Chase asked me recently whether stable elements actually decay. It is the kind of question that sounds simple until you pull on it, and then it keeps coming. The short answer is: not exactly, but it depends entirely on what you mean by stable.
The longer answer is more interesting.
Stable Is a Label, Not a Property
In nuclear physics, radioactive decay is the process by which an unstable nucleus sheds energy by emitting radiation, transforming into a different nucleus in the process. The rate at which a population of atoms decays is characterized by its half-life: the time required for half the atoms in a sample to undergo decay. Half-lives span an extraordinary range, from fractions of a microsecond for highly unstable isotopes to timescales that dwarf the age of the universe.
“Stable,” in this context, is a practical label we apply to isotopes whose half-lives are either too long to measure directly or only calculable from theory. It is not a statement that no decay is occurring or ever will occur. It is a statement that we cannot observe it on any human timescale, and in many cases on any cosmic timescale either.
Consider Tellurium-128. Its half-life is approximately 2.2 × 10²⁴ years, the longest of any isotope whose radioactivity has been confirmed. That figure is roughly 160 trillion times the current age of the universe. In a gram of Tellurium-128, you would expect to observe a decay event perhaps once every several centuries. It is worth noting that this figure was not directly measured; it was inferred from geochemical analysis because the decay rate is so vanishingly slow that direct measurement over any achievable timescale is essentially impossible. For comparison, the longest directly measured half-life belongs to Xenon-124, at 1.8 × 10²² years, confirmed by the XENON1T experiment and published in Nature in 2019 after observing 126 decay events over a year of operation using two tons of liquid xenon. That experiment, buried 1,500 meters beneath the Gran Sasso mountains in Italy to shield it from cosmic ray background noise, is a remarkable illustration of how far experimental physics will go to catch nature in the act.
So when physicists call an element stable, they mean it in the way an actuary might call a 40-year-old healthy: not that nothing will ever happen, but that the probability is so low over any practical horizon that the distinction between “will not decay” and “has not decayed and is unlikely to decay” is operationally meaningless. For most purposes, that is good enough. For the question Chase was asking, it is not.
The Double Beta Decay Wrinkle
It is also worth pausing on the mechanism behind Tellurium-128’s extraordinary longevity, because it reveals something about why “stable” is so hard to define cleanly. Tellurium-128 decays via double beta decay, a process in which two neutrons simultaneously convert into two protons, emitting two electrons and two antineutrinos in a single event. This simultaneous two-body transformation is governed by the weak nuclear force, and its improbability is not merely quantitative but qualitative: it requires two independent quantum mechanical tunneling events to occur at the same instant. The rarity of that coincidence is what produces the spectacular half-life.
Many isotopes conventionally listed as stable have been theoretically shown to be capable of double beta decay, or other decay modes including alpha decay, with half-lives so long that we have never observed a single event. Bismuth-209 was considered unambiguously stable for most of the history of nuclear physics until 2003, when a research team at the Institut d’Astrophysique Spatiale directly observed its alpha decay with a half-life of approximately 1.9 × 10¹⁹ years. That experiment used 31 grams of bismuth and a cryogenic detector sensitive enough to measure the heat deposited by individual decay events. Bismuth-209 was not less stable the day after that paper was published. We simply knew more about it. The decay was always happening. We had just never been watching carefully enough.
This is the epistemological core of Chase’s question. What we call stable is really a statement about the limits of our instrumentation and our patience, not about nature drawing a hard line.
The Proton Is Different
For every isotope discussed above, the nucleus contains both protons and neutrons, and the decay modes involve rearranging or shedding nuclear constituents. But hydrogen-1, ordinary protium, is just a single proton. There are no neutrons to rearrange. Asking whether hydrogen-1 decays is really asking whether the proton itself decays. And that is a genuinely open question in fundamental physics, not merely a question about measurement limits.
Grand Unified Theories, or GUTs, are a class of theoretical frameworks that attempt to unify the strong nuclear force with the electroweak force at very high energies. Most GUT models predict that proton decay is possible, typically via the channel p → e⁺ + π⁰ (a positron and a neutral pion) or p → ν̄ + K⁺ (an antineutrino and a charged kaon). The proton would accomplish this by violating baryon number conservation, a symmetry that the Standard Model treats as exact but that GUTs predict is only approximate. The predicted half-lives, depending on the specific model and the energy scale of unification, generally fall in the range of 10³⁴ to 10³⁶ years.
The experimental effort to detect proton decay has been going on for decades and is one of the most technically demanding programs in physics. The flagship experiment is Super-Kamiokande, a detector containing 50,000 tonnes of ultrapure water buried one kilometer beneath Mount Ikeno in the Kamioka mine in Gifu Prefecture, Japan. The logic is straightforward: if you have enough protons in one place and watch them long enough, statistics suggests you should eventually see one decay, even at half-lives approaching 10³⁴ years. A 50,000-tonne tank of water contains roughly 3.3 × 10³³ protons. At a half-life of 10³⁴ years, you would expect to see a few events per year.
Super-Kamiokande has been watching since 1996. In nearly three decades of operation, across hundreds of kiloton-years of exposure, it has seen nothing unambiguous. The most stringent current lower bound, from a 2020 analysis published in Physical Review D, puts the partial lifetime for p → e⁺ + π⁰ at greater than 2.4 × 10³⁴ years at 90 percent confidence. A 2024 analysis of the p → e⁺ + η channel sets a lower limit of 1.4 × 10³⁴ years. Each non-detection eliminates another slice of the parameter space available to GUT models and forces theorists to push their predicted half-lives higher, into ranges that strain even Super-Kamiokande’s sensitivity.
What makes this extraordinary as an experimental enterprise is what the detector is actually doing. It is not measuring decay products directly. It is watching for the Cherenkov radiation produced when a charged particle moves through water faster than light travels through water. A decaying proton produces a positron and a pion, the pion immediately decays to two photons, and the whole event produces a distinctive ring of blue light in the tank. The experiment has been staring at 50,000 tonnes of water for thirty years, looking for a specific pattern of blue flashes. So far: nothing.
The Two Possible Universes
The absence of observed proton decay places us in one of two genuinely distinct physical universes, and we do not yet know which one we inhabit.
In the first universe, baryon number is only approximately conserved, GUTs are broadly correct, and the proton decays on a timescale we simply have not reached yet. This universe eventually ends with all matter dissolving into radiation and leptons across timescales of 10³⁵ years or longer. It is a universe with a far future but not an infinite one, at least not for matter as we know it.
In the second universe, baryon number is an exact conservation law, not an approximation. If that is true, the proton has nowhere to decay to. It is genuinely, absolutely stable in a way that nothing else in nuclear physics is. Not stable-because-we-cannot-measure-it, but stable in the way that charge conservation is stable: protected by a fundamental symmetry of nature that admits no exceptions.
We cannot currently distinguish between these possibilities experimentally. The non-detections at Super-Kamiokande are consistent with either. What the experiment can do, and continues to do with each additional year of data, is narrow the range of GUT models that remain viable. Its successor, Hyper-Kamiokande, currently under construction, will hold 260,000 tonnes of water, roughly five times the sensitive volume, and should either detect proton decay within a decade or push the lower bound high enough to rule out most of the remaining GUT candidates.
So the answer to Chase’s question has two parts. For everything except hydrogen, “stable” means the half-life is either unmeasurably long or only theoretically nonzero, a boundary of measurement rather than a boundary of nature. For hydrogen, the question touches something genuinely unresolved at the foundations of physics: whether baryon number is a true law or an approximation, and whether the proton will outlast the universe or simply outlast our patience.
We are still watching.