The fundamental science of matter, energy, space, and time
Motion, forces, energy, and momentum. Newton's laws govern everyday objects at non-relativistic speeds.
Heat, temperature, and energy transfer. The four laws govern all energy transformations.
Electric and magnetic fields unified by Maxwell. Light is an electromagnetic wave.
Physics at atomic/subatomic scales. Wave-particle duality, superposition, entanglement.
Physics at high speeds. Time dilation, length contraction, mass-energy equivalence.
Gravity as spacetime curvature. Black holes, gravitational waves, the expanding universe.
The Standard Model of elementary particles — quarks, leptons, bosons, and the Higgs field.
Light, sound, and wave behavior — reflection, refraction, diffraction, interference.
| Constant | Symbol | Value | Significance |
|---|---|---|---|
| Speed of Light | c | 2.998 × 10⁸ m/s | Maximum speed in the universe |
| Planck's Constant | h | 6.626 × 10⁻³⁴ J·s | Quantum of action |
| Gravitational Constant | G | 6.674 × 10⁻¹¹ N·m²/kg² | Strength of gravity |
| Elementary Charge | e | 1.602 × 10⁻¹⁹ C | Charge of a proton/electron |
| Boltzmann's Constant | k_B | 1.381 × 10⁻²³ J/K | Links temperature to energy |
| Avogadro's Number | N_A | 6.022 × 10²³ mol⁻¹ | Particles per mole |
| Fine-Structure Constant | α | 1/137.036 | Strength of electromagnetism |
| Electron Mass | m_e | 9.109 × 10⁻³¹ kg | Lightest charged lepton |
1st (Inertia): An object at rest stays at rest; an object in motion stays in motion, unless acted on by a net force.
2nd (F=ma): The net force on an object equals its mass times acceleration.
3rd (Action-Reaction): For every action, there is an equal and opposite reaction.
u = initial velocity, v = final velocity, a = acceleration, t = time, s = displacement
Momentum p = mv is conserved in all closed systems.
In elastic collisions, kinetic energy is also conserved. In inelastic collisions, KE is converted to heat/deformation.
Orbital velocity: v = √(GM/r). Escape velocity: v_e = √(2GM/r)
k = spring constant, L = pendulum length, g = 9.81 m/s²
Zeroth: If A is in thermal equilibrium with B, and B with C, then A is with C. (Defines temperature.)
First: Energy is conserved: ΔU = Q − W. Heat added minus work done.
Second: Entropy of an isolated system never decreases. ΔS ≥ 0.
Third: Entropy approaches zero as temperature approaches absolute zero.
| Process | Constant |
|---|---|
| Isothermal | Temperature (T) |
| Isobaric | Pressure (P) |
| Isochoric | Volume (V) |
| Adiabatic | No heat exchange (Q=0) |
Entropy is a measure of disorder or the number of microstates a system can occupy. The Second Law explains why time appears to flow in one direction — systems naturally evolve from ordered to disordered states.
The heat death of the universe is a state of maximum entropy where no more work can be extracted.
Conduction: Q/t = kA(ΔT/d) — heat flows through a material.
Convection: Heat transferred by fluid motion. Drives weather and ocean currents.
Radiation: P = εσAT⁴ (Stefan-Boltzmann). All objects emit electromagnetic radiation.
Matter changes state at constant temperature by absorbing or releasing latent heat.
| Transition | Energy |
|---|---|
| Solid → Liquid (melting) | Absorbs |
| Liquid → Gas (boiling) | Absorbs |
| Gas → Liquid (condensation) | Releases |
| Liquid → Solid (freezing) | Releases |
k = 8.99×10⁹ N·m²/C² (Coulomb's constant)
Series: R_total = R₁ + R₂ + …
Parallel: 1/R = 1/R₁ + 1/R₂ + …
Kirchhoff's Laws: current at junctions sums to zero; voltages around a loop sum to zero.
Moving charges create magnetic fields. Changing magnetic fields induce electric fields (Faraday's Law). This interplay produces electromagnetic waves — light.
| Type | Wavelength |
|---|---|
| Radio | > 1 mm |
| Microwave | 1 mm – 1 m (approx) |
| Infrared | 700 nm – 1 mm |
| Visible | 400 – 700 nm |
| Ultraviolet | 10 – 400 nm |
| X-ray | 0.01 – 10 nm |
| Gamma | < 0.01 nm |
Lenz's Law: induced current opposes the change that caused it.
Transformers step voltage up or down: V₁/V₂ = N₁/N₂. AC power generation and transmission depend entirely on electromagnetic induction.
Wave-Particle Duality: All matter and energy exhibits both wave and particle properties depending on how it is observed.
Superposition: A quantum system exists in all possible states until measured.
Entanglement: Two particles can be correlated such that measuring one instantly determines the state of the other, regardless of distance.
Uncertainty: Certain pairs of properties (position/momentum, energy/time) cannot both be known precisely.
When electrons are fired at a barrier with two slits, they create an interference pattern — behaving as waves. But when you detect which slit each electron passes through, the pattern vanishes and they behave as particles.
Observation fundamentally changes the outcome. This is the measurement problem at the heart of quantum mechanics.
| Model | Year | Description |
|---|---|---|
| Thomson | 1897 | Plum pudding (electrons in positive mass) |
| Rutherford | 1911 | Nucleus with orbiting electrons |
| Bohr | 1913 | Quantized electron orbits |
| Quantum | 1926 | Probability clouds (orbitals) |
Each electron is described by four quantum numbers:
n (principal): energy level (1, 2, 3…)
l (angular momentum): orbital shape (0 to n−1)
m_l (magnetic): orientation (−l to +l)
m_s (spin): ±½ (up or down)
Pauli Exclusion: no two electrons in an atom share all four quantum numbers.
Lasers: Stimulated emission of photons — light amplification by quantum transitions.
Transistors: Quantum tunneling and band structure underpin all modern electronics.
MRI: Nuclear spin alignment in magnetic fields.
Quantum Computing: Qubits exploit superposition and entanglement for exponential parallelism.
Quantum Cryptography: Eavesdropping is physically detectable via wavefunction collapse.
Einstein's two postulates: the laws of physics are the same in all inertial frames, and the speed of light c is constant in all frames.
At v = 0.87c, γ ≈ 2 (clocks run at half speed). At v = 0.9999c, γ ≈ 70.
Gravity is not a force but the curvature of spacetime caused by mass and energy. Objects follow geodesics (shortest paths) through curved spacetime.
Gμν = curvature, Tμν = mass-energy, Λ = cosmological constant
✓ Gravitational lensing — light bends around massive objects (confirmed 1919)
✓ Gravitational time dilation — GPS must correct for it
✓ Gravitational waves — ripples in spacetime (LIGO detected 2015)
✓ Black holes — regions where spacetime curvature becomes infinite
✓ Expanding universe — GR predicts cosmic expansion (Hubble, 1929)
At the event horizon, escape velocity equals c. For the Sun: r_s ≈ 3 km. For Earth: r_s ≈ 9 mm.
Hawking radiation: quantum effects cause black holes to slowly radiate. A black hole with mass M will evaporate in time t ≈ 5120πG²M³/(ℏc⁴).
One twin travels at near-light speed to a star and returns. Due to time dilation, they age less than the stay-at-home twin. This is real — astronauts returning from the ISS are slightly younger than they would have been on Earth.
GPS satellites: time runs faster in weaker gravity (+45 μs/day) but slower due to orbital speed (−7 μs/day). Net correction: +38 μs/day, or GPS would drift by 10 km/day without it.
Elementary particles that make up protons and neutrons. Never found in isolation (confinement). Carry fractional electric charge.
| Quark | Charge | Mass (approx) |
|---|---|---|
| Up (u) | +2/3 | 2.2 MeV |
| Down (d) | −1/3 | 4.7 MeV |
| Charm (c) | +2/3 | 1.28 GeV |
| Strange (s) | −1/3 | 96 MeV |
| Top (t) | +2/3 | 173 GeV |
| Bottom (b) | −1/3 | 4.18 GeV |
| Lepton | Charge | Mass |
|---|---|---|
| Electron (e⁻) | −1 | 0.511 MeV |
| Muon (μ) | −1 | 105.7 MeV |
| Tau (τ) | −1 | 1,777 MeV |
| Electron neutrino (νe) | 0 | < 1.1 eV |
| Muon neutrino (νμ) | 0 | < 0.17 MeV |
| Tau neutrino (ντ) | 0 | < 18.2 MeV |
| Boson | Force | Mass |
|---|---|---|
| Photon (γ) | Electromagnetic | 0 |
| W⁺ / W⁻ | Weak nuclear | 80.4 GeV |
| Z⁰ | Weak nuclear | 91.2 GeV |
| Gluon (g) | Strong nuclear | 0 |
| Higgs (H) | Mass field | 125.1 GeV |
| Graviton (?) | Gravity | 0 (theoretical) |
| Force | Range | Relative Strength |
|---|---|---|
| Strong nuclear | ~10⁻¹⁵ m | 1 |
| Electromagnetic | Infinite | 10⁻² |
| Weak nuclear | ~10⁻¹⁸ m | 10⁻⁶ |
| Gravity | Infinite | 10⁻³⁸ |
The Standard Model unifies electromagnetic, weak, and strong forces. Gravity remains separate — the great unresolved challenge of physics.
Every particle has a corresponding antiparticle with opposite charge. When a particle meets its antiparticle, they annihilate, releasing energy as photons.
The Big Bang produced equal amounts of matter and antimatter. Why there is more matter than antimatter today — baryogenesis — is one of physics' great unsolved mysteries.
Dark Matter: ~27% of the universe's energy density. Does not interact electromagnetically — invisible but gravitationally detected.
Dark Energy: ~68% of energy density. Causes accelerating expansion of the universe.
String Theory: Proposes fundamental strings vibrating at different frequencies instead of point particles.
Supersymmetry: Predicts partner particles for all Standard Model particles (not yet observed).