What is the difference between theory and law in science?

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For example: theory of relativity and law of gravity.
I googled this but answer wasn’t clear to me.

In: Other
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A law has been proven. Gravity. You see the ball drop.

A theory is something that cant be proven, but is supported by so much evidence it cannot be false. Atomic theory, for example. We cannot see atoms, and we never will. But there is so much evidence for them that they have to exist

In science a law is a **description** of an observed phenomenon. Often this takes the form of a mathematical equation describing the relationship between observed phenomenon.

A theory in contrast is an **explanation** of why a phenomenon exists or what causes it. They run the range of completely untested guesses to enormously supported explanations accepted by basically everyone as correct; there is no “graduation” from one thing to another via consensus or evidential support, a theory is always a theory no matter how well or little it is accepted.

A law is a universal truth. Regardless of the situation the law will always occur.

For example, in Geology we have 4 laws.

1)The Law of Superposition

2)The Law of Original Horizontality

3)The Law of Uniformatarianism

4)The Law of Cross-Cutting

No matter where you are in the universe these laws will always prove true. Superposition states that if you have two rocks. The rock on top is ALWAYS younger than the rock on the bottom.

A theory means it could become a law but we have no evidence to back it up. An example in Geology is the Core-Dynamo theory. This is the idea our planets magnetic fields are formed in the core. Harrison Schmidt an Apollo astronaut proved the theory true when he collected this rock [https://en.wikipedia.org/wiki/Troctolite_76535](https://en.wikipedia.org/wiki/Troctolite_76535) from the lunar surface. But we only have one example. We have to drill to our own core to prove it to be universal.

~~There isn’t much difference. A law is supposed to be more thoroughly tested than a theory, but when people name something, they might not correctly choose whether to call it a law or a theory.~~

~~Often theories or laws were named “the Theory/Law of _____” a long time ago, and the original term became part of the way people referred to them. For example, Relativity might be considered a law, but people have been calling it “The Theory of Relativity” for a long time, so the word Theory is, to the people using it, just part of the name. So the distinction loses its meaning.~~

It was pointed out that this wasn’t entirely correct. The central point – that people use a term because it’s what they have heard, and that term might not be the correct one – is right, but it appears that I wasn’t using the scientifically correct definitions of the terms.

Not sure if this will be completely satisfactory but hope it points to a direction.

Laws are typically more narrow statements of how things work while a theory might encapsulate several laws and be a broader or more general statement.

For example consider that the Newtonian theory of motion has 3 famous laws. Or the various laws (Gauss, Faraday etc etc) that are encapsulated by Maxwell’s book on the Theory of Electromagnetic fields.

This does not mean that “laws” are somehow less important or significant than “theories”. These terms are just a general and not precisely used way to categorize areas of study or discovery.

Ever seen a book called “<something>, Theory and Practice”?

The “Practice” part tells you if you drop an apple, it will fall to the ground. This is enough to know **what** will happen, based on other people trying it and seeing what happens. Everybody can understand this and apply it in their daily lives.

The “Theory” part explains **why** the apple falls to the ground. The average person may or may not need to know this, but it’s there just the same. This is where you go when you want a deep understanding of the subject… in this case a physicist or engineer.

In this example, the “Practice” is the same as a “Law”.

Put another way, technicians understand practice. Engineers understand theory. But those are big words for a 5 year old.

Let’s look at gravity specifically here, since it is an interesting case.

You can drop something and watch what happens: it moves downward, assuming you are on Earth. That’s just an observation of the phenomena. If you got very specific in your observations, you could say: it moves at a specific velocity towards the center of the Earth. Neat.

Now you could turn that last observation into something of a “law” if you wanted: it would just be the equation you’d use to calculate exactly what that phenomena would be. We usually only elevate these to “laws” if they prove exceeding useful or historically important.

Note that a “law” (or any other equation of this sort) would _not_ tell you _why_ it happens. It would just tell you that it _does_ happen. So Boyle’s law is simply a statement that the “that the pressure of a given mass of an ideal gas is inversely proportional to its volume at a constant temperature.” It doesn’t tell you why this is the case (to explain _why_ required a lot more work). Hooke’s law is simply “the strain in a solid is proportional to the applied stress within the elastic limit of that solid.”

OK. So _why_ does our original phenomena (you drop something, it goes downward) happen? That’s where the theory comes in. Does it happen because, as Aristotle believed,that whatever you dropped is made up of “earth” and/or “water” elements, and these elements naturally move towards the ground? Or does it happen because, as Newton held, there is an invisible attractive force called gravitation that anything with mass emits? Or, does it happen because, as Einstein argued, mass is warping the structure of space-time, making a movement towards the center of Earth’s gravitational mass the shortest distance in space-time? Each of these are theories. They are _why_ explanations.

(I teach history of science at a STEM school, and I always delight in asking students, after explaining Aristotle’s theory of gravitation, what the modern answer is. They _always_ recite Newton’s answer, because that is what is intuitive to them. I congratulate them on being 100 years behind the times.)

For these theories to be very useful, we need to be able to distinguish between one or all of them being right or wrong. Einstein’s theory, for example, has some slightly different predictions about how gravity works than Newton’s, and we can (and have) used instruments to confirm that reality meets Einstein’s approach better than it does Newton’s (Newton’s works fine for a certain approximation). That doesn’t mean Einstein’s theory is true, but it does mean it is probably more true (or more useful) than Newton’s theory. It is possible that in the future we will have a theory that better explains gravity even better than Einstein’s theory (there are some things that it does not explain quite right, so there is probably more needed).