[nostrademons]

Right, but I'm saying that it's all modeling choices, all the way down. Extend the model to include thermal energy and most of the time it holds again - but then it falls down if you also have static electricity that generates a visible spark (say, a wool sweater on a slide) or magnetic drag (say, regenerative braking on a car). Then you can include models for those too, but you're introducing new concepts with each, and the math gets much hairier. We call the unified model where we abstract away all the different forms of energy "conservation of energy", but there are a good many practical systems where making tangible predictions using conservation of energy gives wrong answers.

Basically this is a restatement of Box's Aphorism ("All models are wrong, but some are useful") or the ideas in Thomas Kuhn's "The Structure of Scientific Revolutions". The goal of science is to from concrete observations to abstract principles which ideally will accurately predict the value of future concrete observations. In many cases, you can do this. But not all. There is always messy data that doesn't fit into neat, simple, general laws. Usually the messy data is just ignored, because it can't be predicted and is assumed to average out or generally be irrelevant in the end. But sometimes the messy outliers bite you, or someone comes up with a new way to handle them elegantly, and then you get a paradigm shift.

And this has implications for understanding what machine learning is or why it's important. Few people would think that a model linking background color to likeliness to click on ads is a fundamental physical quality, but Google had one 15+ years ago, and it was pretty accurate, and made them a bunch of money. Or similarly, most people wouldn't think of a model of the English language as being a fundamental physical quality, but that's exactly what an LLM is, and they're pretty useful too.

[jcgrillo]

It's been a long time since I have cracked a physics book, but your mention of interesting "fundamental physical quantities" triggered the recollection of there being a conservation of information result in quantum mechanics where you can come up with an action whose equations of motion are Schrödinger's equation and the conserved quantity is a probability current. So I wonder to what extent (if any) it might make sense to try to approach these things in terms of the really fundamental quantity of information itself?

[jerf]

Approaching physics from a pure information flow is definitely a current research topic. I suspect we see less popsci treatment of it because almost nobody understands information at all, then trying to apply it to physics that also almost nobody understands is probably at least three or four bridges too far for a popsci treatment, but it's a current and active topic.

[ogogmad]

This might be insultingly simplistic, but I always thought the phrase "conservation of information" just meant that the time-evolution operator in quantum mechanics was unitary. Unitary mappings are always bijective functions - so it makes intuitive sense to say that all information is preserved. However, it does not follow that this information is useful to actually quantify, like energy or momentum. There is certainly a kind of applied mathematics called "information theory", but I doubt there's any relevance to the term "conservation of information" as it's used in fundamental physics.

The links below lend credibility to my interpretation.

https://en.wikipedia.org/wiki/Time_evolution#In_quantum_mech...

https://en.wikipedia.org/wiki/Bijection

https://en.wikipedia.org/wiki/Black_hole_information_paradox