# Empirical and fundametnal law

In school they gave us a handout about what is a law in physics. I read the text several times but I couldn't clearly understand the difference between an empirical and a fundamenal law. Can you explain in a simple way the difference between those terms? Or give some examples, anything? Thank you in advance.

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An empirical law is a law that somehow fits the data well, but nobody has any idea WHY it works. Plancks radiation law prior to the 1920's is a good example.

A fundamental law is a law that is derived, logically from deeper principles. For example, the Euler-Lagrange equations that describe the motion of a body follow from the principle of least action.

So.. an empirical law isn't proved or just doesn't have an explaination? Based on experience?
And can you give me simpler examples.. I haven't heard of Plancks radiation law or the Euler-Lagrange equations because we haven't studied those in school.
(Sorry for being so dumb and asking too stupid questions, but I have to have a clear idea of these before going back to school, it will be my first year of studying physics )

Gza
In many cases, we'll discover a law empirically before deriving it from deeper principals. A good example of this is Galileo's relationship between distance and time for a falling body (d=10t^2, metric units). At the time of discovery, this law was empirical, since there wasn't a theoretical basis for it, he just played around with inclined planes and figured it out. It wasn't until Newton came along with F=ma (a fundamental law) as well as the universal law of gravitation, that we figured out Galileo's relationship was nothing more than a special case of this.

EDIT: Apologies to Dimitri for my statement of F=ma as a fundamental law. It's really F=dp/dt, but F=ma looks less intimidating .

I think I got it . Thx a lot :) Now I'll be able to complete my homework.

Gza said:
EDIT: Apologies to Dimitri for my statement of F=ma as a fundamental law. It's really F=dp/dt, but F=ma looks less intimidating .
Good man.

Arwen, don't worry about it. I know several people who got their BSc without ever thinking about these things, so you are definately on the right track.

Galileo
Homework Helper
Haha, I never realized there were two kinds of laws untill a few years ago.
I had a lot of trouble understanding 'why' some things were true and when I asked about it I'd get some weird answer I didn't understand.
It's good you get these things in school, it may save you from some trouble I had.

Keplers laws are emprical, and they can be deduced from Newton's laws of motion and gravitation.
However, Newton's laws of motion can be shown to be true in the macroscopic realm from quantum mechanics and Newton's law of gravitation can be seen to be an approximation from general relativity.

So does that make Newton's laws empirical whereas they were fundamental before? They come from the result of experiments after all, as do all laws.