How many laws explain everything we know about nature, and what are they?

[andrewkirk]

The other day, as I was struggling through my quantum mechanics text, I realized that the only physical laws presented in the text were the four postulates of QM, the last of which is Schrödinger's equation. These are presented around page 150. The first 150 pages establish the background needed to understand what the postulates mean, and why they are necessary in order to explain things like interference patterns that cannot be explained by classical physics. The subsequent 500 pages appear to be explaining a variety of subtle and complex techniques that can be used to derive conclusions from these postulates. Maybe there will be one or two more postulates or laws introduced later on – eg I haven't got up to spinors yet – but it certainly looks like the laws of QM can be stated in a very small number of postulates.

Similarly, general relativity seems to boil down to one tensor equation which, together with a postulate that free particles will move along geodesics, encompasses everything we know about gravity and Newton's first two laws of motion.

This got me wondering whether everything we know can actually be expressed in a very small collection of laws, and all the libraries full of science books are about:

• the experimental reasons why those laws currently seem to be the best explanations
• the theory needed to understand the laws (eg hilbert spaces, tensor calculus, differential geometry)
• the myriad subtle and complex techniques that have been developed for practically applying those laws to make predictions and explanations of phenomena

So now to my questions:

1. Is everything we know about chemistry theoretically derivable from the postulates of quantum mechanics?
2. Is everything we know about biology and geology derivable from the laws of chemistry and physics?
3. Is it possible to state everything we know about physics in a very small number of laws? The idea here is to identify a minimal set that doesn't include any law or observation that can, at least theoretically, be derived from other laws in the set, even if we don't have such a derivation at this stage.
4. What would such a minimal set of laws be? My initial guess would be that we need Einstein's field equation, the quantum mechanical postulates, some or all of the laws of conservation (mass-energy, momentum and angular momentum; do we need all three, or are some derivable from other laws?).
5. Do we need Maxwell's equations or are they derivable from the QM postulates?
6. Ditto for the strong and weak nuclear forces.
7. Which of the laws of thermodynamics do we need to state because they can't be derived from anything else?
8. What else?

I am intrigued by the idea of being able to write everything we know about nature (or rather, everything we need in order to be able to theoretically derive, given enough time and cleverness, everything we know about nature) on one or two pages.

 

[cmb]

In regards physics; watch this video:



It may get pretty close to answering much of the substance of your questions.