The strangeness of physics isn't a bug of small scales or weak intuition — it's how
reality actually works. Cottrell answers profound questions with
thought experiments and honest math, organized from the very big
and the very small to the in-between
world we live in — and finally to the "not things": math, infinity,
and abstraction. Along the way: yes, the universe is a bit of a smart-ass.
How to read this
Diagrams first, then the four parts
The opening sections visualize the book's signature ideas — the scale of the
universe, time dilation, the double-slit experiment, and the "do colors exist?" perception
puzzle. After that, a card for each of the book's four themed chapters.
The book's spine
A ribbon from the cosmos to the abstract
The four parts are a guided zoom: from the largest things (galaxies, spacetime)
down through the smallest (atoms, quanta), back to the human-scale "Goldilocks realm," and
finally off the physical map entirely into pure mathematics.
Big Things · Relativity
Why moving clocks run slow
Because the speed of light c is the same for everyone,
something else has to give: time and distance themselves bend. The gamma factor measures
exactly how much — and it explains the Twin Paradox without ever invoking acceleration.
The Gamma Factor
γ = 1 / √(1 − v²/c²)
As v approaches c, γ blows up:
time dilates, lengths contract, mass grows. Gravity does the same thing — clocks lower
in a gravity well run slow, because gravitational and inertial acceleration are
equivalent.
The Twin Paradox isn't a paradox.
The traveling twin ages less not because she accelerated, but because her path through
spacetime is more "curved." In spacetime geometry a straight path maximizes
elapsed time — the inverse of ordinary geometry. And simultaneity is observer-dependent:
there is no universal "now."
Spacetime Interval
S² = c²t² − x² − y² − z²
The one invariant all observers agree on.
Einstein 1905
E² − P²c² = m²c⁴
Yields both E = mc² and E = Pc for light.
Hubble's Constant
H₀ ≈ 70 km/s/Mpc
Expansion is a rate-per-distance, not a speed.
Small Things · Quantum Mechanics
The double-slit experiment
Young's experiment is the clearest demonstration that everything — light,
electrons, even 810-atom molecules — passes through both slits at once and interferes with
itself. Fire particles one at a time and the interference pattern still builds up. Quantum
superposition is real, and it applies at all scales — it's just harder to see in big, warm,
noisy systems.
A "measurement" is any interaction that conveys information
— no conscious observer required. Watch which slit the particle takes and the fringes fade;
watch partially and they fade partially. From the outside, measurement produces
entanglement, not magic collapse — which is the heart of the Many Worlds picture.
And Bell's theorem (1964) proved the randomness is irreducible: entangled photons reach
2√2 ≈ 2.83 where any hidden-variable theory caps at 2.
In-Between Things · Perception
Do colors exist?
The book's title question. Light has wavelength; "color" is what three types of
cone cells in your eye make of it. Color is a subjective construct, not an objective
feature of the world. A screen only needs to fool your three cones to fake any color you can
see — and the rainbow's coloring is, in Cottrell's words, a "shared illusion."
400 nm · violet500 nm600 nm700 nm · red
Three cones, probably evolved to spot ripe fruit. Your brain
infers color from the ratio of these three signals. Mantis shrimp have 16 cone types;
many animals see ultraviolet or infrared we can't. Almost every science image of non-visible
light is "false-color." So: colors don't exist out there — they exist in here.
In-Between Things · Electromagnetism
Maxwell: light IS an electromagnetic wave
Four equations describe all of electricity and magnetism. From them, Maxwell
derived that self-sustaining oscillating electric and magnetic fields travel at exactly the
speed of light — proving light itself is an electromagnetic wave. The result unsettled physics
for 40 years, until Einstein resolved it with special relativity.
Gauss · E
Electric lines
Field lines begin and end only on charges.
Gauss · B
No monopoles
Magnetic field lines always form closed loops.
Ampère
Currents curl B
Currents and changing E-fields create curling magnetic fields — electromagnets.
Faraday
Changing B curls E
Changing magnetic fields create curling electric fields — every generator and AC line.
Cottrell: "I suspect that when Maxwell first did this
math he cartwheeled all the way back to Edinburgh."
The gallery
The most mind-bending questions
A sampler of the book's best Q&As, one from each part. Each is answered
faithfully and a little irreverently.
Big Things
Did the Big Bang explode into empty space?
No. Space itself expanded. That's why the Cosmic Microwave Background is still
everywhere — its light started out everywhere. Those photons, now ~14 billion years old,
were redshifted from gamma rays to microwaves; the matter that emitted them is now ~46
billion light-years away.
Small Things
Are atoms 99.99% empty space?
No. Electrons are standing waves — "spherical harmonics" spread through the
whole atom like a ringing bell — not tiny dots zipping around. Asking "where exactly is
this electron?" isn't just hard; it's meaningless.
In-Between Things
Could a lab-made black hole eat the Earth?
No. Any black hole we could make is far too small to swallow matter, and it
would evaporate via Hawking radiation almost instantly. Living things don't break the
second law of thermodynamics either — they're open systems fed by the Sun's low-entropy
energy.
Not Things
Why does π never repeat?
It's proven, not just observed. Repeating decimals are always rational; a 1946
calculus proof shows π can't be written as a/b. Related: 0.999… equals exactly 1, because
both sequences converge to the same limit — and "the difference is zero" is how equality
is defined for real numbers.
Small Things
Can quantum teleportation beat light speed?
No. It transfers an unknown quantum state (not matter) via a
pre-entangled pair plus an ordinary classical "same/different" message — and that classical
message is mandatory, so nothing outruns light.
Not Things
Are some infinities bigger than others?
Yes. Counting numbers, integers, and rationals are all the same "countable"
size (aleph-null). The real numbers form a strictly larger infinity — proven by Cantor's
diagonal argument. Whether anything sits between them is undecidable from standard axioms.
The full walkthrough
The four parts
Each chapter bundles roughly a dozen question-and-answer essays. The colored
left edge marks which of the book's four scales you're in.
Part I · the largest scales
CHAPTER 1Big Things: Cosmology, Relativity, Gravity, and Space
Sixteen interconnected Q&As grounded in thought experiments and vivid analogies. The spine
is special and general relativity: the invariance of light's speed forces time and space to
bend, there is no universal "now," and the Twin Paradox is resolved by the geometry of
spacetime paths, not by acceleration. The chapter also covers large-scale cosmology — dark
energy, the Big Bang as an expansion of space, the CMB — plus practical curiosities
like why planets are spheres, why disks form in space, and why "faster than light" expansion
is a category error.
The constant speed of light makes time and distance relative; γ quantifies dilation, and gravitational time dilation (lower = slower) follows from the equivalence principle.
The Twin Paradox: the traveler ages less because her spacetime path is more "curved" — a straight path maximizes elapsed time, the inverse of Euclidean geometry.
Simultaneity is observer-dependent (the Alice-and-Bob train-lightning thought experiment); there is no universal clock.
Dark energy (equation of state w = −1) drives accelerating expansion, is ~75% of the universe's energy, and doesn't thin out as space grows.
The Big Bang wasn't an explosion into space — space itself expanded; the CMB is everywhere because it began everywhere.
Accretion explains flat disks: inelastic collisions average out random orbital planes; the Sun holds 99.86% of the solar system's mass.
Expansion is measured in km/s per megaparsec (H₀ ≈ 70), so calling it "faster than light" is "not even wrong."
Highlights & key equations
γ = 1/√(1−v²/c²) — gamma factor: time dilation, length contraction, relativistic mass
S² = c²t² − x² − y² − z² — the Spacetime Interval, relativity's one invariant
E² − P²c² = m²c⁴ — Einstein 1905, unifying energy, momentum, and mass
"Saying the universe expands faster than light is akin to 'green is bigger than happy' — it's not even wrong."
Alexander Friedmann added the scaling factor a(t), predicting an expanding universe before it was observed.
The Kola Superdeep Borehole: the deepest hole drilled, 7.6 miles, abandoned when it got too hot too fast.
Part II · the smallest scales
CHAPTER 2Small Things: Quantum Mechanics and Particle Physics
About fifteen Q&As tracing wave-particle duality from Newton through Einstein and de Broglie,
anchored in Young's double-slit experiment. The central theme: quantum strangeness is a
fundamental feature of reality at all scales, just harder to see in large, warm, noisy systems.
Essays cover true randomness (Bell's theorem), the measurement problem, quantum computing,
teleportation, antimatter, and particle-physics basics — insisting throughout that quantum
weirdness is not supernatural and consciousness plays no role.
The double-slit experiment is foundational: everything tested — up to 810-atom molecules — goes through both slits at once, interfering even one particle at a time.
Bell's theorem rules out hidden variables: entangled photons hit 2√2 ≈ 2.83 where classical probability caps at 2 — quantum randomness is irreducible.
A "measurement" is any information-conveying interaction; no conscious observer needed. From outside, measurement produces entanglement, not collapse.
Shor's algorithm breaks RSA via quantum parallelism + a quantum Fourier transform that extracts the period r; succeeds 40%+ of the time.
Quantum teleportation moves a state (not matter) using a pre-entangled pair plus a mandatory classical message — so it can't beat light speed.
Atoms aren't mostly empty: electrons are standing waves spread through the atom; "where is the electron?" is meaningless.
Many Worlds isn't universes popping into being — it's what quantum laws look like applied universally; "collapse" is the view from inside one branch.
Highlights
"God has a serious gambling problem" — Cottrell on Bell overturning "God doesn't play dice."
De Broglie wavelength of a cannon-fired kitten: λ ≈ 6.5×10⁻³⁶ m — visible fringes would need a screen ~330 quadrillion light-years away.
Chien-Shiung Wu's 1956 cobalt-60 experiment: first demonstration of parity violation — the weak force has genuine "handedness."
QED's electron g-factor is accurate to better than one part in a trillion — like measuring NYC-to-Paris to a tenth a hair's width.
The Scanning Tunneling Microscope "sees atoms the way a blind person sees the world… with a pokin' stick."
Anyons: quasi-particles in 2D systems that can take any spin, not just integer or half-integer.
Part III · the human scale
CHAPTER 3In-Between Things: Energy, Materials, and Everyday Physics
The "Goldilocks realm" of human-scale physics, where electromagnetic and gravitational forces
compete and complexity flourishes. Each Q&A takes a deceptively simple everyday question and
digs into the real physics beneath — from the subjectivity of color and the optics of wet
stones to Maxwell's equations, carbon dating, entropy and life, and the (non-)danger of
lab-made black holes. The unifying theme: the in-between scale is where physics is richest,
most surprising, and most directly observable.
Do colors exist? Color is a subjective construct of three cone types (mantis shrimp have 16); screens fool just our three; the rainbow's coloring is a "shared illusion."
Wet/polished stones look darker and more colorful: surface reflection consolidates light one direction; subsurface scatter picks up the stone's colors; water reduces the index-of-refraction jump.
The atmosphere rotates with Earth — it's thinner than people think (7 km if compressed); topography drags it; hurricanes are shaped by the Coriolis effect.
Energy is a conserved abstract quantity in many forms; there's no "pure energy." E=mc² just adds rest-mass to the ledger.
Everything is technically quantum, but "wavy" effects show best in light; the Pauli exclusion principle is why matter is solid; transistors and lasers depend on QM.
Carbon dating: cosmic rays make C-14 continuously; its 5,730-year half-life plus the law of large numbers makes decay extremely predictable.
Maxwell's four equations, explained visually — and his derivation that light is an EM wave traveling at exactly c.
Also: surviving a particle beam (Bugorski), harmless lab black holes, life not violating the 2nd law, and why high-speed water acts like concrete.
Highlights
"The coloring of the rainbow is nothing more than a shared (albeit reliable, consistent, and pretty) illusion."
Mantis shrimp hold the record: 16 cone-cell types in each of thousands of eyes.
Anatoli Bugorski (1978) accidentally put his head in a proton beam at the U-70 synchrotron — and survived to finish his PhD.
Feynman: "in physics today, we have no knowledge of what energy is."
The Bragg peak: charged particles dump most energy where they stop — exploited in proton therapy.
Maxwell derived c from EM constants: v = 1/√(ε₀μ₀) = 2.99×10⁸ m/s.
Part IV · off the physical map
CHAPTER 4Not Things: Math, Infinity, Chaos, and Abstractions
The book steps away from physical reality into pure mathematics and logic, arguing that math
is inherently human — as much a creation as love or the rules of poker — yet produces absolute,
irrevocable truths anyone can discover. The survey ranges over the topology of knots in higher
dimensions, the ubiquity of Fourier transforms, the precise meaning of chaos, the hierarchy of
infinities, a real proof that π is irrational, primality and RSA, why 1/0 can't be defined, and
fractional derivatives.
Knots exist only in 3 dimensions for strings; in 4+ any knot unties via a "lift trick." Generally, an N-sphere can knot in N+2 dimensions.
Fourier transforms decompose signals into frequencies — behind MP3/JPEG, EQ, and (less obviously) Heisenberg uncertainty, since FT of position is momentum.
Chaos isn't randomness: it's deterministic dynamics with exponential sensitivity (positive Lyapunov exponents). Weather caps at ~a week; orbits are predictable for millennia.
A Theory of Everything would supply equations, not understanding — the three-body problem is provably unsolvable in general.
Infinities come in sizes: rationals are countable (aleph-null), reals are strictly larger (Cantor's diagonal); the Continuum Hypothesis is undecidable.
π's non-repeating decimal is proven: a 1946 calculus proof shows it can't be a/b.
RSA is secure because factoring large products is hard; defining 1/0 as a number forces 1=0. Fractional derivatives use Euler's Gamma function. And 0.999… = 1.
Highlights
"Math is a scaffold that allows our mind's reach to exceed its grasp."
The Dragon Curve: fold a strip repeatedly, open the folds to 90°, and the path never crosses itself.
Hilbert's Hotel: a full infinite hotel can still take infinitely many new guests by doubling room numbers.