In this post, I argue that, in the grand scheme of the description of the physics of all reality (all objects in reality), the designation of which scientific assertions are “the laws” and which assertions are “the initial conditions” is relative and informal. A similar statement can probably be made about other branches of science too, especially “hard” science like chemistry.
At the end of the day, science is made up of a body of assertions that have been tested against the scientific method. The ways in which we come up with these assertions can differ (as I discuss in my post on the validity of theories in physics), but ultimately we can argue that nature doesn’t distinguish between different kinds of assertions in any way other than their validity as backed up by observation and evidence.
To give an example, consider classical electromagnetism. This is described by Maxwell’s equations along with the Biot-Savart law, which are typically together considered “the complete description” of electromagnetism. In other words, these comprise all the “laws” of the subject. However, when they are applied to a particular situation, we generally need to know more beforehand about the situation in order to draw more specific conclusions. In this context, such “situational data” is typically labeled as “initial conditions” that are fed into the electromagnetism laws. However, in other contexts, that situational data itself is seen as a law! For example, if we were to apply the laws of E&M to study a particular substance, we might accept assertions about the magnetic permeability of that substance to be our initial conditions. However, when studying a subject that classifies properties of substances (say in physical chemistry), we would instead view such assertions as laws.
Said another way: if I walked into a room blindfolded and didn’t know what the charges on objects were or what their velocities or trajectories were, then I couldn’t make any predictions about those objects just from Maxwell’s equations and Biot-Savart. I’d need more information about the situation to say anything further. That additional information can come from other laws (e.g., laws describing how charges move in certain kinds of metals versus other elements.) But do we then think that those laws are necessary to be included to provide the “complete” description of electromagnetism? What does “complete” really mean here? In the context of Maxwell’s equations, we may consider any other information to be “initial conditions” that we can feed into the equations to derive predictions. But it seems in general that the choice of labeling which claims are “the” laws and which claims are initial conditions is actually relative.
