What a headache. I watched “Batman vs. Superman” last night and it was kind of painful.
I will admit right out that I liked some parts of that movie, but quite a lot of it I did not. If you haven’t seen the movie, beware, there will be some *SPOILERS* here.
The reason I’m bringing this up on a physics blog is because I’m getting sort of tired of seeing nuclear weapons misused in popular media. I think people just don’t understand how they work.
At a critical juncture near the end of ‘Batman vs. Superman,’ it suddenly became a good idea for the U.S. government to just shoot a nuclear missile at everybody and sweep the entire Superman vs. DoomsDay incident under the rug. This may have met a pass with me under other circumstances since it is a comic book movie and can’t be expected to comprehend the direction to reality even if given a compass and a map, but I have spent some time learning about how ballistic missiles, nuclear weapons and EMPs all work.
To begin with, the fact of the matter is that you don’t just shoot off a nuclear tipped ballistic missile as if it were an antiaircraft missile. With the antiaircraft mission, there is an entire collection of detection and targeting functionalities associated with the weapon. If the weapon is radar guided, a radio frequency pulse must be sent out by a convenient radar to illuminate the target and the missile must have radio detection equipment on-board in order to receive that pulse. If the weapon is heat guided, it must have some kind of infrared eye sensor. These weapons implicitly contain some expectation that the target is moving during the flight and that the weapon must be steered in order to score a hit, necessitating guidance fins and machineries with which to steer. Further, the weapon typically has some way of telling that it’s close enough to the target in order to go off and do damage. Here is a heat seeking missile:
It has a sensor at the front and steering surfaces all over it.
Here is Standard Missile 3:
Standard Missile 3 is a weapon with an antiballistic missile mission, meaning that it’s fired to kill a ballistic missile. Again, note that it has sensors on it and steering surfaces all over it. You could launch one of these and nail a superhero flying around in the upper atmosphere… never mind that Superman has the old “I’m rubber, you’re glue” infantile adjustment of being basically impervious to everything.
Here is a submarine launched ballistic missile:
This is a Trident missile. In contrast to the previous weapons, I draw your attention to the outside of this vehicle. Note the smooth lines. It has essentially no steering surfaces at all. During launch, it is steered by reaction wheels and (maybe) exhaust gimbaling. That is not super agile steering. I also checked on the guidance package: it uses star sighting and inertial guidance. It’s a ‘ballistic’ missile, meaning that it follows a basically preset parabolic flight path and uses no specific guidance to adjust its flight, much like a bullet. What this means is that the ballistic missile steers while it’s falling out of the sky, not really while on the way up. Further, star sighting is a system where the missile takes a look at the stars in the sky around it and uses that to judge its orientation… it contains no mechanism for telling how near it is to a target that might be encountered in space. The Trident is a rather typical ballistic missile, which is intended to deliver these things:
The thing with all the cones on it is a MIRV, a rather vicious sounding acronym that means “Multiple Independently targeted Reentry Vehicles.” This is the part of a ballistic missile that really maneuvers in order to aim the weapons. During the coast phase of the flight, the platform carrying the warheads (the cones) uses small jets to adjust its trajectory and then it kicks off warhead after warhead, which reenter the atmosphere unguided and strike their intended target. Keep in mind that targeting doesn’t have to be tremendous accurate with a nuclear warhead; off by a mile or two is ‘good enough.’
In the movie, the nuclear missile is more or less just a symbolic gesture of ‘the biggest thing humans can do’ when faced with this fight. Is there anything people can do? Not really, just throw a nuclear missile over that way and hope for the best. This is one of the things I like least about superhero movies: the 7 billion members of the human species are sort of reduced to this gaggle of chickens running around with their heads cut off, except this one guy, who just has to step in to save everyone. Who can do anything about it? Nobody but Bruce Wayne! The best anybody else will manage is an explosive stuffed in a wheelchair or maybe an insane ramble followed by some tinkering with a very user friendly piece of superpowerful, supersmart alien technology that is apparently too stupid to know that it’s talking to a person. Can humans do anything? No way; they mostly just run in circles screaming. All rambling aside, the real point is that a nuclear missile is actually a very honed, complicated system with an extremely specific task: none of the nuclear missiles currently plugged into silos here in the continental U.S. would be capable of beaning an incoming meteorite let alone a wayward man of steel.
The weapon needed to shoot at Superman and Doomsday would be more like the SM-3 than the Trident and, I expect, it would be specifically designed to tackle the mission at hand. I would suggest that some very motivated defense contractors could produce such a weapon in 18 months and probably would have after the previous Krytonian invasion. The technology is basically all there and little new engineering is need. The Pentagon is constantly reevaluating their fighting capabilities and probably wouldn’t be running around like a decapitated chicken, contrary to Hollywood fantasy.
Despite what it looked like, we could suppose that the weapon deployed against Supes and Baddie was some sort of nuclear tipped SM-3 variant. So, suppose that Superman does what he did and they all end up climbing up out of the atmosphere, whereupon the nuclear weapon is detonated.
Clearly the resulting explosion seriously hurt Superman. I’ll live with that, okay. There are some thermodynamic issues with Doomsday “Getting stronger as he absorbs Energy,” but there are also issues with Superman flying, so I guess I can’t be too picky: it is a comic book movie. I can even accept that maybe Supes could die on Doomsday’s spike because he was weakened by Kryptonite when a nuclear explosion was not otherwise enough to kill him. The lack of coherent sense in it all just is since nothing happening in these movies is confined by what can actually happen.
Ahead of all these other things, I will focus for the sake of the blog on the poor depiction of what happens with a nuclear explosion in low earth orbit. A nuke detonated on Hiroshima is a totally different animal from a nuke detonated above the atmosphere. A different weapon even. Something very special happens when you set a nuclear weapon off high in the stratosphere.
A nuclear weapon goes off by a critical mass nuclear chain reaction. The weapon core is imploded by a series of conventional explosives, crushing the core down so that the radioactive atoms of the weapon are in closer proximity to one another. These atoms, usually Uranium or Plutonium, are unstable nuclei which fall apart at some slow rate by a fission reaction, where the Uranium or Plutonium nucleus splits into parts and expels neutrons. If such nuclei are pushed very close together, the neutrons from one splitting event flying around crashing into surrounding nuclei and cause those nuclei to fall apart also, shooting out more neutrons. The act of splitting gives up a tiny bit of mass into energy as high energy light in the form of gamma rays. The initial rate of the explosion is very fast, something approaching the speed of light across the width of the weapon: nanoseconds as the gamma-rays emerge and less than milliseconds for the whole explosion to take place and the mass of the weapon to be consumed by it. The gamma ray pulse standing right in front of the weapon would be so powerful that it would turn all normal matter right there into an ionized gas of nuclei stripped of their electrons –the quantum transition for a electron absorbing a gamma ray is for the electron to simply jump out of orbit around whatever nucleus was holding it and fly away at some velocity close to the speed of light. For the most part, the energy of the explosion is initially stored in this powerful wave of gamma-rays, which you can’t directly ‘see’ per se since the chemical reaction which allows for sight is not compatible with the energy of gamma-rays.
If the bomb is exploded on the ground, a large amount of the gamma-radiation slams into nearby matter, converting those gamma-rays into kinetic energy in electrons and atomic nuclei, which in turn broadcast that energy into whatever they interact with, downgrading gamma-rays into smaller quanta of thermal energy or lower energy light, which in turn get subdivided further, more or less making a lot of heat and a lot of visible light and certainly a lot of moving material with significant amounts of kinetic energy. This translates into a blinding blast wave of sound and heat which moves as a powerful concussion.
If the bomb is detonated high in the atmosphere or in space, the energy of the gamma-rays produced by the explosion is deposited into matter in a different way. It mostly hits the atmosphere in a place where the atoms of the atmospheric gases do not interact with each other as frequently as they do near the surface, which allows the energy being conveyed from the bomb to be diverted into fewer extraneous paths. Electrons knocked from the atoms of atmospheric gases fly through the atmosphere at relativistic speeds without interacting with anything except the Earth’s magnetic field, producing a powerful electrical current that generates a huge electric field, reaching its peak strength in 5 nanoseconds and persisting about a microsecond. It’s a huge, coherent pulse! The resulting field hits the ground with a strength of roughly 50,000 volts per square meter (edit: the units here are actually volts per meter), sensitive to the geometry of the Earth’s magnetic field as the electrons spiral along the magnetic lines. The conveyed power is of an intensity of 6.6 megawatts per square meter (for comparison, sun light at Earth is only 1.3 kilowatts per square meter, or 5000 times weaker). In a way, the electrons stripped from the atmospheric gases convert the gamma-rays into a very powerful radiowave/microwave pulse. At the surface, this huge voltage causes motion of electrons in every conductor absorbing the pulse, mostly at above the breakdown voltage, killing everything electronic that you care about capable of providing Facebook or Snapchat. This is called the E1 pulse of the nuclear EMP and the strength of the pulse increases with increasing altitude of the nuclear detonation.
The E2 pulse takes place a moment later, about a microsecond to a second after the explosion. This is an incoherent pulse of radiofrequency noise as the remaining scattered gamma-rays knock loose other electrons. It’s much like the spark of noise caused by a lightning bolt.
There is also an E3 pulse of low energy radiowaves as the Earth’s magnetic field sloshes around due to the explosion, causing spikes of power to be deposited in long conductors, like power lines, which may knock out electrical power.
Now then, why do I care about this? Because the conventional crappy comic book cliche of towing the nuclear bomb out of the atmosphere to prevent it from causing harm to innocent civilians below is just that, a crappy, poorly considered cliche. Would real life military risk hamstringing themselves by just randomly lobbing a nuke into an uncertain situation over a big, populated city of people that they are supposed to be defending? Gotham and Metropolis would both have been subject to a massive power outage, at the very least, which would have knocked out anybody’s ability to use radar to track Superman or Doomsday –especially since an EMP renders radar useless for a moment, never mind the big booming visible electrical current arcs that Doomsday keeps sending out, which are actually lower energy than a nuke anyway since you can see them (yes, you can see a nuke, just keep in mind that the parts which don’t burn your eyes out are not necessarily the most powerful parts.)
So then, the symbol of a nuclear weapon really should be respected. I feel that a movie with heroes is much more believable if the power of such a weapon isn’t simply used as a blind analogy to show just how powerful a superhero is. It’s like a Chuck Norris joke. Using a nuclear weapon on superman just to show that he can walk away from it is just stupid: there is no ‘stuff’ in our comprehensible physical universe that can remain intact from this sort of treatment at point-blank range. I mean, really, is Supes made of neutronium? If you say ‘yes,’ you really don’t know how ridiculous that sounds. Neutronium powered by sunlight, huh? What story would you ever be able to tell where the jeopardy to normal people is believable and the hero remains relatable? A story working around the actual power of a nuclear weapon would be more interesting to me. I truly hated “Watchmen,” but there is something to be said for the character of Dr. Manhattan. So you upped the ante to nuclear weapons already, where do you go in the next story? Freeza?
(Small edit a long time after the fact: 10-13-16)
Suppose conservation of energy. A nuclear bomb of 1 Megaton strength releases 4.2 x 10^15 Joules in ~1 microsecond. 1 Watt/m^2 of light intensity is 1 Joule/(1 sec*m^2). The intensity of sunlight is about 1.3 kW/m^2. Superman is standing point blank in the blast of a nuclear explosion. The shot is very close and superman occludes 1% of the solid angle where the energy from the bomb is emitted uniformly across a sphere, and he absorbs that 1% completely. Suppose now that superman’s healing quantum yield is about one to one, meaning that he can resist one quantum of energetic damage absorbed by exerting an equivalent amount of energy –this is a generous estimate; few processes in nature have a perfect quantum yield. It’s like postulating that superman is better than a perfect refrigerator, which is appropriate, since he’s a superhero! How long would superman need to rest in the sun in order to recover the amount of energy he exerted to resist the nuclear explosion?
Laying in the sun, Superman would need ~3.2 x 10^10 seconds to recover his energy. That is 1024 years!
Really sets the scale, doesn’t it?