I was reading blog articles as I was wont to do and I stumbled over a blog entry on ScreenRant about the deadliest Marvel superheroes. Most of the article is very tongue and cheek and can be taken with a grain of salt. I felt no alarm until I read the #1 entry placing Hank Pym (Scott Lang) as the deadliest Marvel superhero.
Why do I mention this on a physics blog? Well, when somebody uses the words, “It’s thanks to actual science,” they have essentially just shot themselves in the head and invited me to take pictures of the mess. I have a definite love-hate relationship with superheroes to begin with…
Here’s how the article begins:
It seems only fitting that the superhero who seems the most out of his depth, and literally the smallest would pose the biggest threat, but he does – and it’s thanks to actual science. The movie, like the comics, tries to base Scott Lang’s powers and the Ant-Man suit in actual quantum and atomic science. They explain that the suit doesn’t shrink the wearer, exactly, but uses Pym Particles to shrink the distance between the wearer’s atoms. In other words, an object’s mass stays the same, but is just compacted by removing some of the negative space between the molecules it’s made up of.
I can live with how this starts out. Sure thing, the suit shrinks the dead space in atoms, which is definitely quite a lot of volume since atomic radii are around half an angstrom (10^-10 meters) while nucleii are about five orders of magnitude smaller (10^-15 meters). Never mind that there’s not really any quantum mechanics in this statement, it is livable if fantastical territory. ‘Tries to base’ is a fair statement in so much as a squirrel can try to build a skyscraper out of acorns.
As any comic book fan knows, Ant-man gets his power by retaining his man-sized strength when shrinking down to microscopic size. Yeah, fine, okay, that follows. I even sat still through the laymen’s description of microscopic black holes formed by the large hadron collider and the horrific name dropping of ‘Stephen Hawking,’ as if using his name instantly grants legitimacy. Where I cracked loose was in the following paragraph.
By shrinking to a size smaller than any observable particle, but doing it with all of his mass, Scott would, according to actual science, have created a black hole with a ton more mass than would actually be needed to keep it stable. Stable long enough to start pulling in the matter around it – which happens to be Earth, and everyone on it. He might escape and save the day, but according to the science that the movie lays out itself, Ant-Man wouldn’t just be the greatest killer in the history of the planet… he’d be the last.
Um no. Just, no.
You need to chase around these damn journalists with a rolled up newspaper to keep them from shitting all over the science they are claiming to quote. Just no. Not even…
I wanted to grab him by the lapels and shake him really hard. Did you bother to learn anything about what the science actually says before you wrote word one of that paragraph above?
Just because you have a black hole doesn’t mean that it’s necessarily a threat to the existence of the Earth. Black holes do what they do usually because they have a lot of mass, but mass conservation is actually a real thing. Without actually eating anything, any particular stellar scale black hole has no greater mass than the star that formed it and therefore no greater gravity than that star. If our sun were replaced miraculously right at this second with a black hole of equal mass to our sun, the Earth would continue to orbit as it always has and would do so until the end of time. Gravity is proportional to mass, even in general relativity (where you start thinking about mass-energy, but the energy part is usually very small). You don’t notice the peculiarities associated with black holes until you get very very close to them. In the case of a black hole the mass of our sun (1.99×10^30 kg), the event horizon, the place where light can’t escape, is only 2967 meters in radius (roughly 30 football fields, about the distance of a 3k run). That is in comparison to a radius of the sun of 696 Million meters. That’s 234,000 times smaller. To see the general relativistic effects to any significant degree, you have to be a distance of thousands of meters from the event horizon because the gravity force tends to fall off approximately as 1/radius^2. Once you get out to the radius of Earth’s orbit, Newtonian physics rules and none of the crazy space-time stuff applies to a significant enough degree to screw up most of your calculations. This is all relative to a mass the size of the sun.
Consider now a mass the size of a typical man, say 70 kg. How small would he have to get in order to have an event horizon? Easy, you work the Schwarzchild radius equation. For a 70 kg man, that radius would be about 1×10^-25 m. How small is that? That is 10 billion times smaller than the scale radius of the nucleus of an atom (10^-15 m). For a sense of the size difference here, the distribution of the nucleus of an atom would be on roughly the same scale (10 million to several billion kilometers) as the solar system would be around the sun-sized black hole. Parking our man-sized black hole at the center of an atomic nucleus, most of the nuclear volume would be at Newtonian physics scale distances from this tiny black hole. That’s the nucleus, I’m not even talking about the radius of an orbiting electron.
Now then, since the original author invoked the Q-word without adequately thinking anything through, let’s see what quantum mechanics has to say about any of this. In order for a mass as tiny as an electron to be trapped within the event horizon of the Pym black hole, it must be located within the distance of the event horizon, a radius of 1×10^-25 m. Here we just turn around and use the Heisenberg Uncertainty Principle, which tells how tightly a particle can be localized. In this, for an electron-sized mass to be confined within the event horizon at 100% certainty, that electron would also end up with a momentum distribution of 1.01×10^-9 kg*(m/s)… if you divide out the mass of the electron, this requires the electron to be moving at an aphysically high velocity of 1.12×10^21 m/s. Wickedly pathological because it’s breaking the speed of light by roughly twelve orders of magnitude. The chances of finding even an electron within the Pym event horizon are catastrophically nil. Confining something like a proton would have a slightly less aphysical result, but still quantum mechanically impossible.
One can even ask the question: does Scott Lang/Hank Pym have enough gravity to hold onto a single electron the way a proton can hold down an electron by electrical forces? In this case, the force factor for the electrical charges is about 10^11 bigger than the gravity force, meaning that a stable ground level eigenstate for Pym holding a single electron gives an orbital radius of probably meters… meaning that the rest of the universe would strip that electron free by normal processes. As such, Pym can’t even fake being his own atom.
My conclusion: Hank Pym/Scott Lang can’t make a black hole strong enough by human mass alone to effect the rest of the universe anytime in the age of the universe, let alone eat the earth or deflect the course of any wayward positrons without making a deliberate effort to be in the way. My other conclusion: blog authors say lot’s of shit without firing a single neuron to see if what they’re saying is anything but nonsense.