physics01 · an interactive textbook

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The four pillars of the universe — mechanics, electromagnetism, thermodynamics, and the quantum — with labs you can touch.

Classical Mechanics Newton, 1687

Everything that moves obeys three laws. Force changes momentum. Energy is never created or destroyed — only moved around. Master F = ma and you can predict cannonballs, planets, and roller coasters.

The Second Law

F = m · aforce = mass × acceleration

Push something and it accelerates in proportion to the push, in inverse proportion to its mass. This one equation runs all of engineering.

Conservation of Energy

E = ½mv² + mghkinetic + potential = constant

A falling object trades height for speed. The books always balance — energy is the universe's one unforgeable currency.

Gravitation

F = G·m₁m₂ / r²every mass pulls every other mass

The same inverse-square law that drops your coffee keeps the Moon in orbit. Falling is just orbiting interrupted by the ground.

Lab 1 — Projectile Motion

Galileo's insight: horizontal and vertical motion are independent. Set an angle and speed, fire, and watch gravity do the only thing it knows.

Electromagnetism Maxwell, 1865

Four equations unified electricity, magnetism, and light itself. Charges make fields, changing fields make each other, and the resulting wave travels at exactly c — which is how we discovered light is electromagnetism.

Coulomb's Law

F = k·q₁q₂ / r²charges attract or repel, inverse-square again

Same shape as gravity, but 10³⁶ times stronger. The reason you don't fall through your chair is electrostatic repulsion between electrons.

Ohm's Law

V = I · Rvoltage = current × resistance

Voltage pushes, resistance pushes back, current is what gets through. Every circuit you've ever used is this sentence.

The Speed of Light

c = 1 / √(ε₀μ₀)falls straight out of Maxwell's constants

Two numbers measured in a lab with charges and magnets predicted the speed of light before anyone connected them. Possibly the greatest "oh." in science history.

Lab 2 — Wave Superposition

Two waves overlap and simply add. Where crest meets crest: constructive interference. Where crest meets trough: cancellation. Slide the wavelength and source separation.

Bright bands = constructive interference · dark bands = destructive. This is why the double-slit experiment works — and why noise-cancelling headphones work.

Thermodynamics Boltzmann, 1870s

Heat is motion. Temperature is the average jiggle of atoms. And entropy — the universe's tendency to spread out — is why time has a direction and why you can't unscramble an egg.

The First Law

ΔU = Q − Wenergy in = heat added − work done

Conservation of energy, restated for engines. You can't win — the house always balances the books.

The Second Law

ΔS ≥ 0entropy of an isolated system never decreases

You can't even break even. Disorder grows; that's the arrow of time. Every refrigerator, star, and thought you have pays this tax.

Boltzmann's Equation

S = k · ln Wentropy = how many ways the atoms can arrange

Carved on Boltzmann's tombstone. Entropy is counting: there are vastly more disordered arrangements than ordered ones, so disorder wins by sheer numbers.

Quantum Mechanics Planck → Schrödinger, 1900–1926

At small scales nature stops being definite. Particles are waves of probability until measured, energy comes in packets, and knowing position exactly means knowing nothing about momentum.

Planck's Quantum

E = h · fenergy comes in discrete packets

Light isn't a smooth stream — it arrives in grains called photons. h is tiny (6.6×10⁻³⁴), which is why the world looks smooth to us.

Uncertainty Principle

Δx · Δp ≥ ħ/2position and momentum can't both be exact

Not a measurement flaw — a property of reality. A particle doesn't have a perfectly defined position and momentum at once.

Wave–Particle Duality

λ = h / pevery moving thing has a wavelength

Electrons diffract like waves. You have a wavelength too — about 10⁻³⁵ m. Unmeasurably small, so you get to stay solid.

Lab 3 — The Quantum Coin

A qubit can be in superposition: heads and tails at once until observed. Set the probability, flip, and watch the Born rule — |amplitude|² gives the odds.

The histogram converges on |α|² — probability is the square of the amplitude. That squaring is the Born rule, and nobody knows why.

Relativity Einstein, 1905 / 1915

The speed of light is the same for everyone — so time and space must flex to compensate. Moving clocks run slow. Gravity is not a force but the curvature of spacetime itself.

Time Dilation

Δt′ = γ · Δtγ = 1/√(1−v²/c²) — moving clocks tick slower

GPS satellites gain 38 microseconds a day from this (plus gravity). Without the correction, your maps would drift 10 km daily.

Mass–Energy Equivalence

E = m · c²mass is frozen energy

c² is enormous: one gram of mass holds the energy of a small nuclear weapon. The Sun burns 4 million tonnes of itself per second.

Spacetime Curvature

Gμν = 8πG/c⁴ · Tμνmatter tells space how to curve; space tells matter how to move

Gravity isn't a pull — you're following the straightest possible path through bent spacetime. Black holes are where the bending wins.