"α changes from 1/137 to 1/128" — this "change" is a different axis from the "moving over time" of Bonus 5
"The fine-structure constant changes from 1/137 to 1/128" — some people really do say this. But it is a change along a completely different axis from the "\(\alpha\) drifting with the ages" story we handled in Bonus 5. This one is the running we did in Episode 6, Part 1 — the value changes not with time, but with the energy you slam things together at (the fineness at which you look). Mix the two up, and you get an accident: you mistake "an accelerator result" for "the universe having changed." The second installment of the trilogy sorts out the two ways \(\alpha\) moves, cleanly.
First, what's actually happening. Recall the picture from Episode 6, Part 1. Around the electron clings a thin coat of \(e^+e^-\) pairs welling up out of the vacuum, hiding a bit of its charge (screening). Look coarsely (at low energy) and you're outside the coat, so \(\alpha\approx 1/137\); look finely (at high energy) and you've slipped inside the coat, where the unhidden, stronger charge shows through and \(\alpha\approx 1/128\). The rough boundary is around the mass of the \(Z\) particle (about 91 GeV).
The same electron, in the same era, viewed by changing only the measuring energy.
The everyday world (low energy) → \(\alpha\approx 1/137\) ／ the \(Z\)-particle scale (~91 GeV) → \(\alpha\approx 1/128\).
The era hasn't changed, and this isn't about the distant universe — it's a laboratory fact you can reproduce in an accelerator right now.
So when you hear "\(\alpha\) becomes 128" and brace yourself thinking "has the universe changed since long ago?!", that's mixing up the axes. What's moving here isn't time \(t\), it's the fineness of your look = energy \(\mu\). Same phrase, "\(\alpha\) moves," but the axis it runs along is entirely different.
The "\(\alpha\) moving with time" we handled in Bonus 5, and the "\(\alpha\) moving with energy" of right now. The same-named quantity can move along two independent axes. Let's compare them head-on in a table.
| α moving with time (Bonus 5) | α moving with energy (this piece; Episode 6, Part 1) | |
|---|---|---|
| Axis it moves along | the universe's time t | the fineness of your look = energy μ |
| Example values | α may differ between now and 13.8 billion years ago | 1/137 (low E) → 1/128 (~91 GeV) |
| Is it physics? | real physics (shows up in observations) | real physics (shows up in observations) |
| Which constant do you blame? | gauge = free (e, or ε₀, or ħ — your choice) | no choice. Physics uniquely fixes it: "the coupling (charge) runs" |
| What about c and ħ? | fixing them is a gauge choice | they don't run at all (they aren't couplings) |
| How to check it | cosmology (quasar absorption lines, Oklo, atomic clocks) | accelerators (LEP, etc.) — reproducible right now |
| How certain | evidence for variation is unsettled and contested | an established fact |
In the figure below, watch how differently the two knobs bite. Turn the energy knob and \(\alpha\) runs hard (1/137→1/128). Turn the time knob, on the other hand, and \(\alpha\) stays almost flat — because observations pin it down tightly.
Here is the deepest point of this piece, and the very core of the contrast with Bonus 5. In Bonus 5, "when \(\alpha\) moves, whether you make \(e\), \(\varepsilon_0\), or \(\hbar\) the one that moves is a gauge (bookkeeping) freedom." But running has no such freedom. Physics (vacuum polarization) uniquely fixes that what runs is "the coupling constant = the charge \(e\)."
The reason is that \(c\) and \(\hbar\) don't run in the first place. These two aren't "couplings (strengths of a force)"; they are the kinematic conversion factors that link energy to frequency, and momentum to wavelength. Raise the energy, and there's no reason for \(c\) and \(\hbar\) — the conversion rates — to change what they convert. What runs, i.e. depends on energy, is only the coupling that expresses the strength of the interaction. So "blaming \(\alpha\)'s running on \(\hbar\)," that bookkeeping reassignment, simply doesn't hold up here.
α moving with time: you can choose which constant to blame (a gauge freedom remains).
α moving with energy: the mover is fixed to e (the coupling) — no choice. α(μ) is a uniquely determined, definite observable at each energy.
The conclusion. The people who say "\(\alpha\) becomes 1/128" are turning only the "fineness of your look" knob, while holding time, c, ħ, and every other constant fixed. They are doing none of the gauge reassignment — "which constant to blame" — of Bonus 5. That the moving factor is fixed to \(e\) (the coupling) is likewise not a choice but a consequence of the physics of vacuum polarization. So "128" is textbook quantum field theory (QED), and it lives on a different shelf from the varying-constants claim that "the universe has changed since long ago."
The axes are different, but there is a place where the two meet. Build a theory in which "\(\alpha\) really does move with time," and that motion feeds back into the way-of-running rule (the β function) and the contents of the vacuum. So varying-α theorists discuss time variation on top of the running framework. A different axis, but standing on the same stage (quantum field theory) — that's the precise picture.
Note that "nearly flat on the time axis" in the figure is a schematic expression. In reality atomic clocks pin it to \(|\dot\alpha/\alpha|\lesssim 10^{-17}\)/year, and even quasar observations claiming variation come out, order-of-magnitude, at around \(10^{-6}\) over the age-of-the-universe scale — nothing like the 7% of the energy axis. That's why we draw it "nearly flat."
"1/137 becomes 1/128" is running that moves with energy (the fineness of your look), not time. Through screening by vacuum polarization, the finer you look the stronger the charge appears and the more α grows — a fact already checked in accelerators. It is a different axis from the "α moving with time" of Bonus 5, and moreover running has no gauge freedom of "which constant to blame" — physics uniquely fixes that what runs is the coupling (charge), and c and ħ don't run in the first place.
So seeing "128" and thinking "the universe has changed" is mixing up the axes. α moving with time is unsettled and contested; α moving with energy is an established fact. The same-named quantity can move along two independent axes — the first thing to do is tell which one you're talking about. That was the second installment of the trilogy.
Print / make a PDF: ⌘+P (Ctrl+P on Windows). On screen, the slider lets you see how differently the energy axis and time axis bite. "See the answer" opens each solution.