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I initially asked this question on Physics Stack Exchange, and was then redirected here. I would very much appreciate the input of any physicists who might be reading this.

I'm writing a science fiction story in which I need a devastating weapon of mass destruction that is far worse than nuclear bombs. For some reason, I'm fascinated by the idea of a "proton-decay bomb", a hypothetical device that triggers proton decay in a chain reaction.

I'm no physicist, and as far as I know proton decay is not something we have observed or can make happen, let alone in a chain reaction, but this doesn't really matter in the context of my story, because believe it or not, the weapon plays only a very marginal role. Nonetheless, while I am asking the reader to suspend their disbelief in terms of whether such a bomb is even possible, I would like to give a non-technical description of its probable effects that is as accurate as possible.

The way I imagine it, a proton-decay bomb would cause protons to decay in a chain reaction that eventually dies out. (If it didn't, the bomb would just be a useless doomsday device that would destroy everything, attacker included.) That is the only assumption I'm asking you to make.

Now, I must admit that up until a second ago I probably had the wrong idea about what proton decay is, as I imagined it would mean the proton splits into its three constituent quarks, but on Wikipedia it says proton decay is actually about protons turning into pions or positrons. I don't know if the proton splitting into the three quarks is at all a sensible idea, so I leave it up to whoever wants to answer if that is a possible mechanism for the bomb.

Whichever way the bomb works, I imagine the reaction would be exothermic, thus leading to a huge blast, probably an equally huge shockwave, and a flash. I also suppose other particles would be created in the process and fired all around the blast site at very high speeds, possibly causing additional damage in the form of radiation, on top of the disintegration of matter that is the main effect of the bomb. For example, if for some reason the bomb made protons decay while leaving neutrons alone, the leftover neutron radiation could spread past the area disintegrated by the blast and cause further damage to biological tissue.

Is this description at all plausible? Would there be other effects I didn't think of? Is it possible to speculate on the order of the events that would follow once the bomb is set off?

If the idea of a proton-decay bomb is so impossible that no amount of suspension of disbelief can make up for it, alternative suggestions are welcome!

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    $\begingroup$ "I don't know if the proton splitting into the three quarks is at all a sensible idea,": quarks don't exist in isolation. If you try to separate two quarks, at some point the gluon field between them will produce another quark/antiquark pair and you end up with two pairs of quarks. Trying to pull quarks apart just ends up converting energy into more quarks. So yeah, proton decay might be a thing, but is something very different from just splitting apart into quarks. $\endgroup$ Commented Apr 6 at 13:31
  • $\begingroup$ @Nicola Proton decay is as far as i know that naturally happens overtime. A very long time to be exact like after all black holes disappear from radiation. Your weapon would probably speed this process. I don't know if this causes a chain reaction but it could destroy all matter in a given area. $\endgroup$ Commented Apr 6 at 14:08

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We're already talking theoretical physics here so pardon me if not everything here is purely based in known quantum mechanics.

We actually do know that protons can decay by the weak interaction into neutrons, but for protons not bound in unstable nucleons this process is hypothesized to take an extremely long time - roughly twenty-four orders of magnitude longer than the Universe has existed. We can assume that it virtually never happens except in unstable nucleons.

How proton decay works

So how does proton decay work? Well, it involves the weakest of the four fundamental forces, aptly named the weak interaction. The weak interaction is the only known mechanism by which a particle's "flavor" can change; that is, conserving things like charge and mass, it can change one kind of particle into another. A proton has three constituent quarks: two up quarks and a down quark. During the weak interaction, an up quark emits a $W^+$ boson, which then almost-immediately decays into a positron and an electron neutrino. The electron neutrino disappears at nearly the speed of light, and the positron goes off to do its own thing, while what's left is a down quark. Then, outside the non-strongly-interacting positron, we have two down quarks and one up quark, a.k.a. a neutron. This process is known as $\beta^+$ decay, since it emits a positively-charged positron (anti-electron).

Conversely, one of a neutron's down quarks can undergo a similar process, emitting a $W^-$ boson ($W^+$ and $W^-$ are each other's antiparticles) and turning into an up quark and producing an electron and a proton. Again, this only occurs in unstable nucleons. This reverse process is known as $\beta^-$ decay, because it emits a negatively-charged electron. It is never the case that a proton's singular down quark or that a neutron's singular up quark undergo the weak interaction because that would produce a $\Delta$-baryon rather than a proton or neutron, which are much more massive; there would have to be a large energy input for that to happen.

How to weaponize it

The weak interaction is very weak (hence the name); so weak that it actually doesn't even exist on large scales. Not like "is so weak beyond this scale that it's negligible", it literally has an strength of exactly zero beyond a certain scale. This is due to the fact that the $W$ bosons are massive: so-called "virtual particles" carrying a force are only allowed to exist for a certain period of time inversely proportional to their energy; for other virtual particles like photons, you can have virtual particles travelling infinite distance because you can just make their energy continuously lower, but the mass-energy of the heavy $W$ bosons adds an upper limit to the distance and time they can travel before they just blip out of existence and turn into other particles.

What we need is some sort of weak boson accelerant: a material or field that causes the rate at which $W$ bosons are emitted to increase. This would cause weak interaction rates to skyrocket and cause protons to start decaying into more-stable neutrons very fast, essentially by making nucleons universally "less stable" and making them undergo radioactive $\beta^+$ decay when they realistically shouldn't. We will have to handwave this: there is no known mechanism by which the production of weak bosons could be accelerated, except by just globally increasing the weak isospin in an area.

Actually, that sounds perfect! The weapon itself is an isospin amplifier field generator: it causes the apparent weak isospins of particles in a given region to become much larger suddenly, and uses a large amount of "ignition" energy to allow that to happen (probably powered by a large nuclear bomb, although the result will be much worse as we soon will see).

Wait, what's weak isospin?

Each fundamental force has an associated observable charge: the electromagnetic force has electric charge, gravity has mass, the strong force has color charge (which is frankly too weird to even try and get into), and the weak force has weak isospin.

Particles with higher weak isospin more rapidly decay into more stable particles because they produce more $W$ bosons over a given time period. You can think of it as how "hard" a particle decays via the weak interaction, like how hard an electrically-charged particle gets pulled by another.

What the result is

Oh my, have we created something horrible. Suppose we activate our proton decay bomb and have the isospin amplifier field trigger weak decay in just one kilogram of water: a simple fuel, but a sufficient one nonetheless. In one kilogram of water, there are roughly 55.5 moles of $\text{H}_2\text{O}$, equivalent to about $3.34\cdot10^{25}$ molecules of water. Each molecule contains ten protons, meaning that we've just proton-decayed $3.34\cdot10^{26}$ protons.

That doesn't mean much, but consider what that means: we just produced that many positrons as well. The positron mass is around $9.1093837\cdot10^{-31}\text{ kg}$, so we just produced about 0.00002711 kilograms of antimatter (equivalent to 0.02711 grams, 27.11 milligrams - more antimatter than has ever been artificially produced by humankind to date).

How much energy is then released when these positrons inevitably collide with the electrons that once orbited the atoms and molecules in the water? Well, if we assume 100% mass-energy conversion rate (which is generous but not unexpected if we're dealing with massive charges suddenly attracting each other), then $E=mc^2$, giving $2.4362900434\cdot10^{12}$ joules released. That's equivalent to about five thousand tons of TNT. Not bad, but one must also consider the other consequences: neutron radiation. We just produced a ton of neutrons in addition to positrons, and those neutrons are going to be damaging to most biological tissue they come across. Even though it was only a 5 kT TNT bomb, the region it was detonated in won't be habitable for a very long time.

We can also scale it up, too. If we have about 36 cubic feet of water (roughly one ton), the net energy released just in the antimatter annihilation blast becomes five million tons of TNT, and the neutron radiation would probably sterilize everything in a very wide radius. If you have a cylindrical tank 10 feet in radius and 10 feet tall filled with water (definitely huge, but not unobtainable), that totals 88960 kilograms of water (about 89 tons), which results in around 445 megatons of TNT of explosive power. Aside from rivalling the world's most powerful nuclear weapon, the Tsar Bomba, which measurably altered the Earth's rotation and sent shockwaves all the way through the planet, this proton-decay bomb will likely add a few thousand tons of explosive power just due to neutron radiation alone; there will be no survivors.

Overall, the radiation would probably begin insanely fast neutron activation and irradiate the landscape for many thousands of years to come, aside from coming with a massive mushroom cloud.

Improving it further as if it needed improvement

Why not use pressurized hydrogen as an isospin amplifier field fuel rather than water? Water is notoriously dense, and when you use water you're also using all those dead-weight neutrons that come with the oxygens. Pressurized hydrogen would allow you to store the same mass in a more space-efficient way, and also allow you to load it into a shape that somewhat resembles a normal missile so that you can annihilate your enemies from afar.

TL;DR

Yes, your description is plausible

You don't even need a chain reaction - you can just trigger the field on a heap of fuel and watch the antimatter do the work. That's assuming you can't just trigger the field on whatever you want - this is already a device capable of turning atoms into piles of neutrons and positrons, so if you can selectively generate a field directly inside your enemy's skulls, you don't really need the bomb anyway.

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    $\begingroup$ Pretty good, but you've missed a few things - 1) protons don't decay into neutrons, it's the other way around (proton plus electron plus neutrino is still less rest mass than a neutron); 2) the weak force doesn't go to literally zero strength, it just decays exponentially instead of inverse-square. $\endgroup$ Commented Apr 7 at 4:05
  • $\begingroup$ That's by far the most detailed answer I've ever got on Stack Exchange! I'm surely going to accept it, but I want to give the thread a little more time in case anyone else wants to contribute anything. $\endgroup$
    – Nicola
    Commented Apr 7 at 6:37
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    $\begingroup$ Of course!! I'm glad you like my answer <3 I do a lot of actual physics in my life and it's fun to be able to apply it in a more whimsical way. $\endgroup$ Commented Apr 7 at 19:32
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One way to imagine this is to presume that protons do naturally decay, as required by some theories, but that your hypothetical weapon simply speeds up the process by many orders of magnitude. Since the half-life of the proton is known from observations to be at least 10E34 years, some substantial speed-ups will be required.

The simplest route for the decay is to produce a positron and a neutral pion. That pion will immediately decay into two gamma rays, and the positron will mutually annihilate with any handy electron. Since the gamma rays from the pion are really quite high-energy, they will likely cause pair production.

This does not seem as if it will cause a chain reaction. It converts matter to energy, and if you can speed proton decay up enough to produce an explosion, rather than a dangerous physics experiment, its behaviour is going to be something like a nuclear explosion. It won't produce the specific profile of radioactive substances that a nuclear or thermonuclear explosion would; it will produce a mixture that depends on what kind of matter you proton-detonated, and how large a proportion of it you detonated before the explosion destroyed the triggering aparatus.

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  • $\begingroup$ I find it useful to replace "years" with "entire histories of the universe" when the exponents get bigger than 10. "At least a trillion trillion entire histories of the universe" has more umf than 10^34. $\endgroup$
    – g s
    Commented Apr 8 at 4:25

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