What if a magnetic field could enter a superconductor only in discrete packets? In a superconducting loop, Cooper pairs share one coherent phase. For that phase to close on itself, only certain winding states are allowed. The loop therefore adjusts its persistent current in steps as the applied field changes, enabling SQUID magnetometers and quantum sensors.

Four lines describe every known elementary particle and three of the four forces. The first gives the force fields, the second how matter feels them, the third how particles get mass from the Higgs field, and the fourth the Higgs field itself, whose potential sits off-centre at v ≈ 246 GeV. P.S. Gravity is not in it.

Nothing can beat light in a vacuum, but particles can outrun light in water. In water, light travels at about 225,000 km/s. Electrons knocked loose by gamma rays from the fuel go faster than that and leave a cone of light behind them, the optical version of a sonic boom: Cherenkov radiation. Its spectrum rises toward short wavelengths, so the glow is blue.

This super famous line from 1926 underlies atoms, chemical bonds, semiconductors and lasers. iħ ∂Ψ/∂t = −(ħ²/2m)∇²Ψ + VΨ. The left side says how the state changes in time; the right side is its total energy, kinetic plus potential. Solve it for a harmonic trap and the energies come out evenly spaced, with the lowest never reaching zero: ½ħω.

Zeroth: temperature exists. First: energy is conserved, ΔU = Q − W. Second: the entropy of an isolated system never decreases, so heat flows from hot to cold on its own. Third: absolute zero can be approached but never reached in a finite number of steps.

Air over the top of a wing does not "catch up" with the air below it. It gets there first. The equal-transit-time explanation is a myth. The wing's shape and angle turn the flow downward: pressure drops above and rises below, and pushing air down means the air pushes the wing up. Bernoulli and Newton describe the same flow. Every streamline here is computed from ideal flow around a Joukowski airfoil.

Nearly every law of physics is a differential equation. Orbits, waves, heat flow, radioactive decay, quantum states, turbulence and the expansion of the universe are all solutions of the twelve equations here.

A teaspoon of neutron star would weigh about 2 billion tonnes. All three are what is left when a star runs out of fuel. Electrons hold up a white dwarf; neutrons and nuclear forces hold up a neutron star. Above roughly 2 to 2.3 solar masses, nothing known can stop the collapse, and a black hole forms.

E = mc² is the special case of a body at rest. The full relation is E² = (pc)² + (mc²)², a right triangle with rest energy and momentum as its sides. For a proton in the LHC the triangle is almost flat; for light, with no mass at all, it collapses to E = pc.

It took 115 years to find every particle in the Standard Model. The electron came first, in 1897. Quarks showed up inside protons at SLAC in 1968. The top quark took until 1995, the tau neutrino until 2000, and the Higgs boson until 2012: 48 years after it was predicted.

Eight zooms take you from Earth to the edge of the observable universe. Earth, the Moon's orbit, the Solar System, our stellar neighbourhood, the Milky Way, the Local Group, the Virgo Supercluster, Laniakea, and everything light has had time to reach us from. The last panel is about 7 × 10¹⁹ times wider than the first: nearly 20 orders of magnitude.

A guitar string's overtones are whole-number multiples of its lowest note. An ideal drumhead's are not. The modes of a circular membrane vibrate at 1, 1.59, 2.14, 2.30, 2.65... times the fundamental, set by the zeros of Bessel functions. Those uneven ratios are why a simple drum gives a thud instead of a clear pitch.

Stars of 3, 4 and 5 times the Sun's mass start motionless on a 3-4-5 triangle, 300 to 500 AU apart. There is no neat formula for what happens next; it has to be computed step by step.

In graphene, electrons can pass through a potential barrier with almost no reflection at normal incidence. Their chirality suppresses backscattering, a quantum effect known as Klein tunneling. At oblique angles, reflection returns.

Quantum tunneling lets a particle cross a barrier even when E < V₀. Inside, its wavefunction decays as ψ(x) ∝ e^(−κx), but does not vanish. For width a, T ≈ e^(−2κa), so thinner barriers are much easier to cross.

Decoherence occurs when a quantum system becomes entangled with its environment. The off-diagonal terms that encode phase coherence decay as ρ₀₁(t) = ρ₀₁(0)e^(−Γt). Interference fades, leaving a state that behaves like a classical mixture.

A symmetric theory can have an asymmetric ground state. For V(φ) = −μ²|φ|² + λ|φ|⁴, φ = 0 is unstable, so the field settles into one of many equivalent minima. The laws remain symmetric, but the chosen vacuum does not.

Black holes to true scale, from Cygnus X-1 (a 125 km event horizon) to TON 618.

Noether’s theorem links symmetry to conservation. If the action remains unchanged under a continuous transformation, δS = 0 ⇒ dQ/dt = 0 then a conserved quantity must exist. Time-translation symmetry gives energy conservation. Space-translation symmetry gives linear momentum. Rotational symmetry gives angular momentum. The theorem, proved by Emmy Noether in 1918, applies across classical mechanics, electromagnetism, general relativity, and quantum field theory. It explains why conservation laws are not isolated rules, but mathematical consequences of how nature remains unchanged under transformation.

Repeatedly measuring whether a quantum state has changed can inhibit its evolution. The effect comes from the short-time quadratic decay law. Physical measurement interactions repeatedly reset the state, keeping its survival probability high.