Quantum observers with knowledge of quantum mechanics break reality

Bohmian mechanics violates it by not applying to arbitrary subsystems, but only to the universe as a whole (i.e. parts of the universe cannot be treated as quantum-mechanical systems themselves, because they don't have their own pilot waves)

One of the corollaries/interpretations of Sanov's theorem is that, generally speaking, when faced with an astonishingly improbable outcome (e.g. flipping 9,000 heads and 1.000 tails out of 10,000 independent coin flips), no statistical test can differentiate between "that improbable occurence with a fair coin" and "an unfair coin" - the fair coin, when it does something improbable, with have (with overwhelming probability) a specific tilted distribution that looks unfair.

TL;DR By grouping states together (human choice), certain arrangements seem more probable than others.

It would be nice to say that there’s a 50% chance that I measured 0, but how exactly do you get that in a rigorous way from the state vector above?

To make everything complicated, the answer should not treat the experimenter part of the universe specially.

Once we settle on stuff with position, then we have to ask how that stuff changes. One option is that we specify accelerations; that's Newton's way.

Another option is to specify velocities. That is the Bohm way. Specifically, the velocity is derived from the wave function of quantum mechanics. It is basically the derivative of the wave function, normalized and made real. Done. You can see a simple derivation of the equations here: https://en.wikipedia.org/wiki/De_Broglie–Bohm_theory#Derivat... The first one derives Bohm's equation very quickly and simply from the starting wave relation equations of Einstein and de Broglie.

The complication is that the wave function is a function of the configurations of all the particles. Thus, to get the velocity, one technically needs the positions of all of the particles of the universe. Practically, one only needs the positions of entangled particles, but still. It is a non-trivial setup though the most basic, natural setup one could possibly have given particles and a wave function. Also, the particle positions do not influence the wave function evolution. This is rather unusual.

For the Dirac wave function, it is even simpler. That object directly gives the velocity of the particles; no derivative needed.

Contrast this with MW which says, I guess, that the fundamental thing that we are concerned with is the wave function. It does not seem that particles exist in any meaningful sense in that theory. It is as if we are machines able to track a singular aspect of the change of an abstract vector in Hilbert space. It is not clear why this vector is often represented as a function on configuration space when there is no configuration of stuff. The theory essentially says that actual reality is nothing at all like what we perceive. I would think an honest account of a theory which only has a wave function would be to formulate the theory on an abstract Hilbert space and derive configuration space and, thus, configurations from that. Not very likely, by the way.

Reality may be deceptive, but I certainly prefer to start with theories in which our experience is explained in a pretty simple and straightforward way: it looks like stuff is over there because there is stuff over there. We have singular experiences because a single experience is what actually happens.

Also note that in Bohmian mechanics, we specify the initial wave function and the initial particles and then evolve the system using differential equations. All of the operator stuff, collapse, etc., comes out of that evolution; we don't need to have any special considerations about them. The quantum formalism becomes analogous to thermodynamics, not a fundamental theory, but a useful practical one replacing the individual evolutions with some useful shorthand. In MW, there is this question of how to model an experimental situation. Where are the measurement operators coming from? What is a subsystem? In BM, these things arise essentially by conditioning on the configuration of the environment. In certain situations, this will give rise to roughly an isolated system evolving according to its own Bohmian dynamics. The measurement interaction is then represented by an operator, or its generalization, depending. But all of that emerges from the basic differential equations evolving the universe.

It is not clear to me how easy it is to do that kind of analysis in MW. After all, there is no singular experience to break it down to, there is no subsystem, there is no definitive experiment being done. It is not really clear how one would falsify a theory which, more or less, assumes everything happens.

Paradoxical traps or thought experiments filled with holes?

MW is even more undefined in terms that we cannot even construct a measurement/singular interaction... (it is always derivative of total system state)

Edit: Add the state change in the measurement

(|z+> + |z->)|obs> => |z+,obs+> + |z-,obs->

First there is an electron in one of two states, and the observer is uncorrelated. After the measurement, the observer becomes correlated with the electron.

I don’t think there’s any way for Bob to determine whether the particle stream has been measured by Alice or not.

Don't you think that there is an observable difference between a particle that has been already observed (i.e the wave function has collapsed) and a particle that has not been observed yet (i.e. the wave function has not collapsed)?

An uncollapsed state is a placeholder - constrained by statistics, but with no definite value. A collapsed state has a definite value along some measurement basis.

Entanglement is a different phenomenon.

Uncollapsed entangled pairs remain unmeasured by anyone. Either Alice or Bob can collapse the state of an entangled pair by measuring one item in the pair. This constrains the possible results the other person can find when they measure the other object (if that's a word that even applies in QM...) in the pair.

The correlation isn't obvious unless the results are compared, so neither experimenter can see it on their own.

But there has to be collapse - or decoherence, or a measurement, or some kind of interaction - for the correlations to become observable at all.

In physics if something doesn't have its own math then it is just an opinion. You can't prove it, you can't debunk it, you can have different one. Ultimately it doesn't matter.

For me Copenhagen interpretation becomes absurd from the moment it states that observer matters. Each observer is just lots of particles and the fact that they arranged to have eyes and brain can't possibly matter for the basic laws of physics.

It's like watching animated movie and saying "I observe moving Donald Duck". There's no Donald Duck. What you see is 24 completely separate slightly differnt pictures per second of something that give you an illustion that Donald Duck exists and he is moving.

It's perfectly fine to say Donald Duck is moving when you are considering Earth orbiting the Sun, but when you are talking about particles and quantum it misleads you into thinking Schrodinger's cat should be dead and alive before you open the box.

Conversly, thinking about "paricles" not as specks of dust but as whole fuzzy clouds may give you a lot of new intuitive understanding of what's actually happening. Like when you drop planetary model of atom and you consider orbitals. Then you can understand chemical bonds better. Things that didn't make sense earlier, like benzene make now perfect sense, orbital hybridisation brings new explanations.