Physics

Photoelectric effect

Light comes in discrete quanta, not continuous waves

Einstein's photoelectric explanation used Planck's E=hf to predict that higher frequency light ejects faster electrons

Einstein's photoelectric explanation used Planck's E=hf to predict faster electron ejection with higher frequency light

Brownian motion

Einstein's 1905 paper proved the existence of atoms by explaining pollen's random motion

Special relativity

Albert Einstein's special relativity paper introduced time dilation

Relativity of simultaneity

Simultaneity depends on the observer's motion

Einstein's mass-energy paper was only three pages

Einstein's 1905 paper was just three pages long

Criticism of the theory of relativity

Michelson-Morley experiment null result

Lorentz transformation

Lorentz transformations relate space and time coordinates between two inertial frames

nothing with mass can reach the speed of light

Nothing with mass can reach light speed because Lorentz factor γ → ∞ as v → c

Mass–energy equivalence

E=mc²

Riemannian geometry

Riemannian geometry is essential for understanding curved spacetime

Einstein field equations

Einstein field equations relate spacetime curvature to energy-momentum tensor

Derivation of the Schwarzschild solution

Schwarzschild solution describes spacetime around a massive, non-rotating spherical mass

Schwarzschild metric

Schwarzschild radius at r=2GM/c² marks the event horizon

Kerr metric

Kerr metric describes rotating black hole spacetime

Gravitational lensing formalism

Light bends around massive objects due to spacetime curvature

Tests of general relativity

Light bent by the Sun confirmed Einstein's predictions

Time dilation

Clocks run slower in stronger gravitational fields

Error analysis for the Global Positioning System

GPS satellites must correct for relativistic effects to avoid 10 km/day position drift

Friedmann equations

Friedmann equations govern cosmic expansion in homogeneous and isotropic models

Cosmological constant problem

Vacuum energy predicted 10^120 times too large

Stern–Gerlach experiment

Stern-Gerlach experiment showed quantized angular momentum

Physical paradox

Einstein argued entanglement implied either hidden variables or nonlocality

Bell's theorem

Bell's theorem disproves local hidden-variable theories

Aspect ratio (image)

Bell inequality violations confirm quantum nonlocality

Measurement in quantum mechanics

Quantum states describe probabilities, not certainties

Copenhagen interpretation

Wavefunction collapse is fundamental

Many-worlds interpretation

All outcomes occur in branching parallel universes

Quantum decoherence

Quantum decoherence explains wavefunction collapse through environmental interaction

Path integral formulation

Feynman showed a particle takes all possible paths simultaneously

Feynman diagram

Feynman diagrams revolutionized theoretical physics

Dirac equation

Dirac equation implies existence of antimatter

Spin (physics)

Spin is an intrinsic form of angular momentum carried by elementary particles

the Pauli exclusion principle forbids

Fermions cannot occupy the same quantum state

Spin–statistics theorem

Spin-statistics theorem links particle spin to statistics

Quantum tunnelling

Quantum tunneling allows particles to pass through barriers they cannot classically surmount

Casimir effect

Casimir effect arises from quantum vacuum fluctuations

Aharonov–Bohm effect

Electrons experience phase shifts due to electromagnetic potentials without magnetic fields

Entanglement swapping

Entanglement swapping transfers entanglement between particles

Eastin–Knill theorem

No quantum error correcting code can have a continuous symmetry acting transversely on physical qubits

Noether's theorem

Noether's theorem links continuous symmetries to conservation laws

Symmetry (physics)

Symmetry leads to energy conservation

Angular momentum operator

Angular momentum operator conservation

Gauge theory

Gauge theories are invariant under local transformations

Spontaneous symmetry breaking

Spontaneous symmetry breaking occurs even when laws retain symmetry

Higgs mechanism

W and Z bosons have masses around 80 GeV/c²

Goldstone boson

Goldstone theorem states every spontaneously broken continuous symmetry produces a massless boson

CP violation

CP violation discovered in 1964 neutral kaon decays

CPT symmetry

CPT symmetry is conserved in all physical phenomena

Second law of thermodynamics

Entropy of isolated systems never decreases

Boltzmann's entropy formula

Boltzmann's entropy formula: S = k ln Ω

Demon (thought experiment)

Maxwell's demon challenges the Second Law of Thermodynamics by suggesting information can decrease entropy

Uncertainty principle

Landauer's principle resolves: erasing one bit of information dissipates at least kT ln 2 of energy

Carnot cycle

Carnot efficiency limit: η = 1 - T_cold/T_hot

Equipartition theorem

Equipartition theorem: Each degree of freedom contributes ½kT of energy at thermal equilibrium

Maxwell–Boltzmann distribution

Probability of a state with energy E is proportional to e^(-E/kT)

Bose–Einstein condensate

Bosons collapse into the same quantum state at near absolute zero

Fermi–Dirac statistics

Fermi-Dirac statistics govern fermions' energy distribution

Arrow of time

Arthur Eddington coined the term "arrow of time" in 1927

Standard Model

Standard Model's particle content: 6 quarks, 6 leptons, 4 gauge bosons, 1 Higgs

QCD (quantum chromodynamics) describes

QCD vacuum state characterized by non-vanishing gluon and quark condensates

Asymptotic safety

Quarks interact more weakly at higher energies, earning the 2004 Nobel Prize

Solitary confinement

Free quarks are never observed; they're always bound in hadrons

the electroweak unification achieved

Electroweak unification describes EM and weak forces as aspects of the same force

Higgs boson

Higgs field permeates all space, giving mass to particles

Neutrino astronomy

Neutrinos rarely interact with matter

Supersymmetry

Every fermion has a bosonic partner and vice versa

String theory

Fundamental objects in string theory are 1D strings vibrating in 10 or 11 dimensions

Hierarchy problem

Weak force vs. gravity: 1024 times stronger

Cold dark matter

Dark matter makes up about 27% of the universe

Strong CP problem

Strong CP problem: why does QCD not violate CP symmetry?

BCS theory

BCS theory explains superconductivity through Cooper pairs of electrons

Cooper pair

Cooper pairs are bound electrons with opposite spin and momentum

Topological insulator

Topological insulators conduct on the surface but insulate in the bulk

Quantum Hall effect

Hall resistance Rxy is quantized in units of e²/h

Fractional quantum Hall effect

Hall conductance quantized at fractional values of e²/h

Bose–Einstein condensation of quasiparticles

Bose-Einstein condensation occurs at ultralow temperatures

Ising model

The Ising model describes ferromagnetism using interacting spins on a lattice

Renormalization group

Renormalization group (RG) explains physics changes with observation scale

universality means in phase transitions

Universality in phase transitions implies identical critical exponents across diverse systems

Anderson localization

Anderson localization traps waves in disordered media

Chandrasekhar limit

Chandrasekhar limit is 1.4 solar masses

Type Ia supernova

Type Ia supernovae have a consistent peak luminosity

the Olbers' paradox asks

Olbers' paradox questions why the night sky is dark despite infinite stars

Cosmic inflation

Cosmic inflation explains the universe's uniform temperature

the CMB power spectrum tells us

Cosmic microwave background (CMB) radiation fills all space in the observable universe

Baryon acoustic oscillations

Baryon acoustic oscillations (BAO) provide a "standard ruler" for length scale in cosmology

Big Bang nucleosynthesis

Primordial nucleosynthesis produced hydrogen, helium, and traces of lithium

Penrose–Hawking singularity theorems

Penrose-Hawking singularity theorems predict gravitational singularities under certain conditions

Hawking radiation

Black holes emit Hawking radiation and evaporate over time

Fermi paradox

Information paradox questions black hole information fate

Black-body radiation

Ever wondered why some objects glow red-hot?

Physics beyond the Standard Model

Could the universe be hiding clues about its deepest secrets?

Black hole information paradox

Black holes, once thought to trap everything, might actually leak secrets through Hawking radiation

Twin paradox

Ever wondered why space travel affects aging differently for astronauts?

Theory of relativity

Can gravity bend light?

History of genetics

Did you know pea plants helped uncover genetic secrets?

Electric charge

Does speeding up a charged particle change its electric field?

Theory of everything

Can there be more to reality than we see?