What’s up with nuclear weapons?

By Katja Grace, 27 February 2015

When nuclear weapons were first built, the explosive power you could extract from a tonne of explosive skyrocketed. But why?

Here’s a guess. Until nuclear weapons, explosives were based on chemical reactions. Whereas nuclear weapons are based on nuclear reactions. As you can see from the below table of specific energies and energy densities I got (and innocuously shortened) from Wikipedia, the characteristic scale of nuclear energy stored in things is about a hundred thousand times higher than that of chemical energy stored in things (by mass). And in particular, there are an empty three orders of magnitude between the most chemical energy packed into a thing and the least nuclear energy packed into a thing. This is perhaps to do with the fact that chemical reactions exploit the electromagnetic force, while nuclear reactions exploit the strong fundamental force.

Storage material	Energy type	Specific energy (MJ/kg)	Energy density (MJ/L)	Direct uses
Uranium (in breeder)	Nuclear fission	80,620,000[2]	1,539,842,000	Electric power plants (nuclear reactors), industrial process heat (to drive chemical reactions, water desalination, etc.)
Thorium (in breeder)	Nuclear fission	79,420,000[2]	929,214,000	Electric power plants (nuclear reactors), industrial process heat
Tritium	Nuclear decay	583,529	?	Electric power plants (nuclear reactors), industrial process heat
Hydrogen (compressed)	Chemical	142	5.6	Rocket engines, automotive engines, grid storage & conversion
methane or natural gas	Chemical	55.5	0.0364	Cooking, home heating, automotive engines, lighter fluid
Diesel / Fuel oil	Chemical	48	35.8	Automotive engines, power plants[3]
LPG (including Propane/ Butane)	Chemical	46.4	26	Cooking, home heating, automotive engines, lighter fluid
Jet fuel	Chemical	46	37.4	Aircraft
Gasoline (petrol)	Chemical	44.4	32.4	Automotive engines, power plants
Fat (animal/vegetable)	Chemical	37	34	Human/animal nutrition
Ethanol fuel (E100)	Chemical	26.4	20.9	Flex-fuel, racing, stoves, lighting
Coal	Chemical	24		Electric power plants, home heating
Methanol fuel (M100)	Chemical	19.7	15.6	Racing, model engines, safety
Carbohydrates(including sugars)	Chemical	17		Human/animal nutrition
Protein	Chemical	16.8		Human/animal nutrition
Wood	Chemical	16.2		Heating, outdoor cooking
TNT	Chemical	4.6		Explosives
Gunpowder	Chemical	3		Explosives

Thus it seems very natural that the first, lousiest, nuclear weapons that anyone could invent would be much more explosive than any chemical weapon ever known. The power of explosives is mostly a matter of physics, and physics contains discontinuities, for some reason.

But this doesn’t quite explain it. Consider cars. Turbojet propelled cars seem just fundamentally capable of greater speeds than internal combustion engine propelled cars. But the first turbojet cars that were faster than internal combustion cars were not much faster—it looks like they just had a steeper trajectory, which passed other cars and kept climbing. I’m not sure what caused this pattern in the car case specifically, but I hear it’s common. Maybe people basically know what current technology is capable of, and introduce new things as soon as they can be done at all, rather than as soon as they can be done well.

Anyway, we could imagine the same thing happening with nuclear weapons: even if nuclear power was fundamentally very powerful, the first nukes could have made use of it very badly, exploding like a weak chemical explosive the first times, but being quickly improved.

But that isn’t how nuclear weapons work. For a nuclear weapon to be less explosive per mass it would need to contain less fissile material, be smaller (so the outside casing is more of the mass, and so that fewer neutrons hit other atoms), or be less well contained (so fewer neutrons hit other atoms). But to get a nuclear explosion going at all, you need to get enough neutrons to hit other atoms that the chain reaction starts. Nuclear weapons have a ‘critical mass‘. I’m not sure how much less powerful the first nuclear weapons could easily have been than they were, but measly inexplosive nuclear weapons were basically out.

So the first nuclear weapons had to be much more explosive than the chemical explosives they replaced, because they were based on much more powerful reactions, and primitive nuclear weapons weren’t an option.

So nuclear weapons were basically guaranteed to revolutionize explosives in a single hop: even if humanity had known about nuclear reactions for hundreds of years, and put a tiny amount of effort into nuclear weapons research each year, humanity would never have seen feeble, not-much-better-than-TNT type nuclear weapons. There would just have been no nuclear weapons, and then at some point there would have been powerful nuclear weapons.

It is somewhat interesting that this is not what happened. Physicists mostly came to believe nuclear weapons were plausible from about 1939, and within a few years America spent nominal $19Bn (roughly 1% of 1943 GDP, but spread over a few years) on nuclear weapons, and built some. So our story is that progress in explosives was very slow, and then America spent a huge pile of money on it, and then it was very fast, but the progress was independent of the massive influx of funding.

That sounds surprising. But perhaps the influx of funding was because of the large natural discontinuity visible in the distance? Why would you ever spend small amounts of money every year, if it was clear at the outset that you had to spend a gajillion dollars to get anywhere? If there wasn’t much requirement for serial activities, probably you would just save it up and spend it in one go. America didn’t save it up though—they tried to build nuclear weapons basically as soon as they realized it was feasible at all. So it looks like nuclear weapons were just discovered after it was cost-effective to build them.

But if it was immediately cost-effective to build nuclear weapons thousands of times more powerful than other bombs, then isn’t the requirement that nuclear weapons be fairly powerful irrelevant to the spending? If it was worth building powerful bombs immediately, then what does it matter if it is possible to build lesser weapons? Not really, because cost-effectiveness is relative. If is only possible to buy toothpaste in a large bucket, you will probably pay for it, and it will have been a good deal. However if it’s also available in small tubes, then the same bucket is probably a bad deal.

Similarly, if nuclear weapons must be powerful, then there’s a decent chance that as soon as they are discovered it will be cost-effective to spend a lot on them and make them so. However if they can come in many lower levels of quality, the same large amount of spending may not be cost effective, because it will often be better to spend an intermediate amount.

So a requirement that nuclear weapons be very explosive when they are first built could at least partly explain the huge amount of spending. And the inherently large amounts of energy available from nuclear reactions still seems relevant: any given amount of development will be cost-effective when it is more costly, if it is more effective compared to the alternative.

This also appears to fit in with an explanation of the further coincidence that there happened to be a huge war at the time. That is, the war made all military technologies more cost-effective, and thus made it more likely that when nuclear weapons became feasible to develop, they would already be cost-effective. However the war also makes it more likely that high quality weapons would already be cost-effective compared to cheaper counterparts, thus partly undermining the proposal that the large expenditure was due in part to nuclear weapons requiring a minimal level of quality.

Here’s another plausible explanation for the large expense: because of their extreme explosiveness, nuclear weapons were very cost-effective at the time they were first considered. That is, they could have been produced a lot more cheaply than they were. However, due to the war, America was willing to pay a lot to make them come faster. In particular, America was willing to keep paying to make them come faster up until the point when they were roughly as cost-effective as older weapons, taking into account the upfront cost of making them come faster. This would explain the large amount of spending, and perhaps also why it aligned so well with what America could barely afford. It also explains why nuclear weapons appear to have been very roughly as cost-effective as older weapons. However on its own, it seems to leave the large amount of spending and the large amount of progress as coincidences.

In other ways, this story is in line with what I know about the development of nuclear weapons. For instance, that enriching uranium via several different methods in parallel was around half of the cost of the Manhattan project, and that the project was a lot more expensive than other countries’ later nuclear weapons projects.

Perhaps the inherent explosiveness of nuclear weapons made them very cost-effective, and thus able to be sped up a lot and still be cost-effective? (Thus connecting the expense with the explosiveness) But if nuclear weapons had been too expensive already to speed up much, it seems we would have seen a similar amount of spending (or more) over a somewhat longer time. So on this story it seems the heavy spending didn’t cause the high explosiveness, and the high explosiveness (and thus cheapness) didn’t seem to cause the steep spending.

It seems there was probably one coincidence however: a physics discovery leading to weapons of unprecedented power was made just before the largest war in history, and it’s hard to see how the war and the discovery were related, unless history was choreographed to make Leo Szilard’s life interesting. Perhaps the weapons and the war are related because nuclear weapons caused us to think of WWII as a large war by averting later wars? But the World Wars really were quite large compared to wars in slightly earlier history, rather than just the last in a trend of growing conflicts. If there is at least one coincidence anyway, perhaps it doesn’t matter whether the massive expense is explained by the unique qualities of nuclear weapons or merely by the war inspiring haste.

In sum, my guesses: nuclear weapons represented abrupt progress in explosiveness because of a discontinuity inherent in physics, and because ineffective nuclear weapons weren’t feasible.  Coincidentally, at the same time as nuclear weapons were discovered, there was a large war. America spent a lot on nuclear weapons for a combination of reasons. Nuclear explosions were inherently unusually powerful, and so could be cost-effective while still being very expensive. They also required investment on a large scale, so were probably invested in at an unusually large scale. America probably also spent a lot more on nuclear weapons to get them quickly, because they were so cost-effective under the circumstances.

My guesses are pretty speculative however, and I’m not an expert here. Further speculation, or well-grounded theorizing, is welcome.

(image: Oak Ridge Y-12 Alpha Track)