The Map of Quantum Physics

I’ve been fascinated with quantum physics for a long time, so much so that I completed a PhD in it. I wanted to share the subject with you, so I created this map of quantum physics to outline the ideas within the field, set some boundaries, and introduce you to various concepts that you can explore further if you’re interested. Approaching a complex subject like this can be challenging because it’s hard to know where to start and how all the concepts relate to each other. Hopefully, this will help put everything in context.

First, let’s look at the layout of this map. In the northwest, we have the foundations of quantum physics. As we move south, we transition through quantum phenomena to quantum technology. In the southeast, we find the academic disciplines of quantum physics. At the center is quantum theory, and in the northeast, we explore the theoretical future of quantum physics, beyond what we currently know. That is your quantum forecast for this video. I’ve also made a poster of this available, so if you’re interested, check it out in the description below. Now, without further ado, let’s get started.

The theory of quantum mechanics developed from a set of mysteries in the late 1800s and early 1900s, where reality didn’t quite match the models of physics at the time. We now refer to these older theories as classical physics. There were several clues that pointed to a deeper model of reality. For instance, when light shines through a gas, the gas absorbs and emits specific frequencies of light, known as atomic spectra. This phenomenon lacked a classical explanation, leading to confusion about the stability of atoms. According to classical physics, electrons should continuously radiate energy and collapse into the nucleus. The source of radioactivity was also unknown.

When observing a hot body like the Sun, it emits electromagnetic radiation across various frequencies, a distribution known as blackbody radiation. However, the observed distribution from black bodies did not match the predictions of classical physics. Additionally, shining light on certain metals can cause electrons to be emitted, a phenomenon known as the photoelectric effect. This experiment demonstrated that light behaves not only as a wave but also as a stream of particles, marking the first indication of wave-particle duality. All these mysteries can only be explained through the laws of quantum mechanics.

Let’s take a look at the foundations of quantum mechanics. A cornerstone experiment is the double-slit experiment, where electrons are fired through two thin slits, creating an interference pattern on a detector behind. This pattern is characteristic of waves and serves as further experimental evidence for wave-particle duality. In quantum mechanics, all particles are described as waves through a mathematical construct called a wavefunction. The evolution of this wave over time is governed by the famous Schrödinger equation. However, we can never directly observe these quantum waves; we only detect particles. From the wavefunction, we can predict where particles are likely to appear, but we must first apply a mathematical process called the Born rule to derive a probability distribution.

Quantum mechanics tells us that the universe is fundamentally probabilistic; we cannot know exactly where a particle will appear, only the probability of its location. This leads us to the Heisenberg uncertainty principle, which states that quantum objects do not have definite values for certain pairs of properties, such as position and momentum. This can be illustrated with two images: one showing a particle with a definite position but unknown momentum, and the other showing a motion blur that indicates momentum but leaves the position uncertain.

Another significant equation is the Dirac equation, which extends the Schrödinger equation to include special relativity and describes particles with high kinetic energy. Bell’s theorem is another foundational concept, proving that the uncertainty in quantum mechanics is not due to our ignorance of hidden variables but is a fundamental aspect of the universe. This also leads to the concept of non-locality, which we will encounter later.

Next, we discuss energy quantization, where objects like electrons can only possess certain discrete energy levels when they are in atoms. This is where the term “quantum” in quantum mechanics originates. This quantization occurs because their wavefunctions can only vibrate in specific ways. If we simplify the atom to one dimension, the energy field of the proton can be visualized as a bucket shape, with the electron being attracted to the proton and wanting to fall to the bottom of the bucket. However, as a wave, the electron can only exist in certain modes, similar to the vibrational modes of a guitar string, with higher frequency modes corresponding to higher energy levels.

This also implies that quantum objects always possess a minimum amount of energy known as zero-point energy, which applies not only to electrons in atoms but to everything, including empty space itself.

I understand that this is a lot to absorb if you’re new to the subject. Don’t worry if these terms are confusing; the purpose of this video is to introduce you to various concepts in quantum physics so you know they exist. I can’t cover every detail, or we would be here indefinitely. However, if you want to explore any of these concepts further, I’ve created a playlist of other videos that cover many of them. There are still many gaps in our understanding, and I plan to address them in the future, so if you want to stay updated, consider subscribing to this channel for more information.

Now, let’s continue and examine the interesting properties we observe in quantum systems through quantum phenomena. Particles in quantum mechanics possess many properties. I’ve already mentioned position and momentum, but there are others, including spin, which is a crucial property. Particles are categorized into two groups: bosons, which have integer spin and can occupy the same quantum state, and fermions, which have half-integer spin and cannot share the same quantum state, as described by the Pauli exclusion principle.

Superposition is another property where a particle has a probability of being in multiple states simultaneously, such as being in two different locations at once. This means its wavefunction has values in two different places, although measurement will yield a definite location. While the idea of particles existing in multiple places at once may seem perplexing, it is entirely natural when considering waves; for example, any point on the ocean’s surface is a superposition of countless waves.

You may have heard of Schrödinger’s Cat, a popular illustration of superposition, although it is not particularly helpful. It was originally intended to highlight the absurdity of quantum mechanics, as cats cannot be alive and dead simultaneously. This is true, but not because superposition isn’t real; we now understand that larger objects like cats lose their quantum behavior due to decoherence.

Decoherence occurs when a quantum object interacts with its environment, causing it to lose its quantum characteristics. This process bridges the gap between the quantum realm and our macroscopic world, and coherence is disrupted when measurements are made.

Entanglement occurs when the wavefunctions of two or more particles interact and combine, resulting in them behaving as a single quantum entity. This means that the properties of the entangled particles will be correlated, even if they are separated by vast distances. This phenomenon, where the wavefunction describing a particle extends far beyond the particle itself, is known as non-locality, which is another aspect that does not occur in our everyday experiences.

Several other intriguing phenomena arise solely in quantum systems, including quantum tunneling—the ability of particles to cross narrow barriers due to their wavefunction penetrating through them; superconductivity—the capacity for electrons to move without resistance at low temperatures; and superfluidity—the ability of fluids to flow without viscosity. Other examples include the quantum Hall effect, which involves the quantization of conductance in two-dimensional materials, and the Casimir effect, an attractive force at short distances caused by the exclusion of large quantum waves between two plates.

An important concept in examining the quantum behavior of large systems is phase transitions, which involve shifts from one collective behavior to another. These are analogous to the different phases of matter—solid, liquid, and gas—but in quantum phase transitions, factors such as temperature, pressure, and applied magnetic fields play significant roles.

Whenever we discover new and interesting behaviors in physics, one of the first questions is whether we can leverage this knowledge to develop innovative technologies. Many technologies we use daily exploit the remarkable properties of quantum systems. For instance, lasers utilize a process called stimulated emission to generate beams of light composed of many photons that share the same frequency and phase. Atomic clocks maintain incredibly precise time by using the frequency of light from a specific hyperfine transition in cesium atoms, forming the basis of our global positioning system.

The band theory of solids describes the energy levels of electrons in various solid materials and underpins the semiconductor industry, which has led to numerous technologies, including solid-state transistors—the fundamental building blocks of every computer—LEDs, CCDs used in digital cameras, and solar panels that convert sunlight into electricity.

Electron microscopes, scanning tunneling microscopes, and atomic force microscopes enable us to observe objects that are too small to be seen with optical microscopes, as they can resolve details smaller than the wavelength of visible light, allowing us to visualize viruses or atoms.

Magnetic resonance imaging (MRI) techniques are employed in biology and chemistry, for example, to examine the interior of our bodies. These techniques utilize large superconducting magnets to generate substantial magnetic fields, along with the most sensitive magnetic sensors in existence, known as superconducting quantum interference devices (SQUIDs), which consist of a loop of superconducting wire containing an insulating gap called a Josephson junction.

New technologies are being developed and refined in the realm of quantum information. Quantum cryptography leverages entanglement to create communication that is exceptionally secure, forming the foundation of the quantum internet. Quantum teleportation refers to the ability to perfectly transfer the quantum state of an object from one location to another.

Quantum bits, or qubits, serve as the building blocks of quantum computers, which utilize superposition and entanglement to create states that are nearly impossible to simulate on classical computers. The challenge lies in engineering large groups of qubits that can maintain coherence long enough to perform computations, which is a complex task. However, the potential is enormous because their combined superposition allows them to explore an exponential number of states simultaneously, placing them in a different complexity class compared to the classical computers we use every day.

There are numerous exciting applications for quantum computers, but my favorite is quantum simulation—the ability to model a quantum system, which could be revolutionary for discovering new materials with entirely new properties or for solving computationally intensive tasks like protein folding.

Now, let’s move on to the various fields of quantum physics research. These include condensed matter physics, quantum biology, cold atom physics, quantum chemistry, nuclear physics, particle physics, and theoretical physics.

Condensed matter physics focuses on studying large systems of many atoms in solid or liquid forms, seeking to understand their collective behavior on a quantum level. I’ve placed this here because condensed matter physics encompasses many of these other fields, and condensed matter theory describes the quantum behavior of collections of electrons in solids, explaining collective phenomena like superconductivity and the energy bands of semiconductors.

There are numerous unsolved problems in condensed matter physics; for example, we still lack a theoretical model that explains how high-temperature superconductivity works. In a sense, the frontier of condensed matter physics is complexity, as the subject investigates complex combinations of many atoms, resulting in various materials with different physical and electronic properties. The potential avenues for study are virtually limitless due to the endless combinations.

Quantum biology examines the role of quantum mechanics in biological systems. Many biological processes are challenging to explain without involving quantum mechanics, such as the efficiency of energy transport in photosynthesis, magnetoreception in birds, and the mechanisms behind our sense of smell and sight, as well as how enzymes accelerate chemical reactions.

Cold atom physics, which evolved from condensed matter physics, studies gases that are controlled in magnetic or optical traps and cooled to ultra-low temperatures using laser cooling and other techniques. Cold atom physics investigates many exotic phases of matter, such as Bose-Einstein condensates and Rydberg matter, and explores their behavior, including quantum phase transitions and quantum spin systems. Cold atom experiments can also serve as quantum simulators and sensors, such as gravity sensors.

Since quantum mechanics describes the behavior of electrons in atoms, it also lays the groundwork for the basic principles of chemistry. The Schrödinger equation is used to describe the electronic structure of atoms and how molecules bond and move, a process known as molecular dynamics. Solving the quantum mechanics of molecules is computationally intensive, making computational techniques essential in quantum chemistry. A popular approach is a method called quantum Monte Carlo.

Nuclear physics focuses on the nucleus of the atom and the processes by which nuclei can join in nuclear fusion or split apart in nuclear fission, along with the particles and energy involved in these nuclear reactions. Applications of nuclear physics include nuclear power, nuclear weapons, nuclear medicine, and techniques such as MRI, ion implantation, and radiocarbon dating.

Particle physics, which evolved from nuclear physics, aims to understand the fundamental particles of the universe and their interactions. Experiments in particle physics are conducted in large particle accelerators, where high-energy particles collide to create new particles from the energy of the collision. This field is also referred to as high-energy physics.

The standard model of particle physics describes all known fundamental particles, which have been discovered over many decades, the most recent being the Higgs boson. Feynman diagrams are useful tools for visualizing particle interactions, simplifying the equations of quantum field theory into more manageable illustrations.

The theories within the standard model include quantum electrodynamics, which describes the electromagnetic force; electroweak interactions, which encompass the weak force; and quantum chromodynamics, which describes the strong force. In the standard model, these are all quantum field theories, where particles are understood as excitations of quantum fields that govern their interactions.

There may be other undiscovered particles in the universe. Some researchers propose that dark matter could consist of particles known as weakly interacting massive particles, while the significant discrepancy between the weak force and gravity, known as the hierarchy problem, may be addressed by supersymmetric particles. Thus, the frontier of particle physics involves exploring new methods to investigate the landscape of potential particles at very high energies.

Now, let’s discuss the field of quantum theory, which, although I’ve placed it in this section, actually encompasses the entire map with specific applications in each field. Here are some key aspects of quantum theory worth noting.

The core of quantum physics consists of the postulates of quantum mechanics, which establish the foundational rules. The path integral formulation of quantum mechanics offers an elegant method for calculating particle motion by integrating over every possible path the particle can take. Hilbert spaces serve as a useful framework for describing all possible states of a quantum system within a vast multidimensional space.

The symmetries of quantum mechanics are crucial for understanding conservation laws, which dictate the outcomes of particle interactions based on initial conditions. This is where we encounter the limits of our current knowledge of quantum physics. Two primary areas of theoretical work are focused on extending existing models: interpretations of quantum mechanics, which seek to clarify the counterintuitive implications of the wavefunction, and quantum gravity, which aims to reconcile quantum field theory with general relativity to create a grand theory of everything.

The measurement problem lies at the heart of quantum mechanics interpretations. When we measure a quantum object, its wavefunction abruptly changes upon detection. The laws of quantum mechanics do not provide an explanation for what occurs at the moment of measurement. Furthermore, we do not know if the wavefunction is genuinely real. These conceptual challenges are what the various interpretations of quantum mechanics attempt to address.

For many years, the Copenhagen interpretation was the default perspective, but other popular interpretations include pilot wave theory, the many-worlds interpretation, and quantum Bayesianism, among others. It is too extensive to cover all of them here, but I’ve created another video that delves into this topic.

They are termed interpretations because we currently lack experiments to determine which are valid and which are not; thus, they represent a collection of intriguing ideas rather than established physical theories.

Quantum field theory is the most comprehensive description of reality we possess, merging quantum mechanics with special relativity. However, we know it is not complete, as it does not incorporate general relativity and gravity. Numerous attempts are underway to unify quantum mechanics and general relativity into a grand unified theory. The two main candidates are string theory and loop quantum gravity. String theory, also referred to as M-theory, unifies all consistent versions of string theory.

Testing theories of quantum gravity is challenging because it requires extremely high energies, necessitating a particle accelerator the size of the solar system, with detectors the size of Jupiter. Currently, the best prospects for identifying signatures of quantum gravity involve observing high-energy processes in the universe; signatures from the Big Bang or black holes may provide valuable insights, making this an active area of research.

That’s it—an overview of quantum physics. Congratulations on reaching the end! This is a lot to digest, so don’t worry if you didn’t grasp everything on the first pass. You can always rewatch the video or refer to this image in the future.

This part of the video was sponsored by Brilliant. If this video has inspired you to learn more about quantum physics or improve your math and science skills, Brilliant is an excellent resource. It offers a variety of courses where you can learn and solve problems at your own pace. They have a dedicated section for quantum physics, and actively learning through problem-solving enhances your understanding far more than just watching videos. As I’ve discovered many times, nothing challenges your comprehension like a good question. It’s a fun and engaging way to continue learning.

If that sounds appealing, visit brilliant.org/dos or click the link in the description below, which helps me out as they recognize you came from here. The first 200 people to do so will receive a 20% discount on the annual subscription, granting access to all premium content.

As I mentioned at the beginning of the video, I’m selling this map as a poster, available in my DFTBA store. A big shoutout to everyone who provided feedback on Twitter, especially @physgal and @chriferrie for their contributions. If you’d like to support my work further, I also have a Patreon page. In any case, I’ll continue creating more videos aimed at making science easier to understand. Thank you for watching, and I’ll see you soon!