T he laws of nature are the fundamental principles that govern how things work in our universe. But there is one “law” that stands out from the others. In 1905, Albert Einstein published one of the most impressive ideas in scientific history: the theory of special relativity. The predictions of special relativity are mind-blowing and often bizarre and have made it into popular culture. The length of objects depends on how fast they are moving, and even time is not independent of motion. The faster one travels, the slower one ages. This often leads to seemingly contracting statements like the following. The center of our galaxy is 50,000 light years away. That means that light traveling at, well, light speed, would arrive there in 50,000 years. However, a spaceship traveling at only 99.9999% of light speed would make it in about 70 years. However, all of these contradictions can be resolved, and in fact, the logic and implications of special relativity are perfectly consistent. For example, the spaceship traveling to the center of the galaxy would arrive there after 70 years as measured by the crew of the ship. But on Earth, more than 50,000 years have passed. In fact, special relativity is one of the best and most accurately tested theories of all time. So why did I say in the title that special relativity is not a law of nature?

Let me explain, how I would understand the term “law of nature”. It is something that tells us how some object in the universe must behave. From that perspective, the theory of electrodynamics, encoded in Maxwell’s equations, is a law of nature because it tells us how electromagnetic fields are created, how they change in time, and what makes them change. But why is special relativity not a law of nature? Ok, it tells how space and time, and motion are intricately related. That would actually qualify as a law of nature. But special relativity is much more than that! It is a meta-law of nature! It tells us how laws of nature must behave! Any law of nature must satisfy the requirements of special relativity. If a candidate for a law violates a single requirement of special relativity, it must be wrong. Or at least, it cannot be fundamental, it cannot be the last word.

The two fundamental requirements of special relativity are:

The first requirement is quite reasonable for a meta-law. The second is not necessarily reasonable, but it is an experimental fact that has been checked over and over again to the utmost precision. These two innocent-looking requirements actually impose rather strict constraints on how a law of nature can look like. This is all encoded in a clever 4-dimensional formalism (Lorentz covariance), which would make a good topic for another article. But let’s look at two easy examples, how special relativity rules out possible laws of nature. Look at the Schrödinger equation:

which describes the behavior of particles in quantum mechanics. It is a wave equation, and if you try to solve it for some system (like the hydrogen atom), you get results that are in very good agreement with experiments. So clearly, this looks like a law of nature. But does it satisfy the requirements of special relativity? The answer is no! Although highly successful in giving very accurate predictions on low-energy quantum particles, the form of the Schrödinger equation immediately shows that it cannot be fundamental. In special relativity, space and time are treated as peers. That is encoded in the language of Lorentz covariance. But here in the Schrödinger equation, time and special are treated very differently: time appears with a first derivative, whereas space appears with second derivatives. So the Schrödinger equation cannot be the last word. And in fact, quantum field theory was the answer to that problem. That doesn’t mean that the Schrödinger equation is completely wrong or useless. It just means that it is only applicable in a certain domain, for slowly moving, low-energy particles. But it is not fundamental.

As another example, consider Newton’s law of gravitation:

where F is the force acting on a body of mass m which is a distance r away from some other body of mass M. But suppose that the body M starts to move away from m. Special relativity implies that nothing can travel faster than light, not even information. But from Newton’s law of nature, the body m immediately feels that the body M has moved. So that information would have to travel at infinite speed, which is not possible. So again, this law cannot be fundamental. The relativistic theory that has superseded Newton’s law of gravitation is, of course, the other one of Albert Einstein’s masterpieces, his general theory of relativity. In a way, one could say that special relativity is more general than general relativity, but that’s yet another story.

In conclusion, special relativity is not just a law of nature that tells us how objects must behave. It is a meta-law of nature that tells us how laws of nature must behave in order to be considered true and accurate. We have seen with examples such as Schrödinger’s equation and Newton’s law of gravitation that the requirements of special relativity do not always hold, thus disqualifying them from being fundamental laws. With this power to constrain laws of nature, special relativity really stands out among all other theories.