Quantum mechanics is the cornerstone of modern physics, is considered by many physicists and philosophers to be the best physical theory ever developed, and is the foundation upon which the technologies that power the modern world are built. It has withstood almost a century of experimental tests and discoveries remarkably well and remains as accurate today as it was a near century ago. Indeed, to date, quantum mechanics has not yet been found to provide an incorrect result. This truly is, without hyperbole or exaggeration, extraordinary.

This chapter of the QBook examines the history and structure of quantum mechanics and provides a conceptual framework for the chapters that follow. Crucially, this chapter does not provide a comprehensive overview of all the facets and features of quantum mechanics — quantum mechanics far too conceptually complex and concerns far too many phenomena to be adequately addressed in brief — and the reader will not walk away with a complete understanding of quantum mechanics. Instead, this section seeks to provide sufficient general historical and intellectual context to assess the implications of quantum mechanics for war, peace, security, and our understanding of reality (worldview).

II. A Short History of Quantum Mechanics

Quantum mechanics is the branch of physics which describes the behaviour of systems (atoms, particles, etc) at the atomic and subatomic scale. Before diving into what exactly this means, it is helpful to first examine the context from which it arose, which is dramatically known as the Ultraviolet Catastrophe.

In the late 1890s, physics was plagued by the blackbody problem. In essence, this problem concerns how a blackbody — such as a piece of coal or iron — can emit red light at temperatures in the hundreds of degrees, and emit white light when heated to several thousands of degrees. Physicists, such as Lord Rayleigh, attempted to model this phenomenon using classical thermodynamics, but their calculations predicted that the energy released would approach infinity as wavelengths decreased into the ultraviolet range. Obviously, this is impossible, and physicists knew that something was wrong with their models. Indeed, these calculations yielded nonsensical results because Newton’s laws assumed energy was continuous and was emitted continuously. Max Planck was the first to see through this and, in 1900, Planck proposed that energy is discrete and is emitted discretely as quanta. Planck argued that there was a fundamental quantum of action — as if one could walk at eight kilometres an hour, or nine, but not eight and a half. Energy became granular, and with this quantum hypothesis the quantum revolution began.

At this stage, Planck’s thought his quantum of action was merely a useful mathematical trick for removing the infinities engendered by classical thermodynamics and it was Albert Einstein, not Planck, who developed the quantum hypothesis into the first quantum theory. In 1905, Einstein extended Planck’s quanta to light in order to explain the photoelectric effect, and in doing so he argued that light was granular and that light quanta — which are now known as photons — were real components of reality. Einstein’s view went against the consensus that light was a wave, and his ideas were initially considered outlandish, though he was eventually vindicated.

Several years later, and following Ernest Rutherford’s discovery of the atomic nucleus, Niels Bohr and Arnold Sommerfeld further extended the concept of quanta to atoms and developed what is now known as the Old Quantum theory. This was a peculiar mix of quantum and Newtonian laws which the English physicist A.S. Eddington described as like using “the classical theory on Mondays, Wednesday, and Fridays, and the quantum theory on Tuesdays, Thursdays, and Saturdays.” It worked well enough and managed to predict the light spectra of the elements, but it was unwieldy, required regular adjustments and updates to keep up with new experimental results, and there was a general sense that it was incomplete. In particular, the Old Quantum theory made it clear that electrons could only occupy certain orbits in atoms, but it was unknown why these specific orbits were allowed and others were not. It was this question which occupied a young Werner Heisenberg’s mind and led him to develop the basis of modern quantum mechanics.

One sleepless night, Heisenberg arrived at a solution. “The idea,” he later wrote, “suggested itself… that one should write down the mechanical laws not as equations for the positions and velocities of the electrons, but as equations for the frequencies and amplitudes of their Fourier expansion.” Heisenberg abandoned all that was assumed to exist and set about creating a new mechanics which only used observable variables and their relations. He ordered these observables into tables, and these tables perfectly matched all experimental results. Heisenberg published his Matrix Mechanics in 1925, and a flurry of advancements soon followed. Erwin Schrödinger published his Wave Mechanics in 1926, Paul Dirac introduced his Transformation Theory that same year, and by the fifth Solvay Conference, in 1927, quantum mechanics was proclaimed a closed theory.

There were many other significant contributions and developments in this period, and it was not until the 1930s that the formalism was standardised by Dirac and John von Neumann, but that is the quick history of the development of quantum mechanics.

For more on the history of the Solvay Conferences please visit the Solvay Science Project.

This chapter consists of five parts:

• part one, this part, presents an overview of this section of the QBook;
• part two provides a general history of quantum mechanics;
• part three examines what it is that quantum mechanics is;
• part four describes the key concepts of quantum mechanics;
• part five interrogates the potential implications of quantum mechanics for international relations (IR) theory;
• and finally, part six provides a glossary of quantum-related concepts and terms.

With the historical origins of quantum mechanics out of the way, we can turn to the question of “what exactly quantum mechanics is?” That might sound like an odd question. Quantum mechanics is also known as ‘quantum theory’ and ‘quantum physics,’ so surely the answer is that quantum mechanics is a theory of physics, or a physical theory. Indeed, this is a common answer, and it is often tacitly assumed that quantum mechanics is a physical theory. But is it?

The philosopher of science Timothy Maudlin argues that quantum mechanics is not a physical theory. In Philosophy of Physics: Quantum Theory, Maudlin writes that all physical theories must “clearly and forthrightly address two fundamental questions: what there is, and what it does.” In other words, a physical theory must have an ontology (what there is) and an account of dynamics (what it does). Quantum mechanics provides neither, and thus ‘quantum theory’ is a misnomer. To become a physical theory quantum mechanics can be paired with a so-called ‘interpretation’ that fills in these blanks. Many interpretations exist, but they are all predictively equivalent — at least according to the experiments currently available to us — and there is no way to say which are right or which are wrong. Further, not all interpretations have ontologies or dynamics. For example, the Copenhagen Interpretation — which is often said to be the most popular interpretation amongst physicists — fulfills neither of Maudlin’s categories and so, even when quantum mechanics is paired up with the Copenhagen Interpretation, it cannot be considered to be a physical theory.

What then is quantum mechanics? This is a highly contentious question, and no single answer will receive universal ascent, but the simple answer is that quantum mechanics is a model. This might sound underwhelming — after all who wants a model, we want to know about reality — but models are a key part of science. In fact, they may be the key part. Science seeks to understand reality, and to do so models are constructed and tested against observations. The goal here is not to create a 1-to-1 model which encompasses all the mess and noise of the real world, but to develop models which are good enough and reveal the essential features of the systems being studied. Indeed, creating a 1-to-1 model would mean recreating the thing we are trying to understand in the first place. Thus, to understand the model we’d need to make other models — what’s the point of that?

So, quantum mechanics is a model which tells us that reality operates differently to how we thought it did. What this means for reality is highly contested and the subject of much ongoing debate, but in the absence of an interpretive consensus we can still learn a from the essential features of quantum mechanics.

Christopher A. Fuchs is one of the creators of QBism and one of the deepest thinkers on the foundations of quantum mechanics. Watch our interview with him to hear some of his views on the interpretation of quantum mechanics and more:

The essential features of quantum mechanics vary from interpretation to interpretation, and theorist to theorist, and it is impossible to cover all of the diversity of opinion here. Instead, this section provides and overview of the ideas, concepts, and features which crop up most often when discussing quantum mechanics. The following descriptions attempt to balance brevity with accuracy and clarity and should be considered general descriptions rather than definitive definitions.

In 1930, Paul Dirac introduced the concept of quantum superposition in his seminal textbook on quantum mechanics, The Principles of Quantum Mechanics. Dirac wrote:

“We must now imagine the states of any system to be related in such a way that whenever the system is definitely in one state, we can equally well consider it as being partly in each of two or more other states. The original state must be regarded as the result of a kind of superposition of the two or more new states, in a way that cannot be conceived on classical ideas. Any state may be considered as the result of a superposition of two or more other states, and indeed in an infinite number of ways. Conversely any two or more states may be superposed to give a new state, even also when they refer to different positions of the system in space.”

Sound complicated? It is! And it isn’t. Let’s break superposition down into simpler terms.

In quantum mechanics, what is known about a particle — its initial state — is input into the Schrödinger equation to calculate how it will change over time. The particle is represented as a wave function and said to be in a quantum state. Wave functions represent the probabilities of a range of possible measurement outcomes and thus, rather than being a single state, a quantum state represents a range of possible states. This is referred to as a superposition. When the quantum state is measured, we find out which state the particle occupied and the wave function is said to collapse into one definite state. Additionally, the quantum states (wave functions) of multiple particles can be superposed together, and this is also referred to as a superposition. For example, one can take the wave functions of three particles (or more) and combine them to arrive at the quantum state for this system which is represented by its own wave function. This is not as simple as adding the wave functions together, but it is nothing more esoteric than a sum.

Ultimately, when a particle is said to be in a superposition, all this means is that it is represented by a wave function which, in turn, represents a number of possible measurement outcomes. It does not mean that the particle is in two places at once. It simply means that, between measurements, we can only provide probabilistic descriptions of the properties of quantum systems.

Entanglement is one of the more mysterious features of quantum mechanics and, consequently, has long been a favourite amongst charlatans, mystics, crackpots, and others who wish to connect quantum mechanics with pseudoscientific or religious ideas. This largely arises from the fact that entanglement is poorly named. It is possible that Erwin Schrödinger’s original German word for it, verschränkung — which translates to ‘interlacing’ or ‘interweaving’ — is more fitting, but his translation of verschränkung to entanglement introduced a false sense of conceptual clarity. For example, the word entanglement suggests that things are tangled — like a ball of yarn, shoelaces, or spare cables in a draw. However, there is nothing which suggests that entangled quantum systems are physically ‘tangled.’ Indeed, these systems can be separated by great distances.

Entanglement is a particular type of superposition that occurs when isolated quantum systems (particles or any other subatomic entity) interact in such a way that their quantum states cannot be described independently. After this entangling interaction the probabilities of these systems become correlated so that one can infer the state of one system by measuring the other system. So, if particle a and particle b are entangled, one can know the state of particle a by measuring particle b. Crucially, entanglement is a correlation not a causation, and, thus, a better name would be ‘quantum correlation’ or ‘quantum correspondence.’

Again, the physical meaning of entanglement is highly contested and remains open to various interpretations. While it is a highly perplexing feature of quantum mechanics, it does not prove, in and of itself, that there are invisible webs or links connecting all parts of the universe, or that particles can communicate faster than light. Nonetheless, this mysterious phenomenon plays a crucial role in many modern quantum technologies.

In quantum mechanics, the state of a particle is represented by a wavefunction. This wave function describes the probability distribution of a particle’s properties — such as its position, momentum, or spin. When two or more wavefunctions overlap, their amplitudes can add up or cancel out — constructive or destructive interference — leading to different probabilities of finding the particle in certain regions of space. Crucially, in quantum mechanics the particles do not need to be fired together to interfere with one another. Single particles, fired one at a time, still produce interference patterns.

Wave-Particle duality arises from the fact that, depending on how they are measured, quantum states may present as wave-like or particle-like. So, if you measure a photon one way it will look like a wave and if you measure it another and it will look like a particle. So, which is it? Some have argued that the fundamental units of reality are waves, others have argued that they are particles with waves, and yet others that they are neither particles nor waves, but something else altogether. There is no reason to prefer one interpretation over another, but it is clear that quantum objects are not particles in the sense of a grain of sand, nor waves like those at the beach. ‘Particles’ and ‘waves’ are both metaphors for these subatomic entities. They are not exact descriptions — if they were they wouldn’t be metaphors. Perhaps, it is better to think of these quantum entities as similes. That is, quantum entities are like waves and like particles. Ultimately, the appropriate ontology for quantum mechanics remains an open problem.

Since the development of modern quantum mechanics in the 1920s there have been several attempts to incorporate into, or ‘quantise,’ international relations and international relations theory. The first attempt to do so occurred a mere few months after the 1927 Solvay Conference that marked the birth of modern quantum mechanics. At a meeting of the American Political Science Association, William Bennet Munro called on political scientists to draw on the new physics, arguing that “A revolution so amazing in our ideas concerning the physical world must inevitably carry its echoes into other fields of human knowledge.” Munro’s call was ultimately unheeded, but over the next century many other scholars of politics and international relations have come to draw upon quantum mechanics.

Today, modern quantum international relations argues that traditional, Newtonian approaches to the study of international relations are severely limited. These Newtonian approaches rely on outdated assumptions — for example, they often argue that States behave like billiard balls that interact with each other in predictable ways — and fail to account for a large variety of social and political phenomena. Quantum international relations, on the other hand, argues that international relations should be approached as a complex, dynamic system, where the behaviour of one actor can have an unpredictable and non-linear effects on other actors. However, despite nearly a century of interdisciplinary entanglements the subfield of quantum international relations remains in its infancy (see Der Derian and Wendt, 2022). Further, despite the numerous attempts to quantise international relations there is no disciplinary consensus as to how quantum international relations should be systematically pursued and developed.

The best-known and most influential proposal for a quantum social science comes from Alexander Wendt. However, rather than describing Wendt’s proposal it is better to let him speak for himself:

This page presents a glossary of some key quantum terms. As with all brief descriptions, these are not exhaustive definitions and should be treated as a starting point for further exploration and not as the final word on the subject.

Atom: A unit of matter composed of a nucleus — containing protons and neutrons — and surrounded by electrons.

Bayesian Probability: Bayesian probabilities are subjectivist probabilities which measure an agent’s degree of belief about something.

Bohmian Mechanics: Bohmian Mechanics — alternatively known as the de Broglie-Bohm theory, pilot-wave theory, and the ontological interpretation — is an ontic interpretation of quantum mechanics which posits the existence of hidden variables. In this interpretation all particles are accompanied by undetectable pilot-waves which guide them.

Causality: The principle that present and future events are influenced by past events.

Complementarity: The principle of complementarity was proposed by Niels Bohr as an explanation for why quantum systems display seemingly contradictory properties. For example, when measured one way a quantum system might appear as a particle and measured another the same system might appear as a wave. To Bohr, these two manifestations were not contradictory, but complementary descriptions of the underlying quantum reality. Quantum reality is not susceptible to classical descriptions (such as particles or waves) and physicists must accept these approximate complementary descriptions as complete descriptions.

Copenhagen Interpretation: The Copenhagen Interpretation is an approach to the interpretation of quantum mechanics associated with Niels Bohr and Werner Heisenberg. However, accounts of the Copenhagen Interpretation vary greatly, and it is more accurate to speak of Copenhagen Interpretations. Regardless, the principles of complementarity and uncertainty are universally agreed to sit at the heart of the Copenhagen Interpretation. Broadly, the Copenhagen Interpretation is an epistemic interpretation which argues that quantum states, as described by wave functions, are complete descriptions of quantum reality and that it is impossible to know anything more. Crucially, wave functions are not considered to be ontic entities, but epistemic functions which “represents a tendency for events and our knowledge of events.”

Decoherence: A process in which a quantum system ‘collapses’ into a single state and loses its quantum properties. Interpretations vary n whether they consider decoherence to be an ontic, epistemic, or credal process.

Determinism: The philosophical doctrine that all future states are determined by the laws of physics acting upon present states — all events result from prior causes.

Dynamics: The branch of mechanics which examines the behaviour of systems under the action of forces and other physical constraints.

Entanglement: A phenomenon that occurs when two or more particles interact, and the quantum states of these individual particles can no longer be described independently of each other. It is commonplace to say that these particles are then entangled, however it is more accurate to say that the probabilities of the quantum states of these particles are entangled. Entangled systems appear to be influence each other nonlocally.

Entropy: A measure of the disorder of a physical system.

Epistemology: The branch of philosophy concerned with the study of knowledge and what can be known.

Everettian Quantum Mechanics: An ontic interpretation of quantum mechanics which contends that wave functions are ontologically real and significant. There are no ‘collapses’ in Everettian Quantum Mechanics and thus all possible outcomes are argued to exist on independent ‘branches’ that all coexist. However, what these branches represent — and what is branching — is highly contested. Some argue that the universe itself is branching, and that every interaction leads to the creation (branching) of a new ‘world,’ while others argue that it is ‘mind’ or ‘moments’ that branch. Accordingly, Everettian Quantum Mechanics has diverged into the Many Minds, Many Moments, and Many Worlds interpretations. Broadly, these are all referred to as ‘Many Outcomes’ interpretations.

Field: A physical system which is spread out in space, such as magnetic fields.

Hidden Variables: Unobserved, or unobservable, variables which are postulated to explain the various curiosities extant in quantum mechanics.

Initial Conditions: The known details of a system

Locality: The principle that systems are only directly influenced by what is nearby in space and time.

Nonlocality: Any phenomenon which does not meet the requirements of locality, such as systems which are separated in space influencing each other. Contrary to popular belief nonlocality is not a necessary feature of quantum mechanics and many interpretations of quantum mechanics are unambiguously local.

Ontology: The branch of philosophy concerned with the study reality and what exists.

Quanta: The particle side of wave-particle duality. Also, the smallest transactable unit of something. For example, a photon is a quantum of light as it is impossible to have half a photon.

QBism: QBism, which was formerly known as Quantum Bayesianism, is a credal approach to the interpretation of quantum mechanics which argues that quantum mechanics is a single user decision theory. According to QBism, quantum mechanics is a tool an agent uses to make predictions about the outcomes of experiments.

Quantum International Relations: A rapidly evolving subdiscipline of international relations which considers quantum mechanics to be of material and philosophical importance to social and political affairs.

Quantum Consciousness: A group of hypotheses that argue that consciousness is rooted in quantum phenomena. These hypotheses range from the belief that quantum effects play a key role in the emergence of consciousness to the belief that consciousness is a key part of reality itself.

Quantum State: A complete description of a physical system according to quantum mechanics.

Schrödinger’s equation: An equation used in quantum mechanics to describe the evolution of a wave function.

State: The configuration of a system at a specified time.

Uncertainty Principle: A principle introduced by Werner Heisenberg that states that it is impossible to simultaneously measure both the position and momentum of a particle.

Wave function: Wave functions are representations of the quantum state of a system. The evolution of a wave function is described by Schrödinger’s equation. Interpretations vary as to whether wave functions are considered to be ontic, epistemic, or credal constructs.

Wave-particle duality: A principle of quantum mechanics which states that elementary particles can be described as both waves and particles depending upon their context.