Physics

Before any law, the equipment: what a quantity is, what a unit is, and how to tell a real result from a rounding artefact. Skip this and every later module quietly punishes you.

• What a measurement actually isIf I hand you a number, what has to be true for it to mean anything?
• Dimensional analysis as a reasoning weaponCan I guess the form of a law before I derive it?
• Uncertainty, significant figures, error propagationHow wrong is my answer, and how do I say so honestly?
• Fermi estimationHow do I get within a factor of ten of an answer I have no data for?
• Vectors, coordinates, and why frames matterWhat part of a description is the world, and what part is my choice of axes?

Galileo's insight that motion needs no cause, made quantitative by Newton. This is the first time in your education that a few lines of algebra genuinely predict the future.

• Describing motion before explaining itCan I describe how something moves without knowing why?
• Projectile and two-dimensional motionWhy can I treat horizontal and vertical motion as two separate problems?
• Newton's three laws, read as definitionsIs F = ma a discovery, or a definition of what we mean by force?
• Friction, tension, normal force, dragWhich forces are fundamental and which are bookkeeping for something messier?
• Circular motion and centripetal forceIf speed is constant, why is there any acceleration at all?

The shift from forces to conservation laws. Instead of integrating the whole messy interaction, you compare the before and the after — which is why this module feels like a cheat code.

• Work and the work–energy theoremWhy is ½mv² the combination that matters, and not mv or mv³?
• Potential energy and conservationWhat does it mean for energy to be 'conserved' if I cannot point at it?
• Momentum, impulse, and collisionsWhy does momentum survive collisions that destroy kinetic energy?
• Rotational kinematics and dynamicsWhy does the same mass resist spinning differently depending on where it sits?
• Angular momentum and gyroscopesWhy does a spinning top refuse to fall?
• Universal gravitation and Kepler's lawsCan one inverse-square law produce all three of Kepler's rules?

Everything that returns to where it started obeys nearly the same equation. Learn it once here and you will meet it again in circuits, in quantum mechanics, and in the LIGO detector.

• Simple harmonic motionWhy does almost every small oscillation look like a sine wave?
• Damping, driving, and resonanceWhy does a small periodic push build into a catastrophe?
• The wave equation and superpositionWhat do a string, a sound, and light have in common mathematically?
• Sound, beats and the Doppler effectWhat exactly moves when sound travels?
• Fourier: every wave is a sum of sinesIs the decomposition into sines a convenience, or a fact about the world?

Two descriptions of the same thing: thermodynamics from the outside, statistical mechanics from the inside. The moment they connect is one of the great unifications in science.

• Temperature, heat, and the zeroth lawWhat is temperature actually measuring?
• The first law and thermodynamic processesIf energy is conserved, why can I not run an engine on ocean heat?
• Entropy and the second lawWhy does the universe have a preferred direction in time?
• Kinetic theory and the Maxwell–Boltzmann distributionCan I derive pressure from nothing but billiard balls?
• Ensembles and the partition functionWhy does one function encode every thermodynamic quantity?

Faraday's great conceptual gift: stop thinking about action at a distance and start thinking about a condition of space itself. Everything after depends on taking the field seriously.

• Charge, Coulomb's law, and the field conceptIs the field a bookkeeping device or a real thing?
• Gauss's law and the power of symmetryHow can I find a field without ever doing an integral?
• Electric potential and energyWhy is a scalar easier to work with than a vector, and what do I give up?
• Conductors, capacitors, dielectricsWhy is the field inside a conductor always zero?

The single most beautiful moment in classical physics. Four laws, one added term, and light falls out of equations that were never about light.

• Current, resistance and DC circuitsWhat is actually flowing, and what is actually doing the pushing?
• Magnetic fields and forcesWhy is magnetism just electricity seen from a moving frame?
• Ampère's law and Faraday inductionWhy does only *change* in a field produce a current?
• Maxwell's equations assembledWhat breaks if I leave out the displacement current?
• Electromagnetic waves — and lightWhere does c come from, if I never measured light?

Optics is where classical physics is at its most complete and also where it first fails. The double slit is the hinge between this module and everything quantum.

• Geometric optics: reflection, refraction, lensesWhy does light bend when it enters glass?
• Interference and diffractionHow can adding light to light produce darkness?
• PolarizationWhat does a photon 'know' about the angle of a filter?
• The double slit, and why it will not go awayWhat happens if I send the particles through one at a time?

Newton's approach asks what force acts at each instant. Lagrange and Hamilton ask which whole path nature chooses. The second question turns out to be the one quantum mechanics and field theory are built on.

• The principle of least actionWhy would nature 'choose' a path in advance?
• Lagrangian mechanics and generalized coordinatesHow do I make constraint forces vanish from the problem entirely?
• Noether's theoremWhy is anything conserved at all?
• Hamiltonian mechanics and phase spaceWhat if I treat position and momentum as equals?
• Chaos and nonlinear dynamicsIf the laws are deterministic, why can I not predict the weather?

One postulate — the speed of light is the same for everyone — and absolute time collapses. Nothing here requires mathematics beyond algebra, which makes the strangeness harder to dismiss.

• The two postulatesWhat do I have to give up to keep the speed of light constant?
• Time dilation, length contraction, simultaneityWhose clock is really running slow?
• Lorentz transformations and spacetime diagramsWhat quantity do all observers agree on?
• Relativistic energy and momentumWhat is E = mc² actually saying?
• Four-vectors and invariantsHow do I write physics so the frame never appears?

The experiments that classical physics could not survive, and the strange machinery built to replace it. Take the postulates seriously as postulates — most confusion comes from trying to picture them.

• The experiments that broke classical physicsWhat exactly did classical physics get wrong, and by how much?
• Wave–particle duality and de BroglieIf light is a particle, is an electron a wave?
• The Schrödinger equationWhere does this equation come from — can it be derived?
• Particle in a box, tunnelling, the harmonic oscillatorWhy are energies quantized without anyone imposing it?
• Uncertainty and what ψ meansIs uncertainty about my ignorance, or about the world?

The move from wave mechanics to linear algebra on Hilbert space. Once you see quantum mechanics as geometry in a complex vector space, the paradoxes become structural rather than mystical.

• Hilbert space, operators, Dirac notationWhat is a quantum state, stripped of all pictures?
• Angular momentum and spinWhat is spinning, exactly?
• The hydrogen atomCan one equation produce the entire periodic table's structure?
• Identical particles and the Pauli principleWhy does matter take up space?
• Perturbation theory and approximation methodsWhat do I do when the equation cannot be solved exactly — which is almost always?
• Entanglement and Bell's theoremCould the particles have agreed on their answers in advance?

Gravity is not a force. It is the geometry of spacetime, and matter tells that geometry how to bend. The mathematics is demanding; the central idea fits in one sentence about a falling man.

• The equivalence principleCan I tell the difference between gravity and acceleration from inside a sealed box?
• Curved spacetime and the metricWhat replaces the Pythagorean theorem when space bends?
• Tensors and geodesicsHow do I write laws that no choice of coordinates can corrupt?
• The Einstein field equationsWhat is on each side of G = 8πT, in plain language?
• Black holes, waves, and cosmological solutionsWhat does the theory predict that nobody expected?

Where quantum mechanics meets 10²³ particles and produces the entire material world — including the device you are reading this on.

• Phase transitions and critical phenomenaWhy do wildly different systems behave identically near a critical point?
• Crystal structure and band theoryWhy is one solid a metal and the next an insulator?
• Semiconductors and the transistorHow does doping a crystal let you build a switch with no moving parts?
• Superconductivity and superfluidityHow can resistance be exactly zero rather than merely small?

What the atom is made of, what those pieces are made of, and where that regress finally stops — plus the four or five places where it visibly does not stop.

• Binding energy, fission and fusionWhy does iron sit at the bottom of the energy valley?
• Radioactivity and decay lawsWhy is decay exponential, and why can nothing predict a single atom?
• The Standard ModelWhy these particles, and why exactly three generations?
• Symmetry, gauge theory and the Higgs mechanismWhere does mass come from if the equations forbid it?
• Neutrinos and what the Standard Model missesWhat are the known holes in the best theory we have?

The deepest layer of established physics: reconcile quantum mechanics with special relativity and particles stop being fundamental. Fields are, and particles are what excitations of fields look like to a detector.

• Why fields, not particlesWhat goes wrong if I insist on a wavefunction for one relativistic particle?
• Canonical quantization and the scalar fieldHow do I quantize something with infinitely many degrees of freedom?
• The Dirac field and antimatterWhat did Dirac do to the wave equation to make it relativistic?
• QED, Feynman diagrams and renormalizationWhy do the infinities cancel, and is that legitimate?
• Path integralsCan I reformulate all of quantum mechanics as a sum over histories?

Apply everything so far to the largest object there is. The remarkable thing is that it works — and that 95% of what it describes is still unidentified.

• Stars: how they live and dieWhat holds a star up, and what happens when it stops?
• Galaxies and the cosmic distance ladderHow do we know how far away anything is?
• The expanding universe and the Big BangWhat is expanding, and what is it expanding into?
• CMB, inflation, dark matter and dark energyWhy do we believe in things we cannot see, and what would change our minds?

Information turns out to be physical, and physics turns out to be informational. This module is where quantum mechanics stops being a description of nature and becomes a technology.

• The qubit and quantum gatesWhat can a qubit do that a probabilistic bit cannot?
• Entanglement as a resource, and teleportationWhat is actually transmitted in quantum teleportation?
• Quantum algorithms: Deutsch, Grover, ShorWhere does the speed-up actually come from?
• Decoherence and quantum error correctionHow do you protect a state you are not allowed to look at?
• Building a quantum computerWhat is physically hard about this, and what is merely expensive?