These discussions around Bell's theorem, the Many-Worlds Interpretation (MWI), and the challenges of deriving the Born rule continue invoking the interplay between epistemic frameworks and ontological commitments. A significant point of contention is whether MWI can account for the correlations observed in entangled systems without additional postulates, such as collapse, and how these correlations map onto the observer accounts and global description perspectives. There are interpretational gaps that persist.
John’s description of branching in the Many-Worlds Interpretation (MWI) assumes that decoherence ensures each branch corresponds to a distinct outcome of a quantum measurement. This can be expressed using the density matrix ρ in a composite system-environment state: ρ=∣ψ⟩⟨ψ∣,where ∣ψ⟩=i∑ci∣si⟩∣ei⟩. Decoherence suppresses off-diagonal terms in ρ, effectively yielding a mixed state: ρ′=i∑∣ci∣2∣si⟩⟨si∣. Consider the correlations in entangled systems that violate Bell's inequality. These correlations are quantitatively expressed as deviations from the CHSH inequality: S=∣E(a,b)+E(a′,b)+E(a,b′)−E(a′,b′)∣≤2, where E(a,b) represents the expectation value of measurements along directions a and b. Experimental results consistently show that S>2, as predicted by quantum mechanics but inconsistent with local hidden variable theories (Bell, 1964, p.195). In MWI, these results follow from the unitary evolution of the wavefunction. The wavefunction for an entangled pair, ∣ψ⟩=21(∣↑⟩A∣↓⟩B−∣↓⟩A∣↑⟩B), evolves unitarily under the Schrödinger equation. Decoherence ensures that interference terms vanish in the density matrix describing macroscopic observers, giving the appearance of distinct "branches." However, Bruce keeps raising the critical challenge: how do these branches remain correlated across spacelike separations? In MWI, the correlations are not post-measurement artifacts but inherent to the global wavefunction. The key is the consistency enforced by the universal wf's structure, which ensures that for any measurement basis, the resulting "branches" respect the original entanglement. The reduced density matrix formalism explicitly demonstrates this: ρA=TrB(∣ψ⟩⟨ψ∣), yielding probabilities consistent with the Born rule. Yet, the Born rule itself remains elusive within MWI's framework and demands further clarification, as acknowledged by Carroll (2014, p.18). Critics like Brent and Bruce argue that without an explicit derivation of the Born rule, MWI fails to fully account for observed probabilities. This is valid but reflects a broader epistemological gap. Probabilities, as noted, have different interpretations: frequentist, Bayesian, and, uniquely in computational contexts, "objective" probabilities derived from "subjective probabilities" (Everett used "subjective probabilities" iirc, and Bruno's refinement was terming them "objective" in this sense). In this framework, probabilities emerge not as axioms but as limits of frequency operators over the ensemble of computations or histories: Something akin to: n→∞limn1i=1∑nPi≈PBorn, where PBorn=∣⟨ψ∣ϕ⟩∣2. This connects subjective perspectives (what the observer experiences) to 3p descriptions (what the formalism predicts), which is insufficiently addressed/incomplete in MWI or collapse approaches and open with Bruno's approach iirc (correct me, if otherwise). The merit of this kind of approach is that observer experience is no longer outside the scope of the clearest ontology. Now, consider the Gödelian critique. All frameworks—whether MWI, collapse postulates, or alternatives like Invariant Set Theory (Palmer, 2009)—assume arithmetical or stronger foundations. Gödel's incompleteness theorems (Gödel, 1931) demonstrate that within any sufficiently rich formal system F, there exist true statements T that are unprovable within F. Explicitly: ∃T(T∈True∧T∈/Provable in F). Applied to quantum mechanics and ontology, this indicates that any framework aiming for ontological finality will inevitably encounter unprovable truths if it includes arithmetic or its use in its formulations. For example, the observer's role versus the formalism's predictions remains a gap that cannot be fully bridged within any single system. Collapse postulates introduce "magic" by assuming the wavefunction's reality only to dismiss it post-measurement, while MWI faces the unresolved challenge of deriving probabilities without external axioms. The whack-a-mole nature of these discussions therefore may find an explanation in this incompleteness. Every attempt to resolve one gap (e.g., deriving Born within MWI) introduces others (e.g., defining the observer). As Saibal notes, local hidden variables fail due to Bell's theorem, but Bruce counters that this implies non-locality within standard QM. Both points reflect the limits of purely formal reasoning without acknowledging the epistemic/ontological split. In conclusion, these discussions risk circularity if participants prioritize defending their preferred interpretations over collaborative inquiry. Recognizing the limitations imposed by Gödelian constraints and the potential irreducibility of observer perspectives relative to global descriptions is essential. While frameworks like MWI or collapse postulates have epistemic value, they are better seen as tools for exploring the boundaries of what can be explained or inspiration for developing new problems and possible application, rather than as definitive ontological inquiry. The quest for consensus may remain elusive, but acknowledging these limits instead of giving in to the whack-a-mole discourse may mitigate circularity risk. Work has to be done from all sides. Have a great weekend, whether collapse or in some world, or while riding computations. On Friday, November 22, 2024 at 1:59:10 PM UTC+1 John Clark wrote: > On Thu, Nov 21, 2024 at 6:01 PM Bruce Kellett <[email protected]> wrote: > > *>> The spin of 2 electrons has been quantum mechanically entangled. One >>> electron is given to Alice and the other to Bob. Alice and her electron >>> stay on earth but Bob takes his electron and gets in a near light speed >>> spaceship and after 4 years is on Alpha Centauri. And after 4 years Alice >>> picks a direction at random, calls that "up" and measures the spin of her >>> electron in that direction with a Stern Gerlach magnet.* >>> *At that instant the universe splits into two, in one Alice has the spin >>> up electron and Bob has spin down, and in the other universe Alice has spin >>> down and Bob has spin up.* >>> >> >> *> Bob is at a spacelike separation, and does not know either the angle >> of Alice's measurement, or her result. * > > > *And that's why the resulting correlation is so weird, not paradoxical but > definitely very weird. * > > > *This 4-way split, two branches for Alice and two for Bob* [...] > > > > > > *That is incorrect. There is only a two-way split:1) Alice sees up and Bob > sees down.2) Alice sees down and Bob sees up.There is no universe in which > both electrons are spin-up, and there is no universe in which both > electrons are spin-down. This is because the laws of physics (a.k.a. > Schrodinger's Quantum Wave) forbids it. As soon as Alice measures her > electron and sees what her spin is she knows for certain that she will be > in the same universe where Bob sees that his electron has the opposite > spin. And a similar statement could be said about Bob and his electron. * > > *> How does that happen, exactly? * > > > *Are you sure you really want to know EXACTLY? The short answer is it > happens because of the [COS (x)]^2 polarization rule, but you said you > wanted all the details about how that apparently innocent sounding rule > could lead to a violation of Bell's inequality and put philosophers in a > panic. I'm not sure you really want all the details but about two weeks ago > somebody else asked the same question you did and I went into much more > detail. I'm not going to rephrase what I wrote then I'm just gonna repeat > it because I don't think anybody actually read it the first time:* > *== * > > > > *If you want all the details this is going to be a long post, you asked > for it. First I'm gonna have to show that any theory (except for super > determinism which is idiotic) that is deterministic, local and realistic > cannot possibly explain the violation of Bell's Inequality that we see in > our experiments, and then show why a theory like Many Worlds which is > deterministic and local but NOT realistic can.* > > *The hidden variable concept was Einstein's idea, he thought there was > a local reason all events happened, even quantum mechanical events, but we > just can't see what they are. It was a reasonable guess at the time but > today experiments have shown that Einstein was wrong, to do that I'm gonna > illustrate some of the details of Bell's inequality with an example.* > > > > > > > > > > > > > > > > > *When a photon of undetermined polarization hits a polarizing filter there > is a 50% chance it will make it through. For many years physicists like > Einstein who disliked the idea that God played dice with the universe > figured there must be a hidden variable inside the photon that told it what > to do. By "hidden variable" they meant something different about that > particular photon that we just don't know about. They meant something > equivalent to a look-up table inside the photon that for one reason or > another we are unable to access but the photon can when it wants to know if > it should go through a filter or be stopped by one. We now understand that > is impossible. In 1964 (but not published until 1967) John Bell showed that > correlations that work by hidden variables must be less than or equal to a > certain value, this is called Bell's Inequality. In experiment it was found > that some correlations are actually greater than that value. Quantum > Mechanics can explain this, classical physics or even classical logic can > not.Even if Quantum Mechanics is someday proven to be untrue Bell's > argument is still valid, in fact his original paper had no Quantum > Mechanics in it and can be derived with high school algebra; his point was > that any successful theory about how the world works must explain why > his inequality is violated, and today we know for a fact from experiments > that it is indeed violated. Nature just refuses to be sensible and doesn't > work the way you'd think it should. I have a black box, it has a > red light and a blue light on it, it also has a rotary switch with 6 > connections at the 12,2,4,6,8 and 10 o'clock positions. The red and blue > light blink in a manner that passes all known tests for being completely > random, this is true regardless of what position the rotary switch is in. > Such a box could be made and still be completely deterministic by just > pre-computing 6 different random sequences and recording them as a look-up > table in the box. Now the box would know which light to flash.I have > another black box. When both boxes have the same setting on their rotary > switch they both produce the same random sequence of light flashes. This > would also be easy to reproduce in a classical physics world, just record > the same 6 random sequences in both boxes. The set of boxes has another > property, if the switches on the 2 boxes are set to opposite positions, 12 > and 6 o'clock for example, there is a total negative correlation; when one > flashes red the other box flashes blue and when one box flashes blue the > other flashes red. This just makes it all the easier to make the boxes > because now you only need to pre-calculate 3 random sequences, then just > change every 1 to 0 and every 0 to 1 to get the other 3 sequences and > record all 6 in both boxes.The boxes have one more feature that makes > things very interesting, if the rotary switch on a box is one notch > different from the setting on the other box then the sequence of light > flashes will on average be different 1 time in 4. How on Earth could I make > the boxes behave like that? Well, I could change on average one entry in 4 > of the 12 o'clock look-up table (hidden variable) sequence and make that > the 2 o'clock table. Then change 1 in 4 of the 2 o'clock and make that the > 4 o'clock, and change 1 in 4 of the 4 o'clock and make that the 6 o'clock. > So now the light flashes on the box set at 2 o'clock is different from the > box set at 12 o'clock on average by 1 flash in 4. The box set at 4 o'clock > differs from the one set at 12 by 2 flashes in 4, and the one set at 6 > differs from the one set at 12 by 3 flashes in 4.BUT I said before that > boxes with opposite settings should have a 100% anti-correlation, the > flashes on the box set at 12 o'clock should differ from the box set at 6 > o'clock by 4 flashes in 4 NOT 3 flashes in 4. Thus if the boxes work by > hidden variables then when one is set to 12 o'clock and the other to 2 > there MUST be a 2/3 correlation, at 4 a 1/3 correlation, and of course at 6 > no correlation at all. A correlation greater than 2/3, such as 3/4, for > adjacent settings produces paradoxes, at least it would if you expected > everything to work mechanistically because of some local hidden variable > involved.Does this mean it's impossible to make two boxes that have those > specifications? Nope, but it does mean hidden variables can not be involved > and that means something very weird is going on. Actually it would be quite > easy to make a couple of boxes that behave like that, it's just not easy to > understand how that could be. * > > > > > > > > > > > > > > *Photons behave in just this spooky manner, so to make the boxes all you > need it 4 things:1) A glorified light bulb, something that will make two > photons of unspecified but identical polarizations moving in opposite > directions so you can send one to each box. An excited calcium atom would > do the trick, or you could turn a green photon into two identical lower > energy red photons with a crystal of potassium dihydrogen phosphate.2) A > light detector sensitive enough to observe just one photon. Incidentally > the human eye is not quite good enough to do that but frogs can, for frogs > when light gets very weak it must stop getting dimmer and appears to flash > instead. 3) A polarizing filter, we've had these for well over a century.4) > Some gears and pulleys so that each time the rotary switch is advanced one > position the filter is advanced by 30 degrees. This is because it's been > known for many years that the amount of light polarized at 0 degrees that > will make it through a polarizing filter set at X is [COS (x)]^2; and if X > = 30 DEGREES (π/6 radians) then the value is .75; if the light is so dim > that only one photon is sent at a time then that translates to the > probability that any individual photon will make it through the filter is > 75%.The bottom line of all this is that there can not be something special > about a specific photon, some internal difference, some hidden local > variable that determines if it makes it through a filter or not. Thus if we > ignore a superdeterministic conspiracy, as we should, then one of two > things MUST be true:1) The universe is not realistic, that is, things do > NOT exist in one and only one state both before and after they are > observed. In the case of Many Worlds it means the very look up table as > described in the above cannot be printed in indelible ink but, because Many > Worlds assumes that Schrodinger's Equation means what it says, the look up > table itself not only can but must exist in many different versions both > before and after a measurement is made.* > > *2) The universe is non-local, that is, everything influences everything > else and does so without regard for the distances involved or amount of > time involved or even if the events happen in the past or the future; the > future could influence the past. But because Many Worlds is non-realistic, > and thus doesn't have a static lookup table, it has no need to resort to > any of these non-local influences to explain experimental results.* > > *Einstein liked non-locality even less than nondeterminism, I'm not sure > how he'd feel about non-realistic theories like Many Worlds, the idea > wasn't discovered until about 10 years after his death.* > * John K Clark See what's on my new list at Extropolis > <https://groups.google.com/g/extropolis>* > 7hn > > > >> -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion visit https://groups.google.com/d/msgid/everything-list/617c4449-e43f-4d32-b022-7e5f74abc853n%40googlegroups.com.
