# A Theory Of Everything

Physicists have a concept of a hypothetical “theory of everything”. There’s a Wikipedia page on it. Basically, general relativity describes how gravity works, and it is relevant for very large objects, the size of planets or stars. Quantum mechanics describes how nuclear and electromagnetic forces work, and it is relevant for smaller objects, the size of human beings or protons. And these two models don’t agree with each other. We know there is some error in our model of physics because we don’t have any way of smoothly transitioning from quantum mechanics to gravity. A “theory of everything” would be a theory that combines these two, one set of formulas that lets you derive quantum mechanics in the limit as size goes down, and lets you derive general relativity in the limit as size goes up.

It would be cool to have such a theory. But personally, I feel like this is a really narrow interpretation of “everything”.

Consider quantum mechanics. You can use our laws of quantum mechanics to get a pretty precise description of a single helium atom suspended in an empty void. In theory, the same laws apply to any system of the same size. But when you try to analyze a slightly more complicated system - say, five carbon atoms - the formulas quickly become intractable, either to solve exactly or approximately.

The point of laws of physics is to be able to model real-world systems. Different forces are relevant to different systems, so it makes sense to think of our physical theories along the dimension of “what forces do they have a formula for”. And in that dimension there is basically one hole, the gap between quantum mechanics and general relativity.

But there is a different dimension, of “how many objects are in the system”. In this dimension, we have an even larger gap. We have good laws of physics that let us analyze a small number of objects. Quantum mechanics lets us analyze a small number of basic particles, and classical mechanics lets us analyze a small number of rigid bodies. We also have pretty good laws of physics that let us analyze a very large number of identical objects. Fluid mechanics lets us analyze gases and liquids, and we can also analyze things like radio waves which are in some sense a large number of similar photons.

But in the middle, there are a lot of systems that we don’t have great mathematical laws for. Modeling things between the size of DNA or a human finger. Maybe you essentially have to be running large-scale computer simulations or other sort of numerical methods here, rather than finding a simple mathematical formula. But that’s okay, we have powerful computer systems, we can be happily using them. Perhaps, rather than expressing the most important laws of physics as brief mathematical equations, we could be expressing them as complicated but well-tested simulation software.

To me, a real “theory of everything” would be the code to a computer program where you could give it whatever data about the physical world you had. A video from an iPhone, a satellite photo, an MRI, the readings from a thermometer. The program creates a model, and answers any question you have about the physical system.

Of course we aren’t anywhere near achieving that. But that seems appropriate for a “theory of everything”. “Everything” is just a lot of things.