Episode 6: force is an exchange of carriers → Episode 7: lining up the four forces on a single table and comparing them
In Episode 6 we saw that all four forces run on the same mechanism ── "an exchange of carriers." So how do their strengths differ? Here the lesson of Episode 1 pays off ── the absolute value of a force (in newtons) depends on your choice of units, and as it stands it can't be compared. To line them up fairly, you have no choice but to measure with the number that has no units ── the coupling constant. The star of the sister series "Cosmology That Clicks," \(\alpha\) (the fine-structure constant ≈ 1/137), was precisely the "dimensionless strength" of the electromagnetic force. Line the four up dimensionlessly and the orders of magnitude are astonishingly far apart ── and then the mystery of why the weakest force, gravity, somehow rules the universe stands out in sharp relief.
To answer "which is stronger, electromagnetism or gravity?", you have to put both on the same ruler. But the value of a force is in newtons, and change the units and the number changes too (Episodes 1 and 2). So for each force we use a coupling constant ── a ratio with the units gone capturing "how strongly that force acts between two elementary particles." For electromagnetism, that is \(\alpha=e^2/4\pi\varepsilon_0\hbar c\approx 1/137\).
| Force | Dimensionless strength (rough) | Carrier | Range |
|---|---|---|---|
| Strong force | \(\alpha_s \sim 1\) | Gluon | Short (confinement) |
| Electromagnetic | \(\alpha \approx 1/137 \sim 10^{-2}\) | Photon | Infinite (1/r²) |
| Weak force | \(\sim 10^{-6}\) (effective at low energy) | W, Z | Extremely short |
| Gravity | \(\alpha_G=\dfrac{G m_p^2}{\hbar c}\sim 10^{-38}\) | Graviton (hypothetical) | Infinite |
The shock of this table is that the strengths are spread across about 36 orders of magnitude. Set the strong force to 1 and gravity is \(10^{-38}\) ── a 1 with 38 zeros after the decimal point. The difference is so vast it feels wrong to lump them under the single word "force." And gravity is, of the four, the weakest by a landslide.
This is the crux of the episode. In daily life and across the cosmos, what holds us to the ground, keeps the Moon in orbit, builds the stars, and binds the galaxies together is gravity. The weakest of all, yet on large scales it wins outright. Why? The reason is not strength, but whether things cancel or pile up.
Electromagnetism: charge comes in plus and minus, and matter is neutral. The more you gather, the more it cancels out, and the net is nearly zero. It's orders of magnitude stronger, yet in a large object it can't show its face.
Gravity: mass (energy) is positive only. There's no cancellation, so the more you gather, the more it just keeps piling up. On top of that, it reaches out to infinity.
So for a large, neutral lump (a planet, a star), it's gravity ── weak but never cancelling ── that wins.
In the figure below, watch what happens as you make the object larger (increase the number of particles): the net electromagnetic force stalls because of cancellation, while gravity keeps piling up and overtakes it at some size. Electromagnetism, which per particle is \(10^{36}\) times stronger, loses to gravity in a large object ── this is what "weakest yet dominant" really means.
The conclusion of Episode 7. The "strength" of the four forces can't be compared in newtons; it only carries meaning through the coupling constant, with the units gone. Episode 1's "the absolute value is a convention, the ratio is the physics" applied directly to comparing forces. And phrases like "gravity is weak" and "the strong force is strong" were pointing at the size of the dimensionless coupling all along. The sister series' \(\alpha\) was the electromagnetic version of that.
• Strength can be compared only dimensionlessly (\(\alpha_s\sim1,\ \alpha\sim10^{-2},\ \text{weak}\sim10^{-6},\ \alpha_G\sim10^{-38}\)).
• Whether a force is "dominant" isn't decided by strength alone ── what matters is whether it cancels (electromagnetism) or piles up (gravity) and its range.
• Each force's individuality (strength, range, carrier) gets one more layer peeled back next time, in the "running."
The dimensionless strengths in the table are rough orders of magnitude. In particular, the weak force's "\(\sim10^{-6}\)" is an effective weakness at low energy because its carriers W and Z are heavy; its intrinsic coupling is comparable to electromagnetism (electroweak unification). The strong force's \(\alpha_s\sim1\), too, changes greatly with the energy you probe at, as we'll see next time. \(\alpha_G\) is the value using "proton mass against proton mass" as the reference; change the reference particle and the number changes (gravity depends on mass, so making it dimensionless requires a reference).
The figure is a schematic showing the contrast of "cancels / piles up," and it simplifies the relation between particle number and force (gravity ∝ N², while the electromagnetic net depends on the degree of neutrality). The particle number at which the crossover happens is conceptual too.
The strengths of the four forces can't be compared in newtons; they line up only through the coupling constant, with the units gone ── strong force \(\sim1\), electromagnetism \(\alpha\sim10^{-2}\), weak force \(\sim10^{-6}\), gravity \(\alpha_G\sim10^{-38}\). A spread of about 36 orders of magnitude. Episode 1's "the ratio is the physics" was the foundation for comparing forces. The sister series' \(\alpha\) is the electromagnetic version of this.
And the weakest force, gravity, rules the universe not through strength but because it piles up without cancelling. Electromagnetism, however many orders of magnitude stronger, is neutralized by its plus and minus and vanishes in a large object. Gravity piles up with mass and reaches out to infinity. ── Next time we'll see that this "strength" isn't a fixed value but runs with the energy you probe at. It's Episode 6 of the sister series' running, seen from the side of force.
Print / save as PDF: ⌘+P (Ctrl+P on Windows). On screen, use the slider to watch gravity overtake electromagnetism as you make the object larger. Click "See the answer" to open each solution.