" ... formal ways of describing the variables in psi ... something like a science with quantities and units and such ... "
What I would suggest, in relation to such a splendid appetite for formal methods and scientific ways as is implicit in your remark, is as follows.
Feynman wrote,
I think I can safely say that nobody understands quantum mechanics. ... Do not keep saying to yourself, if you can possibly avoid it, 'But how can it be like that?' because you will get 'down the drain', into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that.
but if that is true, it is because we are
not yet ready to understand quantum mechanics.
The mold of human cognition (this might sound better in German and should probably include some word like
zeitgeist) has not yet developed to the point where it can possibly understand quantum mechanics.
But we
get more ready to understand it by doing exactly what Feynman said not to do, which is to mull over the question, 'But how can it be like that?'
In previous centuries, the same thing applied to Newtonian mechanics.
At one time, humanity could not possibly embrace intellectually the idea that the universe is made of little billiard balls bouncing around and that was all there was to it. It made no sense, the idea simply would not lodge in the human mind.
It's even unclear to what extent Newton himself was intellectually at home in a Newtonian universe. According to Leibniz,
Sir Isaac Newton and his followers have also a very odd opinion concerning the work of God. According to their doctrine, God Almighty wants to wind up his watch from time to time: otherwise it would cease to move. He had not, it seems, sufficient foresight to make it a perpetual motion.
But gradually, over a long period of time during which people kept asking themselves Feynman's forbidden question, 'But how can it be like that?', the mold of human cognition developed to the point where eventually people really could feel at home in a billiard ball universe. By about the twentieth century, vast numbers of people really did naturally feel that this is how things just are. And those people, of course, could not possibly believe in psi.
Well, now the time has arrived for the next step. Actually, that time arrived at least a hundred years ago, but these things move slowly.
Let the quantum question, 'But how can it be like that?', lodge well in our minds, and after a few hundred more years the answer will come.
It doesn't have to be only physicists who do this. It doesn't even have to be primarily physicists who do it. It is a matter of the common mode of cognition of humanity as a whole, to which everyone contributes.
Mulling the question, continually, 24 hours a day, dreaming and awake, is helping the development of the mold of human cognition.
Would you agree?