Physicist Portraits Vol. 1 Pixel Sticker Sheet

10 pixel-art physics stickers on one A5 (5.83″ × 8.27″) white kiss-cut sheet: Physicist Portraits Vol. 1. Every character below has its own sticker page with the full physics panel.

Emmy Noether

Noether's theorem says that every continuous symmetry of a system's laws comes with a conserved quantity. Symmetry under shifts in time gives conservation of energy, shifts in space give momentum, and rotations give angular momentum.

Q = Σ_i (∂L/∂q̇_i) δq_i

Q: conserved Noether charge (momentum for a shift, angular momentum for a rotation) (kg·m/s, J·s); L: Lagrangian (J); qᵢ: generalised coordinates (lengths or angles) (m, rad); ̇qᵢ: generalised velocities (m/s, rad/s); ε: small symmetry parameter (a length for a shift, an angle for a rotation, a time for a clock shift) (m, rad, s); δ qᵢ: direction of the symmetry shift (its size is carried by ε)

Émilie du Châtelet

Kinetic energy grows with the square of speed, so twice the speed carries four times the energy. Du Châtelet used experiments with balls dropped into clay, where the dent depth grew with the square of the speed, to argue for this 'vis viva' measure.

E_k = ½mv²

E_k: kinetic energy (J); m: mass (kg); v: impact speed (m/s); g: gravitational acceleration (m/s²); h: drop height (m); F: average resisting force of the clay (assumed constant) (N)

Chien-Shiung Wu

In Wu's experiment, cobalt-60 nuclei were lined up by a magnetic field, and the electrons from their beta decay came out preferentially opposite to the nuclear spin. A mirror image of that experiment would show the reverse, so the weak force distinguishes left from right.

⁶⁰Co → ⁶⁰Ni* + e⁻ + ν̄_e

J: nuclear spin (axial vector) (J·s); pₑ: electron momentum (polar vector) (kg·m/s); ̂P: parity (mirror) operation

Galileo Galilei

Galileo found that a falling body's distance grows with the square of the time. In equal time intervals the distances covered go in the ratio of the odd numbers 1, 3, 5 and so on, which is the signature of constant acceleration.

d = ½gt²

d: distance fallen from rest (m); g: gravitational acceleration (m/s²); t: time (s); d_n: distance covered in the n-th equal time interval (m)

Isaac Newton

Newton's second law says force equals the rate of change of momentum. His law of gravitation says every two masses attract with a force proportional to their product and inversely proportional to the square of their distance, and together they explain falling apples and planetary orbits.

F = dp/dt

F: net force (N); p: momentum (kg·m/s); G: gravitational constant (m³·kg⁻¹·s⁻²); m₁, m₂: masses (kg); r: separation (m)

James Clerk Maxwell

Maxwell added one missing term, the displacement current, to the known laws of electricity and magnetism. With it the four equations are consistent and predict waves moving at the speed of light, which showed that light itself is an electromagnetic wave.

∇·E = ρ/ε₀, ∇·B = 0

E: electric field (V/m); B: magnetic flux density (T); ρ: charge density (C/m³); J: current density (A/m²); ε₀, μ₀: vacuum permittivity, permeability (F/m, N/A²); c: speed of light (m/s)

Michael Faraday

Gauss's law relates the electric flux through a closed surface to the charge inside it. In a closed conductor at equilibrium the charges sit on the outside, so the field in an empty cavity is zero, which is why Faraday was safe inside his charged cage.

∮_S E·dA = Q_enc/ε₀

E: electric field (V/m); dA: outward area element of a closed surface S (m²); Q_(enc): charge enclosed by S (C); ε₀: vacuum permittivity (F/m)

Nikola Tesla

Power lost in a wire is the current squared times the resistance, so sending power at high voltage and low current wastes much less. Transformers, which only work with alternating current, step the voltage up or down in proportion to the number of turns on each coil.

V(t) = V₀ sin(ωt)

V: voltage (V); V₀: peak voltage (V); ω: angular frequency (rad/s); V_s, V_p: secondary, primary voltage (V); N_s, N_p: turns on secondary, primary; P_(loss): resistive power loss (W)

Ernest Rutherford

Rutherford fired alpha particles at gold foil and some bounced almost straight back. His formula, with its steep dependence on 1/sin⁴(θ/2), only works if the positive charge sits in a tiny, dense nucleus.

dσ/dΩ = (zZe²/(16πε₀E))² / sin⁴(θ/2)

dσ/dΩ: differential cross section per solid angle (m²/sr); z: charge number of the alpha particle (2); Z: charge number of the target nucleus (gold: 79); e: elementary charge (C); ε₀: vacuum permittivity (F/m); E: kinetic energy of the alpha particle (J)

Hideki Yukawa

Yukawa proposed that nuclear forces come from exchanging a massive particle, so they fade out exponentially beyond a range of about ħ/mc. Turning the observed short range around predicted the mass of the carrier, later identified as the pion.

V(r) = −(g²/4π) e^(−r/R)/r, R = ħ/(mc)

V(r): potential energy between two nucleons (J); g: coupling strength (g²/4π has units of energy times length here) (J^(1/2)·m^(1/2)); r: separation (m); R: range of the force (m); λ: Yukawa's range parameter, the inverse of R (he took 5×10¹² per centimetre) (m⁻¹); ħ: reduced Planck constant (J·s)