So, a friend of mine is participating in an RPG campaign, in which his character has the absurd ability to transmute one material to any other material. The rules are that the materials must preserve mass (so, 50g of water can become 50g of lead, but not 100g of hydrogen), and that they can’t form machines; nothing more than basic shapes or blobs. So he maybe could conjure a sword but not a handgun, and not a piece of wood.
Naturally, being a complete jerk, he immediately started looking for ways to break this. I tried to help, and the best thing I was able to find was Hydrogen-7, an isotope which undergoes a 4n decay at a half-life on the order of 10^-23 seconds. by my calculations, this gives 6 kilotons of TNT equivalent (~25 PJ) per pound from that reaction (assuming all of it decays, which essentially all of it will essentially instantly, given that half-life). However, my lack of knowledge of nuclear physics keeps me from feeling confident in that number.
In short:
are my calculations right? In particular the assumption of 1 MeV per neutron decayed, but also if I’m missing any aspects of this stuff that are obvious to someone who knows nuclear physics.
Pound for pound, what known isotope or compound (non-elemental compounds, even complex ones, are fine here) will release the most energy in an explosive timescale? (to be simple, I’ll just say <1 second)
Less-energetic but otherwise “interesting” suggestions are very welcome.
Calculations:
Hydrogen 7.
453.592/7= 64.799 mols/lb
4*avogadro's constant= 2.4E24 neutrons released per mol
2.4E24*64.799= 1.56E26 Neutrons released per lb
assuming 1 MeV average energy per neutron
1.56E26 MeV
25 PJ
5977 tons of TNT equivalent
If antimatter is allowed, then he’s not going to be able to do any better than that. Specifically, he’s going to want a pound of positrons: Any sort of baryonic matter is going to waste most of its annihilation energy in useless neutrinos.
I suppose that the game master might further add a conservation of charge requirement, which would mean he’d have to instead go with an equal mixture of electrons and positrons, for half the total yield.
Thanks! I completely forgot about antimatter. I assume he could get away with that.
The energy released by mass m of antimatter magically appearing on earth should be 2m*c^2, right? So for a pound of matter, roughly 8E16 J or roughly 19 megatons. Yikes!
If you’re looking for non-atomic, non-anti-matter, just plain chemistry, there’s always FOOF.
Were I a DM with a player who wished to pursue the most violent transmutation possible, I would mention an odd sidenote in the history of such researchers, in which they all died in inexplicably huge explosions…
You can do almost as good as antimatter (close to 50%) without antimatter.
Conjure up a mass of electrons compressed into a small volume. Almost all of the overall rest mass will be in the EM field, not the individual electron masses. Once conjured, it will explode very energetically.
If charge conservation is imposed, you can do much better with antineutrons (or if that’s considered cheating, then antihydrogen, antideuterium, or more neutron-rich antisotopes). Back of the envelope, I get about 85% useful yield, in comparison to 50% for an electron/positron mixture.
Antimatter has a 100% yield as noted by Chronos if you don’t need to keep the new blob neutral. But your point that you can create energy through the spatial configuration is a good one.
Arguably it’s (roughly) 200% yield, since you get 2 kg of mass-energy from 1 kg of input antimatter. A kg of electrons is only 99% (or whatever).
If charge conservation is required, then just separate all the electrons and protons and compress them individually. I think the protons will start emitting beta rays as you compress them and convert to neutrons, but no one said this has to be a stable configuration :).
I did a bit of looking around and it seems like about 50% of the energy in antimatter annihilation is carried away by neutrinos. That’s no fun–I don’t think you’d notice that energy even if you were standing right next to the annihilation (even assuming you weren’t distracted by the gamma rays). The kilogram of electrons might actually provide more useful destructive energy.
That matches Chronos’s number above, but it’s not right. Most of the energy released will be kinetic and will be deposited by the daughter particles in-flight over a few to tens of nanoseconds. A large fraction of the initially not-kinetic energy will also soon appear as kinetic energy of lighter mesons through decays, or directly as photons since many of the daughters have electromagnetic decay modes. At the end of the day, it’s mostly just a portion of the rest mass of charged pions and muons that gets lost in the wind.
Revisiting my back-of-the-envelope calculation, I’m amending my estimate to a 94% yield for antineutrons (or actually 189% if we scale to the initial blob mass).
The consequences of free-form transfiguration have been explored in Harry Potter and the Methods of Rationality as well as several of its meta-fanfictions. (“You are NOT to transfigure anything into a pound of free electrons! It’s very important that you never try this. Do you understand how crucial this is? Because we considered just snapping your wand and obliviating you!”)
How much of a baryon annihilation depends on how much room you’re giving it before interacting with its surroundings. But I suppose that the most natural case is where you have very little room, in which case you’ll mostly be dealing with pions, which’ll interact just fine. The pions will eventually decay further into neutrinos and other things, but that would be well after your explosion.
In any event, making positrons will mean that you don’t have to worry about neutrinos at all, since they annihilate directly to photons. Good old more-than-weakly-interacting photons.
And if you’re allowing sufficiently tightly-packed electrons, I don’t think that there’s actually any known upper bound to the energy. Certainly, the size of the electrons themselves (if any) is known to be smaller than the size corresponding to their total mass (which is one of the major arguments for the necessity of renormalization). But I suspect that this falls afoul of the same rule as “no machines”, which is probably actually more like “no fine details”.
The annihilation products will include a number of species: pions, rhos, etas, and more. The most common particle will be a neutral pion which decays instantly (for our purposes), and it never decays into neutrinos. That energy is 100% useful. The same is true for several of the heavier species.
The less numerous charged pions do need to hit something to efficiently dump their kinetic energy, but half of them will go downward into the ground (assuming our RPG character is not flying out in thin air[sup]*[/sup]) and will dump their KE straight away. For those that don’t run into bulk material within 80 feet or so, their daughter muons will still range out, keeping the overall efficiency high (if not as high as for the downward-going pions).
Most relevant processes will be complete within 100 nanoseconds, and all relevant processes will be complete within 20 microseconds, so all of this is within the explosion time frame.
Agreed, solely positrons is clearly a winner if you can have net charge, but for neutral material baryons are the better bet by far.
[sup]*[/sup] although I suspect baryons still win in that scenario, though I haven’t run the numbers
I just love that all of these links are to Derek Lowe. And dang you for beating me to the most recent. But would a solvated crystal be okay for the parameters?