There have been a number of attempts to derive/justify the Born rule, including the self-locating uncertainty approach that Carroll and Sebens develop (I haven't looked at their paper, but they probably cite earlier works in the same vein). Not everyone is convinced that such justifications are (a) not circular, and (b) do not smuggle in assumptions that are not present in the starting interpretation. But adjudicating this debate is way beyond my pay grade. — SophistiCat

That's fine. At any rate, the justification for the Born rule boils down to the following claims:

1. On the Everett interpretation, measurement leads to initial self-locating uncertainty. An observer can have complete knowledge about the relative states of the system, but not which particular state they have just measured. This raises the question of how to quantify their uncertainty in terms of probabilities.

2. If the state amplitudes are equal, the observer should initially be indifferent about which state they have measured. So the states can simply be counted to calculate the probability that a particular state has been measured.

3. If the state amplitudes are not equal, they can be mathematically factored into states that do have equal amplitudes. And again the states can be counted to calculate the probability. The number of factored states exactly tracks the square of the initial amplitude, so it is equivalent to applying the Born rule.

The main assumption is the indifference rule which seems reasonable to me.

I just want to take issue with your characterization of probabilistic theories as "acausal." What you are talking about is causal determinism, and the keyword here is determinism. You can, of course, put your foot down and insist that causality necessarily implies determinism, but, as far as your arguments here are concerned, causality may as well equal determinism, because you are not actually talking about any aspect of causality other than it being deterministic. So for your purposes, causality is a redundant concept, since all that you are talking about is determinism. And I suspect that you only bring it up for rhetorical purposes (everyone wants to preserve causality in our theories, right?) — SophistiCat

It would be great if everyone wanted to preserve causality in their theories but that is what the Copenhagen interpretation explicitly rejects. The idea that the universe is inherently probabilistic implies that the probabilities are a brute fact and inexplicable.

Naturally since the Everett interpretation directly maps the quantum formalism onto the world, then a deterministic formalism leads to a causal (or, if you prefer, deterministic) theory. But it's worth noting that the theory describes and predicts behavior, it does not prescribe it.

Probability can still be baked in the universe even with a causal interpretation. The cause may be inherently probabilistic, which is one of the possible interpretations of the Bohm quantum potential initial conditions. Hence, the reason Bohm suggested that his interpretation is causal yet non-deterministic. — Rich

That raises the question of the status of the Born rule under such interpretations. It would seem that the Born rule could only be postulated, not explained or derived.

well if you accept that the universe is not causally closed, the whole problem goes away. But apparently that is too high a price. — Wayfarer

That's a possible response. But if you make a distinction between the universe and reality, then it just pushes the issue back a level. That is, is reality causally closed (recast as the Principle of Sufficient Reason rather than in physical terms)?

Yes. Before quantum mechanics came along, it was assumed that probability reflected a lack of knowledge about the world (i.e., it was an epistemic issue). But quantum mechanics suggested that probability was baked into the universe at the most fundamental level, violating causality. Which irked Einstein and prompted him to say that "God does not play dice with the universe".

So the problem for a causal interpretation (as Everett and de Broglie-Bohm are) is to explain how probability arises in a causal universe. In particular, if the wave function describes a state evolving into a superposition of two states where one state has an amplitude of 1 and the other has an amplitude of 2, then why should the probability of observing them be in the ratio of 1:4? That is the squared rule that is the Born rule.

If that can be explained in a causal framework then it restores the idea that probability reflects a lack of knowledge about the world, it's not fundamental.

It's about the connection between causality and probability which is really a philosophical issue not a physics issue.

No, this is what we would be committed to if we interpreted light as a flow of classical particles. But the Copenhagen interpretation does not do that. — SophistiCat

I agree that is true.

It is committed to the same thing that the fully-quantum theory is committed to, plus a little extra - but that extra does not show up until the measurement occurs at the detectors, at which point the "extra" makes no observable difference. — SophistiCat

There still remains the issue that the probabilities that the Copenhagen interpretation predicts are inexplicable since it rejects causality. They are simply a brute fact about the universe.

It seems an unnecessary bullet to bite, especially when there are live causal alternatives.

You do not need to assume causality, or anything else besides the operation of standard quantum mechanics, in order to obtain that result. You said so yourself: the Copenhagen interpretation makes the same prediction. It follows the standard solution all the way up to the moment of detection, at which point it says that the superposition state collapses into one of the eigenstates - acausally, as you say, but following the Born rule for probabilities. And since in this case the superposition is degenerate, the result is perfectly predictable, even assuming the Copenhagen interpretation: the wavefunction has to collapse into one particular position eigenstate with probability 1, simply because there is only one non-zero eigenvalue. — SophistiCat

I agree with all you say above but would add that the probabilities themselves also have no causal explanation under the Copenhagen interpretation (i.e., the Born rule is postulated).

So where do you get probability 0.5? And what does this have to do with causality? I don't understand. — SophistiCat

This is when considering a single beam splitter in isolation. When one photon is sent into a beam splitter, there are two position eigenstates - one for the reflection path and one for the transmission path with 0.5 probability for each.

The MZI experiment shows that this cannot be the scenario at the second beam splitter. If only one photon were entering the second beam splitter, then a photon should be found at the second detector half the time. But it's not. This is what I was trying to convey with the "Alice rolling sixes" analogy. It is highly improbable that on multiple runs a single photon entering the second beam splitter would always be found at the first detector purely by chance.

But this is what the Copenhagen interpretation is committed to by denying causality. The results that it predicts are inherently inexplicable on its own premise.

So, if not one photon, then what is entering the second beam splitter? Well, the wave function tells us exactly what is happening. It says there is a photon entering a beam splitter from the upper path and a photon entering a beam splitter from the lower path. Those states in turn split, two of the states destructively interfere and the other two states constructively interfere resulting in a final state with probability 1.

n the MZI experiment the standard quantum mechanics calculation gives the probabilities at the detectors as 0 and 1. Any interpretation of quantum mechanics had better yield the same probabilities, otherwise it doesn't even qualify as an interpretation. Are you saying that the Copenhagen interpretation predicts probabilities other than 0 and 1 in this case, or fails to predict anything specific? — SophistiCat

The Copenhagen interpretation makes the same prediction but it denies that there is a causal explanation for the probabilities. But, if causality is assumed, then the MZI experiment shows that a beam splitter cannot be sending a photon exclusively one way or the other with 0.5 probability (or else a photon would arrive at either detector with 0.5 probability, not 0 and 1). So there must be some underlying causal factor operating in beam splitters in the same way that there must be some underlying causal factor operating in Alice (or her die) such that she always rolls sixes.

(As an aside, this very special case where probabilities neatly collapse into all or nothing is uniquely favorable to the Everett interpretation, which otherwise faces a prima facie problem with specific observed frequencies of outcomes. In contrast to the Copenhagen interpretation, which happily assumes the reality of probabilistic outcomes as a matter of principle, the Born rule is difficult to justify in the context of Many Worlds. When they are not making popular presentations, like the one by David Wallace that you linked, Everettians tie themselves into knots trying to make sense of these probabilities. And this is where, I am afraid, the prima facie appeal of the MWI as the "no-interpretation" interpretation dissipates.) — SophistiCat

I don't think it follows from "no-interpretation" that the natural interpretation should be trivial and obvious. A case in point is that it was decades before the Everett interpretation arrived on the scene.

Anyway, the partial Everettian answer is that the probability describes a system's self-locating uncertainty when it interacts with another system (e.g., whether a photon finds itself in the reflection path or transmission path of the beam splitter). So it is directly related to the physical processes of splitting and interference. This is nicely characterized by the second beam splitter in the MZI experiment where both processes are involved.

It is necessary to discard the concept of "things" (as determinists continue to insist on) and treat quantum as a process that is in continuous flux. How does a process become a thing? That is exactly the role of the mind as it seeks to create a canvas to create on. — Rich

We perceive things that emerge as the result of dynamic processes. So we may more-or-less agree here.

Also, it seems to me that what you mean by non-determinism isn't an absence of sufficient causality (since you deny randomness), but simply that causal agents can exercise autonomy. Which I agree with.

If we do agree, then our substantial difference is really over whether actions in the universe can be non-local. But I'll leave it there for now.

Why do you continue to insist that quantum theory = randomness? — Rich

I'm not saying that at all. On the Everett interpretation, the quantum state contains the complete information about the system and that state evolves deterministically.

On the standard de Broglie-Bohm interpretation, the quantum state does not contain the complete information about the system. Nonetheless a photon has a specific position and momentum and follows one specific trajectory as governed by the pilot wave.

Is that your view?

Bohmian is causal but not deterministic — Rich

What is the difference between causal and deterministic here? Is there a sufficient cause for the photon always ending up at detector 1? Or is it just a chance occurrence in each instance?

Are you suggesting that there is an interpretation that doesn't use the same Schrodinger/Bohmian equations and is getting better predictions? — Rich

No.

I don't understand. If an interpretation gives us the correct result (i.e. the result predicted by the formalism and validated by experiments), then where is the problem? Or are you under the impression that a "non-deterministic interpretation" is contractually obligated to give a non-deterministic result for every conceivable measurement? — SophistiCat

No. It is in principle possible that Alice could roll a dice a million times and get a six every time. That result is no less likely than any other string of results for a million rolls. But her non-random-looking result begs for an explanation in a way that random-looking results don't.

So the Copenhagen interpretation correctly predicts that a photon in the standard MZI experiment will always end up at the first detector despite passing through beam splitters. But that raises the question as to why. What is the causal explanation for that non-random-looking result?

For the Copenhagen interpretation, the Schrodinger equation is equivalent to asserting that Alice just always rolls sixes. Each formalism gives the correct predictions and no causal explanation exists.

The problem is with the plausibility of that idea.

So I want to ask you. You keep saying that the Mach-Zehnder interferometer experiment would be inexplicable under any interpretation other than the Everett interpretation. So what do you think the result of the experiment would look like if the Bohm or the Copenhagen interpretation was true? — SophistiCat

My argument using the MZI experiment is against non-deterministic interpretations.

According to such interpretations, the photon always turns up at the same detector (with certainty), but without a sufficient cause. So God not only plays dice but he always rolls a six.

The result of the experiment would look the same. But the result would be inexplicable.

Provide references and I'll see if I have the time to study it. — Rich

Here's a talk by David Wallace (philosopher of physics) where he gives the reasoning for treating quantum states as real with reference to the MZI experiments. It's aimed at a general audience.

Here's a longer and more technical version of the above talk that gets into the math and philosophical/foundational issues. He discusses ontology (first video), Occam's razor (at 48 mins) and probability (second video).

Still, quantum theory remains probabilistic though in Bohm's model there are real causal agents - including "information". — Rich

There are similarly real causal agents in Many-Worlds. Quantum mechanics describes and predicts the behavior of quantum systems, it doesn't prescribe it.

It is not. I've read enough about it to understand there are lots of questions and issues to consider when using the apparatus and setting up the device depending upon what the experimenter is studying. But for some reason, you are using this as evidence of what??

In any case MZI is just an apparatus, not an experiment. — Rich

Sending a photon through the MZI is the experiment.

The main issue to consider is that the photon always ends up at detector 1. With certainty. This result has no classical explanation.

It also cannot be explained by supposing that the relative quantum states describing each photon path are mere possibilities, since possible states cannot cause real interference effects.

So the experiment is evidence that the relative quantum states described by the Schrodinger equation have physically real referents.

Someone would have to analyze and compute the quantum potential effects throughout the apparatus. I have not found a specific study on this problem. However, to revert to some deterministic, many-works interpretation based upon this one situation, given all of the other issues regarding quantum measurement problems, would be slightly "extravagant". — Rich

The MZI experiment is a simple and crystal-clear demonstration of quantum behavior without any stochastic elements. The point is that introducing stochasticity or indeterminism into a theory doesn't actually help explain quantum behavior.

This paper discusses a way to analyze the experiment utilizing the concept of quantum erasing. No deterministic interpretation of quantum mechanics is required.

Single photon quantum erasing: a demonstration experiment
T L Dimitrova1 and A Weis — Rich

The paper doesn't describe any mechanism by which the experiment works (which wasn't the purpose of the paper, it was only to demonstrate the phenomenon of single photon quantum erasing which all interpretations would accept anyway).

Bohm's model would simply say that the quantum potential is at near certainty at the point of the slit. However, the quantity potential is subject to "information fluctuations", for example: the Delayed-Choice scenario. Note the use of choice. It is causal but not deterministic. — Rich

In the Mach-Zehnder interferometer experiment there's no slit, only two beam splitters, two mirrors and two detectors.

In a single beam-splitter experiment, a photon that is directed through the beam splitter is detected on either the reflection or transmission path with 50% probability of each.

For a one-world explanation of the MZI experiment, there must be a photon that passes through the second beam splitter either from the left path or from the lower path. Yet the photon always arrives at detector 1 and never at detector 2. So the second beam splitter doesn't seem to be behaving like a beam splitter.

How does quantum potential or information fluctuations explain the above discrepancy? Do the photons always choose to go to detector 1 despite the presence of the beam splitter?

You just proved, with a single experiment, that quantum theory is deterministic. How did I miss it? — Rich

It's not a proof but it is a possible explanation.

Can you (or anyone else) outline a non-deterministic process that explains the Mach-Zehnder interferometer experiment?

You are using quantum states as if they are baseballs. — Rich

Actually baseballs are described by quantum states (just as photons are).

The only way to bring determinism back is in what Bell described as the "extravagant" Many-Worlds Interpretation, which still leaves us in a probabilistic world only now "we" have been also smeared over an infinite, every growing number of worlds. Everett's interpretation makes Copenhagen downright sensible. — Rich

There's no need for an infinite number of worlds. The Mach-Zehnder interferometer experiment can be explained by two relative states (or worlds). The states don't continue to split but instead merge into a single state at detector 1 which is why the photon is detected there with certainty.

You might not like it, but it is a coherent explanation. As opposed to the Copenhagen interpretation which doesn't offer an explanation at all.

The quantum state is analogous to the classical state in Newtonian Mechanics
— Andrew M

Yes, I dispute this. — Rich

Okay, let's agree that they are different. Do you agree that quantum states evolve deterministically according to the Schrodinger equation?

Quantum state??? And how does that figure into determinism? You mean that state that is spread out as a probabilistic wave function? — Rich

The quantum state is analogous to the classical state in Newtonian Mechanics. Quantum states evolve deterministically according to the Schrodinger equation. Do you dispute this?

The wave function describes states that produce real interference effects such as the states describing the two paths in the the Mach-Zehnder interferometer experiment. Mere probabilistic states cannot interfere.

What you are omitting, conveniently is what happens when an additional slit is opened after the photon passes through the first slot. I've experiment doesn't make determinism. However, one experiment does destroy it. Determinism is all our nothing. — Rich

All experiments have a deterministic explanation if quantum states are physically real.

Are you figuring on proving that Quantum is deterministic and local in this thread? — Rich

No, only that a coherent explanation is available. Do you have an explanation of the Mach-Zehnder interferometer result in non-deterministic terms?

2) Science says that events are non-deterministic. If they were we could throw out Schrodinger's equation and replace it with Newton's. But, alas, science decided 100 years ago that Newton's Laws do not correspond to experimental evidence including Bell's Inequality which demonstrate non-locality. — Rich

1. The Schrodinger equation uniquely determines a system's quantum state at a future time. It is instead measurements of the system that are (sometimes) uncertain. The relationship between the determined quantum state and measurement uncertainty is the interpretational issue.

2. Bell's inequalites actually demonstrate that counterfactual definiteness and locality can't both be true. So locality can still be true if counterfactual definiteness is false.

The Mach-Zehnder interferometer experiment shows how both of those points play out. When the reflection and transmission paths between the beam splitters are the same length, a single photon directed through the interferometer will always arrive at detector 1 and never at detector 2.

This is easily explained in local, deterministic terms. But can you (or anyone else) explain the result in terms of probabilities or non-determinism?

Here is another quote, and I can pull out thousands like it:

"Quantum mechanics is indeterministic, "

https://www.scientificamerican.com/article/quantum-physics-free-will/ — Rich

That's a quote specifically about measurement, not the Schrodinger equation. In that same article the author says, "Also, at a deep level, quantum mechanics is not random at all. Schrödinger’s equation is completely deterministic and time-symmetric."

As it happens, the De Broglie–Bohm theory is also deterministic. Here's a quote from David Bohm:

In contrast to the usual interpretation, this alternative interpretation permits us to conceive of each individual system as being in a precisely definable state, whose changes with time are determined by definite laws, analogous to (but not identical with) the classical equations of motion. Quantum-mechanical probabilities are regarded (like their counterparts in classical statistical mechanics) as only a practical necessity and not as an inherent lack of complete determination in the properties of matter at the quantum level.") — David Bohm

There are "deterministic" interpretations of quantum mechanics.
— prothero

Which interpretation would this be? I know of no such interpretation, since inherently the Schrodinger equation (which is Quantum physics) is probabilistic. There is no getting away from this. — Rich

The Schrodinger equation is deterministic. From SEP:

"Given the state of a system at t and the forces and constraints to which it is subject, there is an equation, ‘Schrödinger's equation’, that gives the state at any other time U|vt> → |vt′>. The important properties of U for our purposes are that it is deterministic, which is to say that it takes the state of a system at one time into a unique state at any other, ..."

The Everett (Many Worlds) interpretation is based solely on the above dynamics and so is a deterministic interpretation.

Each sense and each emotional feeling has had to go through your personal cognitive and physiological process. Therefore stating that your experience of the world is unique to you. The only way to counteract the quaila controversy is to get everyone to view the world through the same lens, which at this point in time is not possible. — Anonymys

Unique experience doesn't imply that the world can't be understood objectively, it only implies that the objects of one's experience may be different. I think its worth defining our terms to see what the real controversy is.

According to the Oxford dictionary, "Subjective":

[1] Based on or influenced by personal feelings, tastes, or opinions.
[2] Dependent on the mind or on an individual's perception for its existence.

"Objective":

[1] (of a person or their judgement) not influenced by personal feelings or opinions in considering and representing facts.
[2] Not dependent on the mind for existence; actual.

The first meaning for each term is essentially pragmatic. When Alice said it was raining, did she actually look or is she just giving her opinion based on how she feels? In this sense, I think it's clear that we can be objective. But there is no implication that an objective judgement can be reached independent of experience. Alice is required to look.

The second meaning for each term is closer to the philosophical sense. Is there rain independent of Alice's perception of it? Yes there is. But there is still a fundamental role for the subject here which is to define the terms which allow such judgments to be made (in this case, the term "rain"). And such definitions depend on experience.

I would summarize this as "the view from somewhere". The world exists independently of us, but the representation of it depends on human experience (which, by definition, is qualitative).

This, I think, avoids the dualism that is often implicit in these discussions where one is supposed to either reify subjectivity on the one hand (whether cast as "qualia" or "mind") or else eliminate human experience from objectivity on the other hand. It's a false choice.

Tell me what Pascal's 'imperative of stupidity' is when you find out. — Nils Loc

It seems to be a Nietzschean summary of Pascal's Wager.

Nietzsche: 'On the Genealogy of Morality' and Other Writings

But again, what is the motivation behind the mathematics? What is the problem that the maths is trying to solve? Why go to the bother? — Wayfarer

The problem is to predict the behavior of particle systems which classical mechanics cannot do. What distinguishes quantum mechanics from classical mechanics is that a quantum state can be a linear superposition (i.e., multiplicity) of component quantum states. Take the multiplicity out and you're back to classical mechanics.

The interpretation that comes closest to reality, for me, is Carlo Rovelli's RQM — daldai

Great to hear another perspective.

The way I would characterize RQM is as quantum mechanics with a relativist premise. That is, RQM defines reality in terms of the interaction between systems. So, in the double-slit experiment, it would be real for the particle/apparatus system that the particle has gone through a particular slit. But it would also be real for an independent observer that the particle is in a superposition of going through both slits.

According to RQM, this is not a contradiction since no comparison between observables can be made until the observer and particle/apparatus system have interacted. If they do interact, then the observer will find that they agree that the particle has gone through a particular slit and so reality is then defined for the entire observer/particle/apparatus system.

Is that how you understand RQM?

But I have learned that if you can accept the idea that there are parallel universes, which myself and many others thinks is an absurd idea, then clearly there is no line of argument that can be used against it. — Wayfarer

The multiplicity is inherent in the mathematics of quantum mechanics - its not something that can just be ignored as if it weren't there. That's why the Everett model just is unitary quantum mechanics and is falsifiable on that basis (for example, it would be falsified if a physical collapse mechanism were discovered). And it is why the Bohm model, while also realist, is necessarily a different physical model requiring non-local action (with the multiplicity relegated to the pilot wave).

And, as I responded, the fact that it implies 'two Alices' means that, as far as I am concerned, it is not realistic. — Wayfarer

Heliocentrism was once considered unrealistic. Same with 4D spacetime. Reality doesn't seem too concerned with what we consider realistic.

I mist-stated the position. There is an Alice in both of them. I initially said that Alice is in both of them. The reference to an objective identity doesn't work. — noAxioms

It's interesting to see what the math says here. A quantum state can itself be in a linear superposition of quantum states which, for a two-state system, can be represented as psi = psi_1 + psi_2.

So, in the double-slit experiment, we can refer to the (absolute) quantum system that is the particle that is emitted and arrives at the back screen at a location predicted by the interference pattern. We can also refer to the two (relative) quantum systems that are the two distinct particles that go through each slit. So there are three quantum systems, each with its own quantum state, and each with distinct and real identities.

Absolutely. All in one universe so we can actually explore the phenomenon. — Rich

Agreed. For example, see the interaction-free measurements such as the Elitzur–Vaidman bomb tester.

I think it can be stated that the phenomenon of quantum entanglement undermines scientific realism, but again that's a philosophical observation. — Wayfarer

I think that's true for classical scientific realism. But, of course, quantum entanglement has a straightforward realist explanation on the Everett model as outlined earlier in this thread.

B) An a never ending,, growing number of unverifiable, unknowable universes. — Rich

If true, then the same would apply to the Bohmian pilot wave.

To summarize:

[1] The Everett model - realism plus quantum mechanics (the relative states of the wave function equally exist, also called "worlds" or "branches").

[2] The Bohm model - realism plus a classical modification of quantum mechanics (non-local, incompatible with special relativity and quantum field theory).

[3] The Copenhagen model - quantum mechanics with a wave function collapse postulate (inherently random, wave-particle duality, paradoxes including EPR, Schrodinger's cat).

Of course, one can buy into an infinite number of universes to avoid non-locality. But then, what is being observed in all of these experiments? Bohm would say the quantum potential acting at a distance. — Rich

What is being observed is the correlation due to the initial preparation of the entangled pair of particles. If they have been prepared in a state where they have opposite spins, then that's the way they stay regardless of the distance they travel apart.

It's a philosophical choice. Local action or spooky action.

Thank you. Perhaps one of them has indeed gone through the looking glass. — Wayfarer

"Who in the world am I? Ah, that's the great puzzle!" - Alice

Any physicist who regards a field as a real thing, has got a very strange ontology. It cannot be visualized as a mattress with springs, because numerous fields can occupy the same place, and mattresses can't do that. — Metaphysician Undercover

Fair enough. See https://xkcd.com/895/

So - two 'Alices'? — Wayfarer

Yes, that's the result of the unitary evolution of the quantum state per the Schrodinger equation.

How does that obviate the apparent fact of 'action at a distance'? If the measurement of this particle here, fixes the spin of that particle over there, isn't that still 'action at a distance'? — Wayfarer

The initial superposition that expresses the entangled particle pair is:

[1a] particle A is spin-up and particle B is spin-down +
[1b] particle A is spin-down and particle B is spin-up

When Alice measures the spin of particle A she becomes entangled with the superposition, which evolves to:

[2a] Alice measured particle A as spin-up and particle A is spin-up and particle B is spin-down +
[2b] Alice measured particle A as spin-down and particle A is spin-down and particle B is spin-up

Within each quantum state, Alice knows what she measured and so can deduce what the other particle's spin in that same quantum state must be. But no action at particle B occurred, so it doesn't matter how far away particle B is before or after Alice's measurement.

Ok. A violation of Bell's Inequalities which is designed to test .....?? — Rich

That just is the test. What the violation of Bell's inequalities means is that, at most, only one of the following can be true:

[1] Locality, or
[2] Counterfactual definiteness

If 2 is false (as is asserted by the Everett model), then the violation of Bell's inequalities do not demonstrate non-locality.

http://www.sciencemag.org/news/2017/06/china-s-quantum-satellite-achieves-spooky-action-record-distance — Rich

Yes, that was the kind of experiment I was referring to. What the results demonstrate is a violation of Bell's inequalities, not "spooky action at a distance".

The Everett model is a local counterfactually-indefinite theory. Such a theory is not ruled out by Bell's Theorem and so is compatible with experiments that demonstrate a violation of Bell's inequalities.

Ok. It's 'many-worlds" or never-ending branches (multi-verses?) that are interacting with each other (manifestation in one world creates another) non-locally totally entangled (one depended he upon the outcome of the other?). Now, how does Einstein's theory apply to all of these branches whatever they may be? — Rich

The Everett model is local - things only influence their immediate surroundings. Entangled particle pairs do not act or communicate at a distance, their measurement correlation is instead an artifact of being in the same relative quantum state (or branch). The quantum states are all there evolving according to quantum and relativistic laws (e.g., the Dirac equation). However we observe just the relative quantum state (or branch) we are entangled with.

The wheel is what is circular, it is described by "circular", so the wheel is what we claim to be real. Now what is it which is described by the "field"? What is the real thing which "field" is attributed to, as the property of? — Metaphysician Undercover

In Quantum Field Theory, as far as I know, a field is itself regarded as a real physical thing (which can be visualized as a mattress with springs).

Let's put it this way, the experiments that have been designed to test noon-locality gave confirmed non-locality, in the same manner any scientific experiment is interpreted. — Rich

What the experiments have tested for and confirmed is that the measurements of two entangled particles separated by large distances conform to the predictions of quantum mechanics. That is, if Alice measures spin-up then Bob measures spin-down regardless of the distance separating them. The Copenhagen, Bohm and Everett interpretations all agree about the results of the experiment. What they don't agree on is whether they entail non-locality (action at a distance).

On the Everett model, the results do not entail non-locality. They instead entail a linear superposition of states as described by the wave function. That is, one state where Alice measures spin-up and Bob measures spin-down and a second state where Alice measures spin-down and Bob measures spin-up.

Are there equations for inter-universe frame of references? — Rich

It's really one universe with quantum states in superposition as described by the wave function. The relativistic wave equation is the Dirac equation.

Yes, but not-locality has been experimentally observed which is why Bell preferred Bohm's model. Plus it gets around the awkwardness of a never-ending multitudes of universes interacting with each other in a presumably super-non-local manner. — Rich

Non-locality hasn't been experimentally observed. That is an interpretational claim. The Everett model explains EPR-style experiments in a local manner.