Labs
Labs
Virtual experiments: an objective, equipment, step-by-step procedure, then a 3D simulation you can operate yourself.
Newtonian mechanics
Projectile motionNeglecting drag, projectile motion combines uniform horizontal motion with vertical motion accelerated by g.Uniformly accelerated motionConstant acceleration makes velocity change uniformly with time and position vary quadratically with time.Uniform linear motionIn uniform linear motion, an object travels along a straight line at constant velocity; distance grows in proportion to time.Uniform circular motion and centripetal forceIn uniform circular motion, speed is constant but velocity changes direction; centripetal acceleration v²/r requires a net inward force.Newton's three laws, energy, and collisionsThree 3D simulations in one lab: an inclined plane with pulling force and friction, a ball rolling on a track that conserves energy, and two spheres colliding.Work and powerConstant-force work is the force component along displacement times displacement; power measures the rate of doing work.Inertia and balanced forcesAdjust velocity, mass, and applied forces to observe when an object maintains its state of motion.Net force and acceleration on an inclineVary mass, pulling force, slope angle, and friction to see how acceleration depends on net force and mass.Interaction forces and momentum conservationSimulate two colliding spheres to compare interaction forces and total momentum before and after impact.Conservation of mechanical energyWhen only conservative forces do work, a system's kinetic plus potential energy remains constant: K+U=const.Conservation of momentumA system's total momentum remains constant when the net external force is zero or negligible.Gravitation and motion about the center of massExplore two mutually gravitating bodies orbiting their center of mass as mass, separation, and initial speed vary.MomentumMomentum p=mv is a vector describing translational motion; its change is related to impulse.Kinetic energyA mass m moving at speed v has kinetic energy K = ½mv²; net-force work changes its kinetic energy.Gravity and weightMasses attract each other; near Earth, the weight acting on an object has magnitude P = mg.Friction forceFriction opposes relative motion between contacting surfaces; kinetic friction is often modeled as μN.The inclined planeResolving weight parallel and perpendicular to a slope explains motion and friction.Torque and rigid-body equilibriumTorque measures the tendency to rotate about an axis; a rigid body is in equilibrium when net force and net torque both vanish.Moment of inertia and rotational motionMoment of inertia I=∫r²dm measures mass distribution about an axis and is the rotational analogue of inertia.Free fallNeglecting air resistance, an object falling near Earth has gravitational acceleration g ≈ 9.8 m/s², independent of its mass.Gravitational and elastic potential energyPotential energy is associated with position or deformation: near Earth U_g=mgh, and an ideal spring stores U_s=½kx².Elastic collisionsAn elastic collision conserves both the system's total momentum and total kinetic energy.Inelastic collisionsAn inelastic collision does not conserve mechanical kinetic energy; an isolated system still conserves total momentum.Position, velocity, accelerationPosition tells where an object is; velocity describes how quickly and in which direction position changes; acceleration describes how velocity changes.
Thermal physics
Gas lawsExplore how pressure, volume, and temperature of a fixed amount of gas relate in isothermal, isobaric, and isochoric processes.Structure of matter and kinetic theoryMatter consists of microscopic particles in continual motion; absolute temperature is linked to the mean translational kinetic energy of gas molecules.Heat, work, and internal energyExchange heat with gas in a cylinder and track heat, work, and the change in internal energy.Heat transfer and the direction of entropy changeTrack the temperatures of two bodies in thermal contact and their total entropy as heat flows.Heat engines, efficiency, and the Carnot cycleA heat engine converts part of the heat received from a hot reservoir into work and rejects the rest to a cold reservoir; the second law limits its maximum efficiency.Heat and specific heat capacityHeat that changes temperature is Q=mcΔT; specific heat capacity measures how difficult it is to warm a unit mass.Internal energy and its changeInternal energy is a system's microscopic energy; it changes through heat transfer or work done on the system.Ideal-gas equation of stateAdjust temperature, volume, and amount of gas in a cylinder to explore pV = nRT.Melting, vaporization, condensationDuring a phase change, a substance absorbs or releases latent heat; a pure substance's temperature usually stays constant during the transition at fixed pressure.Conduction, convection, thermal radiationHeat moves from hot to cold by conduction, convection, or radiation; multiple mechanisms can occur together.Temperature and its scalesTemperature indicates thermal state; Celsius, kelvin, and Fahrenheit scales are related through fixed points.
Electricity and magnetism
Electromagnetic induction, Faraday–Lenz lawAn induced emf appears when magnetic flux through a circuit changes: $\\mathcal E=-N\,\,d\Phi_B/dt$.Electrical work and powerCurrent transfers electrical energy into other forms. Power is the rate of energy transfer; for a DC circuit, $P=UI$.Electric currentElectric current is the amount of charge passing a cross-section each second; conventional current flows from the positive to the negative terminal through the external circuit.Electric potential and voltageElectric potential is electric potential energy per unit charge; a potential difference determines the change in energy as charge moves.Electric charge and Coulomb’s lawLike charges repel and unlike charges attract; the force between point charges falls with the square of their separation.Electric field and field linesAn electric field describes the electric force on a test charge; field lines show its direction, with their density indicating relative strength.Circuits, Ohm's law, and electromagnetic inductionA 3D circuit with genuinely moving electrons, and a magnet oscillating through a coil to induce an EMF.Coulomb force between two chargesAdjust charge signs and magnitudes and their separation to explore electrical attraction, repulsion, and interaction strength.Faraday–Lenz electromagnetic inductionMove a magnet through a coil and vary its turns to observe induced emf and current.Ohm’s law for a complete circuit and EMFIn a closed circuit with internal resistance r, current is emf divided by total resistance: $I=\mathcal E/(R+r)$.Ohm's law in a direct-current circuitAdjust voltage and resistance to track current, the resistor voltage, and the circuit characteristic plot.Alternating currentAlternating current varies periodically and reverses direction; in a pure resistor, $i=I_0\cos(\omega t+\varphi)$.The Lorentz forceThe Lorentz force is the electromagnetic force on a moving charge, $\vec F=q(\vec E+\vec v\times\vec B)$.Series and parallel circuitsA series circuit carries the same current through its components; parallel branches share the same voltage. These rules determine equivalent resistance.Transformers and generatorsA generator converts mechanical to electrical energy by induction; a transformer changes AC voltage according to its turns ratio.Capacitors and capacitanceA capacitor stores charge and electric-field energy; its capacitance measures charge stored per unit potential difference.Magnetic field and magnetic forceA magnetic field describes magnetic action on magnets and currents; a current-carrying wire experiences F = BIl sin θ.
Optics
Light interference — Young’s experimentTwo coherent slits produce equally spaced bright and dark fringes; the fringe spacing i = λD/a can be used to determine wavelength.Young's double-slit interferenceMeasure the spacing of bright and dark fringes as wavelength, slit separation, and screen distance change.Convex and concave mirrorsA spherical mirror is a reflecting part of a sphere. A concave mirror can converge parallel rays; a convex mirror diverges them and provides a wide field of view.Plane mirrorsWhen a light ray meets a smooth mirror, it changes direction according to a definite rule. The angles of incidence and reflection are measured from the normal at the point of incidence.Refraction of light, refractive indexWhen light crosses a boundary between transparent media, its speed and usually its direction change. The refracted ray bends at the interface.The eye and optical instrumentsThe eye forms a real, reduced, inverted image on the retina; the crystalline lens changes curvature to focus at different distances. Magnifiers, microscopes, and telescopes use lens systems to reveal detail or distant objects.Diffraction of lightDiffraction is the spreading and redistribution of light at an aperture or obstacle; for a single slit, minima satisfy a sinθ = mλ.Polarization of lightPolarization describes the orientation of the transverse electric field; an analyzer obeys Malus’s law, I = I₀ cos²θ, for linearly polarized light.Total internal reflection and optical fibersWhen light travels from a higher- to a lower-index medium above a critical incidence angle, no refracted ray emerges and the light is totally reflected; this guides light in optical fibers.Rectilinear propagation and reflectionIn a transparent, uniform, homogeneous medium, light travels in straight lines. At a smooth mirror, a ray reflects according to a definite law.Dispersion of light and spectraBecause refractive index depends on wavelength, white light separates into colors; in ordinary dispersive glass, a prism typically deviates violet more than red.Converging and diverging lensesA thin lens redirects light by refraction at its two surfaces. For a real object in front of the lens, image position is related to focal length and object distance by the thin-lens equation.
Oscillations and waves
The simple pendulumAt small angles, a simple pendulum oscillates approximately harmonically; its period can be used to measure gravitational acceleration.The spring–mass oscillatorA mass attached to an ideal spring oscillates harmonically, with a period set by its mass and the spring stiffness.Physical and perceptual characteristics of soundPitch relates to fundamental frequency, perceived loudness depends on sound level and hearing, and timbre reflects spectral structure and waveform.Introduction to simple harmonic motionIn simple harmonic motion, displacement varies sinusoidally with time; velocity and acceleration are set by its phase, angular frequency, and amplitude.Introduction to sound wavesSound is a mechanical wave, usually longitudinal in gases and liquids; frequency determines pitch, while amplitude relates to intensity.Introduction to mechanical waves and the wave equationA mechanical wave carries a disturbance and energy through matter; medium particles oscillate about equilibrium.3D wavefronts: circular waves, interference, standing waves, and a quantum fieldFour classical mechanical wavefront patterns, plus a genuinely numerically-solved quantum scalar field for comparison.Damped and driven oscillations; resonanceDamping reduces amplitude; periodic forcing produces driven oscillation, with a large response when the drive frequency is near the natural frequency.Conditions for a standing waveAdjust frequency and length of a string fixed at both ends to observe resonant modes, nodes, and antinodes.Interference of mechanical wavesCoherent waves superpose to form stable reinforcement and cancellation; for in-phase sources, path difference determines the pattern.The Doppler effectRelative motion between a wave source and observer shifts the received frequency; for sound in a stationary medium, approach raises the observed frequency.Energy in simple harmonic motionIn ideal simple harmonic motion, kinetic and potential energies interchange while total mechanical energy is conserved.
Analytical mechanics
Motion in a central field, the Kepler problemThe Kepler problem describes motion under an inverse-square gravitational potential. Symmetry reduces it to radial dynamics and classifies trajectories as ellipses, parabolas, or hyperbolas.Liouville’s theoremHamiltonian flow preserves phase-space volume. For an integrable system with n degrees of freedom, regular invariant level sets are organized as n-dimensional tori.Symmetries and Noether's theoremEach continuous symmetry of the action yields a conservation law: time-translation invariance is associated with energy, and spatial translation with momentum.Generalized momentum and the HamiltonianGeneralized momentum p_i = ∂L/∂q̇_i is conjugate to coordinate q_i; a Legendre transform converts the Lagrangian into the Hamiltonian H.The principle of least actionCompare paths between fixed endpoints and calculate the action of a falling particle to identify the classical trajectory.The Euler–Lagrange equationsThe Euler–Lagrange equations derive motion from a Lagrangian and apply to each generalized coordinate.Hamilton's equations, phase spaceHamiltonian mechanics describes dynamics with canonical coordinate–momentum pairs; phase-space trajectories obey first-order differential equations.Generalized coordinates and degrees of freedomGeneralized coordinates describe a system's configuration after constraints are accounted for; the number of independent coordinates is its number of degrees of freedom.Rigid-body rotation, the gyroscope, Euler anglesThe orientation of a free rigid body has three rotational degrees of freedom. Euler angles provide generalized coordinates for orientation; angular momentum in body and space frames generally point in different directions.
Electrodynamics
Electromagnetic radiation from a dipoleAccelerating charge radiates; in the far zone an electric dipole has a sin²θ angular pattern and average power proportional to ω⁴p₀².Relativistic electrodynamicsElectric and magnetic fields are components of the electromagnetic tensor; Lorentz transformations mix E and B while preserving Maxwell’s structure.Electrostatic fields, conductors, and dielectricsStatic electric fields are sourced by charge; an equilibrium conductor has zero internal field, while a dielectric polarizes in an applied field.The Maxwell equationsMaxwell’s four equations connect charge and current to changing electric and magnetic fields.Electromagnetic waves in vacuumIn source-free vacuum, E and B are mutually perpendicular transverse waves propagating at speed c.Electromagnetic waves in matterMaterial electric and magnetic response changes wave speed, wavelength, polarization, and attenuation.Electromagnetic waves in vacuumExplore the transverse, in-phase electric and magnetic fields and the relation c = fλ.Magnetostatics and the vector potentialSteady currents produce a divergence-free magnetic field; writing B = ∇×A automatically satisfies ∇·B = 0.
Classical statistical mechanics
Phase transitions and critical pointsA phase transition changes a thermodynamic state and is marked by nonanalytic free energy in the macroscopic limit; a critical point terminates a first-order coexistence line.The equipartition theoremAt classical equilibrium, each independent quadratic degree of freedom in the Hamiltonian contributes kBT/2 to the mean energy.Entropy and the generalized second lawStatistical entropy S=kB ln Ω counts compatible microstates; the second law states that total entropy of an isolated system does not decrease.Helmholtz and Gibbs free energiesF=U−TS and G=H−TS are thermodynamic potentials naturally suited to fixed-temperature-volume and fixed-temperature-pressure conditions.Internal energy and enthalpyInternal energy U is a system’s microscopic energy; enthalpy H=U+pV is a thermodynamic potential useful for constant-pressure processes.Maxwell–Boltzmann speed distributionSample molecular velocities in an ideal-gas box and compare the measured histogram with the Maxwell speed law.Statistical ensembles: microcanonical and canonicalA statistical ensemble is a conceptual collection of system replicas used to describe microstate probabilities under specified macroscopic constraints.
Fluid mechanics
Pressure in fluids and atmospheric pressurePressure in a stationary liquid rises with depth; atmospheric pressure is the force per area exerted by the weight of the air.The Venturi tube and airflow past an obstacleA Venturi tube illustrating Bernoulli's law with real fluid particles, and a Lattice Boltzmann simulation of airflow around an obstacle.Archimedes' buoyant force and floatingVary an object's density and volume to observe buoyancy, submerged fraction, and whether it floats, remains suspended, or sinks.Viscosity and the Reynolds numberViscosity describes internal friction in a fluid; the Reynolds number compares inertial and viscous effects to characterize flow regimes.Turbulent flow and the Kármán vortex streetTurbulence features velocity fluctuations and enhanced mixing; flow past a cylinder can shed alternating vortices downstream.Archimedes’ principleAn object immersed in a fluid experiences an upward buoyant force equal to the weight of the displaced fluid.Bernoulli's law in a Venturi tubeAdjust water flow and viscosity to observe speed, static pressure, and losses along a Venturi tube.The continuity equationMass conservation makes the mass flow rate through every section of a steady stream equal.The Navier–Stokes equationsThe Navier–Stokes equations describe momentum balance in a viscous fluid, combining inertia, pressure, body forces, and viscous stress.
Theory of relativity
Relativistic momentum and energy, E = mc²Energy and momentum form the four-momentum; rest mass is invariant and satisfies the energy–momentum relation.Time dilation and length contractionA moving clock accumulates less time between meetings, and a moving object contracts along the direction of motion.Differential geometry and spacetime curvatureThe metric encodes distances and proper time; the Riemann tensor describes spacetime curvature.Minkowski spacetimeSpace and time form a four-dimensional spacetime; events are separated by an interval invariant under Lorentz transformations.The twin paradoxAfter a round trip, the traveler can be younger than the stay-at-home twin because they follow different worldlines and the traveler changes frames while turning around.The Schwarzschild solution and black holesOutside a spherical, nonrotating mass, the Schwarzschild solution predicts an event horizon at the Schwarzschild radius.The equivalence principleWithin a sufficiently small region, a uniform gravitational field is locally indistinguishable from acceleration of the reference frame; this principle motivates general relativity.The Einstein field equationsEinstein’s field equations relate spacetime curvature to matter’s energy, momentum, and stress.Gravitational wavesGravitational waves are propagating spacetime disturbances, emitted strongly by changing, nonspherical accelerating mass distributions.Einstein’s postulates and the Lorentz transformationEinstein’s two postulates lead to Lorentz transformations: physical laws are the same in all inertial frames, and light in vacuum has the same speed c.Mass–energy equivalenceExplore E = mc² through absorbed energy or the photon threshold for electron–positron pair production.
Quantum mechanics
The wavefunction, the Schrödinger equation, and the hydrogen atomA genuine numerical solution of the time-dependent Schrödinger equation in five scenarios, plus a hydrogen-atom electron probability cloud sampled from the exact solution.The quantum harmonic oscillatorThe quantum oscillator has equally spaced levels $E_n=\hbar\omega(n+1/2)$ and a nonzero zero-point energy.The crisis of classical physics and the quantum hypothesisBlackbody radiation and the photoelectric effect motivated energy quanta; light and matter display wave–particle duality.The wavefunction and its probabilistic interpretationThe wavefunction ψ encodes probability amplitudes; |ψ|² is the position probability density, normalized so total probability is one.The particle in a box and quantum tunnelingAn infinite well has discrete energy levels; for a finite barrier the wavefunction decays but remains nonzero beyond it, giving a tunneling probability.Many-body systems and identical particlesExchange symmetry is part of a many-particle state: bosons have symmetric wavefunctions, fermions antisymmetric ones, yielding the Pauli principle.Dirac formalism: quantum states and two-level systemsBra–ket notation compactly represents states and measurements; a two-level system makes coherent evolution and Rabi oscillations explicit.Quantum perturbation theoryPerturbation theory estimates shifts in energy levels and eigenstates when a Hamiltonian is close to a solvable problem.Angular momentum and spinQuantum angular-momentum algebra determines measurement outcomes; Stern–Gerlach experiments reveal quantization and angular-momentum coupling.Uncertainty in position and momentumCompare a wave packet in position space with its momentum spectrum as its width and superposition are varied.The hydrogen atom: energy levels and orbitalsThe Coulomb potential gives hydrogen energy levels indexed by principal quantum number $n$; orbitals $|\psi_{nlm}|^2$ are probability densities, not planetary paths.The Schrödinger equation and wave packetsTrack a quantum wave packet while varying its wave number, width, and potential barrier.Spin and the Pauli exclusion principleSpin is intrinsic quantum angular momentum; the Pauli principle connects fermionic antisymmetry to the impossibility of occupying the same quantum state.Quantum scatteringScattering relates an incident wave to an angular distribution of outgoing amplitudes; the Schrödinger equation and Born approximation predict how an interaction potential shapes it.
Condensed matter physics
Crystal structuresRotate simple-cubic, body-centered-cubic, and face-centered-cubic unit cells and compare their packing fractions.The quantum Hall effectA two-dimensional electron gas in a strong magnetic field develops quantized Hall plateaus; edge states help protect transport.Free-electron gas and the Fermi levelThe free-electron model treats conduction electrons as a fermion gas in a large volume governed by Fermi–Dirac statistics. Filling states at T=0 determines the Fermi surface, Fermi energy, and degeneracy pressure.Band theory and semiconductorsIn crystals, electron states form energy bands; the band gap and Fermi level shape electrical conduction.Bose–Einstein condensation: theoryBose–Einstein condensation is macroscopic occupation of the ground state by bosons at low temperature. For a uniform ideal 3D gas, the critical temperature follows from the density of states; weak interactions, finite size, and trapping modify the threshold and transition.Superconductivity and BCS theoryIn BCS superconductors, an effective attraction pairs electrons into Cooper pairs; their coherent condensate produces a spectral gap and macroscopic electrodynamics.Bose–Einstein statisticsThe Bose–Einstein distribution gives the mean occupation of bosonic states at thermal equilibrium. Bosons are not subject to Pauli exclusion and can share a state; under suitable density and temperature, macroscopic ground-state occupation can occur.Fermi–Dirac statisticsThe Fermi–Dirac distribution describes equilibrium fermion occupations subject to Pauli exclusion. At absolute zero states fill up to the Fermi energy; finite temperature smears the occupation edge.Blackbody radiation and Planck’s lawA blackbody in thermal equilibrium emits a spectrum determined only by temperature. Planck’s law combines electromagnetic mode density with Bose–Einstein photon statistics, resolves the ultraviolet catastrophe, and yields the Stefan–Boltzmann and Wien laws.Topological materialsSome materials are gapped in the bulk yet host distinctive boundary states; topology and symmetry explain their robustness under suitable conditions.
Particle physics
Feynman diagrams and the S-matrixFeynman diagrams encode perturbative terms in scattering amplitudes; the S-matrix connects incoming and outgoing asymptotic states, while vertex factors, propagators, and loop integrals determine amplitudes.Quantization of the scalar fieldQuantizing a scalar field turns each Fourier mode into a quantum oscillator; particle states are field excitations, while the vacuum carries zero-point fluctuations.Particle collisions and curved tracksExplore an electron–positron collision and infer momentum from charged-particle curvature in a magnetic field.The Standard Model: particles and interactionsThe Standard Model describes quarks, leptons, gauge bosons, and three quantum interactions, but excludes gravity and does not fully explain neutrino masses or dark matter.Physics beyond the Standard ModelExtensions such as supersymmetry or grand unification address limits of the Standard Model; they remain research hypotheses, not experimental discoveries.The Higgs boson and Higgs mechanismThe Higgs field has a nonzero vacuum expectation value; coupling to it gives W and Z masses after electroweak symmetry breaking, while the Higgs boson is a field excitation.Quantum chromodynamics (QCD)QCD describes the strong interaction among quarks and gluons carrying color charge; confinement and asymptotic freedom are its central features.Renormalization in quantum field theoryRenormalization absorbs scale-dependent divergences into redefined parameters and fields; observables remain finite, while couplings run with energy scale.The Dirac field and fermionsThe quantized Dirac field describes spin-1/2 particles and antiparticles; anticommutators enforce Fermi–Dirac statistics and the Pauli exclusion principle.Electroweak interactions and QEDQED is the U(1) gauge theory of electromagnetism; electroweak theory unifies it with the weak interaction through SU(2)ₗ×U(1)ᵧ.The weak interaction and CP violationThe weak interaction changes quark and lepton flavor; CP violation in some processes shows that matter and antimatter are not perfectly symmetric under charge conjugation combined with parity.Neutrino physicsNeutrinos are neutral leptons that interact weakly; oscillations among three flavors show that neutrinos have mass and flavor mixing, extending the minimal Standard Model.
Cosmology and astrophysics
Cosmic microwave background (CMB)The CMB is relic light released when the universe became transparent about 380,000 years after the Big Bang. Its temperature map contains tiny fluctuations that seeded cosmic structure.Structure formation and galaxiesTiny density fluctuations in the early universe grow under gravity; dark matter helps form gravitational wells in which gas gathers into galaxies.The Big Bang model and Hubble’s lawOn sufficiently large nearby-universe scales, a galaxy’s average recession speed is proportional to distance. Redshift is an observational signature, not an explosion from a center.Expansion of the universeMeasure the Hubble relation v = H₀d and explore how expansion history and the cosmic microwave background relate to cosmic time.Dark energy and accelerated expansionDistant supernovae, the CMB, and large-scale structure indicate that cosmic expansion is accelerating. “Dark energy” names the component producing this effect in cosmological models.Gravitational waves and multi-messenger astronomyGravitational waves are ripples in spacetime produced by accelerating masses. Combining gravitational signals with light, neutrinos, or cosmic rays probes the same event through different messengers.Dark matterGalaxy rotation curves suggest a gravitating component that does not shine; accelerating cosmic expansion points to a component with negative pressure. The microscopic nature of both remains unknown.
Frontier physics
Optical trapping and laser coolingPhoton scattering provides Doppler cooling, while intensity gradients create dipole potentials that trap atoms.Nuclear structure and nuclear forcesA nucleus is a many-nucleon system bound by residual strong interactions; shell and liquid-drop models capture complementary features.Atomic fine and hyperfine structureRelativistic corrections split atomic levels into fine structure; nuclear–electron magnetic coupling produces hyperfine structure.Fractals in physicsFractal structures exhibit scale-dependent self-similarity over a finite range; fractal dimension quantifies how geometric complexity changes with observation scale.Loop quantum gravitySpin networks quantize spacetime geometry, yielding discrete spectra for area and volume.Nonlinear dynamical systems, fixed points, and bifurcationsNonlinear evolution equations can change stability or their long-term states as parameters vary; fixed points and bifurcations are central tools for analyzing these changes.Lasers and light–matter interactionA laser relies on stimulated emission in a population-inverted medium; resonance governs energy exchange between electromagnetic fields and matter.Bosonic string theory and superstringsOne-dimensional strings vibrate into a particle spectrum; quantum consistency constrains dimensionality and theory structure.Modes of a vibrating stringExplore how harmonics of a one-dimensional string provide an analogy for distinct particle states in string theory.Chaos theory and the butterfly effectA deterministic nonlinear system can be sensitive to initial conditions, causing nearby trajectories to diverge rapidly despite fully specified evolution laws.M-theory and dualitiesDualities relate limits of five superstring theories; M-theory is an 11-dimensional framework without a general microscopic formulation.Quantum cryptographyQuantum key distribution uses measurement disturbance to detect eavesdropping; BB84 illustrates the principle.Nuclear reactions and fissionNuclear reactions conserve charge and nucleon number; fission of heavy nuclei releases energy and neutrons that may sustain a chain reaction.Radioactivity and decay modesUnstable nuclei decay probabilistically; an exponential law describes survival, while each decay mode obeys conservation rules.Qubits and quantum gatesA qubit is a superposition of two basis states; unitary gates act on it, and circuits combine gates with measurement.Quantum entanglement and Bell inequalitiesEntanglement produces correlations incompatible with local hidden-variable models; Bell tests distinguish them from quantum predictions.Quantum error correction and decoherenceQuantum codes protect states without directly measuring encoded information, using compatible syndrome measurements.Quantum algorithms (Shor, Grover)Quantum algorithms use interference and entanglement to speed up selected problems, not every computation.Nuclear fusionFusion combines light nuclei into heavier products. A positive mass defect can release energy, while reaction rates depend strongly on temperature and nuclear cross-sections.The AdS/CFT correspondenceA holographic duality relates gravity in anti-de Sitter space to a nongravitational field theory on its boundary.Plasma physicsA plasma is an ionized medium with collective electromagnetic response; its physics combines particle kinetics, fluid dynamics, and multiscale instabilities.BiophysicsBiophysics uses physical laws and quantitative models to investigate structure, dynamics, and function in living systems across scales.Materials physicsMaterials physics connects microscopic structure, symmetry, defects, and interactions to measurable properties, explaining and designing electrical, thermal, optical, magnetic, and mechanical response.The idea of unifying quantum gravityWhy general relativity and quantum theory call for a common description, and how current research approaches the problem.