Why is the proton (almost) eternal?

Every atom in your body is at least 13 billion years old — and they will stand firm until the end of the universe. Yet a lone neutron only survives about fifteen minutes. Why this staggering difference?

The quietly revolutionary mystery

You know what's extraordinary? You exist. And your atoms exist. And they have existed since primordial nucleosynthesis, about 13.8 billion years ago. The protons that make up the nuclei of your atoms are, with very few exceptions, the same protons that formed in the aftermath of the Big Bang.

No experiment has ever observed a proton decay. The best measurements (notably Super-Kamiokande in Japan) set a minimum lifetime of 10³⁴ years — a number with 24 more zeros than the current age of the universe. For all practical purposes, the proton is eternal.

What about the neutron? Left alone in a vacuum, it lives on average 878 seconds — a bit less than fifteen minutes — before turning into a proton, releasing an electron and an antineutrino. This decay is known as β radioactivity.

The nucleon as a link

Remember Lesson 1: according to TQNT, a composite particle is a link, that is, an assembly of several knots that thread through one another. In TQNT, the proton and the neutron are one and the same link: three intertwined knots — one trefoil (the simplest) and two more complex knots called 7₂.

If you take these three knots and count how many times they wind around one another, you get a number. That number is called the linking number, written Lk (from the English linking number). And it — and it alone — is what tells the proton from the neutron.

• Proton: linking number = +3. This is the optimal linking, the configuration of lowest energy.
• Neutron: linking number = +2. In other words, one loop of linking is missing — as if one of the components had slipped to the side instead of fully engaging.

Why 1.293 MeV exactly?

That missing loop costs energy. It's like a taut rope that isn't quite in place: there is a residual tension. TQNT computes this tension from the geometry of the knots and obtains:

Tension energy between proton and neutron = 1.293 MeV (megaelectronvolts).

Now that is exactly the mass difference measured experimentally: m(neutron) − m(proton) = 1.293 MeV. TQNT reaches this result with no adjustable parameter, purely from the geometry of the knots. It is one of the theory's prettiest successes.

Topology as a shield

Why is the proton so durably stable, when no classical conservation law explicitly forbids it from decaying?

TQNT's answer: because decaying would require changing the topology of the knot, and that operation is mathematically impossible at finite cost. You can deform a knot however you like — twist it, stretch it — and it remains the same topological knot. To turn a trefoil into a 2-crossing knot, you have to cut it. And cutting costs an infinite amount of energy.

More precisely: you would have to climb what is called the Chern–Simons barrier, whose height is colossal. The spontaneous decay rate is on the order of 10⁻³⁶⁸. To give you an idea: the probability that it happens during the entire age of the universe is smaller than the chance of randomly picking one specific atom inside one specific grain of sand somewhere on Earth… raised to the power 1,000.

In short, the proton is topologically stable — but not eternal in the strict sense: the barrier is so high that the theory predicts a lifetime of about 10³⁴ years, precisely the level the future Hyper-Kamiokande detector will probe. A decay observed there would be a spectacular confirmation. And it is because that lifetime exceeds the age of the universe by an unimaginable factor that you are here to read these lines.

The neutron: the slipping loop

The neutron has a suboptimal linking. Its 'extra' loop is not locked in by the topology: statistically, it can come loose. When it does, the neutron settles into the proton-plus-freed-loop configuration, and the freed loop shows up as:

• an electron (which carries away the negative charge the loop was supposed to balance);
• an antineutrino (which carries away the energy mismatch).

This is exactly β radioactivity, as seen in every nuclear physics textbook — but retold as a story of topology readjusting itself, rather than in the language of virtual W bosons of the Standard Model. TQNT predicts a neutron lifetime of 880 seconds against the 878 seconds measured: 0.2% error, once again with no adjustable parameter.

And the other particles?

The same mechanism explains why some particles live a few billionths of a second and others fractions of a zeptosecond. The decay channel available to each particle depends directly on the topology of its link:

• a particle with a free loop can decay via the weak channel (slow);
• a particle with perfect linking can only use the electromagnetic channel (very fast);
• a particle with very strong tensions takes the strong nuclear channel (the fastest of all).

The former lifetime scale (34 states at 0.94 decades) has been archived along with its mass operator. What is derived today is stronger: the very structure of the decay law (the Fermi law and the Sargent rule) comes out of P15 topological reconnection — the muon lifetime is recovered to 0.4%, the W branching ratios to 0.2%, and any unprotected heavy link cascades in ~10⁻¹⁸ s (the “desert theorem”).