries and principles of science in the modern era.  What was clearly demonstrated in this experiment however, is that a subatomic particle, a corpuscle or whatever you wanted to call it, does not have a completely linear and fully deterministic trajectory in the Classical Mechanics sense – as indicated by the fact that the end distribution of said corpuscles against the back screen after they are projected through the double slitted wall appeared to be “random”, i.e. again not fully deterministic.  But what was more odd was that when the experiment was run one corpuscle or particle at a time, not only was the final location on the screen seemingly random individually, but the same aggregate pattern emerged after many, many single corpuscle experiment runs as when a full wave, or set of these corpuscles, was sent through the double slits. 

So it appeared, and this was and still remains a very important and telling mysterious characteristic feature of the behavior of these “things” at the subatomic scale, is that not only did the individual photon seemed to be aware of the final wave like pattern of its parent wave, but also that this corpuscle appeared to be interfering with itself when it went through the two slits individually.  The result of this experiment and the inherent logical conclusions that scientists arrived at, is that the fundamental substratum of existence was not objective in the classical sense, but was also wavelike at the same time.  Furthermore, even when the experiment is performed with just one subatomic particle, the particle itself seemed appeared to be aware of its inherent wave structure, i.e. that the individual particle was interfering with itself, calling into question the notion of objective reality itself.

Furthermore, to make things even more mysterious, as the final location of each of the individual photons in the two slit and other related experiments was evaluated and studied, it was discovered that although the final location of an individual one of these particles could not be determined exactly before the experiment was performed, i.e. there was a fundamental element of uncertainty or randomness involved at the individual corpuscle level, it was discovered that the final locations of these particles measured in toto after many experiments were performed exhibited statistical distribution behavior that could be modeled quite precisely, precisely from a mathematical statistics and probability distribution perspective.  That is to say that the sum total distribution of the final locations of all the particles after passing through the slit(s) could be established stochastically, i.e. in terms of well-defined probability distribution consistent with probability theory and well-defined mathematics that governed statistical behavior.  So in total you could predict what the particle like behavior would look like over a large distribution set of particles in the double slit experiment even if you couldn’t predict with certainty what the outcome would look like for an individual corpuscle.

The mathematics behind this particle distribution that was discovered is what is known as the wavefunction, typically denoted by the Greek letter psi, ψ or its capital equivalent Ψ, predicts what the probability distribution of these “particles” will look like on the screen behind the slate after many individual experiments are run, or in quantum theoretical terms, the wave function predicts the quantum state of a particle throughout a fixed spacetime interval.  The wavefunction was discovered by the Austrian Physicist Erwin Schrödinger in 1925, published in 1926, and is commonly referred to in the scientific literature as the Schrödinger equation, analogous in the field of Quantum Mechanics to Newton’s second law of motion in Classical Mechanics.

This wavefunction represents a probability distribution of potential states or outcomes that describe the quantum state of a particle and predicts with a great degree of accuracy the potential location of a particle given a location or state of motion.  With the discovery of the wavefunction, it became possible to predict the potential locations or states of these subatomic particles, an extremely potent theoretical model that has led to all sorts of inventions and technological advancements since its discovery.  Again, this implied that individual corpuscles were interfering with themselves when passing through the two slits on the slate, which was very odd indeed.  In other words, the individual particles were exhibiting wave like characteristics even when they were sent through the double-slitted slate one at a time.  This phenomenon was shown to occur with atoms as well as electrons and photons, confirming that all of these subatomic so-called particles exhibited wave like properties as well as particle like qualities, the behavior observed determined upon the type of experiment, or measurement as it were, that the “thing” was subject to.

As Louis De Broglie, the physicist responsible for bridging the theoretical gap between matter, in this case electrons, and waves by establishing the symmetric relation between momentum and wavelength which had at its core Planck’s constant (the De Broglie equation), described this mysterious and somewhat counterintuitive relationship between matter and waves, “A wave must be associated with each corpuscle and only the study of the wave’s propagation will yield information to us on the successive positions of the corpuscle in space.”[8]  In the Award Ceremony Speech in 1929 in honor of Louis de Broglie for his work in establishing the relationship between matter and waves for electrons, we find the essence of his ground breaking and still mysterious discovery which remains a core characteristic of Quantum Mechanics to this day.

 

Louis de Broglie had the boldness to maintain that not all the properties of matter can be explained by the theory that it consists of corpuscles. Apart from the numberless phenomena which can be accounted for by this theory, there are others, according to him, which can be explained only by assuming that matter is, by its nature, a wave motion. At a time when no single known fact supported this theory, Louis de Broglie asserted that a stream of electrons which passed through a very small hole in an opaque screen must exhibit the same phenomena as a light ray under the same conditions. It was not quite in this way that Louis de Broglie’s experimental investigation concerning his theory took place. Instead, the phenomena arising when beams of electrons are reflected by crystalline surfaces, or when they penetrate thin sheets, etc. were turned to account. The experimental results obtained by these various methods have fully substantiated Louis de Broglie’s theory. It is thus a fact that matter has properties which can be interpreted only by assuming that matter is of a wave nature. An aspect of the nature of matter which is completely new and previously quite unsuspected has thus been revealed to us.[9]

 

So by the 1920s then, you have a fairly well established mathematical theory to govern the behavior of subatomic particles, backed by a large body of empirical and experimental evidence, that indicates quite clearly that what we would call “matter” (or particles or corpuscles) in the classical sense, behaves very differently, or at least has very different fundamental characteristics, in the subatomic realm.  It exhibits properties of a particle, or a thing or object, as well as a wave depending upon the type of experiment that is run. 

So the concept of matter itself then, as we had been accustomed to dealing with and discussing and measuring for some centuries, at least as far back as the time of Newton (1642-1727), had to be reexamined within the context of Quantum Mechanics.  For in Newtonian Mechanics, and indeed in the geometric and mathematical framework within which it was developed and conceived which reached far back into antiquity (Euclid circa 300 BCE), matter was presumed to be either a particle or a wave, but most certainly not both. 

What even further complicated matters was that matter itself, again as defined by Newtonian Mechanics and its extension via Relativity Theory taken together what is commonly referred to as Classical Mechanics, was presumed to have some very definite, well-defined and fixed, real properties.  Properties like mass, location or position in space, and velocity or trajectory were all presumed to have a real existence independent of whether or not they were measured or observed, even if the actual values were relative to the frame of reference of the observer.  All of this hinged upon the notion that the speed of light was fixed no matter what the frame of reference of the observer of course, this was a fixed absolute, nothing could move faster than the speed of light.  Well even this seemingly self-evident notion, or postulate one might call it, ran into problems as scientists continued to explore the quantum realm.

By the 1920s then, the way scientists looked at and viewed matter as we would classically consider it within the context of Newton’s postulates from the early 1700s which were extended further into the notion of spacetime as put forth by Einstein, was encountering some significant difficulties when applied to the behavior of elements in the subatomic, quantum, world.  Difficulties that persist to this day in fact.  Furthermore, there was extensive empirical and scientific evidence which lent significant credibility to Quantum Theory, which illustrated irrefutably that these subatomic elements behaved not only like waves, exhibiting characteristics such as interference and diffraction, but also like particles in the classic Newtonian sense that had measurable, well defined characteristics that could be quantified within the context of an experiment. 

In his Nobel Lecture in 1929, Louis de Broglie, summed up the challenge for Physicists of his day, and to a large extent Physicists of modern times, given the discoveries of Quantum Mechanics as follows:

 

The necessity of assuming for light two contradictory theories-that of waves and that of corpuscles – and the inability to understand why, among the infinity of motions which an electron ought to be able to have in the atom according to classical concepts, only certain ones were possible: such were the enigmas confronting physicists at the time…[10]

 

The other major tenet of Quantum Theory that rests alongside wave-particle duality, and that provides even more complexity when trying to wrap our minds around what is actually going on in the subatomic realm, is what is sometimes referred to as the uncertainty principle, or the Heisenberg uncertainty principle, named after the German theoretical physicist Werner Heisenberg who first put forth the theories and models representing the probability distribution of outcomes of the position of these subatomic particles in certain experiments like the double-slit experiment previously described, even though the wavefunction itself was the discovery of Schrödinger. 

The uncertainty principle states that there is a fundamental theoretical limit on the accuracy with which certain pairs of physical properties of atomic particles, i.e. corpuscles, position and momentum being the classical pair for example, that can be known at any given time with certainty.  In other words, physical quantities come in conjugate pairs, where only one of the measurements of a given pair can be known precisely at any given time.  In other words, when one quantity in a conjugate pair is measured and becomes determined, the complementary conjugate pair becomes indeterminate.  In other words, what Heisenberg discovered, and proved mathematically, was that the more precisely one attempts to measure one of these complimentary properties of subatomic particles, the less precisely the other associated complementary attribute of the element can be determined or known. 

Published by Heisenberg in 1927, the uncertainty principle states that they are fundamental, conceptual limits of observation in the quantum realm, another radical departure from the realistic and deterministic principles of Classical Mechanics which held that all attributes of a thing were measurable at any given time, i.e. this thing or object existed and was real and had measurable and well defined properties irrespective of its state.  It’s important to point out here that the uncertainty principle is a statement on the fundamental property of quantum systems as they are mathematically and theoretically modeled and defined, and of course empirically validated by experimental results, not a statement about the technology and method of the observational systems themselves.  This wasn’t a theoretical problem, or a problem with the state of instrumentation that was being used for measurement, it was a characteristic of the domain itself. 

Max Born, who won the Nobel Prize in Physics in 1954 for his work in Quantum Mechanics, specifically for his statistical interpretations of the wavefunction, describes this now other seemingly mysterious attribute of the quantum realm as follows (the specific language he uses reveals at some level his interpretation of the Quantum Theory, more on interpretations later):

 

…To measure space coordinates and instants of time, rigid measuring rods and clocks are required.  On the other hand, to measure momenta and energies, devices are necessary with movable parts to absorb the impact of the test object and to indicate the size of its momentum.  Paying regard to the fact that quantum mechanics is competent for dealing with the interaction of object and apparatus, it is seen that no arrangement is possible that will fulfill both requirements simultaneously.[11]

 

Whereas Classical Mechanics, physics prior to the introduction of Relativity and Quantum Theory, distinguished between the study of particles and waves, the introduction of Quantum Theory and wave-particle duality established that this classic intellectual bifurcation of Physics at the macroscopic scale was wholly inadequate in describing and predicting the behavior of these “things” that existed in the subatomic realm, all of which took on the characteristics of both waves and particles depending upon the experiment and context of the system being observed. 

Furthermore, the actual precision within which a state of a “thing” in the subatomic world could be defined was conceptually bound, establishing theoretical limits upon which the state of a given subatomic state could be defined, another divergence from Classical Mechanics.  And then on top of this, was the requirement of the mathematical principles of statistics and probability theory, as well as significant extensions to the underlying geometry which were required to map the wavefunction itself in subatomic spacetime, all called quite clearly into question our classical materialistic notions, again based on objective realism and determinism, upon which scientific advancement had been built for centuries. 

 

Relativity Theory could be grasped intellectually by the educated, intelligent mind.  You didn’t need advanced degrees or a deep understanding of complex mathematics to understand that at a very basic level, Relativity Theory implied that basic measurements like speed, distance and even mass were relative and depended upon the observer’s frame of reference, that mass and energy were basically convertible into each other and equivalent, related by the speed of light that moved at a fixed speed no matter what your frame of reference, and that space and time were not in fact separate and distinct concepts but in order for a more accurate picture of the universe to emerge they needed to be combined into a single notion of spacetime.  Relativity says that even gravity’s effect was subject to the same principles that played out at the cosmic scale, i.e. that spacetime “bends” at points of singularity (black holes for example), bends to the extent that light in fact is impacted by the severe gravitational forces at these powerful places in the universe.  And indeed our measurements of time and space were “relative”, relative to the speed and frame of reference from which these measurements were made, the observer was in fact a key element in the process of measurement. 

If you assumed all these things, you ended up with a more complete and accurate mathematical and theoretical understanding of the universe than you had with Newtonian Mechanics, and one that is powerful enough that despite the best efforts of many great minds over the last 100 years or so, has yet to be supplanted with anything better, at least at the macro scale of the universe. Relativity undoubtedly represents a major intellectual leap in mankind’s understanding of the shape, behavior and underlying laws that govern the physical universal, but a subtle and quite distinctive feature of this model was that it fundamentally relies on the same deterministic and objective realist assumptions which underlie Classical Mechanics as “discovered” and modelled by Newton. 

In other words, Relativity Theory implicitly assumed that objects in the physical do in fact exist, i.e. they were “real”, real in the sense that they had an absolute existence in the spacetime continuum within some frame of reference by some “observer” that also “existed” within the spacetime continuum, each of which could be described, or “defined”, in terms of qualitative data like speed, mass, velocity, etc.  Furthermore, Relativity Theory like Classical Mechanics before it, was framed and built upon the notion that if you knew a set of starting criteria, what scientists like to call a “system state”, as well as a set of variables/forces that acted on said system, you could in turn predict with certainty the outcome of said forces on such a system, i.e. the set of observed descriptive qualities of the objects in said system after the forces have acted upon the objects that existed in the original system state.  This is the essence of the deterministic model of the universe, a principle which underlies the both Relativity Theory as well as Newtonian Mechanics.

It’s quite relevant and important to point out however that in fact these “assumptions” upon which all modern Physics are based – all modern Physics except Quantum Mechanics which is where we’re headed here with this line of reasoning – were quite modern metaphysical assumptions that were a product of the Scientific Revolution more or less.  In other words, a fully deterministic and objective view of reality which came to define early 20^th century physics, although it had roots going back to ancient Greece as we have already pointed out, had not in fact been the prevailing assumptions that governed models of the universe prior to Newton and Einstein, at least not in to the degree of certainty that had been established by these powerful theories and mathematical models and laws that these two great minds had firmly established and had been proven by a variety of experiments and data.  Prior to Newton, the world of the spirit, theology in fact, was very much considered to be just as real as the physical world, the world governed by Science or natural philosophy.  This fact was true not only in the West, but also in the East, and while this idea has been all but abandoned by the Western scientific tradition, it nonetheless to a great extent remains true within the domain of Eastern philosophy which includes and synthesizes the model of the physical world, the intellectual or cognitive world, as well as the spiritual world which is defined and bounded by the domain of the Soul.

But at their basic, core level, these concepts of the atom, electromagnetic force, gravity and Relativity could be understood, grasped as it were, by the vast majority of the educated public, even if they had very little if any bearing on their daily lives and even if didn’t fundamentally change or shift their underlying religious or theological beliefs, or in turn their moral or ethical principles which still remained rooted in Religion for the most part.  Relativity has been “accepted” in the modern era, the so-called Quantum Era, as a basic truth as it were, along with its deterministic and objective realism philosophical and metaphysical assumptions.  What tends to be forgotten however, and not really covered or mentioned in the “scientific” and academic circles which reinforce the “truth” of these theories and laws is that their underlying principles and assumptions do not have any bearing whatsoever on the “subject” in question, i.e. the mental, cognitive or intellectual state of the “observer” whose frame of reference is used for the measurement of these quantifiable phenomena. 

So one of the major and significant implications of the influence and prevalence of modern physics, again leaving aside Quantum Theory for a moment, is that these theories and models completely ignored, and in fact came to represent a sort of intellectual or ontological superiority to, the “act of observation”, and the mode and means of perception itself, one of the driving principles and ideas of Enlightenment Era philosophical inquiry in fact.  The dictum put forth by Descartes as “cogito ergo sum”, i.e. “I think therefore I am” was superseded by a dictum that is perhaps best expressed as “I observe and measure therefore I am”.

Quantum Theory is an altogether different beast however, even though it still falls squarely within the discipline of Physics.  The mathematical laws and their underlying assumptions and principles are very different from, and in fact incompatible at a very basic level with, the mathematical laws and principles that were “discovered” by Newton, Einstein that describe Classical Mechanics and Relativity respectively.  And in order to truly “understand” Quantum Theory, or at least try to come to terms with it, a wholesale different perspective on what reality truly is, or at the very least how reality is defined, is in fact required – hence the continued struggle for a so-called Unified Field Theory of Physics which describes the quantum realm and also takes into account the notion of spacetime and gravity as described by Relativity Theory.  In other words, in order to understand what Quantum Theory actually means, its underlying ontological implications as it were, or in order to grasp the underlying intellectual context within which the behaviors of the underlying particles/fields that Quantum Theory describes can be properly understood, a new framework of understanding, a new description of reality, must be adopted.  What we consider to be “reality”, our objective realism” which underlies Classical Mechanics which has dominated Physics and our modern perspective and definition of “physical reality”, or simply “reality”, since the publication of Newton’s Principia at the end of the 17^th century needed to be abandoned, or at the very least significantly modified, in order for Quantum Theory to be understood in any meaningful way, i.e. in order for some comprehension of the implications of Quantum Theory’s underlying truth about the nature and behavior of the substratum of physical reality, and in turn the role of the “observer” in said reality, to be understood. 

 

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[1] Since Bohr’s model is essentially a quantized version of Rutherford’s, some scholars refer to the model as the Rutherford-Bohr model as opposed to just the Rutherford model.  As a theory, it may be considered to be obsolete given later advancements however, because of its simplicity and its correct results for selected systems, the Bohr model is still commonly taught to introduce students to Quantum Mechanics.

[2] Our current ability to measure the size of these subatomic particles goes down to approximately 10^-16 cm leveraging currently available instrumentation, so at the very least we can say that our ability to measure anything in the subatomic realm, or most certainly the realm of the general constituents of basic atomic elements such as quarks or gluons for example, is very challenging to say the least.  Even the measurement of the estimated size of an atom is not so straightforward as the measurement is dictated by the circumference of the atom, a measurement that relies specifically on the size or radius of the “orbit” of the electrons on said atom, “particles” whose actual “location” cannot be “measured” in tandem with their momentum, standard tenets of Quantum Mechanics, both of which constitute what we consider measurement in the classic Newtonian sense.

[3] In some respects, even at the cosmic scale, there is still significant reason to believe that even Relativity has room for improvement as evidenced by what physicists call Dark Matter and/or Dark Energy, artifacts and principles that have been created by theoretical physicists to describe matter and energy that they believe should exist according to Relativity Theory but the evidence for which their existence is still yet ”undiscovered”.  Both Dark Matter and Dark Energy represent active lines of research in modern day Cosmogony.

[4] Quantum Theory has its roots in this initial hypothesis by Planck, and in this sense he is considered by some to be the father of Quantum Theory and Quantum Mechanics.  It is for this work in the discovery of energy quanta that Max Planck received the Nobel Prize in Physics in 1918, some 15 or so years after publishing.

[5] The Planck constant was first described as the proportionality constant between the energy (E) of a photon and the frequency (ν) of its associated electromagnetic wave.  This relation between the energy and frequency is called the Planck relation or the Planck–Einstein equation: .  It is interesting to note that Planck and Einstein had a very symbiotic relationship toward the middle and end of their careers, and much of their work complemented and built off of each other.  For example Planck is said to have contributed to the establishment and acceptance of Einstein’s revolutionary concept of Relativity within the scientific community after being introduced by Einstein in 1905, the theory of course representing a radical departure from the standard Classical Mechanical models that had held up for centuries prior.  It was through the collaborative work and studies of Planck and Einstein in some sense then that the field of Quantum Mechanics and Quantum Theory is shaped how it is today; Planck who defined the term quanta with respect to the behavior of elements in the realms of matter, electricity, gas and heat, and Einstein who used the term to describe the discrete emissions of light, or photons.

[6] Image illustrates the wave-particle dualistic nature of light, i.e. photons, which are “diffracted” and “interfered with”, like a wave, as they pass through a wall with two slits and come to form a distinctive “wave like” pattern on the screen behind the wall.  Image by Ebohr1.svg: en:User:Lacatosias, User:Stanneredderivative work: Epzcaw (talk) – Ebohr1.svg, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=15229922 from Wikipedia contributors, ‘Double-slit experiment’, Wikipedia, The Free Encyclopedia, 3 December 2016, 23:05 UTC, <https://en.wikipedia.org/w/index.php?title=Double-slit_experiment&oldid=752882651> [accessed 3 December 2016]

[7] The double-slit experiment was first devised and used by Thomas Young in the early nineteenth century to display the wave like characteristics of light.  It wasn’t until the technology was available to send a single “particle” (a photon or electron for example) that the wave like and stochastically distributed nature of the underlying “particles” was discovered as well.  http://en.wikipedia.org/wiki/Young%27s_interference_experiment

[8] Louis de Broglie, “The wave nature of the electron”, Nobel Lecture, Dec 12^th, 1929

[9] Presentation Speech by Professor C.W. Oseen, Chairman of the Nobel Committee for Physics of the Royal Swedish Academy of Sciences, on December 10, 1929.  Taken from http://www.nobelprize.org/nobel_prizes/physics/laureates/1929/press.html.

[10] Louis de Broglie, “The wave nature of the electron”, Nobel Lecture, Dec 12^th, 1929

[11] Max Born, “The statistical interpretation of quantum mechanics” Nobel Lecture, December 11, 1954.