In science, there are many laws that are described mathematically. Some are established from experimentation; others are derived theoretically from other known laws. It has often been pointed out that it is quite remarkable that nature operates in ways that can be accurately described by mathematical equations.
These equations can be categorized into two classes. Some are purely relational between different measurable and deterministic parameters. The idea that a force exerted by an object is equal to the product of the mass and the acceleration of the object is accurately captured by the simple equation F = ma. Each component of the equation is measurable.
The equations in the other category are just as valid, just as true experimentally, but they are somewhat less simple in that they require the addition of an entity that is not measurable. These additional components are called constants, and they may be determined by experiment or mathematical derivation, but they do not change, and they have no physical reality themselves.
An example is the gas law PV = nRT, which consists of 4 measureable parameters (the pressure, volume, temperature and quantity of a gas) and R, the gas constant. The equation doesn’t work without the constant. This is not a question of units, by the way. You can define the other parameters using any kind of units you wish, but when you do the measurements, you will find that PV = nT is never true.
There are many such equations in chemistry and physics, and many such constants. One of the best known is π, a constant of geometry. The area of a circle is determined by its size; namely, its radius or circumference. Its area is
A = πr2.
But what is π? Where did it come from? We don’t know the answer any more than we know why Plank’s constant (h), so important in atomic theory and quantum mechanics, is what it is. We don’t even ask the question, because we know there are no answers.
The values of the physical constants can only be determined by experimental observation. One of the most important such constants is the speed of light. Establishing that this is a constant required some sophisticated experiments and came as a surprise at the time. Knowing what the value of the constant c is allows us to determine many things, including the relationship between mass and energy, as formulated by Einstein:
E = mc2.
But why does light travel at that speed always, and not faster or slower? That question is not part of science as we understand it. .
For me, the philosophical (not scientific) importance of constants lies in the fact that the reason for their values is not subject to scientific enquiry. The idea that there are things that lie outside of scientific investigation – which used to be assumed when speaking of human-related phenomena such as art, music, love, beauty, and so on – has become controversial. Scientism, the belief that all reality is covered by science, has become popular, especially among militant atheists and extreme reductionists.
But the existence of fundamental physical constants proves scientism to be wrong. We don’t need to invoke the emotions one feels when listening to Beethoven, or the source of the creative genius manifested in poetry or painting, to know this. We don’t need to try to defend the concept of love as being more than an evolutionary adaption to reproductive challenges in early hominids. We can look at science itself, to see its limits quite clearly. We need simply ask why π, h, R, c, etc have the values that they have.
We can also ask what the universe would be like if the constants were different, and the answers are both shocking and troubling. In many cases, changing certain constants, even by a small fraction, would lead to a radically different form of reality, usually one in which (among many other changes) there would be no life possible at all. But unless we admit teleology into science – which is forbidden – this answer allows no real insight into the question of why the constants are what they are.
Still, the question cannot be denied as a question, and the answer cannot be denied as being beyond scientific enquiry. This, by itself, demolishes the principle of scientism, for it establishes the reality of questions that are not subject to scientific analysis. Once we drop the illusion that the scientific method as we know it is the only and all-powerful path toward understanding truth, we can make a great deal of progress in learning what other truths await our grasp.