Space-filling

After watching the third Fantastic Beasts movie, and realizing how little of the previous movies I remembered, I decided to go back and watch them. The fantastic beasts are more interesting and plentiful, especially in the first movie. This time around, I found myself pondering the space-filling serpent. According to the Harry Potter Fandom Wiki, it is called an Occamy (and shown in the picture below from the wiki). The ability to grow or shrink to fill space is ‘choranaptyxism’, an invented word in the Wizarding World pulled from the Greek words for ‘space’ and ‘unfolding’. Why not use Latin instead of Greek?

 

Why does the beast grow or fill to shrink its space? I don’t know. Why doesn’t it do so when living in Newt Scamander’s garden of beasts? I don’t know either. Why does Newt ask for a teapot to trap it – shouldn’t any other container do? Possibly, it’s unclear. Maybe Newt says this in the heat of the moment to allow his comrades to focus on a solution. How does this beast change its size to fit its container? I don’t know, but I have speculated on what atomic-level forces might be affected as matter is enlarged or shrunk (it is more problematic than it looks). Then again, this is a fantastic magical beast so maybe the rules of ‘normal’ matter don’t apply as when you cast an Engorgio spell to make a spider larger (to Ron Weasley’s horror) or if (Marvel Comics) Ant-Man shrinks.

 

In an introductory chemistry class, students are taught that gases “take the shape of their container”. The size of the gas particles does not change. Rather, because of their constant motion, the particles whiz around to “fill” the container in their never-ceasing movement. Matter isn’t being resized as the container size changes. The pressure of the gas rises or falls proportionally as the volume of the container is decreased or increased respectively, provided the temperature remains constant (Boyle’s Law).

 

Also in introductory chemistry class, students learn different ‘models’ to represent molecules, one of which is called the space-filling model. This model is sort of like a gas-filled container except that (1) instead of gas particles, electrons are the constantly moving entities, and (2) there isn’t actually a boundary per se – the negatively-charged electrons stay relatively close to the positively-charged nucleus because of electrostatic attraction. The space-filling model comes into play because the electron ‘clouds’ on two different molecules cannot substantially penetrate each other because of the Pauli Exclusion Principle. Were molecules to meet in motion, they would bounce off each other, never passing through each other like ghosts.

 

This reminded me of a vignette in Tom McLeish’s book. Robert Grosseteste was a thirteenth century cleric who became Bishop of Lincoln in 1235. He incorporated what we would today call ‘science’ into his theological thoughts. One thing that puzzled him was the ‘solidity’ of matter. (It’s surprising that students today aren’t puzzled – it is strange!) McLeish writes: “If [Pauli Principle repulsion] were not the case then solid or liquid matter as we know it could not exist – all matter would simply pass through itself… think of a simple version of an atomic picture in which the atoms are really point-like particles – since this is the picture faithful to the ancient Greek atoms – the indivisible ones. At first it seems as if this might be a promising route to explain the matter we experience in terms of its hidden, and simpler, substructure… but in this case classical atomism doesn’t work. If we stay with the idea of point-like particles then solidity simply does not appear.”

 

Why don’t we just give up the idea of point-like particles and use ‘hard spheres’? This isn’t as easy as it looks because it still begs the question as why you have hard spheres. For that matter, classical mechanics (the stuff one learns in physics class) is predicated on using point-charges that give us beautiful and simple equations we can use! Without explaining the ‘bulk’ of atoms, we’re stuck in a circular argument spiraling into infinitesimal point-sized particles (which don’t exist). We had to wait until quantum mechanics to figure out Pauli repulsion – a good seven hundred years after Grosseteste became a bishop.

 

Grosseteste’s idea (in De luce) was to use light as a sort-of explanation. McLeish writes: “… light, unlike atoms, does possess a natural ‘extension’ – open a shutter and it streams in to fill the dusty air beyond uniformly and immediately. If matter cannot of itself (simple and without dimension) fill space, then maybe the operation of light on matter might endow the tiny particles with extension by carrying them, or somehow extendedness into them. Actually, [Grosseteste] is very careful to say that this source of corporality might not actually be light itself, but if not then something very like it… Remarkably, Grosseteste’s insight turns out to be more or less correct… light is space-filling in that it is a wave… the quantum waviness of matter allows it to be solid, and prevents my falling through the chair I am sitting on.”

 

Taking this a step further, Grosseteste “makes an extraordinary leap of imagination: he attempts to apply his theory of local matter to the structure of the universe as a whole. Beginning with a flash of light, the entire universe is filled and expanded by its self-propagation until it has reached huge dimensions. Solidifying in its exterior shell, re-reradiated light from this shell of ‘perfected matter’ then concentrates matter back towards the center, leaving the successive planetary shells in its wake, and the unrefined elements of fire, air, water and earth at the center.” It’s clever. Grosseteste comes up with a ‘Let There Be Light’ creation of Aristotle’s cosmos. As an aside, Grosseteste was also interested in how matter might manifest in different Aristotelian ‘accidental’ forms – because he was interested in how one might explain Catholic theology’s concept of transsubtantation – the bread becomes the ‘body’ of Jesus Christ in some participatory way even though it still looks and tastes like bread to the eater.

 

Is there a creative explanation for the space-filling serpent in the magical world of Fantastic Beasts? I don’t know. I’d love to get my hands on a standard Hogwarts textbook: Magical Theory by Adalbert Waffling might be one. Or maybe Newt’s textbook. But I have a feeling that the explanation will leave me wanting. Or I need to ghostwrite the book with an infusion of the magic of quantum mechanics. Quantum mechanics isn’t astrology, but sometimes feels like it. (That book has been written.) So as you’re sitting on your chair reading this, take a moment to ponder why you don’t fall through it. The weirdness of quantum mechanics that gives rise to the space-filling model of molecules gives us solidity!