What did Einstein mean by “spooky action at a distance”?

You are adding another conditional but nested conditionals still all rely on the first.

We are getting 1 bit of data:0|1; from this entrangled pair.

Fleet1 has Strategy0 in case their measurement reads 0.

Strategy0 requires Fleet2 to act using Strategy2 for the highest probability of success.

Fleet1 also has Strategy1 in case their measurement reads 1.

If Strategy1 also requires Fleet2 to act using Strategy2 for highest probability of success then Fleet1's measurement is useless as Fleet2 can just use Strategy2 in both events.

If instead Strategy1 requires a new Strategy3, and even though you could communicate which of these strategies to choose faster than we know how to communicate that electromagnetically, our 1 bit of information is still useless because you would still have to prepare for both eventualities.

Both pairs: Strategies02 and Strategies13; would equally have to have the same probability of success because if one is favoured over another then using this technique to decide your fleet movements could result in your allowing the possibility for the measurement to order you in a strategy you know is less likely to be successful.

This is what I was trying to get at by using the word 'desirable'.

Fleet2 may appear to be waiting on Fleet1 for orders, but in fact both fleets are waiting on their orders from the first measurement.

From a mathematician perspective, the error is "incompatible probability measure" for events, that's why probability laws don't apply.

Bell's theorem is exactly a well known mathematical theorem "Boole's inequality" which basically tells you, you are doing the math wrong when defining your measure.

About the link between boole's and bell's inequalities : There are tons of paper : A quick search for example https://arxiv.org/pdf/quant-ph/0406004.pdf (I just skimmed it for a few seconds but it's probably talking about the right thing)

In the paper you suggest https://arxiv.org/abs/1508.05949, there is nothing which looks like a probability definition.

Assuming the world is using continuous fields, defining the probability for what register as a discrete event like a "blip" must be done carefully, it's not a trivial thing.

Otherwise when you are taking joint probabilities and condition probability, it just tells you that those are questions you can't ask.

Bonferroni inequalities are also on the wikipedia page of the Boole's inequality https://en.wikipedia.org/wiki/Boole%27s_inequality

>I'm still not sure what probability distribution (or measure) you want to be defined in that paper. Experimentalists generally don't assume any probability distribution in advance, I am not sure why they would need to in this case.

That's the thing, if you try to model it correctly you realize that what you were doing was not the thing to do, and that there is just nothing to see here, apart from yourself asking the wrong question.

Take a zone of space (the detector volume), and define the discrete event "blip" as 1 if somewhere inside the detector volume at instant t0 the field value is greater than 1, or zero elsewhere.

That's all you need : this mean you just expressed an event as a conditional probability. Therefore when you have multiple such events, you are expected to encounter some Boole's/Bell type inegalities (provided that there is information conservation in your model).

Experimentalists are doing circular reasoning. By not assuming an underlying model, they don't realize that the answer they get is due to implicitly defining events as conditional probabilities which don't span a consistent Filtration_(probability_theory), then they try to ask the wrong question, getting an answer which confirm their biases.

QM is a not a model of the world, but a model of what we can observe from the world based on what we observe from the world.

Bell's inequalities tell nothing about how the world works but only tell you that your way of observing the world is wrong.

Notice that in the double-slit experiment, the wave function at different places interacts with itself so as to lower the probability of a photon or electron arriving at a place where it was likelier to arrive with just one slit open.

Informally speaking, that could be seen as an example of different "worlds" (i.e. different places where the photon could be observed to exist) interacting with each other locally so as to effectively lower the probability of observing the photon arriving at some place where it would be likelier to arrive had the different worlds not have interacted with each other. Taking the analogy a bit too far, this seems like if two different worlds interfere with each other so as to cancel each other out. Again, the photon/electron that was likely to arrive at some place, will not likely arrive anymore, and this is purely due to the the wave function interfering with itself.

Wouldn't that mean that there is the possibility that the observed correlations in Bell's theorem could be the result of this phenomenon and not necessarily mean that there is non-local behavior?

That is, couldn't the observed correlations be the result of the different worlds interfering with each other locally, e.g. when the light cones of the different measurements intersect each other, so that some worlds cancel each other out and we don't get to observe them, leading to the correlations that we do indeed observe?

Bell's theorem, as far as I understand, only takes into account what we can observe, but could be falsified if there are "worlds" that we cannot observe, i.e. that are temporally created but stop existing when they cancel each other out by local interactions.

Although, admittedly, I could be completely wrong because I don't understand enough of this to be sure of what I'm saying :)

I think we just don't know enough yet to choose any one interpretation. I hope that at some point we'll find a way to address the measurement problem - either finding that the classical world also behaves quantically or that there is some clear limit between them or that the quantum world behaves classically (least likely).

But until then, we're all just guessing.

Edit: 810 atoms is great, just ~6.023*10^21 more to go and we'll have something that is truly in our range of advertising.

The map is not the territory. A ball is a ball and its motion is its motion, while Newton's equations of motion for that ball are something else.

While it is possible that the MWI is right and the state of the entire universe could be described by a single, universal wavefunction, that wouldn't mean that the universe is that wavefunction, anymore than Maxwell's equations are the electromagnetic field.

Now, there is an interesting question that indeed no one knows the answer to for now: is the wavefunction a direct description of a physical object, or is it just a statistical tool for predicting possible positions of the real objects (waves and particles existing in some duality)?

Also, you shouldn't forget that none of the existing interpretations of QM actually solve the measurement problem, not even MWI. Here is Sabine Hossenfelder's explanation of this [0]:

> In the many worlds interpretation, if you set up a detector for a measurement, then the detector will also split into several universes. Therefore, if you just ask “what will the detector measure”, then the answer is “The detector will measure anything that’s possible with probability 1.”

> This, of course, is not what we observe. We observe only one measurement outcome. The many worlds people explain this as follows. Of course you are not supposed to calculate the probability for each branch of the detector. Because when we say detector, we don’t mean all detector branches together. You should only evaluate the probability relative to the detector in one specific branch at a time.

> That sounds reasonable. Indeed, it is reasonable. It is just as reasonable as the measurement postulate. In fact, it is logically entirely equivalent to the measurement postulate. The measurement postulate says: Update probability at measurement to 100%. The detector definition in many worlds says: The “Detector” is by definition only the thing in one branch. Now evaluate probabilities relative to this, which gives you 100% in each branch. Same thing.

> And because it’s the same thing you already know that you cannot derive this detector definition from the Schrödinger equation. It’s not possible. What the many worlds people are now trying instead is to derive this postulate from rational choice theory. But of course that brings back in macroscopic terms, like actors who make decisions and so on. In other words, this reference to knowledge is equally in conflict with reductionism as is the Copenhagen interpretation.

[0] http://backreaction.blogspot.com/2019/09/the-trouble-with-ma...

Now, you could say that consciousness is a quantity that humans possess a lot of, while photons possess a tiny little amount of, like the Integrated Information Theory people claim. But there is no proof (or even indication, in my opinion) that the IIT 'consciousness' actually captures what we mean by human consciousness.

> It follows that, if true randomness is exhibited by the universe, one that is not generated by rules, then it must be the leftover ingredient. Consciousness is the only leftover ingredient. Everything else we know about physics is deterministic and rule-based.

Randomness is not necessarily a part of QM. For example, in MWI, there is no randomness in the universe - it is perfectly deterministic, as every state of the wave function is realized. In pilot-wave theory, the only randomness is classical - errors in knowing the initial state with absolute precision.

Even if CI or other fundamental randomness interpretations of QM are correct, there is no obvious connection between consciousness and randomness. There are other unknowns in the universe - you could just as easily say that dark matter is consciousness or dark matter is the source of randomness, or dark energy etc.

And only since you briefly mentioned it, free will (as in conscious choice affecting the next state of the universe) is incompatible with QM, as QM is a linear theory, where the next state is uniquely determined by the previous state, especially in MWI.