On the other hand, economics goes on from Homo economicus into a mass of mathiness with very poor empirical correlation except perhaps in very very narrow circumstances.
If by "very narrow circumstances" you mean setting pricing, organizing distribution, predicting the effects of price increases and decreases, determining capital costs, making portfolios, and a whole bunch of other stuff that microeconomics makes precise and in a wide variety of circumstances predictably-correct predictions, sure. There is no economics on the Sun's surface.
It's not billiard physics to general relativity, it's billiard physics to fluid dynamics and predicting the exact route of a stick through a set of rapids.
In economics our biggest complaints are around failure to determine that we're near a singularity and failure to predict behaviour through singularities (in a signal processing sense). It's understandable, as we all strongly care about the path of the stick, yet still unreasonable.
Macro is a decent enough tool most of the time, as are traditional fluid mechanics approaches. What we don't have are ultra precise CFD tools but in our arguments we act like we should/do. Sometimes traders think that they do have a great CFD solution and that's how we get LTCM crashes!
Or to maybe to a more human point, we can carry humans around on airplanes just fine, but don't know how to carry a payload of a nation of humans on a stable and healthy economic vehicle.
So if you want to have some sort of basic theory, any theory at all that really could work with such subjects, you gotta step waaaay back. The rational actor that actually "works" to build a scientific theory is such a general concept that it has literally zero predictive value. It states that actors make consistent choices, but only for identical choice situations. Thus, even if a microsecond passes, we are not in the same choice situation and all sort of rationality is out of the window.
An actor who chooses chocolate first, and then chooses something else the next second while throwing away the chocolate is can still be rational, it's only about the counterfactual of the first choice situation. Yet, one was able to show that this sort of very general rationality is a necessary condition to writing a formal model of human behavior, in other words the homo economicus is just answering the question as to what ground rules we need to model human behavior in the first place. It is truly an immaterial, philosophical object that is used in all science dealing with human behavior.
It's more to the credit of economists that they actually wrote this out axiomatically instead of hiding it in implicit discussion.
Then, economists went and tried to write falsifyable theories based on data and observation. This has been done with more or less success, but let's not forget that economic science still replicates much, much better than something like Psychology or Sociology, also concerned with human behavior.
By the way, applying physical approaches to economics is called econophysics and is a thing that exists. It's not really a thing that is successful, cause if you treat humans as mindless particles who are just behaving according to some ruleset, you are working with hyper-hyper rational actors. But it exists.
Can you give an example?
In terms of micro, yes there are pretty consistent theories as to why and how people use money. Probably the most relevant application thereof are in the microeconomics of banking and in so called microstructure models in finance.
In terms of macro, there is of course also a lot of monetary theory as to why people use money in a certain way.
What does not yet exist is a unified theory linking micro behavior to all aggregates. Such models typically rely on some sort of representative agent, which is known and recognized to be deeply problematic in scientific terms of aggregation. Other approaches exist, of course, such as agent based models. But there is no "theory of everything" yet.
Can economics give rationales? Yes. Peek into any course on the theory of money.
But reasoning from micro behavior to aggregates is difficult in social science. We are currently in the process of figuring out better theories of aggregation, but doing so requires using game theory and decision theory in fully interdependent (so for example networked) contexts trough dynamics, so this as of yet also requires a lot of methodological (read: mathematical) machinery that is not yet developed.
Inverting the question does not obviate the answer to what I asked you. Moreover, as stated your rebuttal question is underspecified: what do you mean by the "dynamics of money" and "stable foundation"? Can I trivially answer this by talking about the relationship between credit and debts, or are you looking for something more specific? You responded to my (very precise and specific) question with a vague, orthogonal dismissal of the entire field.
Why don't you tell me about the "mathiness" in some peer-reviewed economic paper (preferably in a tier 1 journal) that you perceive to only be correlated with real world conditions in "very narrow circumstances"?
You may have taken a statement made in jest literally. Homo economicus is a known fiction. Just as frictionless, airless physics are a known fiction. They're useful, however, for (a) defining a limit or ideal, (b) pedagogical purposes and (c) starting to think about a problem.
Microeconomics makes falsifiable predictions which can be repeated in experiment. (I'll go ahead and quibble over whether macroeconomics is a science. It's closer to an art, like politics. A field with its own rules and lessons worth learning, but without the capacity to experiment and make falsifiable predictions.)