In this post, fundamental concepts related to subatomic particles and quantum mechanics are presented. The objective of this post is to provide you a clear and precise understanding of topics related to quantum mechanics, quantum fields and taxonomy of particles. But before, delving into more on these topics, take a look at the picture below, which has the world’s brighest scientific minds together at solvay conference on quantum mechanics in 1927. Most of the ideas in physics that we see today came from the minds of the scientists shown below.

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Solvay Conference on quantum mechanics at the Institute International de Physique Solvay, Brussels, Belgium, in 1927

Particle

Everything in the observable universe is made up of matter. Matter is made up of atoms that is composed of subatomic particles like electrons, protons, neutrons, quarks, neutrinos, muons, tauons etc. Not all particles are responsible for making matter as some of the particles are responsible for carrying electromagnetic forces. The physics of motion and behavior of such subatomic particles are what we know as Quantum mechanics.

Quantum Field Theory

According to quantum field theory, there is a field for creating each type of subatomic particle. This implies that electrons are created from electron field, quarks are created from quark field and so on and so forth. When we provide energy to the respective field, the field reaches to the excited (high energy) state and then the point in the field which has that excited state creates a particle. So, in simpler terms, fields are creators of particles.

Types of Particles

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Standard Model of particle physics

According to Standard Model of elementary particles physics, particles as shown in the figure below are comprised of the following:

  • Fermions (responsible for making matter)

    • Quarks – up, charm, top, down, strange, bottom. These are written in ascending order of their masses.

    • Leptons – electrons, muon, tau, electron neutrino, muon neutrino, tau neutrino. These are written in ascending order of their masses.

  • Bosons (responsible for carrying electromagnetic forces)

    • Gauge bosons

      • Photons – responsible for carrying electromagnetic force. This is also the basic unit of light. They are massless and travels at the speed of light in a vacuum.

      • W/Z Boson – responsible for carrying weak nuclear force.

      • Gluons – responsible for carrying strong nuclear force. It is used to bind the quarks in the proton and neutrons and therby keeping the protons and neutrons inside the nucleus.

      • Gravitons – responsible for carrying gravitational force.

    • Scalar Bosons
      • Higgs Boson (God Particle) – Higgs Boson is a special particle responsible for providing mass to other particles. Higgs Boson are created in higgs field just like other particles are created in their own respective fields. Higgs field is present everywhere in the universe.

Neutrinos (Ghost Particle)

Neutrinos are nearly massless subatomic particles that have no electric charge and therefore interact rarely with their surroundings (matter).

Hadrons

Hadrons comprises the family of composite subatomic particles that has two members – mesons and baryons. Hadrons are made up of two or more quarks like mesons (two quarks) or baryons (three quarks).

  • Mesons This is a type of composite subatomic particles made up of one quark and one antiquark. They are generally of size greater than compared to baryons but are highly unstable and shortly-lived class of subatomic particles.

  • Baryons This is a type of composite subatomic particles made up of three quarks. The most popular type of baryons that can be seen to constitute the matter are protons and neutrons.

    • Protons – This subatomic particle is made up of two up and one down quark and has positive charge.

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    • Neutrons – This subatomic particle is made up of one up and two down quark and has no electric charge.

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Leptons

This is a type of composite subatomic particles that doesn’t participate in the strong interaction.

  • Electrons – This subatomic particle belongs to the lepton family negative charge.

  • Muons – This subatomic particle contains the negative charge but has higher mass in comparison to electrons.

  • Tau – This subatomic particle is also negatively charged but has much higer mass than muons.

  • Electron Neutrino – This subatomic particle contains no charge.

  • Muon Neutrino – This subatomic particle contains no charge but has higher mass in comparison to electron neutrino.

  • Tau Neutrino – This subatomic particle also has no charge but has much higer mass than muon neutrino.

Wave-Particle duality and Quantum superposition

In the world of quantum mechanics, wave-particle duality describes the notion of dual nature of light and matter. In principle, both light (photon particles) and matter (electron particles) possess the unique quality of behaving both as particles and waves. This duality has been studied under the famous double slit experiment which suggests that the particles behave differently considering whether the an object observer is tracking them or not.

Quantum superposition is a phenonmenon that occurs when a particle that can exhibit all the possible states when unobserved. In reality, a particle exhibits only one state when their location is observed or measured. In an unobserved state, all particles behave as wave and it often described as a wave function. It is only until they are measured or observed that their wave function collapses and we get to know their specific state and location. Now, as weird it as it sounds, the real question that arises here would be is that our conscious mind that creates the reality around us? This implies that nothing is real until we see it because we are generating the reality using our mind.

Quantum Entanglement

Quantum entanglement is a phenomenon that occurs when two or group of particles such as photons are behaviourly linked irrespective of the distance between them. This means that when there is change in the state of one particle in one way, then the state of the other particle will be changed in the other way.

Heisenberg’s Uncertainty Principle

It is one of the famous ideas in physics. In simpler terms, it states that it is impossible to simulatenously estimate the position, \( (x) \) and momentum, \( (p) \) of the particle with absolute accurate precision. In mathematical terms, at any given time if we multiply the particle’s position error and particle’s momentum error, then it is always greater than or equal to half of the reduced planck’s constant \( \hbar \).

\[\Delta x \Delta p \geq \frac{1}{2} \hbar \]

\( \Delta x = \) error in true and measured position,

\( \Delta p = \) error in true and measured momentum,

\( \hbar = \) reduced planck’s constant, and is defined as \( \frac{h}{2\pi} \), where \( h \) is the planck’s constant, precisely, \(6.626 \times 10^{-34}\) joule seconds.

Schrödinger’s equation

The schrödinger’s equation is a mathematical equation that is quite similar to the idea of newton’s second law of motion but with a difference. The difference lies in the fact that newton’s second law of motion, \(F = ma\) describes motion and behavior of a physical system on a larger scale but schrödinger’s equation describes motion and behavior of a physical system on quantum (atomic and subatomic) scale using wave function, \( \psi \).

In the most general form, i.e. time-dependent version, the equation is written as:

\[ H(t) \vert \psi(t) \rangle = i \hbar\frac{\partial}{\partial t} \vert \psi(t)\rangle \]

Important – In quantum mechanics, we denote the quantum state by \( \langle \text{bra} | \text{ket} \rangle \) notation which is a vector in hilbert space. The column vector is denoted in \( | \text{ket} \rangle \) notation as \[ |\Psi \rangle = \begin{pmatrix} a_1 \\ a_2 \\ a_3 \end{pmatrix} \] while the row vector is denoted in \( \langle\text{bra} | \) notation as \[ \langle \Psi | = \begin{pmatrix} a_{1}^* & a_{2}^* & a_{3}^* \end{pmatrix} \] where * denotes the complex conjugate of the coefficient. If we have two vectors, \[ \Psi = \begin{pmatrix} a_1 \\ a_2 \\ a_3 \end{pmatrix}, \qquad \Phi = \begin{pmatrix} b_1 \\ b_2 \\ b_3 \end{pmatrix} \] then their scalar product is written as \[ \langle \Psi | \Phi \rangle = a_{1}^{*} b_{1} + a_{2}^{*} b_{2} + a_{3}^{*} b_{3} \]

\( H = \) hamiltonion operator, that describes a set of operations concerning interactions that governs the state of the system,

\( \psi(t) = \) three-dimensional wave function,

\( i = \) imaginary unit, \( i = \sqrt{-1} \),

\( \hbar = \) reduced planck’s constant.

Useful Resources

Standard Model

All About Neutrinos

Quantum Mechanics Maths