Force That ClicksEpisode 8 ／ Peeling the true nature of force away, one layer at a time

Episode 7: we lined up the four forces as dimensionless numbers → Episode 8: those "strengths" turned out not to be fixed values

A force's strength changes
with how closely you look The coupling constants we lined up last time actually move. Look up close (at high energy) and electromagnetism grows stronger, while the strong force grows weaker.
And far out at high energy, the strengths of three forces draw near a single point ── a whiff of unification.

Tools you'll need: Episode 7's coupling constants, Episode 2's vacuum, a logarithmic graph The coupling "runs" ── strength is a function of how closely you look

In Episode 7 we lined up the four forces by their coupling constants (their dimensionless strengths). \(\alpha\approx1/137\), \(\alpha_s\sim1\)… But these numbers come with a big caveat ── they are not fixed values. The closer you look (the higher the energy), the more a force's strength shifts. In physics this is called the running coupling constant. In our sister series "Cosmology That Clicks," Episode 6, we watched \(\alpha\) grow from \(1/137\to1/128\); now we meet that same phenomenon from the side of the four forces. And as we let them run ── the once-scattered strengths of three forces begin to gather toward a single point far out at high energy. It's a hint that the forces may "originally have been one."

01The vacuum wears a "coat" ── which is why strength changes as you get closer

Why does strength change with how closely you look? The key is the vacuum fluctuations that already showed up in Episode 2. Around an electron drift electron–positron pairs, born from and vanishing back into the vacuum, and they thinly hide (screen) the electron's charge. Seen from far away (coarsely = at low energy) you're outside the coat, so the charge looks weak; get closer (finely = at high energy) and you enter the coat, where the real, stronger charge that hasn't been hidden comes into view.

How the coupling runs

Electromagnetism: the vacuum's coat hides the charge → the closer you look (higher energy), the stronger it appears (\(\alpha:1/137\to1/128\)…).
The strong force: the coat forms the other way around → the closer you look, the weaker it gets (asymptotic freedom, Episode 11).
Both are consequences of "screening by the medium called the vacuum." A force's "strength" was a function of how closely you look.

02Let them run, and three forces converge toward a single point

This is the climax of today's episode. Electromagnetism gets stronger as you get closer; the strong force gets weaker. They run in opposite directions. Which means that as you shift your gaze to much higher energies, the once-scattered strengths gradually draw together. The figure below plots the "inverse strength \(1/\alpha_i\)" of each of the three forces (higher = weaker) against energy (logarithmic). At low energy (left) the three lines are scattered. As you move right ── toward high energy ── the three lines close in on a single point.

Figure: the running of the three forces' strengths (inverse 1/α, higher = weaker). Right = high energy. Scattered at low energy, but converging toward a single point around 10¹⁶ GeV ── a whiff of unification

Energy you're looking at (logarithmic; higher toward the right)10² GeV

electromagnetic weak force strong force

If they gather at a single point, then there the three forces had "one and the same strength" ── a single, indistinguishable force. Our three are merely the branched-off form of that ── this is the idea of grand unification. We'll tackle it head-on in Episode 12, but its doorway lay right here, in the fact that "a force's strength runs."

A connecting voice ── even a "strength" value moves depending on how you look In Episode 7 we said "strengths can only be compared in dimensionless terms." Today, one step further ── even that dimensionless strength moves with how closely you look (with energy). What the sister series kept repeating ── "the surface value moves; what's deep is the 'way it runs' (the rule)" ── applies just as well to the strength of a force. More than the value itself, it's how it runs that gives a force its character. Episode 11's "only the strong force runs upside-down" is a story about this difference in how they run.

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03What the peeling revealed ── strength is set not by place but by "scale"

The conclusion of Episode 8. A force's "strength" is not a fixed attribute the force carries, but a running quantity set by how finely you look (by energy). The screening by the medium called the vacuum produces it. And the fact that three forces running in opposite directions crowd together at high energy is the strongest circumstantial evidence for unification ── the idea that the four (three) forces may originally have been one.

The honest line ── "exactly one point" is an overstatement

With the Standard Model as it stands, the three lines get close but don't meet at a perfect single point (they miss slightly). Add an as-yet-undiscovered symmetry called supersymmetry and the way they run changes, so they draw much closer to a single point at \(\sim10^{16}\) GeV ── that's the famous circumstantial evidence. Even so, "with supersymmetry they match exactly, mathematically" is not strictly correct either; both grand unification and supersymmetry are promising but unestablished hypotheses (the same honest line as the sister series, Episode 6 part two).

The slopes and crossing point of the three lines in the figure are a schematic showing the concept, not a strict reproduction of measured values. Gravity's "running" has a renormalization problem, so it isn't included in this figure (a topic for the finale).

Practice problems

Why does the electromagnetic force "appear stronger the closer (higher-energy) you look"?
See the answer
Vacuum fluctuations (electron–positron pairs) screen the charge, so as you get closer you enter the coat and see the un-hidden, stronger charge. α grows from 1/137→1/128.
What does it suggest that the three forces' strengths draw near a single point at high energy?
See the answer
That at high energy the three may have been one and the same strength ── a single, indistinguishable force (grand unification). Today's three are its branched-off, low-energy form.
Is "a force's strength" a fixed attribute? Episode 8's conclusion in one line.
See the answer
Not fixed. It's a quantity that runs with how closely you look (with energy), produced by the vacuum's screening. What's deep is not the value itself but "the rule for how it runs."

SummaryStrength runs, and three lines going opposite ways crowd together

The coupling constants we lined up in Episode 7 are not fixed values; because of the vacuum's screening they run with how closely you look (with energy). Electromagnetism gets stronger as you get closer; the strong force gets weaker (asymptotic freedom). Because they run in opposite directions, shifting your gaze to high energy brings the three strengths together, and around \(\sim10^{16}\) GeV they begin to gather at a single point ── a whiff of unification, that the forces may originally have been one.

The sister series' "the value moves; what's deep is how it runs" held just as well for the strength of a force. Still, "exactly one point" is an overstatement, and grand unification and supersymmetry are promising but unestablished. ── By now we've peeled away a force's strength, range, carrier, and how it runs. Next time, at last, to the core: where does force come from in the first place? Make a symmetry local, and a force is born ── that's the gauge principle.

Next time ── Episode 9 (the heart of the series) "Where does force come from?" We've been peeling away force's properties, but the last question standing is "why does force exist?" The answer is astonishingly deep ── the moment you allow an ambiguity you can freely choose at each point (local symmetry), a force is born to patch it up. We turn the gauge principle from the sister series' Bonus ⑧ into a main-line story, as the origin of force. It's the endpoint of the peeling.

This document is Episode 8 of the "Force That Clicks" series, a reading piece for high-schoolers and undergraduates who love physics. That coupling constants depend on energy (running coupling constants, the renormalization group) and are screened by vacuum polarization; that the electromagnetic coupling increases at high energy (\(\alpha:1/137\to\)about\(1/128\) at \(M_Z\)) while the strong coupling decreases (asymptotic freedom); and that the three gauge couplings approach one another at high energy, hinting at grand unification (they don't meet exactly in the Standard Model, and this improves to \(\sim10^{16}\) GeV in the MSSM and the like) ── these are established content plus promising hypotheses. Popular phrasings like "they cross at exactly one point / the Standard Model is completely ruled out" are not strictly correct. The figure is a conceptual schematic and does not strictly reproduce measured slopes and intercepts; gravity is not included because of the renormalization problem. ── To print, use your browser's "Print" and choose "Save as PDF" (in the print version the slider and answers are frozen or hidden).

Print / save as PDF: ⌘+P (Ctrl+P on Windows). On screen, raise the energy with the slider to watch the three forces crowd together. Click "See the answer" to reveal each solution.