The laws that govern reality — from falling apples to the fabric of spacetime
What this module covers
Physics is the attempt to describe everything that happens in the universe using the fewest possible principles. It proceeds by experiment, mathematics, and bold theorising — and its track record is extraordinary: the same equations that describe a pendulum also describe a pulsar. This module moves from classical mechanics and thermodynamics through electromagnetism, relativity, and deep into quantum mechanics (the most successful and philosophically disturbing theory humans have ever built), then arrives at particle physics, open frontiers, and cosmology.
The four great theories — explore each
Units & measurement — the bedrock
Physics is quantitative or it is nothing. The International System of Units (SI) defines seven base units — metre, kilogram, second, ampere, kelvin, mole, candela — from which every other unit is derived. The logic behind SI is elegant: units obey algebra, so if you have metres per second squared for acceleration and kilograms for mass, multiplying them gives kg·m/s², which is exactly the Newton, the unit of force. Dimensional analysis alone can often tell you whether an equation is wrong, a trick physicists use constantly. Fermi estimation — making useful order-of-magnitude guesses from sparse data — is the practical face of this: it's how Enrico Fermi estimated the yield of the first nuclear test from scraps of paper he dropped during the blast.
Newton's three laws
Newton's first law (inertia) says a body continues in uniform motion unless acted on by a force — the punch-line being that "rest" and "constant velocity" are physically identical, a Galilean insight Newton codified. The second law, F = ma, is the workhorse: it tells you that force is what causes acceleration, not velocity. Crucially, F and a are vectors — direction matters. The third law (action-reaction) is frequently misunderstood: if you push a wall, the wall pushes back on you with equal force, but on a different object, so the forces don't cancel. That's why you accelerate away from the wall when you push off.
Conservation of energy — Noether's deeper insight
Energy conservation is so fundamental it seems like furniture. But Emmy Noether's 1915 theorem revealed why it must hold: every conservation law corresponds to a symmetry. Energy is conserved because the laws of physics are the same today as they were yesterday — time-translation symmetry. Momentum is conserved because physics is the same here as there — space-translation symmetry. If the universe had different physical laws at different times, energy would not be conserved. This is one of the most beautiful results in all of physics, and it's almost unknown outside physics departments.
Physics timeline — key eras
Gravity — from Newton to Einstein
Newton's law of universal gravitation (1687) says every mass attracts every other mass with a force proportional to the product of their masses and inversely proportional to the square of the distance between them. It works brilliantly for apples, moons, and space probes — but not for Mercury. Mercury's orbit precesses 43 arcseconds per century more than Newton predicts. Einstein's general relativity (1915) gets it exactly right, because gravity is not a force in GR — it is the curvature of spacetime caused by mass-energy. The escape velocity from Earth is 11.2 km/s; from a neutron star it's a significant fraction of the speed of light; from a black hole's event horizon, it exceeds it.
Waves and oscillations
Waves transfer energy without transferring matter. The key properties are frequency (f), wavelength (λ), and wave speed (v = fλ). Resonance — when an external force drives a system at its natural frequency — is both enormously useful (musical instruments, MRI machines) and dangerous: the Tacoma Narrows Bridge collapsed in 1940 because wind-induced resonance matched the bridge's natural frequency. The Doppler effect explains why a passing ambulance changes pitch: the source is moving relative to the medium, compressing wavefronts ahead and stretching them behind. The same effect is used to measure the recession velocity of distant galaxies via redshift.
Thermodynamics — the four laws
The four laws of thermodynamics are sometimes summarised wryly: you can't win (energy is conserved), you can't break even (entropy always increases in an isolated system), and you can't quit the game (absolute zero is unattainable). The zeroth law defines temperature by transitivity. The second law — that entropy never decreases — is the reason time has an arrow. A broken egg never unbreaks not because it's forbidden by energy conservation (it isn't), but because the probability of all the particles spontaneously reassembling into egg-form is so astronomically small it will never happen in the age of the universe.
Escape velocity explorer — drag to compare objects
Maxwell's equations — four equations that unified everything
In the 1860s, James Clerk Maxwell assembled four equations that simultaneously describe electric fields, magnetic fields, and their relationship. The stunning result: when he looked at the speed at which electromagnetic disturbances propagate, he found it was 299,792 km/s — the measured speed of light. Light is an electromagnetic wave. The equations predicted the existence of radio waves, X-rays, and gamma rays decades before they were discovered. Hertz confirmed the prediction of radio waves in 1887. Einstein later said Maxwell's equations were the most important revolution in physics since Newton. They also seeded the incompatibility with Newtonian mechanics that led Einstein to special relativity.
The electromagnetic spectrum — click each band
EM band applications — relative energy per photon (log scale, eV)
Energy per photon = hf. A radio photon carries ~10⁻⁶ eV; a gamma ray photon carries >10⁶ eV — a ratio of a trillion. This is why gamma rays ionise tissue and radio waves don't.
The crisis that led to relativity
In 1887 Michelson and Morley tried to measure Earth's velocity through the luminiferous ether — the medium through which light was assumed to travel. They found no effect whatsoever. This null result was profoundly disturbing: if light requires no medium, what is it? Einstein in 1905 solved it by taking two postulates seriously: (1) the laws of physics are identical in all inertial frames; (2) the speed of light in a vacuum is the same for all observers regardless of their motion. The consequences that follow from just these two axioms are extraordinary.
Spacetime diagram — light cone and causality
Special relativity — the key results
Time dilation: a moving clock runs slow by factor γ = 1/√(1−v²/c²). At 99% of c, γ ≈ 7, so one year passes on the ship while 7 pass at home. This is not an illusion — muons created in the upper atmosphere at 0.998c reach the ground despite their lifetime being only 2.2 microseconds in their own frame. Length contraction: a moving object is shortened in the direction of travel. Mass-energy equivalence: E = mc². The 'c²' factor (≈ 9 × 10¹⁶) explains why a tiny mass converts to enormous energy — the Hiroshima bomb released energy from converting about 700mg of matter into radiation.
General relativity — gravity as geometry
The equivalence principle: there is no experiment you can do inside a closed box that distinguishes free fall from floating in empty space, or sitting still on Earth from accelerating at 9.8 m/s². Einstein extended this to conclude that gravity is not a force but the curvature of spacetime. Mass tells spacetime how to curve; curved spacetime tells mass how to move (John Wheeler's summary). Predictions: gravitational redshift (clocks in strong gravity run slow — GPS satellites must correct for this or accumulate 38 microseconds of error per day, adding 11km of positional error); gravitational waves (confirmed 2015 by LIGO, detecting two black holes merging 1.3 billion light-years away).
Time dilation calculator — special relativity
Black holes — explore key concepts
The ultraviolet catastrophe
Classical physics predicted that a hot object in thermal equilibrium should radiate infinite energy — specifically, that radiated power should increase without limit as wavelength decreases. This was not a small discrepancy; it predicted that everything around you at room temperature should be bathing you in lethal ultraviolet and X-ray radiation, constantly. In 1900, Planck fixed this by assuming that energy is emitted only in discrete packets (quanta) of size E = hf, where h = 6.626 × 10⁻³⁴ J·s. He described this as "an act of desperation" — he didn't believe the quantisation was real. Einstein did.
The photoelectric effect — Einstein's Nobel Prize
Shine light on a metal surface and electrons pop off — but only if the light exceeds a threshold frequency, regardless of intensity. Classical wave theory predicted that more intense light would always eventually dislodge electrons. Einstein (1905) explained this by proposing that light itself comes in quanta (photons) of energy E = hf. A dim high-frequency light source ejects electrons; a brilliant low-frequency source ejects none. This wasn't just a mathematical trick — it meant light was genuinely particle-like, which contradicted Maxwell's undeniable wave description. The tension between these two views is wave-particle duality.
From Bohr to de Broglie — quantisation of the atom
Rutherford's 1911 nuclear model of the atom had a fatal problem: electrons orbiting the nucleus are accelerating (changing direction counts as acceleration), and accelerating charges radiate electromagnetic energy. Classical physics predicted the electron would spiral into the nucleus in about 10 picoseconds. Bohr (1913) fixed this by simply declaring that certain orbits are stable and electrons only emit radiation when jumping between them. He could calculate hydrogen's spectral lines with startling accuracy, but his model was philosophically arbitrary. de Broglie (1924) supplied the missing logic: if light waves behave like particles, particles must behave like waves. The allowed Bohr orbits are exactly the ones where the electron's de Broglie wavelength fits a whole number of times around the orbit — a standing wave condition. Electron diffraction experiments confirmed this in 1927.
The wavefunction — visualising probability amplitude
The Schrödinger equation
The Schrödinger equation is quantum mechanics' equation of motion. Given the wavefunction now, it tells you the wavefunction at any future time — perfectly deterministically. This surprises most people: quantum mechanics is deterministic about the wavefunction, but the wavefunction only gives probabilities for measurement outcomes. The randomness enters not in the time evolution but in the measurement itself. A particle in a box (infinite square well) is the simplest exact solution: the allowed energies are E_n = n²π²ℏ²/(2mL²), quantised naturally because only standing waves fit inside the box — just like Bohr's condition, but now derived rigorously.
The Heisenberg uncertainty principle
ΔxΔp ≥ ℏ/2 is not a statement about measurement disturbing particles. It is a fundamental property of waves: a wave with a well-defined wavelength (definite momentum) extends over all space (indefinite position), and vice versa. This is true for water waves too — it's a mathematical property of Fourier transforms. For quantum particles, momentum is encoded in wavelength, so localising a particle necessarily introduces a spread of wavelengths and hence momenta. Zero-point energy follows directly: the electron in a hydrogen atom can't collapse to the nucleus because that would require definite position, which demands infinite momentum spread, which requires infinite energy. The atom is stable because of the uncertainty principle.
Uncertainty principle — position vs momentum trade-off
Spin — angular momentum with no classical analogue
Spin is intrinsic angular momentum that doesn't correspond to anything rotating. An electron has spin ½, meaning when you measure it along any axis you get exactly +ℏ/2 or −ℏ/2 — nothing in between. The Stern-Gerlach experiment (1922) confirmed this: a beam of silver atoms (with one unpaired electron) passing through a non-uniform magnetic field splits into exactly two lines, not a smear as classical theory predicted. The mathematics uses spinors — two-component complex vectors — that behave differently from ordinary vectors: you must rotate a spin-½ particle through 720° to return to its original state, not 360°. This has been experimentally confirmed using neutron interferometry.
The double-slit experiment — animated
With both slits open and no detector, individual particles build up an interference pattern — as if each particle goes through both slits simultaneously. Place a detector to determine which slit, and the interference pattern vanishes. This is the core mystery of quantum mechanics.
Quantum weirdness — explore the phenomena
Bell inequality violations — experimental results summary
The Bell parameter S: classical (local hidden variable) theories require S ≤ 2. Quantum mechanics predicts S ≤ 2√2 ≈ 2.83. Experimental results consistently find S > 2.
The Aspect et al. (1982), Hensen et al. (2015, loophole-free), and subsequent experiments all confirm quantum mechanics and rule out local hidden variable theories. The universe is genuinely non-local at the quantum level.
Interpretations compared — on key dimensions
Where each major interpretation falls on contested questions
Wavefunction collapse — real or not?
Determinism — is the universe fundamentally random?
Interpretations — explore in depth
The Standard Model — explore the particle families
From QM to quantum field theory
Quantum mechanics describes particles. Relativity requires that nothing propagates faster than light, including the interactions between particles. When you try to combine non-relativistic quantum mechanics with special relativity, you immediately encounter inconsistencies — the number of particles isn't conserved (particles can be created and destroyed), and you need to allow for anti-particles. Quantum field theory (QFT) resolves this by promoting fields (like the electromagnetic field) to be the fundamental objects, and particles are excitations of those fields. An electron is a ripple in the electron field that pervades all of space. The photon is a ripple in the electromagnetic field. This is why QFT is inherently multi-particle and handles creation/annihilation naturally.
Antimatter — prediction and asymmetry
Paul Dirac's 1928 equation for the relativistic electron had two solutions — one with positive energy (the electron) and one with negative energy. Rather than discard the negative solution, Dirac predicted the existence of a positive-charge counterpart: the positron. Carl Anderson discovered it in cosmic ray tracks in 1932, two years after Dirac's prediction. Every particle has an antiparticle; when they meet, they annihilate, converting mass entirely to energy (E = mc²). The deepest puzzle: the Big Bang should have produced equal amounts of matter and antimatter. The universe is almost entirely matter. This matter-antimatter asymmetry is one of physics' biggest unsolved problems.
Standard Model — particle categories by type
The Standard Model has 17 fundamental particles (6 quarks, 6 leptons, 4 force-carrying gauge bosons, plus the Higgs). The Higgs boson, last piece confirmed at the LHC in 2012, gives quarks and leptons their mass via the Higgs mechanism.
Quantum technologies — explore applications
Quantum vs classical computing — capability landscape 2025
Quantum advantage exists for specific problem types, not general computation. In 2019 Google claimed quantum supremacy (a specific sampling task in 200 seconds vs ~10,000 years classically); IBM contested the classical estimate. As of 2025, quantum computers remain noisy and error-prone, with fault-tolerant quantum computing still years away.
Quantum gravity — the hardest problem
General relativity and quantum mechanics are each extraordinarily well confirmed. They are also mutually inconsistent. GR treats spacetime as a smooth, continuous, classical field. QM requires all fields to be quantised and subject to uncertainty. At the Planck scale (10⁻³⁵ m, 10⁻⁴³ s), both theories are needed simultaneously, and both break down. String theory proposes replacing point particles with 1D strings, predicting a spin-2 graviton and requiring 10 or 11 dimensions. Loop quantum gravity quantises spacetime itself, predicting space is discrete at the Planck scale. Neither theory yet makes new predictions that have been experimentally tested. This is the dominant unsolved problem in fundamental physics.
Dark matter and dark energy
Normal (baryonic) matter makes up only about 5% of the universe's energy content. Dark matter (~27%) is inferred from galactic rotation curves (stars move too fast for the visible mass), gravitational lensing, and cosmic structure formation. It doesn't emit, absorb, or reflect light and interacts only gravitationally and possibly weakly. WIMPs (weakly interacting massive particles) are the leading candidate, but decades of increasingly sensitive detectors have found nothing. Dark energy (~68%) causes the accelerating expansion of the universe, discovered in 1998. It may be Einstein's cosmological constant — the energy of the vacuum — or something more dynamic (quintessence). We have no confirmed particle physics explanation for either.
Multiverse proposals — scientific status spectrum
The string theory landscape (~10⁵⁰⁰ possible vacua) and inflationary multiverse are criticised for being unfalsifiable. The many-worlds multiverse follows necessarily from standard QM with no collapse. Bubble universe collisions in eternal inflation could in principle leave imprints on the CMB.
The Big Bang — evidence, not inference
The Big Bang is supported by three independent observational pillars. (1) Hubble expansion: all distant galaxies are receding, with velocity proportional to distance — run time backward and everything converges. (2) Cosmic Microwave Background: the universe was once opaque plasma; when it cooled enough for atoms to form (380,000 years post-Bang), photons were released. We detect them today as the CMB, at 2.725 K, perfectly matching predictions. (3) Big Bang nucleosynthesis: the light elements (H, He, Li) were forged in the first few minutes in exactly the ratios we observe — 75% hydrogen, 25% helium by mass. No stellar process can explain this ratio from scratch.
Stars — nuclear furnaces and element factories
Stars form when gas clouds collapse under gravity. A protostar heats until hydrogen fusion begins (the pp chain or CNO cycle depending on mass). On the main sequence, outward radiation pressure balances inward gravity. When the hydrogen core is exhausted, the star expands to a red giant, fusing helium, then carbon, all the way to iron (Fe-56) — the most tightly bound nucleus, beyond which fusion releases no energy. For massive stars (>8 M☉), the iron core collapses in under a second, bouncing to produce a Type II supernova, briefly outshining an entire galaxy. The explosion seeds space with all elements heavier than iron, forged in the explosion itself (r-process nucleosynthesis). Calcium in your bones was forged in a stellar explosion before the Sun formed.
Stellar fates — by initial mass
Main sequence lifetime scales roughly as M⁻²·⁵ — a 10 M☉ star lives only ~30 million years; the Sun will last ~10 billion years total. The most massive stars live and die while the Sun barely blinks.
Fate of the universe — explore the scenarios
Composition of the universe (energy density)
Dark energy is the dominant component and drives the accelerating expansion. Baryonic matter — everything you can see, touch, and are made of — is a 5% afterthought in the cosmic inventory.