Contents

Physics

Manhattan Project

Classical mechanics

International System of Units (SI) has seven base units: second, meter, kilogram, ampere, kelvin, mole, and candela. Based on the metre-kilogram-second (MKS) system.

Buckingham π theorem: an equation of n variables in k dimensions can be rewritten in terms of n-k dimensionless parameters. For example f(s, kg, m, m/s^2) is 4 variables in 3 dimensions, so we have the dimensionless quantity gT^2/L = 4π^2. Thus a pendulum has period T = 2π sqrt(L/g).

Kinematics studies the geometry of motion, excluding forces and masses.

Newtonian mechanics studies force as a vector. Newton’s laws of motion:

  1. Inertia: objects have constant velocity without external forces. There is no privieged inertial frame.
  2. F = ma.
  3. Conservation of momentum.

Newton’s law of universal gravitation: F = G m_1m_2/r^2, where the gravitational constant G = 7e-11 N m2/kg2.

Forces: normal force, friction, gravity. Projectile motion, inclined planes, circular motion and centripetal acceleration.

Harmonic motion

Lagrangian mechanics

https://archive.org/details/physicsforentert035428mbp

Thermodynamics

Some math at Thermo.

Ideal gas law. PV = nRT.

In information theory, entropy H = -int p log p.

In statistical mechanics, entropy S = k_B * ln(W), where W is the number of microstates consistent with the observed thermodynamic state.

Gibbs entropy S = k_B * H, where H is the entropy of the Maxwell–Boltzmann distribution, in nats.

Change in entropy dS = dQ/T, so Q = integral dQ = integral T dS

A reversible process does not generate entropy (frictionless, etc).

An ideal cycle is reversible, so net work equals the net heat transfer Q = Q_H - Q_C. The Carnot efficiency eta = work / Q_H = 1 - T_C / T_H.

First law of thermodynamics. Conservation of energy (heat and work). Implies that perpetual motion is impossible.

Second law of thermodynamics. Entropy always increases, or equivalently heat cannot flow spontaneously from cold to hot. Implies Carnot’s theorem that the maximum efficiency of a heat engine is the Carnot efficiency.

Third law of thermodynamics. Entropy S = 0 for a perfect crystal at absolute zero. The ground state is a unique state with minimum energy.

1929. Onsager reciprocal relations relate flows in non-equilibrium systems and irreversible processes. 1968 Nobel Prize in Chemistry.

Potential/Flux Heat Electric Diffusion
Temperature Thermal conduction Seebeck effect Soret effect (thermophoresis)
Voltage Peltier effect Ohm’s law Electromigration
Chemical potential Dufour effect Galvanic cell Fick’s law
Stress Thermoelasticity Piezoelectricity Osmosis

An adiabatic process occurs without heat exchange between the system and its environment.

Carnot cycle: Q = delta T * delta S.

  1. Isothermal expansion: W out, Q in, decreases P, increases V.
  2. Adiabatic expansion: W out, decreases T, decreases P, increases V.
  3. Isothermal compression: W in, Q out, increases P, decreases V.
  4. Adiabatic compression: W in, increases T, increases P, decreases V.

Stirling cycle:

  1. Isothermal expansion: W out, Q in, decreases P, increases V
  2. Isovolumetric cooling: Q out, decreases P
  3. Isothermal compression: W in, Q out, increases P, decreases V
  4. Isovolumetric heating: Q in, increases P

Rankine cycle for steam engines: uses lower temperature steam input

  1. Isobaric heating: Q in
  2. Adiabatic expansion: W out, decreases P, increases V
  3. Isobaric cooling: Q out
  4. Adiabatic compression: W in, increases P, decreases V

Brayton cycle for gas turbines and jet engines:

  1. Isobaric expansion: Q in, increases V
  2. Adiabatic expansion: W out, decreases P, increases V
  3. Isobaric compression: Q out
  4. Adiabatic compression: increases P, decreases V

Diesel cycle: high efficiency, low stress.

  1. Isobaric heating: Q in, increases V
  2. Adiabatic expansion: W out, decreases P, increases V
  3. Isovolumetric cooling: Q out
  4. Adiabatic compression: W in, increases P, decreases V, ignites the fuel.

Otto cycle: gasoline engine.

  1. Isovolumetric heating: Q in (burn fuel), increases P
  2. Adiabatic expansion: power stroke
  3. Isovolumetric cooling: Q out, decreases P
  4. Adiabatic compression

Refrigeration

Irreversible cycles:
Vapor-compression refrigeration consists of a compressor, condenser, expansion valve, and an evaporator.

  1. Adiabatic compression: W in, increases T and P
  2. Hot vapor condenses to a hot liquid: Q out.
  3. Hot liquid is isenthalpically expanded using a thermal expansion valve (aka throttle valve) to become cold (and partly gas).
  4. Cold liquid evaporates to become gas, Q in.

Joule–Thomson effect that most gases cool (positive JT coefficient) and most liquids warm up when expanding: used in the Siemens cycle and Hampson–Linde cycle. Irreversible.
https://en.wikipedia.org/wiki/De_Laval_nozzle

Siemens cycle uses the

  1. Compress the gas to increase temperature.
  2. Cool gas by exchanging with environment.
  3. Cool gas by expanding the gas and doing work.

Hampson–Linde cycle is used to liquefy gases with regenerative cooling.
https://en.wikipedia.org/wiki/Hampson%E2%80%93Linde_cycle
https://en.wikipedia.org/wiki/Regenerative_cooling

https://en.wikipedia.org/wiki/Dilution_refrigerator

Absorption refrigerator such as the Einstein refrigerator.

  1. A mixed fluid is heated so the ammonia refrigerant evaporates out. (Hydrogen is used for pressure balance.)
  2. Refrigerant condenses, releasing heat to the environment.
  3. Refrigerant evaporates (absorbing heat) by being absorbed into water.

Dilution refrigerator cools to 2 mK

Sisyphus cooling

Heat equation and diffusion equation are parabolic.

Fluid and continuum mechanics

See also acoustic engineering.

Density and pressure. Buoyant Force and Archimedes’ Principle.

Bernoulli’s principle is the conservation of energy for flows. For incompressible flows, the sum of static pressure, dynamic pressure (kinetic energy), and hydraulic head (gravitational energy) is invariant.

Pitot tube measures stagnation pressure (or total pressure where gravity is not a factor). It is a tube pointing into the flow of liquid and closed at the other end, to convert all the fluid velocity to static pressure.

Venturi effect. In a constricted pipe, velocity increases proportional to the decrease in cross-sectional area, and the increase in kinetic energy causes a decrease in static pressure. A differential pressure sensor can measure fluid velocity.

Viscosity μ is the internal friction force between layers in relative motion.

Navier-Stokes equations describe the motion of viscous fluids.

Fluid dynamics

Doppler effect: change in frequency due to relative motion. Light sources moving away at relativistic speeds are redshifted.

Slosh dynamics model liquid momentum, inertial waves, and resonance. A slack tank has a free surface is subject to zero parallel shear stress. The free surface effect can cause boats to capsize. Mitigate using baffles.

Pumps

https://en.wikipedia.org/wiki/Turbine
Impulse turbine: change the direction of flow, reduces kinetic energy. Pressure drop at nozzle, and no pressure change in the turbine blades. Useful for low flow and high head.

Reaction turbine: pressure changes as it passes the turbine rotor blades. Useful for high velocity and low head.

For a turbine, the degree of reaction is the ratio of the static pressure drop in the blades to total pressure drop in the stage. An impulse turbine only has a stator.
A Pelton wheel is an impulse water turbine where water flows into and turns spoon-shaped buckets. It is optimal for high hydraulic head and low flow rates.

Ships
A ducted propeller improves thrust at very low speeds (tugs and trawlers).

TODO Kort nozzle

Surface ships use waterjets with outlet above the waterline and axial flow impellers. Cavitation occurs at
A pumpjet is integrated behind the hull, axial duct, and stator to reduce rotational energy output. Lower internal pressure (due to higher internal velocity) allows higher speed before cavitation.

An azimuth thruster or azipod can rotate horizontally. It is more maneuverable than a rudder.
harbor pilot
mooring lines to the dock
whitecaps 20 knots

https://en.wikipedia.org/wiki/Fluid_mechanics

https://en.wikipedia.org/wiki/Template:Rivers,_streams_and_springs
https://en.wikipedia.org/wiki/Template:Agricultural_water_management
https://en.wikipedia.org/wiki/Template:Agricultural_water_management_models

Optics

Spectrum: radio, microwave, infrared, visible, ultraviolet, X-ray, gamma ray. Earth atmosphere is visible to radio and visible radiation.

Refraction

Transverse waves oscillate perpendicular to the direction of motion, while longitudinal waves oscillate in the direction of motion.

Polarization is the direction of oscillation, determined by photon spin.

An electromagnetic wave causes electrons in a material to oscillate proportional to the material’s magnetic susceptibility. This induces a phase-delayed wave of lower amplitude at same frequency. Phase 180 destructively interferes (light absorption). Phase 90 slows down the wave.

A rainbow is created when light from the sun enters a water droplet, reflects off the back, and passes back out of the droplet. Refraction causes the light to return at a 42° angle. Dispersion refracts blue light at a larger angle, and after the reflection, red light emerges at a larger angle, on the outside of the rainbow.
The antisolar point is the point on the celestial sphere directly opposite the sun.
A Brocken spectre is a midair shadow cast on fog. Depth perception is difficult, so the shadow can appear larger and further away that it really is.
Heiligenschein or hot spots are bright spots around a shadow in the presence of dew droplets, which act as lenses.

Rayleigh scattering (1971) is inelastic (energy-preserving) scattering due to polarizable molecules smaller than the wavelength of light. An electromagnetic wave causes the molecule to oscillate and radiate light. Blue light is scattered more than red light, so diffuse sky radiation is blue. In sunset, rays pass through up to 40 times more atmosphere, and blue light is scattered away. It scatters up to 0.1% of photons.

Raman scattering is elastic scattering, where a molecule gains vibrational energy from incident photons. It scatters ~1 ppm of photons.

Diffraction is a wave phenomenon. The classical Huygens–Fresnel principle states that every point on a wavefront is itself the source of spherical wavelets. For example, when a plane wave encounters a slit, it creates spherical ripples instead of a shadow. The small opening acts as a point source. For light, the source is a dipole, so waves are only emitted in the forward direction. The secondary waves can interfere with each other, producing bands of high and low amplitude. For light to exhibit wave properties, the slit should be comparable in size to the wavelength.
The double-slit experiment demonstrates wave–particle duality. A source can emit single photons or even electrons which are clearly detectable as individual particles hitting a screen. But the spatial bands still show wave interference.

Fluorescence: emit light at a different wavelength. Antifreeze contains fluorescein to detect radiator leaks.
Phosphorescence: emit light at a later time, usually at a longer wavelength.

Optical fiber: core has a higher refractive index than the cladding.

Optical pumping: add photons with the exact transition energy, achieving population inversion.

Optical module is an optical transceiver between electrical systems and fiber optic cables.

Optical amplifier: pump laser achieves population inversion. Signal light can stimulate excited atoms in the doped core to emit a photon at the same wavelength, which cascades.

An optical circulator is a passive non-reciprocal device, where light entering one port exits the next port with low loss (1 dB) and high isolation (20 dB) of the other direction.

https://en.wikipedia.org/wiki/Dichroism
https://en.wikipedia.org/wiki/Pleochroism

X-rated ptychography requires high energy x-rays.

The dress (2015) is a viral phenomenon about unusually large differences in perceived color. The photo of a blue and black dress under yellow illumination can also be interpreted as a white and gold dress under blue illumination.
https://en.wikipedia.org/wiki/The_dress#See_also

Lateral inhibition of neurons

The spectral power distribution is the radiant exitance by wavelength.
Photopic vision occurs in well-lit conditions (10 to 10^8 cd/m^2) via cone cells, which have peak absorption at 420 nm (blue), 534 nm (bluish green), and 564 nm (yellowish green). Color vision is limited to 400 to 700 nm.
Scotopic vision is vision in dark conditions. Rod cells are most sensitive to 498 nm wavelength.

A Lambertian reflector is an ideal matte surface, with reflected radiance the same in all directions, following Lambert’s cosine law: radiant intensity is proportional to the cosine between the observer’s line of sight and the surface normal.

Color

A staring array uses an array of sensing pixels. A push broom scanner or along-track scanner sweeps a scan line. A whisk broom scanner or across-track scanner sweeps a single detector in 2D.

Projection of an object onto the projection plane or image plane

Relativity

Special relativity is the theory of spacetime. It postulates that the speed of light in vacuum is the same for all observers, and that the laws of physics are invariant in all inertial frames of reference. It predicts mass-energy equivalence, E = mc^2. It is the an approximation of general relativity for flat spacetime or Minkowski space.

In Minkowski space, an event is described by the 4-position (ct, x, y, z). The speed of light converts time units to space units. The metric tensor is 1 0 / 0 -I_3 (metric signature +—).
The spacetime interval is invariant in all coordinate frames, whereas time intervals and lengths are not. Intervals traveled by light are lightlike, with s^2 = 0. Intervals traveled by massive objects are timelike: s^2 > 0. Spacelike intervals have s^2 < 0. The light cone at a given point defines timelike past (causal influences), timelike future (causal effects), and spacelike (causally unrelated events). Simultaneity is relative for spacelike-separated events.
The proper time interval, elapsed time as measured for a clock following the line, is invariant for timelike world lines.
The Lorentz transformation transforms spacetime coordinates between inertial frames with different relative velocities, explaining length contraction and time dilation.
A particle with 3-position r(t) and 3-velocity u = dr/dt has Lorentz factor γ(u) = 1/sqrt(1 - |u|2/c2).
In the instantaneous rest frame where the particle is always at rest, we have dr = 0 and ds^2 = c^2 d𝜏^2. For another frame, we have ds^2 = ct^2 - dr^2. Thus the time dilation is dt = γ(u) d𝜏.
The four-velocity U = dX/d𝜏 = dX/dt dt/d𝜏 = γ(u)(c, u), and the magnitude |U| = c.
The four-momentum P = m_0 U = m_0 γ(u)(c, u) = (E/c, p) for rest mass m_0. We have |P|^2 = m_0^2 c^2 = (E/c)^2 + |p|^2. The energy–momentum relation E^2 = (pc)^2 + (m_0 c2)2 decomposes energy into momentum and rest mass.

Geometrized units set c = 1, dimensionless, making time and length equivalent. Mass is the magnitude of the four-momentum vector, so it must have units of length, so the gravitational constant G = 1. The Schwarzschild radius of a black hole with mass m becomes r = 2m.

Cosmological constant problem. The theoretical zero-point energy from vacuum fluctuations of matter fields and force fields is 1e60 higher than the vacuum energy density implied by the observed cosmological constant.

General relativity is the theory of gravitation. The curvature of spacetime is related to the stress–energy tensor representing the density of energy and momentum. Spacetime curves with matter, propagates waves, bends light, etc.

Lorentzian manifold.

A metric tensor is a bilinear form. It gives infinitesimal distance on a manifold, and allows computing distances on the manifold by integration.

The Einstein field equations are G_{μν} + Λ g_{μν} = κ T_{μν}.

FRW metric (Friedmann–Lemaître–Robertson–Walker or FLRW).
-c^2 d𝜏^2 = -c^2 dt^2 + a(t) dΣ^2
Σ ranges over a 3D space of uniform curvature, and a(t) is the cosmic scale factor that characterizes the expansion of the universe.

ΛCDM (lambda cold dark matter) is the standard model of Big Bang cosmology based on general relativity.
The Hubble constant H = a’/a.
For a Λ-dominated universe, the Friedman equations state that H = H_0 * sqrt(Ω) is a constant, which implies exponential growth.

Consider a perfect fluid described by scalar field ϕ with time derivative ϕ’, pressure P, energy density ρ, potential energy V(ϕ), and four-velocity u_μ.
The energy-momentum tensor is T_{μν}=(ρ+P)u_μ u_ν +Pg_{μν}.
Equation of state parameter w = P / ρ = (1/2 ϕ’^2 - V(ϕ)) / (1/2 ϕ’^2 + V(ϕ)). Positive vacuum energy implies w = -1 and negative pressure.

https://en.wikipedia.org/wiki/Wilkinson_Microwave_Anisotropy_Probe

Quantum mechanics

Quantum states have unit 2-norm. (In contrast, classical probabilities sum to 1 or have unit 1-norm.) A binary state or qubit (a, b) has outcomes with P(0) = a^2 and P(1) = b^2. In Dirac notation, a qubit is a|0> + b|1>, where a is the amplitude of outcome |0>. Stochastic matrices contain columns of nonnegative real numbers that sum to 1. For example, a bit flip is ((0 1) (1 0)).
Negative amplitudes enable quantum interference. Consider the counterclockwise 45 degree rotation matrix ((1/√2 -1/√2) (1/√2 1/√2)). Rotating the state |0> leads to an entangled state, but rotating again causes destructive intereference between the paths to |0>.
Operations are unitary matrices. Amplitudes can be complex numbers so that every unitary operation, such as the mirror transfrom ((1 0) (0 -1)), has a square root.

A wave function \(|\phi\rangle\) represents a quantum state at a fixed time. \(\phi\) maps its domain (e.g. position) to probability amplitudes (complex numbers). The wave function represents a vector in the state space H, the complex Hilbert space over wave functions.
Q: why do we need probability amplitudes?

Born rule. The probability of an observation is proportional to the square of the amplitude of the wavefunction (projection onto the corresponding eigenvector). This implies that \(E[A] = \phi \dot A\phi\). They can be normalized to unit L2 norm and are generally restricted to be square-integrable (L2 norm exists). Operators are unitary, satisfying \(U^*U=UU^*=I\), the complex analogue of an orthogonal matrix which preserves vector norms.

A metric space M is complete if every Cauchy sequence in M has a limit that is also in M (there are “no points missing”).
A Hilbert space H is a vector space that is also a complete metric space with the induced distance function. For a complex Hilbert space, the inner product is conjugate symmetric (aka Hermitian symmetric): \(<y, x> = \overline{<x, y>}\).
A Banach space is a space that is complete under the metric induced by a norm. A Hilbert space is an inner product space that is a Banach space.

An observation collapses the state space so that only outcomes consistent with the observation are possible. The new state is the projection onto the eigensubspace associated with the observation.
An observable represents a measurable physical quantity. The possible result are its eigenvalues. Real-valued eigenvalues imply that an observable is a self-adjoint operator, or a Hermitian matrix in finite dimensions. A Hermitian matrix is equal to its conjugate transpose, the complex analog of a symmetric matrice. More generally, a self-adjoint operator is a linear endomorphism that is its own adjoint. The Hermitian adjoint operator A* generalizes the conjugate transpose of a matrix and is defined as \(\langle Ax,y \rangle = \langle x,A^*y \rangle\).
https://en.wikipedia.org/wiki/Bra%E2%80%93ket_notation

Conjugate variables are Fourier transform duals.
Noether’s theorem states that a symmetry with respect to one conjugate variable implies that the other conjugate variable will not change with time (i.e. it will be conserved).
A Fourier transform maps wave functions over position to wave functions over momentum. (Pontryagin duality)

Complementary properties cannot be measured simultaneously because their observables are incompatible or fail to commute.
The Heisenberg uncertainty principle states that
\(\sigma_x\sigma_p\geq {\frac{\hbar}2}\). For a general operator, \(\sigma_O = \sqrt{E[O^2] - E[O]^2}\) and the commutator is \([A, B] = AB - BA\), and \(\sigma_A\sigma_B \geq \left|\frac1{2i} \langle [A, B]\rangle\right|\).
Quantum entanglement.

Canonical commutation relation. For any conjugate variables \(x\), \(p\), the commutator \([x, p] = i\hbar I\).
\(i\hbar {\frac {d}{dt}}|\psi (t)\rangle =H(t)|\psi (t)\rangle\). The time derivative of a quantum state is \(-i/\hbar H\).
The Schrödinger equation gives the evolution over time as a unitary transformation on the initial state: \({|\psi (t)\rangle =U(t;t_{0})|\psi (t_{0})\rangle }\).

The Hamiltonian operator is the observable corresponding to the total energy of that system. The energy spectrum is the set of possible outcomes obtainable from a measurement of the system’s total energy.
For a single particle of mass \(m\), H = T + V for potential energy V and kinetic energy $T = $.
The momentum operator \(p =-i\hbar \nabla\), and kinetic energy \(T = p^2 / 2m\).

The Planck constant \(h\) is the product of the wavelength lambda of a particle and its momentum p.
For a photon, E = hf. The reduced Planck constant \(\hbar = h/2\pi\) relates energy to angular frequency (radians per second), explaining the photoelectric effect.
Matter waves are also known as de Broglie waves. Momentum \(p = \hbar k\), where k is the wave vector in inverse meters.

Fermi energy is the difference between the highest and lowest occupied single-particle states in a quantum system.

Particle in a box model: in classical systems, a particle can move at any speed, whereas at nm scale, particle energy levels are discretized and it can never have zero energy level.

Quantum harmonic oscillator

Quantum numbers are conserved quantities that can be measured together as eigenvalues of operators that commute with the Hamiltonian.

https://en.wikipedia.org/wiki/Wave_packet
https://en.wikipedia.org/wiki/Particle_in_a_box
https://en.wikipedia.org/wiki/Quantum_harmonic_oscillator
https://en.wikipedia.org/wiki/Quantum_uncertainty
https://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics
https://en.wikipedia.org/wiki/Copenhagen_interpretation
https://en.wikipedia.org/wiki/Wave_function_collapse
https://en.wikipedia.org/wiki/Template:Quantum_mechanics_topics

Quantum information theory

Particle physics

Quantum field theory (QFT) treats particles as excited states of their underlying quantum fields. Particle motion is described by minimizing the action of the Lagragian, a functional of the particle field.
A gauge theory is a field theory where the Lagriangian (the system dynamics) is gauge invariant under local symmetry transformations. The symmetry group (Lie group or gauge group) forms a Lie algebra of group generators. Each group generator produces a gauge field. An abelian gauge theory has a commutative symmetry group.
In the fiber bundle formulation, a gauge theory studies parallel transport connections on vector bundles, principal bundles, and fibre bundles. The theory associates a fiber, a copy of the gauage group G, at each point in spacetime. A fiber bundle is a space that is locally a product space R^d x G, but can have some global twisted topology. A loop representation is in the space of Gauss gauge invariant physical states, avoiding the redundancy of Gauss gauge symmetries.
A Wilson loop W[γ] is a gauge invariant operator arising from the parallel transport of a gauge variable around a closed loop. It is an order operator whose expectation characterizes phase transitions. It is defined as the trace of closed Wilson lines. The confining phase is described by the loop in spacetime traced out by a quark–antiquark pair created at one point and annihilated at another point. The action of the loop E[W[γ]] follows the area law. In the nonconfining Higgs phase, the expectation follows the perimeter law.
The S-matrix or scattering matrix is the unitary matrix connecting sets of asymptotically free particle states.
https://news.ycombinator.com/item?id=40456801

A special unitary group is the Lie group of unitary matrices with determinant 1.
The three Pauli matrices is the observable representing spin in the three spatial dimensions. They are unitary, with eigenvalues 1 and -1. They span the Lie algebra of the SU(2) group.
The eight Gell-Mann matrices span the Lie algebra of the SU(3) group.
https://en.wikipedia.org/wiki/Exponential_map_(Lie_theory)

The Standard Model describes the electromagnetic, weak, and strong interactions. It classifies all known elementary particles into bosons and fermions.
Bosons are the quantized exchange interactions or force carriers for gauge fields: photon (EM), W and Z bosons (weak), eight gluons (strong), and the scalar Higgs boson. They have integer spin and obey Bose–Einstein statistics.
Fermions include quarks and leptons. Fermions have half-integer spin and obey the Pauli exclusion principle and Fermi–Dirac statistics.
Symmetrization postulate: the wavefunction in 3D of a system of identical particles is either totally symmetric (bosons) or totally antisymmetric (fermions) when exchanging two particles. It implies the Pauli exclusion principle that two fermions cannot share the same set of quantum numbers.
https://en.wikipedia.org/wiki/Mathematical_formulation_of_the_Standard_Model

Quantum electrodynamics (QED) is an abelian gauge theory with symmetry group U(1) and the electromagnetic four-potential gauge field quantized as the photon. Theory of wave-particle duality.

Yang-Mills theory is the field theory of special unitary groups.

The weak force SU(2) has three force carriers: W and Z bosons, where W bosons have spin 1 and -1. There are two types of interactions, where current refers to the exchange of the boson.

W bosons mediate charged current interactions. Weak isospin is a 3D vector T with T_3 being important. It is conserved in electroweak and strong interactions. Higgs interactions do not conserve weak isospin but does conserve charge Q = T_3 + 1/2 Y_W. Weak hypercharge Y_W corresponds to the gauge symmetry U(1).

The Z boson mediates neutral current interactions. The weak charge Q_w quantifies the force of the interaction. e- -> e- + Z, and \(Z \rightarrow b + \overline{b}\): an electron emits a Z boson, which decays rapidly.

Weak isospin describes interaction with W bosons; color charge for gluons (strong force).
https://en.wikipedia.org/wiki/Weak_isospin
The Higgs field is the only scalar field with two neutral and two electrically charged components. It is nonzero everywhere, breaking the weak isospin SU(2) symmetry. The Higgs mechanism is responsible for all rest masses in the Standard Model.
Leptons are fermions that do not undergo strong interactions. They can be charged or neutral: (1) electron and electron neutrino ν_e, (2) muon and muon neutrino, and (3) tauon and tauon neutrino. Neutrino oscillation implies that the neutrino has mass. The Koide formula is an intriguing empiral relation between the masses for the three generations. The Deep Underground Neutrino Experiment (DUNE) at Fermilab studies proton decay.

Quantum chromodynamics (QCD) is the nonabelian gauge theory SU(3) of the strong force, which acts on quarks through gluons. Isospin is a symmetry of the strong interaction under the action of SU(2). The isospin operator is vector-valued. I_3 is the eigenvalue of the I_Z projection, which is a Pauli matrix 1/2 𝜏_3.
Gluons come in eight types, identifiable by superpositions of color-anticolor states. The color singlet state (equal probability of all three color-same anticolor states) is excluded. Thus there are eight possible types. In asymptotic freedom, the strong force decreases at high energies and short distances, so that quarks can move freely inside protons.
Quarks have charge +2/3 or -1/3, and come in three generations: (1) up and down, (2) charm and strange, (3) top and bottom. Up and down quarks have isospin +1/2 and -1/2. Heavier generations have isospin 0 and are more rare. Quarks also have color charge (rbg), which ensures color confinement. The gluon field between a quark and antiquark forms a flux tube or string between them with constant force (10 kN), and the work required to separate them quickly exceeds the energy need for a new quark-antiquark pair to appear.
Hadrons are composite particles made up of quarks bound by the strong force. Baryons are fermions with an odd number of quarks, mainly three quarks of different colors. E.g. protons (uud) and neutrons (udd). Mesons are bosons with quarks paired in singlets, mostly pions (quark and antiquark).

CPT symmetry. Any Lorentz invariant local quantum field theory with a Hermitian Hamiltonian.

Photoelectric effect: quantized photon energy proportional to frequency. Can also emit photons: photoluminescence.

Black-body radiation. Quantization is needed to explain why the ultraviolet catastrophe does not happen–why there is not unbounded radiation at high frequencies. The equipartition theorem in classical statistical mechanics states that each degree of freedom (frequency) has an average energy of k_B T. But the number of harmonic oscillator modes per frequency increases unboundedly.

The mass number A is the sum of atomic number (proton number) Z and neutron number N.

Condensed matter physics

Superfluids can flow without energy dissipation.

Superconductors have zero resistance below a critical temperature Tc.

The thermal de Broglie wavelength is the average de Broglie wavelength of particles in an ideal gas at a given temperature. When particles are usually closer than this distance, the gas must be treated as a Fermi gas or a Bose gas: Bose–Einstein statistics or Fermi–Dirac statistics. When particles are further apart, they can obey Maxwell–Boltzmann statistics.

Ionization produces an ion pair: an electron and a positive ion.
A Townsend avalanche is a cascade of gas ionization. An electric field accelerates each freed electron to free additional electrons.
A gaseous ionization chamber has an electric field to prevent ion pairs from recombining. It uses a cylinder with a coaxial anode wire or parallel plates. It lasts longer in high radiation fields.
A proportional counter measures the energy of ionizing particles to determine absorbed dose or distinguish between alpha and beta particles. A medium electric field creates an ion drift region, where the number of ion pairs is proportional to the energy of the ionizing particle. A 1 MeV particle can create about 30,000 ion pairs. Near the anode wire (<1 mm), the field is strong enough to amplify signal through localized avalanches.
A wire chamber uses a grid of wires acting as proportional counters. A micropattern gaseous detector (MPGD) has a sub-millimeter grid. The MicroMegas detector (1992) has a gain of 10,000. A gas electron multiplier consists of a thin polymer sheet layered with copper on both sides, with a voltage difference. Photolithography creates uniform small holes, and a single ion entering a hole can emit up to 1,000 electrons. A triple stack can result in a gain over 1 million.

A cloud chamber is saturated with water vapor. A charged particle traces a track of ionized gas particles, which form condensation centers. A magnetic field results in a radius of curvature of a charged particle proportional to its momentum.
A bubble chamber is filled with superheated liquid. A charged particle creates ions surrounded by vapor, and decreasing the pressure grows the bubbles to visible size.

Compton scattering. A high-frequency photon releases electrons from an atom.
https://en.wikipedia.org/wiki/Cherenkov_radiation
Second: Caesium standard

https://en.wikipedia.org/wiki/LIGO
https://en.wikipedia.org/wiki/Black_hole_thermodynamics
https://en.wikipedia.org/wiki/Holographic_principle
https://en.wikipedia.org/wiki/Bogomol%27nyi–Prasad–Sommerfield_bound
String theory
https://en.wikipedia.org/wiki/History_of_string_theory
https://en.wikipedia.org/wiki/M-theory
https://en.wikipedia.org/wiki/AdS/CFT_correspondence
https://en.wikipedia.org/wiki/Template:Breakthrough_of_the_Year

A particle acclerator accelerates charged particles to relativistic speeds.

Nuclear power plants

The Large Hadron Collider LHC can accelerate protons to 7 TeV in a 17 mi circumference ring.
https://en.wikipedia.org/wiki/COMPASS_experiment
https://en.wikipedia.org/wiki/Super_Proton_Synchrotron
CMS
ATLAS
ALICE
LHCb

A tokamak confines plasma in a toroidal chamber with magnetic coils.

https://en.wikipedia.org/wiki/Template:Beyond_the_Standard_Model

Nuclear reactors have become safer, more modular, with less waste, and more fuel efficient.

Fusion power