What do we mean by nonlinearity in physics? ('cause wikipedia sucks)

[piareround]

Physics teacher and physics professors need to come up with a better definition of nonlinearity if we expect our students to pass any basic physics course. This is because of how education has changed over the past 10 years. I hope in this thread, we collectively as members of this forum can come up with a better definition.So I was learning about Follett's Information Skills Model from Pathways to Knowledge in education class, when I came across this sentence:
http://www.intime.uni.edu/model/information/proc.html
http://www.k12.hi.us/~mkunimit/pathways.htm

"Evaluation by both self and peer is ongoing in this nonlinear information process model and should occur through each stage."

The problem is outlines of the model itself are very linear and cyclically linear in nature at least based on comparing to examples of linearity and nonlinearity in physics. This is mainly because other than in literature, I know no other examples of nonlinearity other than in physics. This got me thinking, how do we really define nonlinearity in physics? Is really that different from how other professions definite it?

However, when I took a quick glance at Wikipedia I found the worst definition for nonlinearity possible:
http://en.wikipedia.org/wiki/Nonlinearity

In physics and other sciences, a nonlinear system is the opposite of a linear system, that is a system that does not satisfy the superposition principle, which means that the output is not directly proportional to the input.

In mathematics, a nonlinear system of equations is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree one. In other words, in a nonlinear system of equations, the equation(s) to be solved cannot be written as a linear combination of the unknown variables or functions that appear in it (them).

I really don't like this definition because there is a lot of physics phenomenon can be broken down into more manageable parts by the super position principle or approximately obeys the superposition principle. There is also a lot of nonlinear phenomena in physics. Furthermore, sound, light, and quantum mechanics electrons in atoms itself serve as the core of how we define to student what superposition is. We use things that can approximately obey superposition to define and introduce what superposition is! We do it before they even learn laws of mechanics, because teachers are not required to teach superposition in 6th and 8th grade! Superposition and waves making up a fundamental part of the new science core standards!

So, are we preparing student to fail through misunderstanding by then turning around an saying these examples of superposition are also not examples of superposition in nonlinearity?I don't think we are preparing students to fail in such a way nor do i believe that we are trying to lie to students. However, the potential for a logical reason for failure is there. Thus, I feel that using superposition as only test of nonlinearity itself, is a poor definition and way of teaching nonlinearity.

So can anyone think of a better physics definition of nonlinear than how Wikipedia defines it? What do we mean by nonlinear in physics?


P.S. The mathematics definition is a bit better of course; however, I am not asking about that. I only post it to show how much in contrast it is to the nonlinear definition they give for it in physics. What I am asking about is for a better definition of nonlinearity in physics not mathematics.

 

[Simon Bridge]

"A system that is not linear" is the best definition of a non-linear system you will get. Sorry.
Instead of trying to define a negative - why not look up the definition of "linear"?

The physics definition is the same as the math definition.

 

[Bobbywhy]

One good starting point is our old standby, Wikipedia:

"In physics and other sciences, a nonlinear system is the opposite of a linear system, that is a system that does not satisfy the superposition principle, which means that the output is not directly proportional to the input.
http://en.wikipedia.org/wiki/Nonlinear_system

Read through this entire page and check the "references", and also, the "see also" suggestions.

 

[stevendaryl]

Linear or nonlinear is about a relationship between two variables. For example, suppose you have a spring hanging from the ceiling. You connect a weight to the end of the spring, and the length of the spring will increase. Then the relationship between weight and length change is linear if the change in length is proportional to the weight added. You put a 1 pound weight on the spring, and the length increases 1 inch. You put a 2 pound weight on the spring, and the length increases 2 inches. Etc.

Mathematically, the relationship between two variables $X$ and $Y$ is linear if there is a constant $C$ such that $X = C \cdot Y$.

 

[Claude Bile]

Nonlinear means not-linear; I don't see how it could be explained any simpler than that.

I don't understand what the problem is.

Claude.

 

[AlephZero]

I don't understand what the problem is.

I think the problem is confusing psycho-babble with science.

Note, the "pathways to knowledge" quoted by the OP should have a "registered trade mark" symbol after it. You don't often find those symbols in real science, in my experience.

 

[dipole]

There are many different kinds of non-linearities, while there is only one kind of linear. So you won't find a definition that exactly describes every scenario - however like everyone else I think the current meaning of the term "non-linear" is perfectly clear to anyone who studies science.

Might wana read into a subject a bit before you waste so much effort going on long tirade in the future.

 

[Claude Bile]

I think the problem is confusing psycho-babble with science.

Aye, the day that physicists change definitions to suit psychologists is the day I give the game away.

Claude.

 

[dauto]

The original poster ought to better explain why he doesn't like the Wikipedia definition. To me it seems to be clear, correct and concise. What else could one ask from a good definition?

 

[Simon Bridge]

I'm with dauto - we need to hear back from OP to make sense of the question.
I understand OP is an 8th grade TA ... so we'd probably benefit from knowing the education level needed here too.
Canvassing past threads suggests an undergrad college level...

 

[BruceW]

in an intuitive sense, linear is exactly how it sounds. A variable is linear in some equation if it appears just as itself, or multiplied by some constant. But if you want to get into the proper mathematics of it, then you need to talk about the theory of linear vector spaces. linear equations and linear differential equations can be used to define a linear vector space, and then things like superposition naturally come about due to the theory.

So, are we preparing student to fail through misunderstanding by then turning around an saying these examples of superposition are also not examples of superposition in nonlinearity?

not 100% sure what you mean here. do you mean we explain light as an example of superposition, but then when we consider light in some material, it no longer obeys superposition? That's because light is linear in the 'microscopic' Maxwell equations, but light is (generally) non-linear when we use the 'macroscopic' Maxwell equations. (for example, if the polarization is a non-linear function of the electric field). But also, this means light does not obey the superposition principle when it behaves non-linearly. So the main thing is that when light is linear, it obeys superposition. But when light is non-linear, then it doesn't obey superposition. (I think wikipedia calls it nonlinear optics).