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. <further mumbo-jumbo here>
There was a time we thought Earth was the only terra firma, then we discovered that the wandering stars were actually planets, some bigger than ours.
There was a time we thought the Sun was singular, then we discovered that every star in the sky is a sun, a galaxy full of them, some bigger than ours.
There was a time we thought that our galaxy was the whole universe, then we discovered that most every fuzzy nebula is a distant galaxy, some bigger than ours.
A hundred billion galaxies, each with a hundred billion stars - and those are just the ones we can see within our horizon! - all to support a bunch of hairless apes? Turns out the universe has no care for economy of stuff. At every step in history of science you could have made an argument of economy, and you would have been wrong. The universe seemingly only cares for economy of rules. Four forces, twelve fields - enough to describe everything that is.
Is it that great of a leap to take one more step and accept that our experience is but one branch of a mind-breaking multitude of the many-worlds branching tree? There is exactly one rule that controls them all - the Born Rule - that’s the kind of economy the universe likes.
I think it IS that great a leap - all the steps before have been steps of magnitudes - we kept finding it was way bigger. But the multiverse idea is one of parallelism - that our universe is one of infinitely many; each way bigger that we could imagine. There IS an economy of stuff in at least THIS universe - a finite quantity, albeit mind numbingly much. My ancestors mutter “enough is enough!” lolz
If it helps assuage your sentiment: the Born Rule enforces a finite quantity of total probability - namely 1. The branching does not create new universes, it merely splits the existing universe thinner, each given 50% (or however much) amplitude. That probability cannot be created or destroyed is a mathematical consequence of the Schrodinger equation.
The you and me here is one small blob of probability, one 10999…999th part of the original universe, but NOT an infinitesmall part - merely finitely small.
You misspoke here - every slice is exactly as big in extent of space as every other, namely one Hubble volume. That probably IS bigger than we could imagine, but that’s not related to quantum mechanics.
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[1] 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.
Or more specifically and even more oddly, the square absolute magnitude of the amplitude, which itself is a complex number ↩︎
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?