Cosmology That ClicksBonus 3 · the tale of a theory that came so close

There was a theory that seriously tried "changing the speed of light." Fine motive, but it slipped in the implementation.

Why VSL Was So Close But Missed The varying-speed-of-light theory (VSL) — a genuine theory that tried to solve cosmic puzzles by changing the speed of light.
The motivating instinct was right. Where it stumbled was the choice of "what to hold fixed."

Tools you'll need: α from Episode 2, Episode 6's "only the dimensionless is physics" what should be held fixed was α, not c

Throughout this series we've used "the speed of light slows" strictly as a way of seeing (a guide-line). But in history there are people who pursued it seriously as a genuine physical theory — the varying-speed-of-light theory (VSL). Albrecht and Magueijo, and Barrow and others, proposed it in the late 1990s. Its aim was admirable and it's still cited. Yet it never became mainstream. This time we'll diagnose "why it was so close but missed" precisely, using the tools we've stacked up in this series — not hunt for a culprit. And that diagnosis becomes exactly the flip-side key to the next topic (under what conditions spatial curvature and slowing light are equivalent).

01The motive was entirely right

What VSL tried to solve is standard cosmology's hard problem, the "horizon problem" — the puzzle that the universe is nearly the same temperature everywhere, though far-apart regions could never have exchanged light signals (we computed this in Episode 4). The mainstream answer is "inflation," a rapid expansion of the early universe. VSL proposed a different road — if the speed of light was much faster in the early universe, light reaches far, contact is made, and the puzzle disappears.

This idea is exactly the same as what you saw in Episodes 1 and 4: "light used to be fast → the horizon widens." So VSL's motivating instinct rings intuitively right for a reader of this series. This deserves full credit. The near-miss was in the implementation, not the motive.

02The stumble — "moved only c, held the others fixed"

The original VSL, while varying the speed of light \(c\) over time, held the other constants fixed — the amount of charge \(e\), Planck's constant \(\hbar\), and so on. Here, recall Episode 2's equation.

Episode 2's fine-structure constant
$$\alpha = \frac{e^2}{4\pi\varepsilon_0\,\hbar\, c}\approx\frac{1}{137}$$

\(c\) sits in the denominator. Hold \(e,\hbar,\varepsilon_0\) fixed and move only \(c\), and — \(\alpha\) moves. As we saw in Episode 6, \(\alpha\) is the unit-free "number of the universe itself" that governs the atomic world. Its changing in time would mean the colors of the light atoms emit, and the rhythms of atomic clocks, drift over the ages.

And as emphasized in Episodes 2 and 6, atomic clocks confirm \(\alpha\) "isn't moving" to the staggering precision of less than \(10^{-19}\) per year. A VSL that moves only \(c\) instantly collides with this observation. Here's the near-miss — it mistook what to hold fixed.

Precisely — it did NOT "hold too much fixed" A common misconception is "VSL was cramped because it held too many constants fixed." But precisely, it's the opposite — the "combination" of what it held fixed was mismatched. If you move \(c\), you should move \(e\) and \(\hbar\) in step to protect \(\alpha\). By fixing each one separately, it accidentally moved the very ratio it most needed to protect, \(\alpha\). What should be protected was not the individual constants, but their ratio.

03The real dilemma — harmless but powerless / powerful but harmful

So what should VSL have done? Here an unavoidable choice appears. Using the series' backbone — "only the dimensionless ratio \(\alpha\) is physically meaningful; moving the dimensionful \(c\) alone is just swapping the standard" — there are only two roads.

Road A: protect α, move c
Move \(e,\hbar\) in step as \(c\) moves, keeping \(\alpha\) constant. Not beaten by atomic clocks.
But — then the change in \(c\) becomes just a relabeling of units, leaving no trace in observation. It has no physical power to "solve" the horizon problem.
→ harmless, but powerless
Road B: actually move α
Move only \(c\) and allow \(\alpha\) to change in time. Then the early-universe physics genuinely changes and it has the power to solve the horizon problem.
But — it instantly collides with the atomic clocks' \(10^{-19}\)/yr and dies.
→ powerful, but harmful

The original VSL essentially chose Road B (or was indifferent to the A-vs-B distinction) and took Road B's punishment. The near-miss was failing to find a "third road" that satisfies both "the power to solve the horizon" and "\(\alpha\) invariant (compatible with experiment)." In the figure below, watch how it gets stuck between the two choices.

Figure: VSL's dilemma. Raise "how much you move c" and the horizon-solving power (green) grows, but α's drift (red) grows too, exceeding the atomic-clock limit.
◇ ◇ ◇

04Why your c·t=constant didn't step on the trap

This is the heart of the episode, and a "return gift" to the earlier ones. The \(c\cdot t=\text{constant}\) universe built up in Episodes 1–4 structurally avoided this VSL trap. The reason: what it moved was different.

The decisive difference

What VSL moved was \(c\) itself (holding the other constants fixed).
What \(c\cdot t=\text{constant}\) really moved was the way of expanding, \(a\propto t\) (straight-line expansion). The change in \(c\) is merely a "rephrasing" of that expansion in the language of the speed of light.

This difference lets it take both sides of the choice.

It gets Road B's "power" without moving \(c\). The work of solving the horizon problem is done not by \(c\)'s variability but by the physics of the expansion law \(a\propto t\) (Episode 4's diverging \(\int c\,dt\); its identity is the \(R_h=ct\) universe). So it gains the solving power without moving \(\alpha\).

It also holds Road A's "harmlessness" at the same time. \(c\cdot t=\text{constant}\) can also be read as a rephrasing (a gauge) that "just writes the expansion in the language of the speed of light," so \(\alpha\) stays invariant. Not beaten by atomic clocks.

Where VSL got stuck between the two choices, your guide-line drew the line "c is a bookkeeping rephrasing; the real thing is the expansion law" and erased the very footing on which one stumbles. VSL clung to "moving \(c\)" and tripped over the bookkeeping of constants. \(c\cdot t=\text{constant}\) didn't cling to \(c\), so there was no place to trip — this is the precise content of "VSL is a near-miss; \(c\cdot t=\text{constant}\) is better reasoned."

Linking voice (the series' backbone) Episode 1 ("moving \(c\) is swapping the standard"), Episode 2 ("what to protect is the unit-free \(\alpha\)"), Episode 6 ("\(\alpha\) is the number of the universe itself") — use all of these and VSL's near-miss diagnoses in one line: "moved the dimensionful \(c\) and failed to protect the dimensionless \(\alpha\)." The series' backbone lets you point precisely to where a genuine, near-miss theory slipped. It works as a "ruler" for judging theories, too.

The honest line — so as not to gloat

This isn't about knocking VSL down to lift up \(c\cdot t=\text{constant}\). VSL is genuine research that posed a valuable question — "can the horizon problem be solved without inflation?" — and stacked up serious calculation. It's just that the lesson learnable from it (= what to protect is \(\alpha\)) happened to be implemented in this guide-line.

And \(c\cdot t=\text{constant}\) (= the \(R_h=ct\) universe) has unpaid homework too — the consistency with the early formation of the elements (Big Bang nucleosynthesis) mentioned in Episode 1. Whether straight-line expansion is compatible with the early abundances of elements is a still-unsettled point of contention. It's not that VSL alone was a near-miss while this side is perfect. Every theory carries unpaid homework somewhere.

Wrap-upWhat to protect was not individual constants, but the "ratio"

VSL's motive — solve the horizon problem without inflation — was right. It stumbled in the implementation: moving only \(c\) and holding the others fixed, it moved the very ratio it most needed to protect, \(\alpha\), and collided with atomic clocks. It arrives at a two-way choice — protect \(\alpha\) and it's harmless but powerless; move \(\alpha\) and it's powerful but harmful. Failing to find the third road was the identity of the near-miss.

\(c\cdot t=\text{constant}\) didn't step on this trap because what it moved was not \(c\) but the expansion law \(a\propto t\), treating the change in \(c\) as a "rephrasing." Don't cling to the dimensionful value; protect the ratio that must be protected — this one point that VSL's near-miss taught us was a direct example of what this series has said all along.

This is Bonus 3 of "Cosmology That Clicks," a reading piece for curious high-schoolers and undergraduates. VSL (varying-speed-of-light theory) is a real cosmological program by Albrecht–Magueijo (1999) and Barrow and others, proposed as an alternative approach to the horizon and flatness problems. That in the original VSL a change in \(c\) is accompanied by a change in the fine-structure constant \(\alpha\), in tension with constraints on \(\dot\alpha/\alpha\) from atomic clocks and spectroscopy (currently roughly \(\le 10^{-19}\)/yr), is a genuine point of contention. The figure is a schematic of the dilemma, not a quantitative theoretical curve. The \(R_h=ct\) (linear-expansion) model also has unsolved points of contention such as Big Bang nucleosynthesis. — To print, use your browser's Print → Save as PDF.

Print / save as PDF: ⌘+P (Ctrl+P on Windows). On screen, the slider shows the tug-of-war of the dilemma.