Cosmology That Clicks

Rewrite cosmic expansion as "the speed of light slowly drops." Derive for yourself that light slows by 2.2 cm/s per year. c · t = constant

The hydrogen electron orbits at 1/137 the speed of light. Compute the strange unit-free number α by hand and confirm it. α = v/c ≈ 1/137

Expand the relativistic energy and the familiar kinetic energy appears. The c→∞ limit where relativity vanishes, in equations. c → ∞ ⇒ v/c → 0

Turn the equation into a recurrence and compute step by step. The graphs recompute live in your browser. Feel how a change of variables speeds it up. c(t) = c₀t₀/t

Close in on the discrete/continuous boundary with the sampling theorem. Watch "aliasing" — a fake wave born from coarse sampling — in motion. f_s > 2 f_max

Even that 1/137 changes with how finely you look (1/137 → 1/128). Repose "why 1/137?" into its correct form. α(fineness) is not constant

Three running forces approach one point at high energy — that's grand unification. How far the dream of "everything from one number" goes, and where it stops. M_GUT ~ 2×10¹⁶ GeV

Proton decay couldn't be tried at 10³⁴ years. But the neutron decays in 880 s, and the 13.8-billion-year-old helium abundance delivers a verdict on c·t=constant — the face-value reading is rejected; the α-invariant gauge is not guilty but unobservable. Γ ∝ Q⁵ / ΔQ/Q ≲ 0.34%

Dissecting the i left over from Episode 3. The moment you localize the phase ambiguity — "choose it freely at each point" — the electromagnetic force is born to patch it up: the origin of α. Experience "trace-leaving ambiguity" via the Aharonov–Bohm effect. ∂ → D = ∂ − iA / origin of α

Turn the same i ninety degrees onto the imaginary axis of time (the Wick rotation): oscillation turns to decay, the quantum to heat, and the period of imaginary time becomes temperature. Overlay c·t=constant and the temperature drops as 1/t — linking to Episode 7's BBN (cosmic cooling). t → −iτ / τ = ℏ/k_BT

A nucleon is one bit, "n or p." As the universe cools and updates can't keep up, the bit freezes and only irreversible erasure (= decay) remains. Landauer's principle (k_BT ln2 per bit) bridges information and energy, rewriting Episode 7's BBN freeze-out. erase 1 bit = k_BT ln2

At last, the mass side. No one can measure the neutrino's absolute mass; only the squared difference Δm² is measurable — Bonus 2's "absolute values are bookkeeping, only the difference is physical," happening for real in experiment. Oscillation is Episode 9's phase of i; the seesaw origin of its lightness shakes hands with the GUT scale. only Δm² is measurable

The fourth force, gravity, shoots up as E² and catches up at the Planck scale — but there it can't be renormalized. The identity of the "edge of the band" the series kept pointing to, and the last, still-open door. gravity ∝ E² / M_Planck ~ 10¹⁹ GeV

A little tale that exposes the lie in a name, with one derivative. H = 1/t decreases with time. The habit of trusting the definition over the name. H = ȧ/a = 1/t

In 1983, humanity stopped measuring the speed of light and fixed its value — because there was nothing left precise enough to compare against. A story about the root of what measuring is. speed = distance ÷ time

A theory that seriously tried to change the speed of light. Right motive, but it slipped in the implementation — it moved only c and failed to protect α. fix α, not c

Make the series' watchword "space stretch = slowing light" rigorous, with two conditions. Where it holds and where it breaks. Bonus 3's lesson becomes the equivalence condition. c_B·a = constant / α invariant

Flip the view from "protect" to "move." The four constants that build α amount to only "three people's worth" dimensionally, so you can fix at most three. Which one is the moving one is a gauge (a choice of bookkeeping). you can fix at most three

α can move along two axes — running with time (gauge freedom exists / still debated) and running with energy (no freedom / an established fact). "128" is the energy story, not the time story. the time axis vs. the energy axis

The energy knob can't be turned forever. Below is the 1/137 floor; above is the electroweak, grand-unified, and Planck wall. Both ends coincide with "where today's physics ends." Closes the trilogy with a reading guide. floor 1/137, ceiling the Planck edge

Yang–Mills won because it chose a description that "doesn't fix" — more precisely, a fixing that keeps the symmetry manifest without breaking the invariant core. The origin of force from Episode 8, seen from behind. freedom of description ↔ rigidity of dynamics

Everything with units is a "convention"; most dimensionless numbers are "26 you can only measure"; only a precious few are pinned to exact values by principle (anomaly cancellation, topology, fixed points). A three-column map closes the constants series. fixing by convention vs. by necessity

Turn the same measuring stick on the tool itself. AI has no grounded units and represents the world by "ratios only"; its embeddings carry a literal gauge freedom. Separating what it's good at (sorting, connecting) from where it's risky (numbers, the fluency trap) closes the series. AI has nothing but ratios

A version that reads cosmic expansion through storytelling and the reveal alone, without equations. For getting the feel first, or for showing others.