Can Axioms Revolutionize Our Understanding of Physics?

[Yaya]

After the idea of deducing theorems and propositions from axioms became widespread in mathematics, our knowledge grew tremendously. Why haven't we done the same for physics ? I have a list of axioms which I think will work for physics but I don't want to release them yet before seeing what other people think. Could this possibly allow us to explain phenomenon such as dark energy and dark matter ? Possibly discover other things as well ?

 

[Vanadium 50]

Physics is not mathematics.

 

[Nugatory]

After the idea of deducing theorems and propositions from axioms became widespread in mathematics, our knowledge grew tremendously. Why haven't we done the same for physics?

Physics is an empirical science, so it operates by proposing hypotheses and testing how well they predict the results of experiments and observations. Theories are judged by how well they describe the universe in which we live, as opposed to axiomatization which judges propositions by their consistency with initial assumptions chosen because they lead to interesting problems.

I have a list of axioms which I think will work for physics but I don't want to release them yet before seeing what other people think.

Please do respect the forum rules about not posting personal theories.

 

[Dale]

There are lots of papers on various axiomatizations of physics. You may want to start with some research on what has already been done and the known problems before you go off proposing your own list of axioms.

However, the fact that you were not even aware of the existing work on this topic pretty much guarantees that your current list of axioms will be fatally flawed. Before you can think outside the box you need to know what is already in the box and before you can know what is in the box you have to at least be aware that there is a box.

 

[hilbert2]

That was the "6th great problem" of David Hilbert, from whom I've stolen my screen name...

https://en.wikipedia.org/wiki/Hilbert's_sixth_problem
But to do "physics", conduct experiments and so on, you also need common sense and learned experience in addition to purely logical axioms.

 

[George Jones]

I like a passage in a book by the (very) mathematical physicist Robert Georch:

"It seems to me that "theories of physics" have, in the main, gotten a terrible press. The view has somehow come to be rampant that such theories are precise, highly logical, ultimately "proved". In my opinion, at least, this is simply not the case - not the case for general relativity and not the case for any other theory in physics. First, theories, in my view, consist of an enormous number of ideas, arguments, hunches, vague feelings, value judgements, and so on, all arranged in a maze. These various ingredients are connected in a complicated way. It is this entire body of material that is "the theory". One's mental picture of the theory is this nebulous mass taken as a whole. In presenting the theory, however, one can hardly attempt to present a "nebulous mass taken as a whole". One is thus forced to rearrange it so that it is linear, consisting of one point after another, each connected in some more or less direct way with its predecessor. What is supposed to happen is that one who learns the theory, presented in this linear way, then proceeds to form his own "nebulous mass taken as a whole". The points are all rearranged, numerous new connections between these points are introduced, hunches and vague feelings come into play, and so on. In one's own approach to the theory, one normally makes no attempt to isolate a few of these points to be called "postulates". One makes no attempt to derive the rest of the theory from postulates. (What, indeed, could it mean to "derive" something about the physical world?) One makes no attempt to "prove" the theory, or any part of it. (I don't even know what a "proof" could mean in this context. I wouldn't recognize a "proof" of a physical theory if I saw one.) "

 

[Herman Trivilino]

After the idea of deducing theorems and propositions from axioms became widespread in mathematics, our knowledge grew tremendously.

That's a process of deduction. There is never anything contained in a conclusion that isn't already present in the axioms.

Physics is a process of induction. Take something like Einstein's famous mass-energy equivalence: $E_o=mc^2$. It can't be proven. Yes, it can be derived from some other assumptions, but that doesn't mean it's necessarily a universal truth that has been proven to be always true.

 

[atyy]

There are many axiomatizations of parts of physics: Newton's 3 laws, the 3 or 4 laws of classical thermodynamics, the microcanonical emsemble of statistical mechanics, Maxwell's equations, the postulates of quantum mechanics, the standard model Lageangian.

 

[bhobba]

Read the following, a copy of which I have, and you will begin to understand why:
https://www.amazon.com/dp/0387493859/?tag=pfamazon01-20

Thanks
Bill