# How are physics formulas derived

1. Mar 20, 2014

### shreder

i was having this argument with a friend that said that physics formulas are found by performing experiments and in his words "changing the variables and watching how the result changes"
i found this ridiculous but i want a professional opinion (because i know that some formulas are in fact found by experiments like the first law of thermodynamics)

so how do physicists find formulas (like E=hf, F=ma or the schrodinger equation)
and are there formulas that can only be found by experiments

2. Mar 20, 2014

### Staff: Mentor

It's some of both. A very common pattern is to discover a purely empirical formula, something that fits with observations, and then with that hint come up with some first principles from which we can derive some more general formula. Some examples:
- Kepler's laws of planetary motion, followed by Newton's discovery of universal gravitation.
- Bohr's completely empirical model of the hydrogen atom, followed by Schrodinger's discovery of his wave equation, followed by the modern discovery that Schrodinger's equation can be derived from some fairly basic axioms.

However, it's important to understand that the more complete and mathematically derived formulas don't actually tell us anything more about WHY the world is the way it is than the original experiments and observations. They just allow us to make better predictions from fewer ad hoc assumptions. That's aesthetically satisfying and often of great practical value, but we're still choosing the math to describe what we observe to be true and rejecting those theoretical frameworks that don't match how the world behaves.

3. Mar 20, 2014

### SteamKing

Staff Emeritus
Not to mention Galileo, who combined keen observations with mathematics, in his study of falling bodies and the motions of pendulums, for example.

http://en.wikipedia.org/wiki/Galileo_Galilei

4. Mar 20, 2014

### dauto

What your friend describes is called empiricism, definitely an important element of scientific investigation. But it is not the only way to find things out. For instance, you can find that atmospheric pressure drops exponentially with altitude above see level by experimentally measuring the atmospheric pressure at different locations up a mountain slope - empirical observation. But you could also assume that air follows the ideal gas law, solve the hydrostatic equilibrium equation making use on Newton's laws along the way and voila you get to the same conclusion. Many important scientific theories were originally proposed by use of logic and theory alone and only later were experimentally confirmed.

5. Mar 20, 2014

### UltrafastPED

As a professional physicist who has also taught - I think that "derivations" start from "known laws", and apply logic and mathematics to derive the formula of interest.

In the case of experimental results you have a mass of data - but prior to the experiment you also had a "theoretical" basis for conducting the experiment. So if I am using electron diffraction to search for phonons in a crystal that has been struck by a laser impulse ... I have a lot of theoretical knowledge already at hand; I will apply that to interpret the experimental results. There will still be some graphing and statistical fitting, but the information being studied will also have some type of expected structure.

I think that "most" physical theories are based on earlier findings of "experimental facts" which could be generalized into "Laws of Nature" - like Boyle's law, or Kepler's laws. It is only after you have a set of accumulated knowledge that the "Great Thinker" can reorganize the material and make it appear that it all come out of thin air and logic.

6. Mar 20, 2014

### DennisN

In addition to the other good replies, I'd briefly describe the process (the scientific method) as an interaction between previous knowledge, theory, experiments, observations and - guesswork!

A clip where Feynman briefly describes the process: