Relativity, quantum theory, fields, and gravity are not rival, separate theories — they are separate corners of a single cube
By the time you have read the "Wakaru" collection this far, relativity, quantum theory, fields, gravity, and cosmology should feel not like separate hard problems but as one continuous landscape. What draws that landscape on a single sheet is this Physics Cube (Bronstein's cube). Physics has 3 fundamental constants that set how strongly the world "acts" — c (the speed of light, relativity), ℏ (the grain of action, quantum), and G (gravity). Treat each of these as a switch that is either "off (ignore it)" or "on (let it act)." Then the combinations of the three switches — 2×2×2 = 8 possibilities — become the 8 corners of the cube, and each corner holds one of humanity's major theories exactly. The origin is Newton; each time you flip a switch a new theory appears; and only the final corner, with all three switched on, is — unfinished. Let's walk through which part of this cube each Wakaru series has been drawing.
What each switch means is exactly the subject of each series so far.
• c (relativity): let the finiteness of the speed of light act. Off (\(c\to\infty\)) and time is absolute; on and space and time become one (Relativity That Clicks).
• ℏ (quantum): let the grain of action \(\hbar\) act. Off (\(\hbar\to0\)) and the world is classical; on and you get superposition and uncertainty (Quantum That Clicks).
• G (gravity): let gravity act. Off and there is no gravity; on and masses attract / spacetime curves.
The refrain the "Wakaru" series has returned to again and again — "Newton is a limit of some ratio," relativity's \(\beta\to0\), the quantum's \(S/\hbar\to\infty\) — is precisely the act of switching a switch off. The origin of the cube (everything off) is Newton's world.
| c | ℏ | G | Theory | Wakaru series |
|---|---|---|---|---|
| — | — | — | Newtonian mechanics | (the classical starting point) |
| c | — | — | Special relativity | Relativity That Clicks 1–5 |
| — | ℏ | — | Quantum mechanics | Quantum That Clicks |
| — | — | G | Newtonian gravity | Force That Clicks (gravity) |
| c | ℏ | — | Quantum field theory (relativistic quantum theory) | Fields That Click |
| c | — | G | General relativity (gravity = curvature) | Relativity That Clicks 6–7 |
| — | ℏ | G | Non-relativistic quantum gravity (limited) | (partial) |
| c | ℏ | G | Quantum gravity / theory of everything | Unfinished |
When people say relativity and the quantum "conflict," they are only talking about the very last corner of this table — quantum gravity, with \(c,\hbar,G\) all switched on. Special relativity and the quantum, far from conflicting, merge happily into quantum field theory (Fields That Click), the most precisely tested theory humanity has. The conflict is not "everywhere" — it is localized at "the last corner."
The figure below is the cube spanned by the three axes \(c\), \(\hbar\), and \(G\). Flip each switch on or off with the buttons below, and the corner you're currently at lights up, showing the name of that corner's theory and the matching "Wakaru" series. Starting from the origin (all off), cross one edge at a time and visit each theory. Only the far corner, with all three switched on, is red — the quantum gravity no human has yet reached.
Seen this way, a map of the whole "Wakaru" collection emerges. Relativity That Clicks is the c axis (special relativity) and the c–G edge (general relativity); Quantum That Clicks is the ℏ axis; Fields That Click is the c–ℏ face (quantum field theory) — and its heart, the gauge principle, is exactly the language of that corner. Force That Clicks is a journey peeling force away from the classical all the way to fields (c–ℏ), crossing the cube. And Cosmology That Clicks looks toward the region of the early universe where c, ℏ, and G all act at once — it was an attempt to reach toward the deepest corner of the cube (the quantum gravity corner). The series that seemed scattered were all lighting up different faces and corners of one and the same cube.
Seven of the cube's corners already belong to humanity. Special relativity, quantum mechanics, Newtonian gravity, quantum field theory, general relativity — every one is precisely tested and has become technology. Only the one remaining corner, quantum gravity with \(c\), \(\hbar\), and \(G\) acting simultaneously, has been unfinished for 100 years. The center of a black hole, the beginning of the universe (the Big Bang), a world where spacetime itself undergoes quantum fluctuations — only there do all three axes of the cube apply. String theory and loop quantum gravity are aiming at this last corner.
But what has come into view across this whole collection is a quieter single attitude — dimensionful quantities (meters, seconds, newtons, and the values of c, ℏ, G) are stage machinery. What decides the shape of the world is only the dimensionless ratios. The lag number \(\varepsilon\), the speed \(\beta\), the action's \(S/\hbar\), the coupling \(\alpha\), the dimension \(d\), the Yukawa coupling \(y\) — in every series, thinking in terms of ratios kept things from getting complicated. What was hard was never the physics; it was the way of seeing that starts from units. Perhaps the cube's last corner, too, will suddenly become simple the day someone finds the right ratio.
The major theories of physics line up at the 8 corners of a cube whose axes are the fundamental constants c, ℏ, G. The origin is Newton; turn on \(c\) for special relativity (Relativity That Clicks), \(\hbar\) for quantum mechanics (Quantum That Clicks), \(c+\hbar\) for quantum field theory (Fields That Click), \(c+G\) for general relativity (the second half of Relativity That Clicks). The "conflict" between relativity and the quantum is only about the last corner = quantum gravity (unfinished), with \(c,\hbar,G\) all on; special relativity and the quantum instead merge happily as quantum field theory.
Each "Wakaru" series was a map lighting up different faces and corners of this cube. And what sets your address is not the axis constants themselves but the dimensionless ratios \(\beta,\ S/\hbar,\ \Phi/c^2,\ \alpha\dots\) — the thread running through the whole collection: "units are stage machinery; what acts are the ratios." The one remaining corner, quantum gravity, too, will someday fit onto a single sheet once the right ratio is found. Think from there, and it doesn't get complicated.
Print / save as PDF: ⌘+P (Ctrl+P on Windows). On screen, the c·ℏ·G buttons switch between the cube's corners (theories).