I've been interested in physics since I was a kid, and read many books on the topic. The thought experiments of Einstein that led to his theories of relativity were some of the earliest topics I encountered. If you have not read of that, do so . . . I will wait.
So we come to the EPR paradox. The new field of quantum mechanics in the 1920s presented this conundrum - that particles could have entangled properties but that those properties would not become determined until a measurement event, at least according to Bohr. But upon one measurement, both particles states would be determined even if they were separated, and this determination would be instantaneous - faster than light.
The EPR paradox received further attention in the 1950s and led to the Bell's Inequalities - describing the paradox in some detail. Bell proposed solutions to the paradox which are each a bitter pill in their own way. Some have received greater press, but there is nothing yet known to choose among them. Two that are most conspicuous are 1) a multiverse - all the outcomes exist in separate parallel universes, and 2) hard determinism - the paradox arises from quantum mechanics being predictive, but spacetime is complete and only one outcome actually exists - always has and always will.
The more I have thought on these options, the less possibility I can grasp for matters spiritual. The multiverse scenario seems ridiculously uneconomical to my admittedly-Calvinist upbringing, but if all outcomes exist, what judgement can there be for how a person lives (i.e. we live in ALL the ways we can). The hard determinism scenario is crystalline. We do not actually have any free will whatsoever - not even the free will to take advantage of being completely inculpable for our actions.
I think there may be a more mystical way of thinking of hard determinism though - a koan, if you will. We are agents of causality within a complete four-dimensional spacetime. We bring the crystalline structure of the universe into existence by virtue of our own existence in some way.
hmm . . . the existing universe; thinner in what respect? the total probability of all outcomes is 1, but in each individual spacetime, there is also an outcome probability of 1 for the future that actually transpires . . . much to contemplate here.
"Thinner" with respect to the Born rule :) It's like if time were a reel of movie film, except that the film had noticeable thickness, say 1cm. Every point in the movie where there is a macroscopic divergence due to a quantum effect is like shearing the film in half, so now you have two ribbons of film each 5mm thick. Like the movie begins with you setting up a machine to measure the spin of an electron along a fixed axis, then the film splits and one movie ribbon continues showing where the dial on your instrument points "up" and in another half-thickness movie ribbon the dial points down. You can conduct more experiments and get more and more shears down to 2.5mm, 1.25mm, etc. Or, if the experiment is set up in such a way that outcomes are not 50/50 but say 90/10, then the first shear is into 9mm and 1mm, the second shear is 8.1mm, 0.9mm, 0.9mm, and 0.1mm, etc - a crazy medusa head of split hairs.
It is not yet clear what this "thickness" or, in another sense, "reality fluid" really is. All we know is that it obeys the Schrodinger equation and that its amplitude^[Or more specifically and even more oddly, the square absolute magnitude of the amplitude, which itself is a complex number] we get at the end of our calculation is exactly equal to the probability of our outcomes. As in, if we look backwards at our film's history, we have ended up in the thicker ribbon of film more often than in the thinner one. And remember, the outcomes don't need to be 50/50, you could set them up to be 90/10. This can't be explained by something like the binomial distribution of a pachinko machine - the 90% outcome really carries some weight to it, some extra thickness of reality.
OK, but if I am put in a box with a radioisotope, a sensor, a hammer and a vial of poison; and I survive the ordeal; my reality will be as real to me and my wife as the other reality where she goes to my funeral too early. Each of those realities - those universes will be equally whole and complete; except for this aspect of thin-ness? If an outcome has a very low probability, in a quantum event, so that it would be remarkably "thin", it will still be a whole separate universe with all the rights and privileges, etc.? So is thin-ness perceptible from within a universe or only a property observable from some higher vantage?
The thin-ness is directly observable retrospectively. We look at our past history and see that we find ourselves in a branch that is much thicker than many of the other possible branches. If we look backwards in time at all the experiments we have ever done, we always mostly end up in the thicker branches than in the more numerous branches. There are versions of us in the thin branches, yes, but we are not them.
For example, imagine you had a weighted quantum 90/10 coin that landed heads 9 times out of 10 on average, and you flipped it 1000 times. If you were just counting distinct universes (thinking that "each universe will be equally whole and complete"), you have 2^1000 distinct branches. Of those, using the binomial theorem, you'd expect that in 99.8% of them the number of heads you see will be between 450 and 550. However, you will most likely not see that. There is a 99.8% chance that you will see at least 870 heads.
If you think that each branch is whole and complete, you cannot explain this. You'd expect to find yourself equally in every branch since they are "all equally distinct", but in practice you do not. You might claim you were just super-lucky that time, but most every time you repeat the experiment you will end up with the same lopsided result. It is as if there is some additional variable you are missing, some value to assign to each branch to describe how "real" it is! That variable is the amplitude, the Schrodinger equation is how you calculate its evolution in time, and the Born rule tells you how to square it to calculate the probability value you need.
This is why I think of probability as "thickness" of the universe. We are just too fixated on counting distinct options, it's hard to think in any another way. So I imagine this thick reel of film, where all the ribbons are identical and stuck together up to the point where some quantum measurement happens, and then some of the ribbons peel off into diverging plotlines. This way you can still count individual "ribbons", it's just that a bunch of ribbons in a thick bundle all carry an identical movie. After some time you may finally stop caring about counting individual ribbons and just take a thickness measurement instead.
I find my hard determinism so much more comforting - there was always a 100% chance I would end up right here! I am right where I am supposed to be, where I *must * be. All those other outcomes, probable or improbably though they may have seemed, they had zero chance! Mere figments of my imagination.
How does hard determinism help you understand the world and shape it into the fashion of your choosing? You flip a 90%/10% coin, you get heads. "It was predetermined that I would get heads!" You flip it again, you get tails. "It was predetermined that this time I would get tails!" Ok then, if you were to flip this biased coin 1000 times, how many heads would you get? "I am not privy to predestination, I can only experience it, but how ever much is predetermined that's exactly how many I will get." Didn't you just reinvent "God's will works in mysterious ways"? I, on the other hand, can tell you exact confidence intervals that, in the large number limit, even converge to an exact number.
Why did you get 900 heads instead of 500? "It was pre-determined". Ok yes, but why was it pre-determined to be 900 and not 500? "That's what it happened to be." Not good enough! I can tell you why, but you cannot tell me. I can predict that if you flipped a 10%/90% coin instead, you would get about 100 heads, but you cannot. I can plant crops knowing that temperature and rain will be favorable in the future, even though I cannot tell the exact weather on any particular day months in advance, while you sit on your hands saying "the weather will be whatever it shall be". Then you will say it was predetermined that you would sit on your hands and that you have no free will to choose otherwise. Then you will starve and die. Meanwhile I will be building solar panel farms and exchanging memes on laser-powered fiberoptic networks. You say you like physics, but you sure are stubborn to use it to your advantage!
If that's really your hangup and you are arguing-from-consequence of some theological catastrophe rather than accepting the universe the way it is, then what's wrong with this postulate for example:
Forget for a moment that you don't like quantum probability, just imagine as a thought experiment that it exists and there are multiple world branches. Stop trying to count the number of distinct branches but look at their relative probability measure specifically. Is the above postulate sufficient satisfy your spiritual desire for a moral principle? Yes, it's weird at first to weigh the value of good such as human life and happiness by something so acerbic as the "square absolute magnitude of the complex-valued quantum amplitude", but if you did it anyway, what would happen?
For example, imagine I tell you:
If you use the postulate I proposed above, there is a clear winner answer, such that in 99.8% of probability measure space, the children are fed, and in only 0.2% of probability measure space they starve. Are you seriously ever going to consider picking "<870", or saying that it doesn't matter what you pick?
So, we are wrestling, I think, with the phenomenon of causality. Conditions observed at time 1 are necessary to the conditions that are observed at (later) time 2. We observe the cause-effect relationship all the time - it seems to be a fundamental property of the universe. Until the 20th century, there was quite a bit of philosophical focus on determinism because the laws of physics seemed so strictly and universally applicable that physicists began to suspect a sufficiently complete observation of conditions at time 1 might predict all future conditions - even for very complex systems. Of course, we know that is not correct now; the predictive power of our theories has been constrained by such effects as quanta and chaos. But being unable to predict the outcome is not the same as the outcome being in doubt, as anyone knows who has ever watched a good detective movie. I do not know how causality is related to hard determinism - principles like quantum mechanics and chaos mathematics seem to make the path of the universe forward in time unpredictable, but they say nothing about whether we are in semi-block time (everything up until the present exists and the future does not yet exist), or block time (everything from the beginning to the end exists).
To take your example of coin flips; in the pre-20th view, a sufficient analysis of forces, positions of air molecules, etc. would give one a precise calculation of the outcome of the flip. In the post-20th view, the coin flip is unknowable until the end because not only do unmeasurably small errors in measurements make it impossible to collect sufficient data for complete analysis, but the outcomes of interactions are indeterministic. And yet, the coin lands heads or tails. So you might say (correct me if I am wrong!) that either both outcomes exist, but in different universes and when we, the observers "collapse the quantum state", we are resolving what might have been into what is (an almost supernatural ability?), or we are perceiving a bifurcation of the universe into two separate ones; the "heads" universe and the "tails" universe. I would say that we live in block time and that our inability to predict the coin toss is a limitation on us, not the universe. The outcome of the toss is a condition in spacetime that is eternal and unchanging, and we will respond to it in the way it is.
In the matter of quotes about morality, some of which I made tongue-in-cheek and some of your own invention, regarding judgement for how one lives or doing good or bad--I'll just say I have no desire for a moral principle in these considerations. The universe seems entirely impersonal and the only so-called spiritual reality we have is what we carry in our own thoughts. I think of the choice between multiverse and hard determinism as possibly an Occam's Razor sort of choice. Can we explain the universe by referring to this one that we perceive directly, or do we need to refer to a vast host of others we cannot?
In regard to moral principles, I think there is no comfort to be had by those seeking such, within this discussion. If I say, the outcome is predetermined, so I cannot change it, so I will act from my own selfish desires - another can call me immoral. If you say, all the outcomes exist so make choices based on probability of good, then don't the bad outcomes exist equally and the choice does not matter? In that case there can be no morality because just like in hard determinism there can be no choice. I think the middle road somehow exists; we are agent's of causality within this one universe and it turns out how it does because of the things we do in it. The fact that we do them of necessity or of free choice is our own internal mental consideration.