Ok, thanks. I had read deeper and indeed just following on many minds, it only has one physical universe. The trick is that it's one quantum, uncollapsed, always in superposition physical world.
The many minds realize the classical world by splitting into many mind-worlds, each seeing one possible quantum result.
Here's what I wrote for introduction into this interpretation. Welcome to join in r/quantuminterpretation.
The story: Based on this paper[https://www.jstor.org/stable/20116589], it seems that the many minds interpretation is an interpretation of some confusing aspects of the many worlds interpretation. I personally feel that many minds is more confusing. Anyway, it accepts the main claim of many worlds, that is to reject the collapse of wavefunction. There’s only one world, but infinitely many minds, which splits into mind-worlds. I coin the term mind-worlds to describe that the world that particular mind sees (no superposition), which is not the same as the physical world (always in superposition).
With one physical universe, there’s no issue on conservation of mass-energy, no issue on which basis which is realized in the physical world. The “price” to pay for this interpretation is to have the mind to be totally not physical and having infinite minds for each sentient being. In particular there can be brains states without an associated mind state. And one brain state corresponds to one mind. The brain can go into superposition, the mind cannot. Each possible brain entangled with measurement result can have one of the infinite minds associated with it. The brain remains deterministic, the mind has the probability. So for each possible minds, we can assign probability of seeing this or that result. This has dualism forced into it and introduces another principle compared to many worlds.
Basically, this interpretation tries to take advantage of the advantages of the many worlds, but still try to account for why we only see one measurement result and never superpositions. That minds never see superpositions is a given in the interpretation and the splitting into different worlds due to different results, is actually the splitting into many mind-worlds. The physical universe remains as one, different minds sees different classical, measured results in their respective mind-worlds. The physical world remains in superposition.
However, we only ever experience one result, so that is in essence a measurement, and the next moment, having another quantum measurement, the whole process of many minds repeats itself, each new measurement splits into more mind-worlds. Quantum results are real, but only relative to each observer (minds) in their own mind-worlds.
The wikipedia table has the properties for this interpretation to be almost the same as many worlds.
I have some difficulty understanding some of these properties given the story above, so I shall just quote and paraphrase from the paper as much as possible.
First, and most important, the Many minds view, MMV (unlike the Splitting worlds view, SWV) is in accord with the fundamental idea of the many worlds interpretation that the entire physical universe, and every physical system, is quantum mechanical in the sense of principles I and II (wavefunction and deterministic evolution law). There is no need to postulate collapses or splits or any other non-quantum mechanical physical phenomena. And so there arises no conflict with conservation laws as we saw on the spitting worlds view.
So yes to universal wavefunction and no to collapse from the above.
Second, the MMV entails that the time-evolution of the whole physical world is completely deterministic, and that the "global mental state" of every sentient physical being (that is: the distribution of mental states among the infinity of that being's minds) is uniquely fixed by the physical state of that being. Unlike the abandoned Single mind view, SMV, the global mental state is unambiguously determined by its physical state and consequently the time-evolution of the global state is, likewise, deterministic.
So yes to determinism.
Third, the MMV is in accord with our very deep conviction that mental states never superpose; consequently it is in accordance with the claim that competent sentient beings can accurately report their mental state.
So yes to observer role.
Fourth, the MMV (unlike the SWV) entails that the choice of basis vectors in terms of which the state of the world is expressed has no physical significance. There is always but one physical world in but one quantum mechanical state on this account; and that state can be equally well written in terms of any complete set of basis vectors. As long as a brain is in a state which can be represented as a super position of B states it will have minds associated with.
So it seems yes to unique history in having one physical world, although wikipedia says no to unique history due to the worlds split being the minds.
Sixth, the account is realist in the sense that it entails that there is a uniquely correct state for the whole universe and in the sense that does not suppose that the state of the universe in any way depends on a consciousness or on what observables an observer decides to measure. In this it contrasts markedly with some "idealist" interpretations which entail that consciousness, by bringing about a collapse or in choosing to measure certain observables, in some mysterious way makes reality (perhaps different realities for different observers). This realism, however, does have the consequence that a mind's beliefs about the state of a system after measurement are typically false. Thus, a mind associated with A that measures the x-spin of an electron in a superposition will at the conclusion of the measurement believe, say, that the x-spin is up (of course some of A's other minds will believe that spin is down). In fact, spin is neither up nor down but rather the system A's brain plus electron (and of course the intermediary measuring devices, etc.) is in a superposition. So A's belief is strictly incorrect. However, it is, we might say "pragmatically correct", in the sense that subsequent measurements of the x-spin by A will, from the perspective of that mind, yield results which agree with its initial measurement.
In essence, the many minds all inhabit this one physical world. This is indeed schizophrenia with a vengeance. I took some time to digest this story. I recommend you to not identify yourself as a mind. Just see the word mind as like an object, not you. Then see the picture that the physical world with its quantum universal wavefunction inhabiting a super large dimensional Hilbert space is always in superposition and the Hilbert space is large enough for each minds to experience different worlds within one physical world. So one person is host to many minds who disagree on what’s exactly happening in the world should the many minds in one person be able to communicate with each other. In essence, it’s every sentient being having infinite minds each, not just one person. Like multiple personality disorder too, but each personalities (minds) only see their own reality, which is only part of the superpositions of the world. Each mind can assign probabilities to see which results will happen in their own mind-world. Presumably each sentient being’s mind which sees the same quantum result shares the same mind-world.
So yes, wavefunction is real. Hidden variables… depends on who you ask. This website [https://www.encyclopedia.com/humanities/encyclopedias-almanacs-transcripts-and-maps/many-worldsmany-minds-interpretation-quantum-mechanics]says yes, the mental states are the hidden variables, and wikipedia says no. Surprisingly, locality is yes, see analysis below. And counterfactual definiteness, like the many worlds is ill-posed. Different minds will observe the different sub worlds within the universal wavefunction. It is the ultimate factually indefinite. As minds never see the superposition of the physical world, and the physical world is always in superposition.
Classical score, taking that hidden variables to be yes, observer role to be yes, no to counterfactual definiteness, no to unique history, we get six out of nine. A bit different compared to many worlds, but same score. Interestingly, for the minds involved, the hidden variables are there to introduce indeterminism into the interpretation.
Double-slit with electron.
The wavefunction for the interference is always in superposition, only different minds sees the electrons appearing in different locations on the screen until the interference pattern emerges. Of course, like the many worlds, some minds will see utterly strange stuffs with very low probability like the electron always just land on one point.
If one choses to try to look at which path the electron goes through, the wavefunction there changes to only have superposition of one of the two slits (discounting the electrons which hits the wall of the double slits, which have their own mind-worlds) and the mind-worlds splits into two reflecting the different slits the electrons go through.
The mind-worlds split into two for each measurement. The physical world retains all the superposition, even after sometime it gets super complicated to keep track of, each minds sees some collapse relative to them, so each minds have much easier time to see the classical world in their mind-worlds inside the quantum physical universe.
For the entangled particle pair, say electron spin which goes into room A and B, the person in room A, Alice measures her set and Bob in room B measures his set. Each of them have half of their minds showing the electron spin up and electron spin down. The whole system of electron entangled pairs, including Alice and Bob along with their measurement apparatus are always in superposition. There’s no collapse of wavefunction, no mystery to be solved. When Alice and Bob meet together and compare notes on their measurement results, then the same minds with the same consistent results will share the same mind-worlds, showing the correlations there. However, each process of measurement, coming together can comparing are local. Thus only those particular minds in the mind-worlds sees something strange unless they use this interpretation to interpret that the physical universe is always in superposition, no collapse. No issue with locality.
Delayed Choice Quantum Eraser.
The single photon emitted from the laser goes into superposition after the first beam splitter, then split into entangled pairs at both paths, meet the second beam splitter, have superposition to go into D1 and D2. The idler parts of the photon superposition either meets with the eraser beam splitter or not then meet D3 and D4 in superposition. There can be minds which sees each of the four possible world results as analysed in the many worlds interpretation and then build them up to possibly have the delusion that they can somehow influence the past via their delayed choice.
Strength: It fixes some weakness of the many worlds, in particular, which basis to split the worlds (refer to decoherence section), and conservation of mass-energy. It seems to be also the only interpretation which can claim one physical quantum world, (although many classical mind-worlds), local version of Bell’s test which doesn’t have superdeterminism.
Weakness (Critique): It’s really hard to get around the crazy notion that our physical body is host to many infinite minds, each thinking that their mind-worlds which reflects a classical world is true but in reality, the physical world is so much stranger for being full quantum and always in superposition without any collapse. It’s as if the minds are there just to fulfil any potential classical way to see the quantum worlds and splits into mind-worlds for that purpose. Many materialists also tends to want to ignore this interpretation as it requires a dualist view of the mind. That the mind is not physical.
Many other interpretations also tends to make the quantum world less weird, this interpretation makes it so much more weird.