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

Why can't you just turn up the brightness to get electrons flying?

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

How can light speed remain constant even when moving?

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

Why can't you ever see a car zoom by at the speed of light?

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

Can two identical particles ever share the same spot in quantum mechanics?

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

Can two particles talk without ever meeting?

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)

Can a clever trickster change the rules of a game?

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

Why can't you split up the strong force like you split up water?

Asymptotic safety

Why do quarks behave differently at high-energy particle collisions?

Solitary confinement

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

the electroweak unification achieved

Ever wondered why lightning and radio waves behave differently?

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

Why do ice cubes vanish in a glass of water?

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

Why is the night sky not bright if there are infinite stars?

Cosmic inflation

Cosmic inflation explains the universe's uniform temperature

the CMB power spectrum tells us

Ever wondered why the night sky glows uniformly?

Baryon acoustic oscillations

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

Big Bang nucleosynthesis

Why did the universe start with just hydrogen and helium?

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?

Introduction to general relativity

Ever wondered why clocks on fast-moving planes tick slightly slower?

Chronology of the universe

Did you know the universe's first 10 minutes shaped everything we see today?

Speed of light

Does moving faster change how fast light travels?

Global Positioning System

How fast-moving clocks tick differently?

Quark

Why can't you see tiny particles called quarks?

Majorana fermion

Are particles that are their own antiparticles real?

Time

Why do astronauts age slower in space?

Michelson–Morley experiment

Did light speed change with Earth's motion through space?

Expansion of the universe

Why does everything in the universe seem to be moving away from us?

Mathematical formulation of the Standard Model

Ever wondered why particles behave so strangely?

Cosmic microwave background

Did you know the universe's baby picture is everywhere?

Black hole thermodynamics

Black holes aren't just cosmic vacuums; they have a temperature and entropy!

Electron

Ever wondered why some materials heat up quickly while others don't?

The Hunt for Gollum

Superconductors defy normal magnetic rules

Weyl semimetal

Ever wondered how some materials behave like magic in the world of physics?

Electron configuration

Why can't two electrons in an atom be identical twins?

Pauli exclusion principle

Why can't two electrons crash into the same spot?

Spacetime

How does time bend around massive objects?

Jahn–Teller effect

Why do some crystals look distorted?

Schwarzschild radius

How can you compress mass to light speed escape?

Dark energy

Why does the universe keep getting bigger faster?

Information

Can black holes erase information forever?

History of physics

Did Dirac's math hint at a shadowy twin of electrons?

Born–Oppenheimer approximation

Why can't we just treat everything in a molecule as moving together?

Navier–Stokes equations

Ever wondered how airplanes stay aloft?

Emergence

Why do simple ingredients create something complex and delicious?

Discovery of cosmic microwave background radiation

Ever wondered how scientists confirm the universe's explosive birth?

Phase transition

Ever wondered how ice melts or water boils?

Virial theorem

Ever wondered why planets don't just fly off into space?

Differential geometry

Can geometry predict the universe's secrets?

Nobel Prize in Physics controversies

Did you know a tiny particle holds the universe's secret?

First observation of gravitational waves

Did Einstein's wildest dreams come true?

Symmetry in quantum mechanics

Can flipping time keep things spinning just right?

Meissner effect

Did you know magnets can disappear in cold metal?

Planck's law

Did you know light behaves differently at tiny scales?

Gunn–Peterson trough

Why can't we see the universe's infancy clearly?

Coefficient of performance

Can a heat pump be more efficient than just heating or cooling?

Thought experiment

Can a cat really be both alive and dead at the same time?

No-cloning theorem

Can you copy a secret recipe perfectly?

Particle accelerator

Does a car's speed affect the force of the wind hitting it?

Erwin Schrödinger

Can light be both a wave and a particle?

Davisson–Germer experiment

Did light behave like waves or particles? Imagine trying to understand a mysterious shadow

Quantum cellular automaton

Can different systems exhibit the same quantum properties?

Nuclear fission

How do stars make heavy elements?

Force

Why can't you push a magnet to make it move?