In a previous post, I explain why the universe is probably not stable, but nevertheless unlikely to be intentionally destroyable even in the limit of advanced technology. Now let's turn our attention to more prosaic risks where exotic physics merely destroys the Solar System, Earth, or just outperforms traditional nuclear weapons on some more local scale.

The basic logic behind any bomb is a self-sustaining chain reaction, in which a carrier converts a unit of fuel and comes out the other side in surplus:

Two conditions make this run away. The reaction must release energy, so the products are more stable than the fuel; and each reaction must produce more carrier than it consumes, so that one reaction seeds the next. A practical third condition is that cannot be so unstable that it decays before the bomb is assembled.

False vacuum decay is the ultimate bomb: is the false vacuum, the empty space we currently inhabit, and is the true vacuum. Because the supply of false vacuum is effectively unlimited, the reaction grows without bound and destroys the universe.

Fission bombs run on the same principle at a more prosaic scale. Consider uranium-235. This has a half-life of 704 million years, and is stable enough that it is still found naturally on Earth, having survived for at least 4.5 billion years. But upon collision with a neutron the nucleus fissions, for example through the reaction The energy comes from the fuel—the uranium splitting into more stable fragments—while the chain is carried by the neutrons. Each neutron can in turn split more uranium-235, and if you assemble a critical mass the result is a nuclear chain reaction, which can be used to power nuclear reactors (if carefully controlled) and nuclear bombs (if not).

Only a handful of fissile nuclides have the properties required to support a nuclear chain reaction; most ordinary matter remains stubbornly unexploded when bombarded with neutrons. Thermonuclear weapons reach much higher yields by using a fission chain reaction to ignite fusion of deuterium and tritium. But fusion itself is not self-propagating. Each joule used to heat the fuel produces on the order of a hundred times as much energy through fusion, but this energy dissipates too quickly to ignite surrounding fuel. Larger thermonuclear weapons can be made, but only by adding distinct stages, each of which traps the energy produced by the previous one to ignite more fuel. ^[1]

So is a self-sustaining fusion burn possible at all? Under the gravitational compression at the core of a star, yes—that is what powers the Sun. Under ordinary terrestrial conditions, no. In Appendix 1 I review why, but hardened empiricists may take additional comfort in the fact that the Trinity test did not ignite the atmosphere, nor have any of the more than two thousand nuclear and thermonuclear bombs that have been detonated since.

Nuclear physics is by now well understood, and it offers no super-weapon beyond the ordinary scaling of a thermonuclear bomb—and certainly nothing that would run away to Earth- or star-busting scales. Are there more exotic options?

Nuclei are probably, but not definitely, stable within the Standard Model

With the exception of gravity, all known physical phenomena—including all of atomic, nuclear, and particle physics—are described by the Standard Model. If we want to understand whether an exotic chain reaction is possible, it is the first place to look. Such reactions are possible only if is more stable than ordinary nuclei, so the question becomes: are nuclei the most stable form of matter?

The Standard Model conserves baryon number: the number of quarks minus the number of antiquarks in a system never changes. Quarks never appear in isolation, but instead form into triplets in larger particles:

• Three quarks form a baryon, baryon number
• One quark and one antiquark form a meson, baryon number
• Three antiquarks form an antibaryon, baryon number

The proton, made of two up quarks and a down quark, is the lightest baryon in the Standard Model and so is stable. ^[2] The neutron also has baryon number 1, but it is slightly heavier than the proton, and a free one decays in about 15 minutes,

With baryon number fixed, all matter can do is rearrange its baryons into a lower-energy configuration. For a nucleus, that configuration is set by a balance of two forces: the residual strong force binds protons and neutrons together, while the electrostatic force pushes the protons apart. In addition, the Pauli exclusion principle prevents any two protons or neutrons from occupying the same quantum state. This means that, energetically, it's favorable to have similar numbers of protons and neutrons to avoid needing to fill up higher energy states. For any given number of nucleons, there is an optimal mix of protons and neutrons and therefore a most stable state.

But are ordinary nuclei really the most stable form of baryonic matter? Two alternative options have been proposed:

• Up-down quark matter: In this phase, up and down quarks are no longer confined within nucleons. For baryon number it is clear this state is less stable than ordinary nuclei, but it is conceivable that larger collections of quark matter are absolutely stable (Holdom et al. (2018)). Such quark matter would be positively charged and behave similarly to ordinary nuclei, just much larger.
• Strange quark matter: In this phase, the up and down quarks are joined by strange quarks (Bodmer (1971); Witten (1984)). Unlike up-down quark matter, strange matter would only be slightly positively charged due to the strange quark's negative charge. Ordinary nuclei do not contain strange quarks and spontaneous decay to strange matter would be extremely suppressed even if strange quarks were ultimately more stable; thus, the apparent stability of ordinary nuclei does not preclude the possibility that strangelets—droplets of quark matter containing strange quarks—are more stable.

The standard belief in the field is that ordinary nuclei are more stable than these alternatives, but the issue is surprisingly hard to resolve. While quantum chromodynamics (QCD)—the theory of quarks and the strong force—should theoretically allow us to resolve the issue, it infamously becomes strongly coupled at low energies and this makes mathematical computations intractable. Computing the proton mass from scratch to a few percent was a significant milestone and required substantial supercomputer time (Dürr et al. (2008)); such computations become exponentially more expensive as the number of quarks involved increases and so a brute-force approach looks difficult.

Experiments are also of limited help. We have never observed strangelets or droplets of up-down quark matter in collider experiments, but given how hard they would be to produce this tells us little. Terrestrial and cosmic-ray searches have likewise come up empty, but that may only mean that astrophysical processes rarely make quark matter either. Neutron stars are the likeliest place to find it, since their enormous pressures and violent formation should facilitate conversion. So far all observations are compatible with conventional neutron stars rather than quark stars, but observational evidence is limited and difficult to interpret; and conversion of neutron stars to quark stars might be very difficult even if the latter are theoretically more stable (Bombaci et al. (2007)).

Overall, I think both theoretical prejudices and the absence of observational evidence favor ordinary nuclei as the true ground state for baryonic matter. If I had to bet, I would assign 5% credence to up-down quark matter being more stable than ordinary nuclei, and 5% to strange matter.

Positively charged strangelets are safe, neutral strangelets are not

Suppose, contrary to the expectations above, that strangelets really are more stable than ordinary nuclei. Ordinary matter is then the metastable phase, and a strangelet can seed the true ground state: with the strangelet playing the role of "something bad" from the opening. An up-down quark droplet, if stable, could behave similarly. How concerned should we be?

This turns out to depend entirely on the charge of the strangelet. Conversion is driven by the strong force and requires contact between the strangelet and nucleus. But electrostatic forces are long-ranged and nuclei are positively charged, and this exponentially suppresses nuclear interactions. Indeed, the light nuclei surrounding us are already unstable to fusion. For example, it is energetically favorable to fuse hydrogen into deuterium (H): But the positively charged protons repel each other so strongly that fusion does not occur under ordinary conditions. Only neutrons are able to fuse with nuclei at low temperatures, but outside of neutron stars they are unstable and found only at extremely low abundance.

Positively charged strangelets would likewise repel nuclei, rendering them inert under normal conditions. In the appendix we calculate what would happen if a positively charged strangelet were to be thrown into the Sun and find that even in this case it would have no effect. But for a neutral, or worse, negatively charged strangelet, no suppression occurs. In this case we find that the strangelet would grow without bound and destroy the Sun. Importantly, the strangelet still remains whole and never divides despite growing to massive size. As a result, while the Sun is eventually destroyed this process takes years to complete, though the brightness of the Sun would double in years.

So, are strangelets positively charged? The up quark has charge while the down and strange quarks have charge . A strangelet carrying equal numbers of up, down, and strange quarks would thus be neutral. But the strange quark is much heavier than the up or down, so we would generically expect strangelets to contain fewer strange quarks and therefore be positive. The issue is not entirely settled, because repulsive gluon interactions between quarks become weaker at higher quark masses and in some models this can allow negatively charged strangelets. Fortunately most calculations do not support this conclusion (Farhi & Jaffe (1984), Madsen (1999), Wen et al. (2006)) and the general consensus is that strangelets should be positively charged, with a typical scaling relation between charge and baryon number of (Madsen (2000)):

If I had to bet, I would give odds that strangelets are positively charged and therefore safe. But I think the probability of the dangerous combination of (A) stable and (B) not-positively charged strangelets is less likely than the naive suggested by independently combining the two probabilities; if sufficiently abundant, these strangelets would cause very visible astrophysical effects, and the absence of these means I think the true probability is probably .

Up-down quark matter, which only contains up and down quarks, is almost certainly positively charged and would therefore be completely benign if stable.

Strangelets would be hard to make

Suppose we are in the dangerous corner of the space: strangelets are stable, and neutral or negative, so a loose one really would consume the Sun. Could someone make one on purpose? This looks impossible with current or near-future technology, though perhaps not for a sufficiently advanced civilization.

One route would be to find some naturally occurring strange matter. Presumably it must be extremely rare, given that we see none of the astrophysical signatures it would produce if abundant. But perhaps some neutron stars have been converted into strange stars, and if so one could harvest strangelets from them. That itself is probably much harder than it sounds—the strange star is tightly bound both by gravity and the strong force—but I would guess it could be achieved.

The harder route is to assemble strange matter yourself. One method is to collide two heavy nuclei at high energy and hope the debris coalesces into strange matter. Experiments at RHIC and the LHC have done exactly this without producing any observed strangelets, positively charged or otherwise. But in any case, we know from cosmic rays that such collisions could not create a dangerous strangelet: heavy nuclei collide at these energies, and far higher, all over the surface of the Moon, and have done so for billions of years (Jaffe et al. (2000)).

Heavy-ion collisions are in any case limited in what they can produce. If a stable strangelet requires some minimum number of strange quarks much larger than one, a fireball that fleetingly contains a handful of strange quarks will never reach it. The only way around this is to build the strangelet by hand, combining hadrons that already carry strangeness. Such hadrons are difficult to produce and have a lifetime of only s; colliding of them together into a strangelet appears very hard, if not impossible, even granting fantastic engineering prowess.

Exotic physics could permit ways to destroy protons, but not autocatalytically

Baryonic matter is stable in the Standard Model because baryon number is conserved. But baryon conservation is an "accidental symmetry" of the Standard Model arising from the mathematical structure of the low-energy effective field theory regardless of the more fundamental underlying physics. Actually, baryon number is already technically broken by subtle non-perturbative effects, and while these have no observable consequences they suggest that there is nothing ultimately sacred about baryon number. Finally, the generic expectation is that theories of quantum gravity do not have global symmetries; black-hole Hawking radiation, in particular, does not seem to respect such symmetries.

If these arguments are correct (and I think they are very strong), the proton itself is unstable and will decay through pathways such as: But if baryon symmetry is violated only by quantum gravitational effects then the expected lifetime of years is much longer than anything we can detect experimentally; current bounds on the proton lifetime are much lower, but still very impressive years.

Spontaneous proton decay is thus only relevant on timescales absurdly longer than the age of the universe. But some theories let the decay be catalyzed. For example, some grand unified theories have magnetic monopoles that catalyze proton decay. They are very heavy, weighing some proton masses, but are stable due to their magnetic charge. But they are not, in and of themselves, very concerning because reactions with protons are infrequent. Under ordinary conditions we might expect a single monopole to catalyze proton decays per second, which means each gram of monopoles destroys a gram of protons every few million years.

Catalysts are scary only if they can self-reproduce through some process which in turn requires that is light: But the above -mediated process is related by crossing symmetry to the spontaneous decay This process is kinematically allowed so long as in which case the observational bounds on the proton lifetime imply a cross-section GeV. At this rate, a particle created on Earth would collide with a proton every years. But even if is fine-tuned to satisfy forbidding regular decay, virtual and would contribute to the process Observational bounds on this process, and on analogous neutron-antineutron mixing within nuclei, again result in an extremely tight upper bound on the cross-section.

Other forms of matter offer no plausible chain reaction

What about the other components of matter: electrons, photons, and neutrinos? Unlike the proton, which is only "accidentally" stable in the Standard Model, these are protected by deeper physical principles that are expected to remain true in more fundamental theories:

• The electron is stable because it is the lightest charged particle.
• The photon is stable because it is the lightest particle; indeed it is exactly massless.
• The (lightest) neutrino is stable because it is the lightest fermion; conservation of angular momentum prevents decay into photons or other bosons.

Because the photon is massless, consistency forces it to couple to a conserved current, so charge is conserved. The only way to violate charge conservation is to give the photon a mass by spontaneously breaking the gauge symmetry, which requires introducing new additional light degrees of freedom which we have no theoretical reason to expect; furthermore the empirical bounds are very strong. The electron could still be unstable if lighter charged particles exist. But charged particles couple universally to the photon, and observational evidence rules out a light new particle with charge (Fung et al. (2023)). It is very implausible such particles exist, and even if they did, electron decay would be exponentially suppressed by the quanta needed to carry off its unit of charge.

Unlike the electron and the photon, the neutrino's stability merely follows from its being the lightest fermion we know of. It is conceivable that lighter fermions exist, and there are no strong bounds against them: neutrinos interact so feebly that we can barely tell whether they decay at all, and a light fermion escapes cosmological limits entirely unless it was thermally produced. But a self-sustaining chain reaction among neutrinos would require extremely contrived dynamics—and we would then have to explain why it had not already run to completion at some point in the history of the universe. In any case, the cosmic neutrino density is tiny, and we would barely notice even if every neutrino were converted into photons.

Now turn to dark matter. Unlike neutrinos, its energy density is substantial. The local halo density corresponds to a blackbody temperature of about 500 K, and so if converted to photons it would cook the Earth. But again, it is extremely hard, perhaps impossible, to contrive theories where dark matter can chain-react, producing substantial visible radiation in the process, yet otherwise remains cosmologically stable and invisible to our detection efforts, while spontaneously reacting so infrequently that we have never observed dark matter explosions.

Tiny black holes are not scary

Let us finally turn to gravity. The inexorable attraction of a black hole might sound scary, but the truth is that gravity is by far the weakest force and so tiny black holes are rather pathetic.

The smallest possible black hole has a mass of 20 g, or about protons, and a horizon length of just m. As we discussed in my post on false vacuum decay, creating these black holes would be extremely hard, probably requiring galactic scale engineering. ^[3] And for all that effort, they evaporate in about s. Even if they somehow didn't evaporate, their cross-sectional area is m, which means even at the sun's core it would capture a proton about every years.

Black hole lifetimes increase with size, but for black holes to pose any real danger they have to hoover up matter faster than they evaporate. Hawking power falls as while Bondi accretion in a dense core rises as , which allows us to estimate:

In other words, a black hole would have to have a mass of a few-hundred-meter asteroid, trapped within a volume the size of a proton, to actually ingest the planet. If you want the planet to be destroyed within a year, you'd need something a billion times more massive again.

Conclusion: There are no super-weapons between the nuclear bomb and false vacuum decay

In this post we have explored a question of leverage: whether a small, buildable trigger can set off a runaway out of all proportion to itself. Brute force is another matter: a civilization operating on astronomical scales could fling asteroids or planets, trigger supernovae, or build enormous lasers, and do immense damage. But a runaway requires a chain reaction, and that chain reaction needs a fuel: something that can convert into a more stable state, releasing energy on the way.

Chemistry gives us feeble explosives, nuclear physics much more powerful ones. Could new physics yield even bigger explosions? The table collects every candidate the Standard Model and gravity provide from the nuclear scale upward, spanning this post and its companion on false vacuum decay:

Fuel	Product	Reaction possible?	Runaway possible?	Comments
Heavy nuclei	Lighter nuclei	Yes	Rarely	Requires a fissile isotope like uranium-235
Light nuclei	Heavier nuclei	Yes	No	Fusion radiates faster than it burns unless confined
Nuclei	Up-down quark matter	Very unlikely	No	Probably isn't stable; would be positively charged, and therefore inert, if it were
Nuclei	Strangelets	Very unlikely	Very unlikely	Strangelets probably do not exist and would probably be positively charged if they did
Protons	Positrons	Probably	Very unlikely	No way to autocatalytically trigger baryon decay
Electrons, photons, neutrinos	Nothing lighter	Very unlikely	Very unlikely	Each is the lightest particle of its kind, with nothing more stable to decay into
Dark matter	Photons	Very unlikely	Very unlikely	An enormous reservoir, but nothing couples to it to release it
Small black hole	Larger black hole	Yes	Very unlikely	Evaporates too fast and captures matter too slowly
False vacuum	True vacuum	Probably	Yes	Probably possible, but probably not intentionally triggerable

The answer appears to be no: there are no new more powerful explosions on the horizon, or, with the potential exception of false vacuum decay, probably ever. The explosion of the first atomic bomb in 1945 had been barely anticipated even a decade earlier, and came as a surprise to all but a handful of physicists. ^[4] But our understanding of physics is far more advanced now than it was a century ago: the Standard Model has passed every laboratory test in the fifty years since it was written down, and astrophysics and cosmology confirm that the same laws hold across the universe. We can thus say with some confidence that the nuclear bomb was a one-off increase in our destructive capabilities.

Appendix 1: Igniting the Atmosphere

Whether a nuclear explosion could ignite a self-sustaining fusion burn in the air was settled during the Manhattan Project by Konopinski, Marvin & Teller (1946) in report LA-602, but it is not the most accessible source and here I will give a basic overview.

Nitrogen-14 is the most abundant nuclide in the atmosphere, and can fuse to form heavier elements through reactions such as: At low temperatures these reactions are exponentially suppressed by the Coulomb barrier and are essentially impossible. As the temperature rises the suppression weakens, and in the limit where every nucleus that meets another reacts, the cross-section saturates near its geometric value, which Konopinski, Marvin & Teller generously bound as m. This is the most favorable case for ignition, so we adopt it as a bound: the true fusion rate at any reachable temperature is smaller, by tens of orders of magnitude. The energy production rate is then where is the nuclide density, MeV is the energy released per reaction, and is the mean relative speed of two nuclides of mass at temperature , where is the Boltzmann constant. Energy production scales quadratically in the nuclide density and with the square root of the temperature.

A parcel of air at temperature produces energy through fusion, but the same hot plasma also radiates. The fusion energy first appears as kinetic energy of the nuclei; collisions with the surrounding electrons quickly thermalise both species to an approximately common temperature ; and the electrons, deflected in the electric fields of the nuclei, emit bremsstrahlung. For a sufficiently small parcel this radiation escapes faster than it is reabsorbed, carrying energy out and cooling the parcel. The loss rate is where is the nuclear charge, the fine-structure constant, the Gaunt factor, and the electron mass. The factor comes from the ion charge times the electron density .

If the parcel heats; otherwise it cools. The fusion reaction thus cannot be self-sustaining so long as the safety factor: Because both and scale as , their ratio is independent of density and temperature and we find that the safety factor is a constant: This is larger than , and so self-sustaining reaction cannot occur.

Our constant is only a first approximation: it assumes the electrons are as hot as the nuclei, the bremsstrahlung is non-relativistic, and the cross-section is saturated. Konopinski 1946 includes corrections to all three. First, the electron gas runs cooler than the nuclei: fusion deposits its energy into the nuclei, and the electrons heat up only indirectly, so they lag behind. Because bremsstrahlung is set by the electron temperature, the cooler electrons radiate less than the estimate assumes, which lowers the safety factor and drives it down as the temperature climbs. Second, the bremsstrahlung rate rises once the electrons turn relativistic (Rider (1995)), which pulls the other way and raises the safety factor at high temperature. Third, below the Coulomb barrier the fusion cross-section is Gamow-suppressed, so at low temperature far fewer collisions fuse than the saturated value assumes; this lifts the safety factor at the cold end, and since the constant- estimate ignores it, there is a conservative floor.

As a result, stays large at both extremes—Gamow-suppressed fusion at the cold end, relativistic radiation at the hot end—but reaches a minimum in between, where the electron-temperature lag dominates.

With help from Claude 4.8, I attempted to reproduce the Konopinski 1946 calculation and their minimum safety factor of . In the process, I discovered the paper contains an error. The expression they give relating the neutron temperature to the electron temperature, is correct. But the relationship between and they plot in Figure 2 and use in Figure 1 and 3 to calculate , is not the above relationship, and I'm not sure what causes the error. I instead find that ; fortunately we are even more safe with the error resolved!

Figure 1 shows the reconstructed under three assumptions about the cross-section, each computed with both bremsstrahlung methods. The flat b curve holds the cross-section at the constant bound m at all energies, ignoring the barrier. The second curve keeps the same 2 b ceiling but applies KMT's own above-barrier suppression factor, The third curve is the most realistic: it replaces KMT's approximate factor with the correct quantum penetration through the barrier (see Appendix 2), and lowers the geometric ceiling to barn. We have no measurement of the cross-section at these temperatures, but measurements of similarly sized nuclei (Kovar et al. (1979)) find peak cross-sections closer to one barn, about half KMT's bound. Each assumption is plotted twice: once with the bremsstrahlung reconstruction above, and once with Rider (1995), whose fuller relativistic treatment cools the electrons harder and pushes the safety factor higher still. Every curve sits above , and the more realistic the assumptions, the safer we are.

Safety factor for nitrogen fusion in air

Similar bounds exist for other nuclear reactions and, because the bremsstrahlung radiation scales as , it becomes stronger for heavier nuclei. Igniting fusion reactions is of central interest to those trying to make nuclear fusion power plants, and detailed calculations show that the only fuels for which ignition is not ruled out are the deuterium-based ones: D–T, D–³He, and D–D. ^[5] All other reactions radiate faster than they burn even at their optimal temperature and so cannot be ignited in thermal equilibrium (Rider (1995)).

Optically thick ignition

The bremsstrahlung argument assumes the radiation escapes, which holds only while the parcel is smaller than the photon mean free path. For a larger region, the photons never escape and instead reach thermal equilibrium with the nuclei and electrons. Because the energy released remains trapped in the region, bremsstrahlung radiation can no longer prevent ignition.

For the reaction to spread, however, it still must produce enough energy to heat the surrounding cold air; advancing the front by one parcel means heating it to some temperature at which fusion becomes meaningful. If the nuclide density is , and each reaction releases energy , then the maximum energy yield is But because a photon gas at temperature has energy density the maximum temperature reachable is Taking m as the number density of nitrogen nuclei in air, MeV as the energy released per reaction, we find that the maximum temperature attainable is

The temperature at which fusion becomes appreciable is set by the Coulomb barrier (see Appendix 2). For two nuclei the Gamow energy is and the thermally averaged rate is suppressed by which becomes appreciable only around K. At the maximum attainable temperature K, the exponent is , so the rate is suppressed by and no fusion occurs.

Appendix 2: Let's throw a strangelet into the sun

Imagine that a strangelet suddenly appeared in the core of the Sun. What would happen?

Neutral strangelet

Let be the baryon number of the strangelet and its radius. The bulk density of the strangelet will be approximately equal to that of nuclei, so that where is the baryon number density of nuclear matter, so that with fm.

Let us first assume that the strangelet is perfectly neutral and remains so as it grows. Let us also assume that any protons that collide with the strangelet are immediately converted to more strangelet. If so, then initially the strangelet baryon number will increase at a rate proportional to its surface area : where is the proton number density of the core plasma and is the average proton thermal speed at the core temperature K. Writing , The number of baryons then grows cubically in time, , so that the radius expands at a constant rate:

This growth rate holds only while the strangelet stays smaller than the proton mean free path, m; beyond that the plasma must be treated as a bulk fluid. In this regime, the energy released by the strangelet increases the surrounding temperature while the pressure remains fixed by hydrostatic balance. As a result, the local number density decreases and hence the strangelet growth slows. Growth becomes limited by the rate at which energy can escape from the strangelet, which in turn is limited by convection: where the convection rate is

with the density of the local proton plasma and the local speed of sound. Ordinarily we expect and , so that convection increases with temperature. But at K, somewhat hotter than typical core temperatures, the radiation pressure comes to match the hydrostatic balance, at which point and convection ceases. As a consequence, reaches its maximum value at a temperature of around , which is only somewhat greater than under ambient conditions. The strangelet itself is close to thermal equilibrium with the surrounding plasma, and since keV is orders of magnitude below the surface energy per baryon, it would remain stable against fissioning.

If each proton colliding with the strangelet releases some fraction of its rest mass as energy, then the power released is We can solve this to find that, once again, the radius increases linearly, but this time at the slower speed: This speed no longer depends on the strangelet's size. The power released and the surface available to shed it both scale as , so the dependence cancels and the radius again advances at a fixed rate—now about a thousand times slower than in the free-streaming regime.

As the strangelet grows its power output increases. But so long as its power output is small compared to the rest of the Sun, it has negligible effect on the global structure of the Sun, and remains invisible to observers. This remains true until the radius reaches: where W is the total power output of the Sun, which takes about years to occur.

Past this point, the Sun becomes increasingly bright as strangelet energy emissions come to dominate regular fusion. The increased radiation pressure causes the Sun to expand, akin to a red giant. Lowered density at the core causes to decrease, slowing but not preventing further strangelet growth.

Over years the luminosity will increase up to the Eddington luminosity of . Above this, the radiative forces acting on the outer layers of the Sun become stronger than the gravitational forces binding them, and the Sun begins shedding mass. At this stage the strangelet has a radius of km and contains a few percent of the entire solar mass. The dynamics of shedding can become quite complicated but the ultimate result is that the vast majority of solar mass becomes dispersed, leaving behind a small strangelet remnant.

Positive strangelet

Now let us repeat the same exercise, but assuming the strangelet has charge: A proton approaching the strangelet must now climb a Coulomb barrier of height

Using the WKB approximation, the absorption cross-section for an incoming proton with energy can be estimated as where is the Gamow energy and where is a finite-size correction that tends to for a point-charge and can largely be neglected for our purposes.

To compute the capture rate we must average this cross-section over the Maxwell-Boltzmann distribution of proton velocities in the plasma. In the latter distribution, the thermal population of particles with energy is suppressed by the Boltzmann factor , where keV. After some gnarly but standard manipulations, one can show that where the Gamow peak energy is The net result is that the average cross-section is exponentially suppressed by a factor of . Already for this gives a suppression factor of ; even at the center of the Sun this means such strangelets would not absorb a single proton over the Sun's entire main-sequence lifetime.

Bonus: neutral strangelet meets Earth

What if a neutral strangelet were created at the Earth's core? Just as in the solar case, growth here will become limited by the rate at which energy can be transported from the strangelet, resulting in a constant expansion rate of: But the equivalent on Earth is much lower than that of the Sun because the local pressure now is only GPa, which reduces down to about W/m, so the strangelet growth rate is It would take about 6 million years for the heat from the strangelet to exceed normal geothermal fluxes, which is about when the effects of the strangelet should first become visible. By 400 million years heat production rivals insolation, by which point the Earth's surface temperature will have been increased well beyond the point of habitability.

1. Thermonuclear weapons also typically include a uranium-238 bomb casing. High-energy neutrons produced by fusion can fission the uranium-238, releasing more energy. This final fission step is typically responsible for the majority of bomb yield. Like the fusion step, it cannot self-propagate. See the Nuclear Weapon Archive for a detailed discussion. ↩︎

2. Technically speaking the Standard Model violates baryon number symmetry non-perturbatively through sphalerons but these can only change baryon number by , which means the proton remains absolutely stable within the Standard Model. Nuclei with baryon number , such as He, could in principle decay via this mechanism, but the lifetime is years. ↩︎

3. This assumes the true Planck scale of GeV. In the very unlikely event that space has large extra dimensions, the effective Planck scale could fall to as low as a TeV and this could place tiny black holes within reach of colliders. Such TeV-scale black holes would still evaporate in s, rendering them harmless. Even if they somehow failed to evaporate, their capture cross-section of m² would mean that they would grow only very very slowly. ↩︎

4. Though it was not entirely unanticipated; (not-very-realistic) nuclear-powered weaponry features in H. G. Wells's 1914 The World Set Free. ↩︎

5. Note the proton-proton and proton-deuterium fusion are strongly suppressed, the former because it requires a weak decay: and the latter because it requires electromagnetic radiation Deuterium is found naturally, comprising about 1 part in every 6700 hydrogen atoms in the ocean. However, while deuterium is not ruled out by the ignition bound—Rider (1995) estimates for pure D-D in pure deuterium—power production scales with while the strength of the bremsstrahlung radiation scales with the total number of electrons and is dominated by their interactions with the highly charged oxygen nuclei. As a result, in ocean water and there is absolutely no risk of ignition. The dense hydrogen surrounding the cores of Jupiter and Saturn is similarly inert. ↩︎