# Difference between Theory and Law

• ffleming7
In summary, a scientific law is a statement that can be encapsulated in a single sentence or equation, while a scientific theory is a framework that includes this law and makes predictions about the results of experiments. The word "law" fell out of favor in physics in the early 20th century, and theories are not considered to be true but rather useful in explaining and predicting phenomena. The layperson's understanding of the word "theory" may differ from its technical definition, leading to misunderstandings. However, when communicating with non-scientists, scientists may use the common meaning of the word.

#### ffleming7

What is the difference between a scientific theory and a scientific law? Is there a fundamental difference or is a scientific law just a scientific theory that is extremely well accepted and supported. If that is the case, why is the Theory of Evolution not a scientific law, considering how much evidence there is supporting it? Also, I believe I have read that there is a Theory of Gravity as well as a Law of Gravity. Is this true? If it is, does that mean there is a fundamental difference between the two?

Thanks for any help.

A law is just a part of a theory that can be stated in the form of a single sentence or a single equation. Newton's law of gravity is the statement that the force by which a particle of mass M acts on a particle of mass m has magnitude GMm/r2 and direction from m to M. Newton's theory of gravity is the framework that contains this law and everything else you need to calculate the motion of particles influenced by this law.

A theory doesn't ever stop being a theory just because sufficient evidence to support it has been found. There's no word that means "theory with lots of evidence to support it".

What Fredrik said. However, as far as I know there are no moderns "laws" in physics, even when a theory can be largely encapsulated in a single equation we simply don't use that word anymore. The word "law" was used up until the beginning of the 20th century or so (the most recent "law" I can think of is Planck's law) but then fell out of favour.

The reasons are -as far as I know- mainly historical. A few hundred years ago many scientists saw it as their job to figure out "God's laws of Nature" and many meant this quite literally: what they envisioned was a library with books where you could look up which laws of nature were applicable to a certain situation; in the same way you could (and can) look up the laws of Humans (the laws in our legal systems).
This is one reason why many laws were formulated in such a "formal" way.
It also explains why there are quite a few "laws" that are by no means "universal" and only applicable to relatively small range of situations, Hook's law being a good example of the latter (only applicable in the linear regime; if you stretch the spring too far it won't work anymore).
Hence, a "law" is by no means neccesarily more "correct" than a theory: A good example is Einsteins theory of gravitation which is "more correct" (applicable in a wider range of situations) than Newtons law of gravitation (the latter is just limiting case of the former),

By the way, I consider the definition of a theory as a statement about some aspect of the real world that has a lot of evidence to support it to be fundamentally flawed, and also inconsistent with how the word is used by physicists. That definition is probably sufficient for any other branch of science (which explains why it's in such widespread use), but physics requires a more sophisticated definition.

I would define a theory as a set of statements that makes predictions about the results of experiments. (I would also require logical consistence, that the number of statements is finite, etc., but I'm not going to go through all the details unless someone asks). This includes statements such as "the Earth is round" and "the Earth is flat". I consider both of those to be theories. The essential property of a theory is that it makes predictions.

It doesn't make sense to categorize theories as either right or wrong, because they are all wrong. Some are just less wrong than others in the sense that their predictions agree with experiments to a higher degree of accuracy.

"I would define a theory as a set of statements that makes predictions about the results of experiments."

That would be a hypothesis.

I don't like they way you phrase it but yor gist is correct about them being right/wrong. I'd say the theory is incomplete, not incorrect. :D

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Perhaps a law is just a theory that's old enough that scientists in those days still thought that theories could be true. Today, we're not really vain enough to believe that our models of the world are true, rather that they are useful. Newton's laws, for example, are not exactly true, as Einstein revealed. However, they are incredibly useful.

The layperson still believes that a law is a kind of super theory, or that a theory is an uncertain guess. But that's rather ironic considering that the theories of relativity correct the Newtonian laws of motion. When scientists use the word theory, they don't mean guess, or something that they're unsure about. This divergence between the popular usage of the word and the professional usage can lead to misunderstandings.

Even so, when scientists communicate with laypeople, they still tend to use the common meaning of "theory", and not the technical one. Carl Sagan, for example noted that "Evolution is a fact. Not a theory." That's probably not something one would say to a biologist.

f95toli said:
What Fredrik said. However, as far as I know there are no moderns "laws" in physics, even when a theory can be largely encapsulated in a single equation we simply don't use that word anymore.

Birk's Law.

Hubble's law

Shannon's law

Laws of black hole thermodynamics (but that's cheating)

Laws of nature/physics still in use

xxChrisxx said:
"I would define a theory as a set of statements that makes predictions about the results of experiments."

That would be a hypothesis.
No, it wouldn't. The word hypothesis refers to something that might be true. That's why it's a useless concept in physics. The standard definition of the word theory has the same problem. That's why I said it's "fundamentally flawed".

xxChrisxx said:
I don't like they way you phrase it but yor gist is correct about them being right/wrong. I'd say the theory is incomplete, not incorrect. :D
That terminology suggests that you can make the theory right by completing it, when in fact you'd have to replace it with another theory. The new theory makes predictions about a range of experiments that includes the range covered by the old theory, but the concepts it defines and uses in calculations can be completely different from what the old theory used (e.g. strings instead of particles, spacetime curvature instead of action at a distance)

I understand why you don't want to call excellent theories like QED or GR "wrong" or "incorrect", but their predictions are wrong, so it makes perfect sense to say that the theories are wrong too.

Ahh very subtle difference on the hypothesis thing, didnt read it well enough.
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I don't like the fact that word theory causes so many problems in everyday life, where to some it means blind speculation. Whereas I tend to see theories as models explaining the facts we see.

Now in the case of gravity. You have Newtons model and GR, they are valied at different points. This is a good example acutally as both are models that are valid at different points in the domain. Within the valid range thay are 'correct', but as a general model they are not. This merely means there are gaps to be sorted out, now if a general model displaces both GR and Newtons model in the future then fair enough.

As technology and knowledge improve, we'll be able to fill in the gaps and get a more complete model. When that is the case I believe the model would be correct to within measureable error, at which point barring semantics you can say the theory is correct.
Now I realize that getting to that point is a virtual impossibility, but I just don't subscribe to that fact that we will never completely understand something and will never have a complete theory.

I can see this getting slightly beyong my level of knowledge, as an engineer Newton is the fella for me.

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xxChrisxx said:
Ahh very subtle difference on the hypothesis thing
Yes, I should probably have emphasized what that subtle difference is. We could say that a hypothesis is "a set of statements that attempt to describe what something is like". My definition of a theory on the other hand is "a set of statements that makes predictions about the results of experiments". That difference is subtle enough to be irrelevant in other sciences, but it's relevant in physics.

Fermat's last theorem - which now is a theorem, I'm told - the proof is gobbledygook to me - given the conventionality of simultaneity, I suppose it's always been a theorem? Or up (down?) in the platonic realm?

Riemann hypothesis

A law is a statement accepted without evidence other than observation and induction. A theory is the logical body that follows from a set of laws. Einstein's special relativity follows from these two laws (taken from Wikipedia):

* The Principle of Relativity – The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems in uniform translatory motion relative to each other.

* The Principle of Invariant Light Speed – Light in vacuum propagates with the speed c (a fixed constant) in terms of any system of inertial coordinates, regardless of the state of motion of the light source.

These two statements are accepted, forming the starting point, and all else is logically deduced from this base. "Laws", "postulates", "axioms", "principles" are all synonyms. Usually these terms are reserved for statements that produce successful theories, as opposed to arbitrary statements generating arbitrary theories.

Werg22 said:
Einstein's special relativity follows from these two laws
This claim (which is also completely standard; it can be found in every text on SR, and probably hundreds of posts at Physics Forums) is my biggest pet peeve in physics. Those statements are ill-defined. I could talk about what's wrong with them for a long time, but I'll just mention the biggest problem here. They use the concept "inertial frame" without a definition, and any definition that's appropriate for SR must in fact include some version of these two statements.

If we really want to use Einstein's postulates in some sort of derivation, we have to do something like this:

* An ill-defined statement can be interpreted as representing a set of well-defined statements.

* We apply this idea to the principle of relativity, and interpret it as a set of well-defined statements: One well-defined statement for each definition of "inertial frame", "law of physics" and what it means for two laws of physics to "be the same" in two coordinate systems.

* Now we make a bunch of other assumptions: a) Physical events are represented by points in R4. b) A function representing a change from the coordinates used by one inertial observer to the coordinates used by another is infinitely differentiable and takes straight lines to straight lines. c) These functions form a group.

* Then we find out which groups of functions are consistent with these assumptions. There are only two: The Galilei group and the Poincaré group.

* Now we interpret the speed of light "postulate" as meaning that the light cone at the origin (which is defined as the set of points satisfying xTη x=η) is invariant under those coordinate change functions that take the origin to itself. This forces us to choose the Poincaré group.

* Now it almost makes sense to say that we have derived the Lorentz transformation from Einstein's postulates, but what we really did was just to find out which ones of the well-defined statements represented by the first postulate were consistent with the other assumptions we made.

A less complicated way to think about Einstein's postulates is as a set of loosely stated guidelines that are meant to help us guess a theory that might be a good description of space and time.

Some common sense definitions from NAS are

Law: A descriptive generalization about how some aspect of the natural world behaves under stated circumstances.

Theory: In science, a well-substantiated explanation of some aspect of the natural world that can incorporate facts, laws, inferences, and tested hypotheses.

http://www.nap.edu/openbook.php?record_id=6024&page=2

bleedblue1234 said:
That discussion is five years old, and, except for post #3, it shows. PhysicsForums has improved *a lot* in the last five years.

xxChrisxx said:
I don't like the fact that word theory causes so many problems in everyday life, where to some it means blind speculation.
That Joe Blow now uses the word "theory" to make his completely random, completely unjustified conjecture sound better does not belittle the term "theory". Theory, in science, is as good as it gets. Hypotheses are laws or theories in the making. Laws are short and simple and answer "what" questions. Theories are broad and deep and focus start answering the much more difficult "why" and "how" questions. Think of it as the difference between kinematics and dynamics.

Some dirty little secrets about science:

Scientific theories cannot be proven to be true. Suppose you hypothesize that all crows are black. Over the years you see thousands of them. All of that evidence does not prove your hypothesis correct. All it takes is for one albino crow to fly by, and BANG! Your hypothesis is dead.

Science works by consensus. That scientific consensus works to distinguish what is accepted science versus what is not, what gets published versus what doesn't, what gets funded versus what doesn't. There's an implicit voting process in science.

Science isn't a democracy. A Nobel-prize winning physicist has a lot more say in what gets published, what gets funded, and what is deemed the best explanation than does a post-doc, even if the Nobel winner hasn't produced much new science for decades. That consensus is needed is partly due to the fact that ...

Most scientific hypotheses are shot down by reality. That stupid albino crow flies by. Scientists know this and want to see some evidence before they jump on the hypothesis-of-the-month bandwagon. Journalists don't know this and regularly get snookered as a result. Example: Back in the 1970s a few climatologists made predictions of global cooling. This was never the consensus view, but because it was a sensational claim, journalists ate it up. Those climatologists were respected scientists. They just got it wrong. That isn't always the case. Another reason consensus is needed is that ...

Science has its share of crackpots. A recent example: Cold fusion. Journalists got snookered in the first time around, and the second, and the third, ... The vast majority of physicists did not. Cold fusion is not a scientific theory. Not yet, at least (and it most likely never will be).

xxChrisxx said:
I don't like they way you phrase it but yor gist is correct about them being right/wrong. I'd say the theory is incomplete, not incorrect. :D

How about 'the theory is supported by evidence'? That gets across (at least to me) that it is neither complete or correct, merely something that fits the observed evidence (where the converse is either an incorrect theory such as the 'flat earth' theory where non of it's predictions are even approximations of observation, or a less good but useful approximation such as Newton's laws for non-relativistic motion or hooke's law for springs)

Moridin said:
Some common sense definitions from NAS are

Law: A descriptive generalization about how some aspect of the natural world behaves under stated circumstances.

Theory: In science, a well-substantiated explanation of some aspect of the natural world that can incorporate facts, laws, inferences, and tested hypotheses.

http://www.nap.edu/openbook.php?record_id=6024&page=2
That's the definition I had in mind when I said that it's...

"...fundamentally flawed, and also inconsistent with how the word is used by physicists. That definition is probably sufficient for any other branch of science (which explains why it's in such widespread use), but physics requires a more sophisticated definition."

How about 'the theory is supported by evidence'? That gets across (at least to me) that it is neither complete or correct, merely something that fits the observed evidence
That phrase is good enough for most situations, but it's not perfect. The first problem is that it suggests that the evidence indicates that the theory might be true. But it's not a theory's job to be true. It's "job" is to predict the results of experiments. The second problem is that the best theories of physics aren't supported by all the evidence. They are actually contradicted by some of it.

xxChrisxx said:
...
Now in the case of gravity. You have Newtons model and GR, they are valid at different points. This is a good example actually as both are models that are valid at different points in the domain. Within the valid range they are 'correct', but as a general model they are not...

The trouble is that the valid range for Newton's model is for particles with no relative motion at all. As soon as anything starts moving, Newton's model becomes an aproximation, a good aproximation for low relative velocities, but nevertheless an aproximation and technically not correct. The exception is that some of Newton's "laws" survive unscathed in the GR regime, especially in terms of proper time. Claiming Newton's model "incomplete" and "just needs a few gaps filling in" is I think just a polite way of saying it is incorrect.

To a certain extent, even some of the solutions to GR such as the Schwarzschild metric are aproximations, because the solution assumes a vacuum and assumes the effect of the mass of a test particle with non zero rest mass on the spacetime is negligable, but at least we are aware of where the aproximations are being made.

ffleming7 said:
What is the difference between a scientific theory and a scientific law? Is there a fundamental difference or is a scientific law just a scientific theory that is extremely well accepted and supported. If that is the case, why is the Theory of Evolution not a scientific law, considering how much evidence there is supporting it? Also, I believe I have read that there is a Theory of Gravity as well as a Law of Gravity. Is this true? If it is, does that mean there is a fundamental difference between the two?

Thanks for any help.

Often Law refers to an empirical rule that approximately describes a specific phenomenon. Newton's Law of Gravitation, the Law of Biot and Savart, Boyle's Law, Gauss's Law of magnetism. There is an endless supply.

To me a theory is a construct that attempts to explain the phenomenon. For instance General Relativity as opposed to Newton's Law. I am not sure what it would be for electromagnetic theory since all of Maxwell's equations is really a set of empirical laws.

Shroedinger's equation is a Law rather than a theory but Quantum Mechanics is a theory.