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What is the difference between a law, a principle, a theory, and a hypothesis in science?
Category: Society
Published: July 24, 2024
By: Christopher S. Baird, author of The Top 50 Science Questions with Surprising Answers and physics professor at West Texas A&M University
In science, the terms principle, law, theory, and hypothesis all have different meanings, even though we often use them interchangeably in everyday life. Scientists intentionally use these terms to mean different things. With that said, scientists can sometimes get clumsy in their language and use these terms in mixed up ways. If that happens, don't treat it like it's a big deal. Ultimately, the important information in a statement is the scientific principle itself and not so much what we choose to call the statement. Also, the exact definition of these terms can be slightly different from one field of science to the next.
Hypothesis
A hypothesis is a guessed outcome of a particular experiment, observation, data analysis, simulation, or mathematical derivation that has not yet been tested. In everyday life, when people say, "I have a theory," this is equivalent to saying in science, "I have a hypothesis." Technically, a hypothesis could be any guess that is testable. However, scientists strive to formulate a good hypothesis, which is a hypothesis that has a reasonable likelihood of being true or of leading to interesting results, and will likely bring about a significant advance in our knowledge. The statement, "other universes exist," is not a hypothesis because it is not testable. On the other hand, the statement, "the total energy of a closed system is locally conserved," is not a hypothesis because it has already been tested and found to be true. The statement, "the sun will be made of cheese tomorrow," is indeed a hypothesis, but it isn't a good one because it has almost zero likelihood of being true and has no theoretically sound way in which it could be true. In contrast, the statement, "the sun will be white tomorrow," is indeed a hypothesis and indeed has a high likelihood of being true, but it's not a good hypothesis because it would not bring about a significant advance in our knowledge.
An example of a good hypothesis was the statement, "there is a supermassive black hole at the center of our galaxy." This statement was a good hypothesis because it was testable, because it was reasonably likely to be true (observations had already identified a very powerful compact object at the center of our galaxy), and because testing this hypothesis would lead to ground-breaking results. In fact, testing this particular hypothesis and finding it to be true led to a Nobel Prize. Often in research, figuring out a good hypothesis and how to test it is the most important step. It can take unique creativity and deep thinking to come up with a good hypothesis and a successful way to test it.
Physical Law
A physical law is a single statement that the universe obeys; whether in physics, chemistry, biology, or other fields of science; that has been experimentally proven to be true in a wide variety of situations and systems. An example is the law of conservation energy. It's a single rule (namely, that the total energy of a closed, local system is always constant in time). Also, it's been proven to be true by a mountain of evidence. Also, it's true in a wide variety of situations—chemical reactions, nuclear reactions, mechanical machines, biological processes, and so forth. Therefore, conservation of energy is indeed a physical law. In fact, conservation of energy is always exactly true (locally*), in all situations and processes, everywhere in the universe. This makes it a fundamental, exact physical law. Fundamental, exact physical laws arise from innate local symmetries present in the framework of the universe, which is why they are always true (at least locally*).
Let's look at these symmetries. Time symmetry gives rise to the law of conservation of energy, spatial translational symmetry gives rise to the law of conservation of momentum, spatial rotational symmetry gives rise to the law of conservation of angular momentum, and electromagnetic gauge symmetry gives rise to the law of conservation of charge. In many cases, laws are considered definitions of parameters. The distinction between a law and a definition is usually not important. For instance, you could say that there is a law of conservation of momentum which is obeyed by the parameter momentum. Or, you could say that the "law of conservation of momentum" is really just the definition of momentum. In other words, "momentum" is defined as the vector parameter of motion that is conserved.
There are also genuine physical laws that are not fundamental or are not exact. These laws are only approximately true or are only true for particular systems. For instance, Newton's law of universal gravitation is only approximately true. In many situations, Newton's law of universal gravitation is so close to being correct that the error that results from using this law is below the sensitivity of your equipment. However, with sufficiently sensitive equipment, you can find that Newton's law of universal gravitation is only approximately correct and that Einstein's theory of gravity—general relativity—is exactly correct. Also, in extreme situations such as near and in black holes, Newton's law of universal gravitation is spectacularly wrong. Despite being neither exact nor fundamental, Newton's law of universal gravitation is still a genuine law. Note that Newton's law of universal gravitation is a law and not a theory because it is a single statement consisting of a single equation.
Conclusions and Facts
A bit of scientific information that is too specific to be true in a wide variety of situations (or to even make sense in a wide variety of situations) is not called a law, but is rather called a "conclusion" or a "scientific fact". For instance, the statement, "Jupiter is bigger than Mars," is a true statement, but it's not a physical law because it's far too specific and is not an equation. We should instead call this statement a scientific fact. Raw data (which could include the results of experiments, observations, and numerical simulations) contains scientific facts which then get condensed down to conclusions. A collection of conclusions can become a law if a single equation is able to accurately describe them and if this equation is true in a broad array of situations and systems.
Rule
Unfortunately, the word "law" is also sometimes used in science to refer to a useful rule that isn't really a genuine physical law. The difference between a genuine law and a rule is that a genuine law arises from a clear, underlying scientific principle that is true for all objects within the same category, even if it is a non-exact law or a non-fundamental law. In contrast, a rule is invented because it makes it easier for humans to remember things, to visualize things, or to calculate things. For instance, Ohm's law is not a genuine physical law. It was invented to make the math easier when analyzing electrical circuit elements. It's not true for all circuit elements. In fact, it's not really true for any circuit element except within a narrow range of voltages. Also, Ohm's law does not arise from a meaningful underlying scientific principle. You can analyze and understand the physics of electric circuits just fine without ever mentioning or using Ohm's law. Ohm's law is therefore a rule of thumb and not a genuine physical law. Other examples of scientific rules are the 18-electron rule in the chemistry of transition metal complexes and Hooke's law for the force provided by a spring. They are both mathematically useful but scientifically unnecessary.
Principle
Often, the term "principle" is used in science to mean the same thing as "law". For example, Bernoulli's principle in fluid dynamics could just as well be called Bernoulli's law. If a distinction is made, a principle is usually broader than a law. A law can be written as a single equation. For instance, the law of conservation of energy is written as ΔE = 0 for a closed, local system. In contrast, a principle is a statement that can become several different equations when applied to different parameters. For instance, Heisenberg's uncertainty principle becomes a certain equation when applied to the position-momentum pair of parameters, but becomes a different equation with the same form when applied to the energy-lifetime pair of parameters. Whereas a law is expressed as a single, specific equation, a principle is usually expressed using conceptual statements. With that said, the terms "principle" and "law" often overlap so much in common usage that it might not be beneficial or enlightening in practice to try to make a distinction.
Theory
A scientific theory is a collection of laws, principles, concepts, and facts united together into a self-consistent framework that has been verified experimentally and is able to accurately describe every aspect of a system or field of study. Whereas a physical law contains a single proven statement, a scientific theory contains a large collection of proven statements. An example is Einstein's theory of general relativity, which accurately describes all aspects of gravity, space, and time, everywhere in the universe.
If you are referred to by name when data, facts, instruments, or techniques are mentioned, such as, "the data from A. Smith was used to calibrate our equipment," then you have made a contribution to science. If you are referred to by name when a conclusion is mentioned, such as, "these results agree with the conclusions of A. Smith," then you have made an even bigger contribution to science. If you get a physical law named after you, such as, "Faraday's law of induction," then you have done amazing, ground-breaking science. If you get an entire theory named after you, such as, "Einstein's theory of general relativity," then you have revolutionized an entire field of study and your name will go down in history as one of the greatest scientists.
*Locally? What do I mean by that? As general relativity makes clear, spacetime is typically warped so that it does not actually have time symmetry or spatial symmetry. This means that the law of conservation of energy and the law of conservation of momentum are not actually true on large scales. However, on small enough scales, a warped spacetime will look locally flat, which means that it will locally have time and spatial symmetry, which then means that the laws of conservation of energy and momentum do indeed hold true locally. Therefore, in this context, "locally" means on a small enough scale that conservation of energy and conservation of momentum hold true.
Also, conservation of energy and momentum can approximately hold true non-locally if you define a spacetime geometry that is asymptotically flat far away from the objects of interest and analyze the energy and momentum globally. For instance, we can reasonably approximate spacetime as asymptotically flat far away from two black holes that are orbiting each other. When the two black holes collide and merge into one black hole, gravitational waves are produced that carry away energy with them. In the limit of traveling far away, these gravitational waves will carry away the same amount of energy as was lost by the two-black-hole system during the merger, meaning that conservation of energy holds true. This energy that is lost mostly comes from the mass-energy of the black holes. This means that the mass of the final black hole will be significantly smaller than the sum of the masses of the two original black holes, typically about 10% smaller.