What's with this desperate need for magic? Of course we know what a photon is. It's the exchange of a certain amount of energy, momentum and angular momentum between two parts of a physical system. How mysterious is that? Why do we not know that? Of course we know this. We are building calorimetric detectors which measure photon energy all the time.

-

You said a photon is "...the exchange of a certain amount of energy, momentum and angular momentum between two parts of a physical system...". If it is an "exchange", then doesn't that mean a photon isn't a "thing" at all? In other words, it's a noun but it's not a physical "thing". Instead, it's an "act".

-

The last time energy was a thing was in the 17th/18th centuries when people were talking about the phlogiston theory of heat. Since the 19th century energy has always been the property of a system to be able to do work on another system. This hasn't changed with the advent of quantum mechanics, there is just a very unfortunate tendency to mistake mass-energy equivalence (correct) for mass-matter equivalence (nonsensical) and to use the word particle for quantum, which carries connotations of some corporal form of energy with it. That is not what the word quantum means.