Breaking Physics
Worldbuilders seem to be exceptionally keen when it comes to creating new laws of nature, and breaking existing ones along the way. There have been times when, on Worldbuilding Stack Exchange, I’ve pointed out that a given premise won’t work in our universe, and someone says that a different universe could have different laws of nature that allow the premise to work. It’s quite the cop-out, but at the same time, it does make one think about how different things could be in a different universe.
There are some scientific principles that can be modified without changing the universe too much, and then there are some scientific principles that cannot be modified without basically rewriting the universe from scratch. Then there are the principles that cannot be changed, under any circumstances. These are often mathematical relations, which lead to blocks that not even the most imaginative worldbuilder can hurdle.
I’d like to use this post to explore all three types, and delve into the nitty-gritty facts about why our universe is the way it is. My examples are all from physics, and so I thought it was appropriate to use a phrase my friends and I tease each other with whenever we’ve come up with an impossible answer to a problem: “Congratulations. You’ve broken physics!”
The first type of principle that I mentioned — the type that can be changed without producing catastrophic effects — is a small category. The issue at hand is that small changes have big effects. Perhaps you’ve heard this before in the context of the butterfly effect: Small changes in the initial conditions of a system end up having major consequences. This simple statement forms the basis of chaos theory. Here, though, the idea is modified: Small changes in the laws that dictate how a system evolves end up having major consequences.
The technical term for one manifestation of this is the fine-tuning problem: If you change the value of any physical constant by even a tiny amount, the universe will be completely different. To take a famous example, if the cosmological constant had a different value, the universe might contract into a singularity like a reverse Big Bang. Worldbuilders are often concerned with constants that play into equations that are more accessible to the layman than the equations of general relativity, such as the universal gravitational constant or the speed of light. But change those and things will be much different. This question and its answers talk a bit about some of the results.
The second type of principle I alluded to is, in my opinion, the most interesting, because it can involve the underlying structure of reality. I’ll use an example that celtschk used in an answer nearly one year ago, and that was expanded upon recently in another answer by Cort Ammon: Noether’s theorem and the Lagrangian formalism of mechanics.
Noether’s theorem — proved by Emmy Noether, who is perhaps the greatest female mathematician of all time, and certainly one of the greatest mathematicians of all time — states that if the action of a system has a continuous symmetry, there is an associated conservation law. Stating it in a slightly less technical way, if the laws of physics don’t change based on some change in the state of the system — whether it be time, space, or something else — then some quantity is conserved, whether it be energy, momentum, or something else (See this question on Physics Stack Exchange for more information.).
If Noether’s theorem is violated, then you can’t describe the universe in terms of any of a number of formulations of the equations of motion expressed in analytical mechanics (The reason has to do with the connection between these formulations and Noether’s theorem via a quantity called an action). These include Lagrangian mechanics and Hamiltonian mechanics. Now, it might seem okay at first — after all, this simply means that these formulations are invalid. But there’s a massive problem: If Lagrangian mechanics is incorrect, then many of the physical laws that describe our world are incorrect. The only solution here is, as Cort Ammon pointed out, to get rid of the idea that the laws of physics are time-invariant — that is, that they don’t change over time. This is a major concession, and one that I think most people wouldn’t be willing to make.
So while you can afford to have Noether’s theorem be inaccurate, you have to be willing to change your entire universe.
Finally, we go to the third type of principle: the type that cannot be changed under any circumstances. It can be hard to distinguish this type from the second type, because often the only way to change a principle is to get rid of certain assumptions, assumptions that we might have taken for granted. These are (type two) cases, though, where reality must be changed at a fundamental level.
Type three cases aren’t necessarily physical laws, but are instead more abstract things that I find difficult to categorize. I’ll go straight to an example: Gauss’s law. Gauss’s law can be stated in two different ways, the differential form and the integral form:
The differential form says that the volume density of the flux of an electric field is equal to the charge density divided by the electric constant. The integral form says that the flux of the electric field is equal to the total electric charge enclosed within a region bounded by a surface divided by the electric constant.
These two equations are identical because of something called the divergence theorem. It is purely mathematical, and thus can’t be violated. There are certain criteria that must be met for it to be applied — Wikipedia states that the volume must be compact, the surface must be piecewise smooth and the vector field must be continuously differentiable — but violating them introduces levels of mathematical weirdness that I think makes it impossible to build a universe. The point here is that if you have a force that satisfies one of the equations, it must satisfy the other. You can’t insert another constant, or change the power of something.
Here’s the point of it all: You can’t change the way the world works without having effects you couldn’t have predicted. Changing the laws of nature is a dangerous game, because the universe is a delicate entity, staying hospitable by only the narrowest margins.
Be careful when playing with physics. You just might blow up the universe.
