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Hypophys: Basic Thoughts on the Development
and Study of Fictional Systems of Physics

Note: I'm not an expert in anything (except maybe 'classical' FNaF lore? lol). There may be errors in my mathematical (or nonmathematical) reasoning in this post. If you think you know better than I do, and have something to correct/contribute, I would be happy to hear it!

A conlang is a constructed language; that is, a language developed by someone intentionally, rather than evolving naturally. The constructor is a conlanger, and the act of construction is conlanging. There exists a rich online culture surrounding the subject, overlapping heavily with worldbuilding circles (that is, the construction and development of fictional worlds). Worldbuilders often want to give their fictional societies a unique language, and may even want to imagine how that language evolved through the society's history. This is specifically called naturalistic conlanging, as it is concerned with conlangs which "could have plausibly developed naturally", applying patterns observed in real naturalistic languages.

Spec-Bio, or "Speculative Biology" (sometimes "Speculative Evolution") is, similarly, the development of fictional "speculative" species and evolutionary trees. The Alien Biospheres video series is a great accessible example of this sort of project, where Biblaridion starts with a dead planet and uses principles of evolutionary biology to trace the (supposedly) plausible evolution of a fictional ecosystem.

Now this is all pretty based so far, but my special interest is not really in linguistics or biology, but physics. Could one realistically apply this same worldbuilding attitude to the fundamental physics of a fictional world? Is a hypophys ("hypothetical physics", coined by me, just now) an achievable project?

Well- Maybe. The most common ways that worldbuilders will try to mess with physics is for a "magic system", and/or for scifi technology (at least, these seem to be the most common; I don't have stats, or anything). If you want to outline the structure of an intergalactic society, you probably want that society to have technology which allows for faster-than-light travel, which, of course, requires designing new physics. But both magic systems and scifi tech are not usually a unique system of physics; rather, they're just adding a bit onto the physics of the real world. Furthermore, they're usually done in a sort of ad-hoc, handwavey, impressionistic, and/or vague way, not having any actual concrete physics model to back up their mechanics.

These are not really what I'm interested in. They may be considered "soft" hypophysing. Homestuck, for example, arguably does some very deep hypophysing, but in a way I would more comfortably consider "metaphysics" than physics. On the "harder" side, there are some scifi stories which explore worlds with different physical constants. These can definitely be interesting, but they're really just real-world physics with some tiny modification. It's not not hypophysing, but it's not quite as radical as what I have in mind.

From the searching I've done, it seems that not many people have made a serious attempt at an original hard-hypophys worldbuilding project, at least at scale, and for good reason. It's just really difficult.

(I imagine there are examples I'm simply not aware of. I should probably look into Flatland, and Unicorn Jelly.)

Why it's difficult

Linguistics, Biology, culture and so on (things worldbuilders usually focus on) are all about large-scale, complex, chaotic, noisy processes. That might sound like it would make plausible worldbuilding harder, but it's the opposite: there's very few hard rules with hard consequences, only broad, fuzzy principles and vague tendencies. There are many, many evolutionary paths that might be considered "plausible", so the worldbuilder has a lot of freedom to express themselves through their systems.

Physics is fundamentally different in that, first off, "plausibility" is no longer a sensible goal. Physics is the very thing that worldbuilding usually strives to be plausible with respect to. It's the ultimate underlying structure behind all those other systems. So, rather than plausibility, what we are interested in is carefully tuning the emergent consequences of our hypothetical physics. We probably want our world, on the human-scale, to look and act a certain way, so we need an underlying system of physics which gives the desired effect. Or, even if we don't have a goal in mind, we probably want to at least know what the large-scale consequences are, exactly.

The trouble is that fully understanding the emergent consequences of a physics theory is very, very difficult. You kinda have to be, well... a physicist, basically. Theories of physics are written in differential equations, which compactify a lot of behavior into what is usually a relativity short line of symbols. Take, for example, Newtonian gravity: \[ m \frac{d^2x}{dt^2} = F_g = Gm \sum_i \hat{r}_i \frac{m_i}{r^2_i} \] Starting from particles in 3D space obeying Newtonian mechanics, this law tells you that your universe will probably be full of large spherical objects (planets) flinging around one another in mostly elliptical orbits. It also tells you that looser, lighter materials will tend to form discs rather than spheres (due to centripetal effects), resulting in planets with rings, and relatively flat planetary systems.

Could you have figured that out just by reading the equation? The only reason anyone knows this is because this equation describes the real world, so it's been studied to death, and compared to actual observation. Our hypophys, on the other hand, is going to be made-up, which means all we can do is use mathematical reasoning (or possibly computer simulation). It takes some amount of serious physics training to even interpret the equation on a basic level, let alone to develop a deep feeling for its consequences.

When we start actually changing things, we're going to crash extremely hard into the "understand the rules before you break them" problem. The laws of physics are, as it turns out, extremely tightly designed, and any small change will very likely cascade into an entirely different sort of world. Since all hypophys is inherently "breaking the rules", a good hypophysicist must have an incredibly deep understanding of the structure of physical theory.

(My own personal understanding is only so deep, of course. Please keep in mind my non-expert status for the duration of this post.)

A simple case study

Here's an obvious idea to toy with: Take the basic Newtonian framework, and swap out gravity with a simple "vertical force". Rather than a world full of planets in orbit, maybe we want a flat world, with one objective "down" direction where all things fall uniformly. Here's a naive attempt: \[ F_y = Ym \hat{y} \] Y gives the force a constant magnitude, y-hat a constant direction, and the m is there so objects of all masses fall at the same rate.

Immediately, we have a problem. If everything falls at the same rate, then the ground is falling beneath you at the same rate you're falling onto it. Accelerating the entire universe uniformly would not actually have any noticeable effect, as far as I can tell. The force may as well not exist, then.

Even looking past that (somehow), we find another immediate problem: We've broken lots of symmetries. Since we've chosen a special "down" direction and elevated it to a fundamentally unique status, our physics is no longer rotationally symmetric. This means that angular momentum is no longer conserved. The force's potential field will also break translational symmetry, which means regular momentum isn't conserved either. Neither is energy.

So, in our own carelessness, we've immediately accidentally broken all the major conservation laws, sometimes considered the most important physical principles. But remember that, apparently, none of this even matters, because the force wouldn't actually have any observable effect...

As it turns out, the only simple way for a force to obey those laws is by varying only with respect to the distance between particles, and those particles' invariant properties (like mass or charge). Furthermore, it must only act along the axis between the particles (or some invariant function of it, if we want to be fancy). All things considered, here's what our force should probably look like: \[ F = Cq \sum_i \hat{r}_i f(q_i,r_i) \] C is a constant, the q's are some invariant property of the particles, the r's are the distances between particles, and the r-hats are unit vectors along the axis between them. As far as I can tell, f can be any smooth invariant function, though I'm sure there's some constraints I haven't thought of. For mainly geometric reasons, I think, the most natural choice is \(q/r^2\). \[ F = Cq \sum_i \hat{r}_i \frac{q_i}{r^2_i} \] Now, does this equation look familiar? Have you scrolled up to compare it with Newtonian gravity, yet?

But, wait, there are more forces in the world than just gravity. The so-called "four fundamental forces" are gravity, electromagnetism, and the nuclear forces. The latter can only be understood with quantum mechanics, which would open up a huge new can of worms. Magnetism would similarly take us to the realm of special relativity. The purely electric (or "electrostatic") force can, however, be understood purely within the Newtonian paradigm. Here's what it looks like: \[ F_e = ke \sum_i \hat{r}_i \frac{e_i}{r^2_i} \] ...yeah.

It seems that the better one understands physics, the more one feels that it couldn't really be any other way. Intellectually, this is a really amazing fact, I think. But for the aspiring hypophysicist, it's a huge headache.

Though, there is definitely still hope. Even though the gravitational and electrostatic force laws look almost identical, their consequences are actually radically different. This is mainly because charges can be negative, while masses can't. If a difference that subtle leads to such a grand effect, then what if, say, we gave our force a vector-valued charge? Or a complex number? Or a spinor? And of course, you can consider other functions of the q's and r's (or even r-hats, though you should probably be careful to keep things rotationally symmetric). Maybe your force goes with \(1/r^3\), or maybe it gets stronger with distance. And this is all still while limiting ourselves to the Newtonian paradigm. There's still no shortage of ideas to explore, though I can't guarantee any of them will give you something coherent, let alone easy to understand.

Some things to consider

So far, I've shown you why hypophysing is very hard. But I don't think it's impossible. The problem of coming up with laws which conform to important considerations, and then getting a feel for their consequences, is what the entire field of theoretical physics is built around, so I'm sure there's plenty of useful tools one could look into. Lagrangians help with symmetries, for example. So, given that it can be done, what considerations should the aspiring hypophysicist keep in mind?

Radical Alienness

I've spent the last section detailing why you "can't" do this or that because it would break this or that symmetry. But of course, you're really free to do whatever you like. The reason I'm being restrictive is because there are certain properties of the everyday world which you probably take for granted, and violating these simple principles will likely result in a radically different kind of world.

But maybe you're okay with that. You are of course free to ditch the classical limit (discussed below) and allow your world to look nothing like the real world. It'll probably be more difficult to figure things out (since you won't have real-world physics to lean on), but it'll probably be difficult regardless, so, y'know. Do as you please.

Be warned, though, that it's very easy to come up with a system which will instantly "collapse" to some very simple state and then stay there forever. You probably want your world to blossom into a multiplicity of complex processes (eg life), as does the real world, but you won't necessarily get that without some intentionality. Maybe look into the field of complex systems for some intuition building?

Classical limits

The emergence structure is definitely an important thing to understand and consider. Quantum Field Theory is the closest thing we currently have to physics-bedrock, with the familiar classical physics of forces and particles only emerging as an approximation for the human-scale world. This is called the "classical limit", and if you want your hypophys to resemble the real world at all, it should probably have one.

But you don't have to get there from quantum mechanics; you could make up a new fundamental framework, and so long as it has a classical limit, the human-scale world will look somewhat familiar. Familiar enough that the concept of forces and momentum and so on should apply in most situations, anyway. You probably also want solids, liquids, and gases, which requires some more specific tuning... Chemistry might be a more difficult aspect to get right without Quantum Mechanics. And if you're going through the trouble of making a unique fundamental physics, you probably also want there to be edge-cases where the classical limit doesn't apply. All that's to say, we should understand how classical limits work.

Special relativity has a simple one: just take the limit for small velocities. The equations of relativistic classical mechanics tend to have lots of terms which are negligible when things are slow (compared to light), so you can recover Newtonian mechanics just by ignoring those terms. Retrieving classical physics from quantum mechanics is more subtle, and depends on your interpretation of the wavefunction. The basic idea, though, is that you just average out all the randomness. You may also look into the emergence from particle motion of thermodynamics (see: statistical mechanics), fluid mechanics, and so on. Your hypophys's more fundamental mechanics might look classical when only certain elements are present, or when this or that charge is balanced out, or at low energies, or when something is in equilibrium, or whatever else you can think up.

I should warn you that keeping quantum mechanics in your hypophys will probably make your life more difficult in the long run (this is my guess, anyway). Working out the classical effects will be difficult, for one. QM/QFT is also very constrained, to my understanding, so they're much more difficult to modify without breaking everything. Special relativity, on the other hand, I personally would suggest maintaining. It actually simplifies classical mechanics quite a bit, tying things together in a neat way, almost to the extent that nonrelativistic physics feels "contrived" without it. QM doesn't really feel that way to me, though that could speak more to my own lack of understanding.

(I'm not familiar enough with general relativity to recommend whether you should use it. It seems to introduce calculation difficulties, but it also might be the most natural way to give gravity to a world with special relativity.)

Anyway, different fundamental physics will give you different fundamental ontologies. Newtonian mechanics is a matter of forces and the motion of bodies through space over time. Relativistic physics essentially replaces forces with fields, and space and time with spacetime (turning "dynamics" into geometry). Quantum mechanics deals primarily with hermitian operators on Hilbert spaces. Your fundamental ontology may make use of probabilities, or constructors, or cellular automata, or information, or boolean logic, or directed graphs, or whatever you like.

(Of course, you're free to ditch all this emergence mumbo jumbo and just make your hypophys fundamentally Newtonian.)

The value of nondeterminism

Worldbuilding projects are often intended for storytelling. In this case, you probably want living agents of some sort, and you probably want a certain level of artistic control over your story. Deriving a coherent narrative all the way from fundamental physics is probably far beyond the capability of any human ever.

The obvious thing to do is make your fundamental physics nondeterministic. This straightforwardly removes a lot of constraints on what you can or can't do with your story. Be cautious, however, with the law of large numbers. Even if your fundamental physics is nondeterministic, it's still possible for the human-scale world to behave deterministically, simply because the randomness all tends to cancel out. This is effectively what statistical mechanics is all about.

Luckily, we don't even need nondeterministic fundamentals to leave space for artistic liberty. Physics is generally only deterministic for closed systems, when the initial conditions are known exactly. Chances are, your story will not exactly specify any initial conditions, nor will the setting of the story be a closed system. And even if it were, nonlinear physics (eg Newtonian mechanics) tend to be chaotic, leading to practical unpredictability. Even if your story is technically impossible, then, it may be that nobody will be able to prove one way or another, because the calculations are too difficult.

Conclusion

This is all I can think to say, for now. I have been thinking about this subject in the background for about as long as I've been seriously studying physics, so I wanted to lay out many of the considerations that've come to me as my understanding has matured. I would like to create at least one large-scale hypophys project in my lifetime, though it does seem quite difficult.

I almost called it a "fictphys" or "physfic".