Cosmology That ClicksEpisode 6, Part 2 · your "everything from one number" becomes physics

Part 1: α was a running number → Part 2: three running forces — what if they meet at high energy?

Do the Three Forces
Meet at a Point? Part 1 showed α "runs." Nature has three running forces — electromagnetic, weak, strong.
If they line up at one point at high energy, "everything from one force" becomes real. That's grand unification.

Tools you'll need: Part 1's "running coupling," reading a graph Do the three runnings cross at one point?

In Part 1 we watched the electromagnetic force strength \(\alpha\) run with "how finely you look" (energy) — growing from \(1/137\) to \(1/128\). And we reposed the question: not "why 1/137," but "where do the running and the mechanism that fixes it come from?" Part 2 steps into the physics that comes closest to the answer. Nature has three running forces — electromagnetic, weak, strong — each running differently. If, at very high energy, the three line up at one point, then there is "one force," and our three branched off from it. Your original dream, "everything comes from one number," here becomes concrete physics: the grand unified theory (GUT).

01Three forces, three ways of running

In the particle world, setting gravity aside, there are three forces: the electromagnetic force (light and electricity), the weak force (which drives radioactive decay), and the strong force (which binds the nucleus). Each has a coupling constant for its "strength," and as we saw in Part 1, they all run with how finely you look (energy). But — they run in different directions.

How the three forces run (Part 1's "vacuum fluctuations" set the direction)

Electromagnetic-type force → stronger at high energy (the screening-peels-away effect from Part 1).
Strong force → weaker at high energy (freer as you get closer = "asymptotic freedom").
Weak force → runs somewhere in between.

Here's the interesting part. In the everyday low-energy world, the three strengths are all over the place (the strong force is strongest, electromagnetism is weak). But because each runs in a different direction, as you go to high energy, the three lines gradually approach one another. If they line up at one point out there, then the three had "one and the same strength" — they were an indistinguishable single force.

Linking to Part 1 What sets the direction of the running is the "screening by vacuum fluctuations" from Part 1. For electromagnetism, the fluctuations hide the charge, so it looked stronger the closer (higher energy) you got. For the strong force, the fluctuations behave differently, so conversely it looks weaker the closer you get. The same "fluctuation" mechanism produces a different running for each force — one picture from Part 1 splits the fates of the three lines.

02Run it — the three lines approach

Plot the three runnings with "how finely you look (energy)" on the horizontal axis and "weakness of the force (the inverse coupling \(1/\alpha\), weaker higher up)" on the vertical. At low energy (left) they're scattered. Move your eye rightward — toward high energy — and watch the three converge. The buttons below switch between "Standard Model" and "adding supersymmetry."

Figure: the running of the three forces' couplings (inverse). Right = high energy. Where the three converge is the candidate "grand unification scale"
electromagnetic-type force weak force strong force

In the plain Standard Model, the three approach but — don't quite cross at one point; they miss slightly. The small triangle the three make doesn't fully close. But add "supersymmetry," a new symmetry not yet found, and the running changes a little, the convergence improves, and around \(2\times10^{16}\) GeV (a super-high energy, roughly a trillion-times-a-trillion the everyday world) they gather nearly at one point. This dramatic approach has been treated as strong circumstantial evidence for both "grand unification" and "supersymmetry."

How high an energy?

The grand unification scale (candidate)

$$M_{\text{GUT}}\sim 2\times10^{16}\ \text{GeV}$$

Particle accelerators today reach about \(10^4\) GeV. The grand unification scale is a trillion times higher — checking it by direct collision is hopeless. So the way to test it relies not on accelerators but on a different prediction — which is proton decay, next.

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03If it's one force — the proton should decay

If the three forces really are one, a startling result follows. What are now separate — "quarks (the stuff of protons)" and "electrons/neutrinos" — become interchangeable relatives in the unified world. Then the proton, long thought stable, should very rarely decay. The most basic building block of matter would not be eternal.

This is a testable prediction. Fill a giant tank with a huge amount of water, watch an enormous number of protons, and wait for even one to decay. Japan's Super-Kamiokande does exactly this. The result — not a single one found yet. From this we know the proton's lifetime is staggeringly long.

The status of proton decay

The proton's lifetime is at least longer than \(10^{34}\) years (the observed lower bound) — roughly a trillion-times-a-trillion the age of the universe (about \(1.4\times10^{10}\) years). No decay has yet been observed.

This "no decay found" puts unified theories through a sieve. The most naive unified theory (the minimal SU(5) model) predicted the proton decays sooner — so it disagrees with observation and is essentially ruled out. To survive, you need a mechanism to make decay slower. A dream can't pass on beauty alone; it must get through the sieve of experiment.

04The honest state of play — the dream has come "halfway"

This is where Part 2 — and the question carried from Part 1 — currently stands. Grading your dream, "everything comes from one number," precisely —

Grading the dream (in current physics)

The force side (electromagnetic, weak, strong) → the storyline of branching from a single \(\alpha_{\text{GUT}}\) genuinely exists (grand unification). Half of it is working.
However → in the Standard Model the three don't fully cross; the supersymmetric version is promising but no superpartners have been found at accelerators; the minimal unified model is ruled out by proton decay — far from established.

And the other half. The electron-to-proton mass ratio named in Part 1 and Episode 2, \(\mu = m_e/m_p \approx 1/1836\), lives in a different room (the mechanism that sets the masses of matter) and comes out of neither \(\alpha\) nor \(\alpha_{\text{GUT}}\). Even if unification tidies up the force side, the mystery of matter's masses (why \(1/1836\)) is left untouched.

In terms of the series' backbone In Episode 2 we planted a flag: "\(\mu=m_e/m_p\) can't be derived from \(\alpha\)." Even with grand unification, the most powerful tool, this flag can't be knocked down — because unification of forces reaches only the "force room," not the "matter-mass room." Exactly how far your dream has come, and where it stops, shows up sharply at this one point. The forces may be unified into one. But why the electron is 1/1836 the mass of the proton, no one yet knows.

The honest line — a step more precise than the common story

It's often said that "in the Standard Model they don't cross, but with supersymmetry they cross perfectly at one point." Strictly, it's not that simple. The possibility that the Standard Model is the low-energy face of a grand unification can't be fully ruled out, and even in the supersymmetric version the three don't cross at exactly one mathematical point (a very small gap remains). "Approaches dramatically" is true, but "matches perfectly" is overstating it — here, as ever in this series, look at reality rather than the name or the common story.

Grand unification is a promising hypothesis with many attractions: particles group neatly into families, and it explains why charge comes in discrete values, among others. But the decisive evidence (proton decay or superpartners) has not been found. Beautiful, promising, yet unestablished — that's the honest state of play.

Practice problems (solvable with this episode)
  1. Why, though the three forces are scattered at low energy, can they approach at high energy? In one line.
    Show answer
    Because the three "run" in different directions. Electromagnetism gets stronger at high energy, the strong force gets weaker, and the difference in running direction brings the lines together. Without running, they'd stay scattered forever.
  2. How many times higher is the grand unification scale \(2\times10^{16}\) GeV than the accelerator reach of \(10^4\) GeV?
    Show answer
    \(2\times10^{16}\div10^4=2\times10^{12}\) — about two trillion times. Direct collision to check it is practically impossible, so we rely on indirect predictions like proton decay.
  3. Name one "different room" mystery that remains even if grand unification unifies the forces, using a quantity from Episode 2.
    Show answer
    The electron-to-proton mass ratio \(\mu=m_e/m_p\approx1/1836\). It belongs to the mechanism that sets matter's masses and can't be derived from the unification of forces (the α side). "Why 1/1836" remains unsolved.

Part 2 wrap-upThe dream has come halfway; half stays open

Part 1 showed "α runs." Part 2 showed three running forces, each running differently, converging at high energy. Line up at one point and it's "one force" — grand unification. In the Standard Model they don't fully cross; the supersymmetric version is promising but unconfirmed; the minimal unified model is ruled out by proton decay. The "force side" of the dream has come as far as a storyline that genuinely exists.

But the "matter-mass side" (why \(m_e/m_p=1/1836\)) is untouched even by grand unification. Your "everything from one number" is half-realized for the forces and stays open for matter's masses — this is not a failure of your reasoning, but a door physics itself cannot yet open. The question reposed in Part 1 let us point precisely to "how far we can go, and where we stop." A good question drew the map of the unsolved — that's the payoff of Episode 6.

This is Episode 6, Part 2 of "Cosmology That Clicks," a reading piece for curious high-schoolers and undergraduates. The running of the three gauge couplings, the fact that they don't fully cross at one point in the Standard Model, that in the MSSM (supersymmetric Standard Model) they cross with much improvement near \(\sim2\times10^{16}\) GeV, that minimal SU(5) is strongly constrained by the non-observation of proton decay, and that the proton lifetime lower bound is of order \(\sim10^{34}\) years, are all established. The popular phrasing "the MSSM crosses perfectly at one point / the Standard Model is completely ruled out" is not strictly correct, and this piece adopts a more accurate wording. The figure is a schematic of the concept, not a faithful reproduction of measured slopes and intercepts. Grand unification and supersymmetry are promising but unestablished hypotheses, and the flavor origin (such as the electron-proton mass ratio) is unsolved. — To print, use your browser's Print → Save as PDF (in the printed version, the toggle and answers are static/hidden).

Print / save as PDF: ⌘+P (Ctrl+P on Windows). On screen, the buttons switch between Standard Model / supersymmetry. "Show answer" opens the solutions.