A Is the wavefunction subjective? How?

[DarMM]

In contrast, other than 0 or 1 probabilities, no single observation can prove a Bayesian probability assignment wrong

Basically I think you are comparing quantum pure states with high entropy classical states with some assignment to all outcomes and concluding objectivity. Rather you should compare like with like. All quantum states with all classical states. Then you will see there is no difference.

Bayesian probability assignments which cover the whole sample space are analogous to mixed states in quantum mechanics, thus there is no difference. You shouldn't compare these to pure states.

 

[DarMM]

And I'm saying that you're wrong. If in classical probability, you only allowed 0 or 1 values for the probability, then probability wouldn't be considered subjective, since disagreements could be objectively resolved. Quantum mechanics is in this situation: Disagreements about the value of the wave function can be objectively resolved.

This might be the post to focus on, disagreements about mixed quantum states can't be resolved in one measurement in general, just as classical probability distributions can't be discarded in one measurement in general.

However in both cases, quantum and classical, there is a subset of mixed states (of which pure states are a special case) which can.

Every quantum case corresponds to the perfect knowledge case of Bayesian probability, and the perfect knowledge case of Bayesian probability is objective.

Basically they don't. Quantum pure states correspond to the perfect knowledge case, quantum states in general do not.

 

[bhobba]

Do you think non-contextuality can be justified via no-signalling? If we made probability assignments that revealed the context and verified them we could know the settings of distant experiments.

I think Kochen-Specker basically says that - but a deeper analysis than I am aware of may show there is an out to that one. Personally I find contextuality ugly which is one reason I do not like interpretations that have it. The way these threads often go forces me to emphasize my dislike for something means absolutely nothing - its simply an opinion. Nature could indeed be contextual.

Thanks
Bill

 

[atyy]

And I'm saying that you're wrong. If in classical probability, you only allowed 0 or 1 values for the probability, then probability wouldn't be considered subjective, since disagreements could be objectively resolved. Quantum mechanics is in this situation: Disagreements about the value of the wave function can be objectively resolved.

Only by people who agree on the same objective facts.

 

[Fra]

Only by people who agree on the same objective facts.

And for them to reach such an agreement they must coexist in the same classical background; where the "quantum inquiries" are defined. And there interactions for all practical purposes be classical.

This is clearly a scenario that does not cover general cases of inside observers, so this stance will not be viable in the QG or unification realm I would say.

/Fredrik

 

[zonde]

Only by people who agree on the same objective facts.

And for them to reach such an agreement they must coexist in the same classical background; where the "quantum inquiries" are defined. And there interactions for all practical purposes be classical.

This is clearly a scenario that does not cover general cases of inside observers, so this stance will not be viable in the QG or unification realm I would say.

/Fredrik

People agreeing on objective facts is basic requirement for doing science. You can not relax this stance and still pretend that your philosophy has something to do with science.

 

[DarMM]

People agreeing on objective facts is basic requirement for doing science. You can not relax this stance and still pretend that your philosophy has something to do with science.

I think what they mean is given a cut, or what Healey calls "the physical situation of the agent", there is a best wavefunction.

In other words given what you currently know there is a "best" wavefunction you should be using like Objective Bayesianism. However agents in two different physical situations (i.e. one will have witnessed a different set of events) won't have the exact same quantum state. Just like Classical Probability Theory.

 

[Fra]

People agreeing on objective facts is basic requirement for doing science. You can not relax this stance and still pretend that your philosophy has something to do with science.

If we are literally speaking of "people" or scientists, they all coexist on the same classical background, and can fapp communicate and compare their observations classically - this is of course not where the problem lies.

"People" here is a metaphor for a information processing agent - a generalisation of an observer - but one that is not necessarily "classical".

Quantum mechanics as it stands relies on a classical background and classical measurement device to be defined. This was i think understood by many of the founders of QM, but often misinterpreted to somehow involve humans or "minds".

We do not need to make the same mistake again. The above paradigm is IMO not making sense in QG, unification attempts or cosmological models. So we desperately NEED to reconstruct a measurement theory, in terms of a non-classical observer. Observers that moreoever is interacting with other observers. The correspondence is that we must recover regular QM and QFT in the appropriate limit of a dominant classical lab frame observer observing a small subsystem.

But we still lack the framework to describe this. But one trait of such a framework is indeed that effective truth values are not necessarily objective. But we should not interpret this as the breakdown of effective human science, i think it rather deepens our understanding to see how "objectivity" can emergent, from a chaotic starting point. That BIG difference is that in this paradigm, the objectivity are NOT hard god given mathematical constraints that need no explanation.

/Fredrik

 

[zonde]

But we should not interpret this as the breakdown of effective human science, i think it rather deepens our understanding to see how "objectivity" can emergent, from a chaotic starting point.

Absence of "objectivity" is subjectivity not chaos. But for any "objectivity" to emerge we need fapp objective communication channels to compare our subjective observations. So we have to assume at least some objectivity to start talking about emergence of "objectivity". This makes your idea about emergent "objectivity" circular.

 

[Fra]

Absence of "objectivity" is subjectivity not chaos. But for any "objectivity" to emerge we need fapp objective communication channels to compare our subjective observations. So we have to assume at least some objectivity to start talking about emergence of "objectivity". This makes your idea about emergent "objectivity" circular.

Yes the subjectivity is the unavoidable observer choice but this is really something you can not escape unless you engage in ontological fantasy. I require that ontologies are the result of a physical inference process, otherwise it is to me metaphysics.

Any comparasiom between two subjective views takes a third perspective. And comparasions are necessarily physical interactions.

This is a chicken and egg situation but circular is i think a bad an inappropriate descriptor as it sounds like a deadlock which it ia not.

I call i evolving. Evolving means progress and revision is made on each comparasion rather than contradictions. Agents that don't revise and negotiate will not be stable and thus not be abundant in nature.

/Fredrik

 

[zonde]

This is a chicken and egg situation but circular is i think a bad an inappropriate descriptor as it sounds like a deadlock which it ia not.

Let's not say that "it does not work" because it sounds like it does not work while I think that it works? - is this what you are saying?

Do you have some valid starting point for your reasoning? What is instead of what is not? And is it consistent with scientific approach? It does not seem so to me.

You have to understand that science does not cover all the thinkable explanations of the world. It covers only limited class of explanations. And it does not seem that your reasoning is anywhere near that "limited class of explanations".

 

[atyy]

People agreeing on objective facts is basic requirement for doing science. You can not relax this stance and still pretend that your philosophy has something to do with science.

"People" is subjective. What is a person?

 

[zonde]

"People" is subjective.

In what sense "people" is subjective?

What is a person?

For example me and you. A person who does the science is a primitive term in context of philosophy of science so it does not require definition.

 

[DarMM]

Basically I think one can argue that given a particular cut/physical situation/observed outcomes that there is a best wavefunction. The same kind of thing Jeffreys and Jaynes had for Classical Probability.

However because there is a Quantum de Finetti theorem you are also fine taking it subjectively like Savage, Ramsey and de Finetti did for Classical Probability.

So you just fall back to the interpretation of Probability theory in general.

 

[A. Neumaier]

Basically I think one can argue that given a particular cut/physical situation/observed outcomes that there is a best wavefunction.

This is not sufficient: Taking the cut to include a lot (system, detector, much environment), the corresponding best wave function should determine all probabilities about (system, detector, much environment), and hence should determine all conditional probabilities when taking the cut more narrowly, e.g., only (system, detector). But this conditional probability is not given by a wave function.

 

[DarMM]

This is not sufficient: Taking the cut to include a lot (system, detector, much environment), the corresponding best wave function should determine all probabilities about (system, detector, much environment), and hence should determine all conditional probabilities when taking the cut more narrowly, e.g., only (system, detector). But this conditional probability is not given by a wave function.

Could you describe what you mean in a bit more detail?

 

[julcab12]

"The wave function cannot be measured (its tiny changes cannot be distinguished by any apparatus that studies the physical system once) which is a good reason to say that "it probably doesn't objectively exist"

Basically, In this sense the complex conjugate square of the wave function that gives the probability for an event to happen, is objective. It is a real number and accumulating measurements with the same conditions always gives the same probability distribution, even though there are levels upon levels of modeling. The wavefunction is the mathematical modeling of what happens when "particle scatters" . It is not the wavefunction that interacts, it is the particle(blurry bunch) which interacts with the boundary conditions of a experiment that can be fitted with a wavefunction which complex conjugate squared gives the probability distribution for the experiment.

 

[atyy]

In what sense "people" is subjective?

For example me and you. A person who does the science is a primitive term in context of philosophy of science so it does not require definition.

"People" is subjective like "measurement apparatus".

 

[Fra]

Let's not say that "it does not work" because it sounds like it does not work while I think that it works? - is this what you are saying?

No, I was basically saying that I read your understanding of "objectivity" as what from my perspective is a deceptive illusion.

But I was trying to put it in more polite manner for the sake of discussion by saying that you make and observation that I partially agree with (that we have a self-referencing situation), but when you say its circular that implies to me you are missing the point.

Do you have some valid starting point for your reasoning? What is instead of what is not? And is it consistent with scientific approach? It does not seem so to me.

You have to understand that science does not cover all the thinkable explanations of the world. It covers only limited class of explanations. And it does not seem that your reasoning is anywhere near that "limited class of explanations".

To connect this to the scientific method, what I am talking about here belongs to the hypothesis generation part. This is the part that Popper tried to sweep under the rug byt instead focus on the deductive falsification events.

But if you have given unification approaches and thoughts you should know that one problem is that faces initial value problems, problems with naturalness etc, simple BECAUSE the state spaces are so large. As smolin etried to explain to death in books, this is a failure of what he calls the Newtonian paradigm. It is actually also related to the "unreasonable effectiveness of mathematics", which when you understand the reason for it is in fact very reasonable. Its effective because it applies to subsystems.

As I said, no one has yet published a theory of framework for this, that to my knowledge is a solution. But let's not avoid facing the problem just because we have no solution.

My staring point means to reconstruct a measure framework, from the perspective of a ficitve information processing agent. This has the advantage that as you scale down the complexity, the state space is NOT infiinte, it rather gets trivially small. The challenge is then to see how relation emerge as these interact and gain complexity. This process of scaling complexity corresponds exactly to the big band and TOE unification level: information processing agents are like spieces that POPULATE the universe, and they are further assocaite to elementary particles, and their RELATIONS encode also spacetime. The Science here is that this is a hypothesis, if this works and reproduces known physics or reducing the number of free parameter,, and thus increases the explanatory power, then it will also yield more predictions that can be tested.

But you can not apply Poppian falsification logic to the process of hypothesis generation! This is not how creative or evoltionary processes work. Most scientis keeps these dirty thoughts to themselves, and only present the "result".

/Fredrik

 

[Stephen Tashi]

Saying that probabilities are relative frequencies doesn't really make sense.

And defining a probability as the relative frequency of an event in a specific population doesn't produce a model of the probability of that event occurring in a "random" trial unless we assume there is a mechanism for independently selecting a member of that population that gives each member of the population the same probability of being selected. So the frequency definition of probability requires a non-frequency concept of probability in order to handle the usual applications of probability.

 

[Stephen Tashi]

. For a specific male, we can come up with different probabilities depending on how much information we have about him. So it's subjective.

Is the fact that people with different information assign different probabilities any more subjective than the situation where two problems in a textbook have different given information and different answers?

Person A with information Y, can claim his assignment of a probability P1 to an event is correct if he does experiments which set conditions as Y and produce results consistent with the value P1. Person B with information "Y and Z" can claim his assignment of a probability P2 to the event is correct if he does experiments which set conditions as "Y and Z" and produce results consistent with P2.

The "subjective" aspect seems to come from the viewpoint of an observer who knows the actual conditions are "Y and Z", and hence regards person A as honest but wrong. Likewise, an observer might know the actual length of the hypoteneuse of a particlular triangle is 10 meters and thus consider people who are working a homework problem where the hypotenuse of a triangle is given to be 8 meters to be honest, but wrong.

 

[A. Neumaier]

stating that the wavefunction is subjective. This means that it is perfectly valid that two different observers use two different wavefunctions to describe the same system. I do not understand how it makes any sense.

Consider the example of the probability for a UK male of 25 years of age to die within the next year. Clearly, this probability is well defined and exists regardless of whether person A and person B agree about it.

This is a misleading analogy.

The right analogy is to consider the example of the probability for John Jones (who happens to be an UK male of 25 years of age, but has many other properties) to die within the next year. This probability depends on which ensemble of people you regard John Jones to belong to. One of these ensembles is the set of UK male of 25 years of age, but another one is the subset of heavy smokers (or nonsmokers, depending on John Jones's habits). Thus different probabilities describe the same person.

Similarly in quantum physics: Once you specify the intended ensemble unambiguously, the state is fully determined by it.

 

[A. Neumaier]

Basically I think one can argue that given a particular cut/physical situation/observed outcomes that there is a best wavefunction.

This is not sufficient: Taking the cut to include a lot (system, detector, much environment), the corresponding best wave function should determine all probabilities about (system, detector, much environment), and hence should determine all conditional probabilities when taking the cut more narrowly, e.g., only (system, detector). But this conditional probability is not given by a wave function.

Could you describe what you mean in a bit more detail?

Given a large system in a pure state with wave function $\psi$, conditional expectations for subsystems are typically not described by wave functions but by density operators.

 

[DarMM]

Woops I should have said "a best state"

 

[A. Neumaier]

Two different predictions about the same event cannot both be correct

Predicting that it will rain tomorrow with probability 40%, and predicting that it will rain tomorrow with probability 60% are both correct, no matter whether it rains tomorrow.

 

[fluidistic]

Predicting that it will rain tomorrow with probability 40%, and predicting that it will rain tomorrow with probability 60% are both correct, no matter whether it rains tomorrow.

One is tempted to fully agree with you if the probability is associated to the knowledge or method of the person who tries to assess the probability.

On the other hand one is tempted to say that the maximum knowledge would lead to a single "correct" probability. For example if we assume that ergodicity holds (I'm probably not using the right word here). Let's say that we have infinitely many times the same system and check whether tomorrow it will rain and make the statistics. We would know with absolute certainty the probability that it will rain tomorrow, i.e. we would get a percentage. It would probably be different from 40% and 60%. People seem to believe that this percentage is the ultimate one, I think. But now it's clear to me that none is the ultimate one, at least when the percentage reflects the knowledge of the observer.

 

[A. Neumaier]

Let's say that we have infinitely many times the same system and check whether tomorrow it will rain and make the statistics. We would know with absolute certainty the probability that it will rain tomorrow, i.e. we would get a percentage.

1. You'll be dead before you have infinitely many independent tomorrows.
2. To give your statistics an objective ergodic meaning you need to include all sufficiently late tomorrows, and presumably there will not be any rain in the very far future of the Earth (if it continues at all to exist indefinitely). Thus it says nothing of interest for us.
3. What you get is only the probability that it will rain on an anonymous tomorrow. The probability whether it rains tomorrow, May 29, 2019, at the Stephansplatz in Vienna will still be definitely 0 (by today's forecast unlikely) or 1 (by today's forecast most likely), though we cannot yet tell for sure which one.

 

[DarMM]

A nice example of subjectivism in the quantum state @fluidistic is the case of two experimenters performing tomography measurements on two qubits.

Say one has the initial prior for the state of:
$$\rho_{+} = \frac{1}{2}\left(|00\rangle\langle 00| + |++\rangle\langle ++|\right)$$

And the other uses:
$$\rho_{-} = \frac{1}{2}\left(|00\rangle\langle 00| + |--\rangle\langle --|\right)$$

with $|\pm\rangle = \frac{1}{\sqrt{2}}\left(|0\rangle \pm |1\rangle\right)$

These are analogous to two overlapping priors in Classical Statistics.

They then perform a measurement on the first qubit in the $\{|0\rangle,|1\rangle\}$ basis and they obtain $1$. The first experimenter will then update the state of the second qubit to $|+\rangle$ where as the second experimenter will update it to $|-\rangle$.

These are actually orthogonal states. The analogue in Classical Statistics is updating to two posteriors with no overlap.

 

[Fra]

Predicting that it will rain tomorrow with probability 40%, and predicting that it will rain tomorrow with probability 60% are both correct, no matter whether it rains tomorrow.

And this makes a difference in one specific scenario: When you try to predict the action of the observer; from the perspective of another observer. This is IMO the trick and insight. The rationality assumption simply means that an external observers best guess, is that each OTHER observer acts randomly as per its subjective p-distributions.

If you repeat this logic, down to micro-observers (ie subatomic structures - not humans) this logic implies that interactions in-between observsers, are encoded by their relative information and subjective p-distributions about each other. From a very far distant dominant observers (laboratory frame) these inside observers, then should form like an equivalence class of "inside-observers" that could also be called gauges. As the choice if inside observers is arbitrary. But one can never reduce away the distant observer. This becomes a problem in cosmological models, when there is no "lab frame" that is dominant.

So in my view, understanding unification of forces, is another side of the same problem, to understand the interaction between observers encoding incomplete truncated p-measures about each others. The latter way of thinking however offers an interesting route to deeper insight.

Similar logical literally explains conflicts in social interactions - the explanation and cause, is simply the different information perspectives. This drives the conflicts. One usually says such problems are solved by mutual understanding in human world, but in physics the "inside observers" are physically constrained and its physically impossible for all obersvers to be in possession of the same information, so some fundamental interactions must be unavoidable.

/Fredrik

 

[A. Neumaier]

The rationality assumption simply means that an external observers best guess, is that each OTHER observer acts randomly as per its subjective p-distributions.

But this is an irrational assumption. Rationally, how other observers act must be determined by sufficient observation (or judgment must be deferred until such observation is available), and not by postulating some a priori subjective distribution for it.

 

[Fra]

But this is an irrational assumption. Rationally, how other observers act must be determined by sufficient observation (or judgment must be deferred until such observation is available), and not by postulating some a priori subjective distribution for it.

Admittedly this is a conjecture; its success depends on wether this conjectures helps solve the puzzle. But as I see it, this conjecture is "natural". It appears to ne to be the least speculative conjecture, and "deferring judgement" works in some human situation, but in a physical interaction this is not an option. Under timepress; assuming we think of interaction between observers as a realtime decision process, sometimes a suboptimal fast choice, rather than a more accurate but more slow considerations is what keeps you alive.

/Fredrik

 

[A. Neumaier]

Under timepress; assuming we think of interaction between observers as a realtime decision process, sometimes a suboptimal fast choice, rather than a more accurate but more slow considerations is what keeps you alive.

Yes, but science is not under time pressure. (Or rather, science done under time pressure is only very rarely good.)

There is no rational substitute for the complete lack of information except information.

 

[Fra]

Yes, but science is not under time pressure.

I think you missed my point. The process under time pressure is not human science, but real world physical interactions.

There is no rational substitute for the complete lack of information except information.

Its my firm understanding that the incompletness and uncertainty of information, and the constrained capacity to process information thrown at an observer, and its associated process is they key to understand unification of forces.

I think that the limitations of this process, is fundamental, and thus nature is faced with a situation of having to make decisions/actions based upon incomplete and incompletely processed information under time pressure.

/Fredrik

 

[PeterDonis]

Admittedly this is a conjecture

Conjectures and personal speculations are out of bounds for PF discussion.

 

[PeterDonis]

unification of forces

...is not the subject of this thread.

 

[A. Neumaier]

The process under time pressure is not human science, but real world physical interactions. [...] nature is faced with a situation of having to make decisions/actions based upon incomplete and incompletely processed information under time pressure.

Ah, you make not observers but Nature the epistemic subject whose knowledge is encoded in the wave function? But Nature never bets, as far as I can tell. How can it have a subjective but rational notion of knowledge?

Do you really think that a measurement device constantly gathers information under time pressure in order to know which result it should produce? Two photodetectors far apart don't have the complexity to gather, store, and process enough information about the nonlocal state of a possibly impinging photon pair to figure out the joint probability with which they should fire...

 

[Fra]

Conjectures and personal speculations are out of bounds for PF discussion.

My apologies.

Some of these discussions - both in btsm and sometimes the "interpretational QM" topics in this subformus are in my opinion typically always in a grey area. Interpretations, philosophical stances and personal conjectures sometimes float together.

/Fredrik

 

[Fra]

Do youreally think that a measurement device constantly gathers information under time pressure in order to know which result it should produce? Two photodetectors far apart don't have the complexity to gather, store, and process enough information about the nonlocal state of a possibly impinging photon pair to figure out the joint probability with which they should fire...

I will pass discussing this in detail as its not the main topic, but a closing comment is that yes I see a measurement device (or any interacting part) as a kind of "information processing" object. I put it in quotes because I view the computation as observer dependent spontanous processes.

/Fredrik

 

[Jehannum]

Predicting that it will rain tomorrow with probability 40%, and predicting that it will rain tomorrow with probability 60% are both correct, no matter whether it rains tomorrow.

Your example is merely a good demonstration that probability doesn't mean much with regard to single events (despite what Mr Spock says).

 

[A. Neumaier]

Your example is merely a good demonstration that probability doesn't mean much with regard to single events (despite what Mr Spock says).

It is a demonstration that it means nothing, from a scientific perspective.

In the form of subjective probability, it may be a useful guide for practical decision in the light of uncertainty. But to confuse subjective probability with science is in my view a big mistake.

 

[Heikki Tuuri]

The wave function is not subjective. If any observer performs a measurement of the system, then the state "decoheres" into macroscopic measurement apparatus and a macroscopic observer. Interference between different outcomes of the measurement is minuscule after that because a macroscopic object is involved.

The true wave function of the system has to be calculated from all the measurements performed on the system. It is natural: every measurement changes the state of the system and, of course, you have to take into account all operations which affected the state.

Some people may know less about the measurement results. They may calculate probabilities with the classic probability calculus where probabilities are real-valued. The wave function is complex-valued.

The true state of a system in classical mechanics depends on all operations which were performed on the system. Some observers may not know all the operations, but that does not mean that the state of the system is subjective.

 

[PeterDonis]

The wave function is not subjective.

It is in some interpretations.

A better way of capturing the part that is indisputably objective would be to say that the preparation process which a given system undergoes is not subjective. By analogy with what you say about classical mechanics: someone making measurements on the system might not know what the preparation process was, but that does not mean the preparation process is subjective.

 

[jlcd]

It is in some interpretations.

A better way of capturing the part that is indisputably objective would be to say that the preparation process which a given system undergoes is not subjective. By analogy with what you say about classical mechanics: someone making measurements on the system might not know what the preparation process was, but that does not mean the preparation process is subjective.

When it is said the quantum state is a tool that we use to predict the probabilities of different results for measurements we might choose to make of the system. Is this valid for the deterministic Schrodinger Equation as well or only when determining the observable via the hermitian operators? Because if the state being a tool to predict probabilities is valid for the entire Schrodinger Equation. Then what equations do you use to model how the atoms or particles interact on their own before we do any measurement?

I know though that the wave functionp psi (x), derived from the Schrodinger equation through its rules of solution, represents all that can possibly be known about the physical state of the object. Before measurement. Surely the object or atoms still use the Schrodinger equation, so how can it just be a tool or subjective.. unless there are other more objective equations for how the atoms really interact that doesn't use the Schrodinger Equation? What is this true objectve equations then called?

 

[PeterDonis]

Then what equations do you use to model how the atoms or particles interact on their own before we do any measurement?

How do you know they're interacting on their own if you're not measuring anything?

 

[jlcd]

How do you know they're interacting on their own if you're not measuring anything?

The particles and atoms or molecules (or moon) would break apart if there are no interactionsamong the particles. So what is the equation(s) for the true interactions even if no humans measure them. If Schroedinger equation as a whole is just a tool for probability or subjective. Then what is the objective equation(s) that are there even when nothing measuring?

 

[PeterDonis]

The particles and atoms or molecules (or moon) would break apart if there are no interactions among the particles.

If we observe that objects made of lots of atoms or molecules hold together, isn't that a measurement?

 

[jlcd]

If we observe that objects made of lots of atoms or molecules hold together, isn't that a measurement?

I mean those that we can't observe like 1 mile inside Pluto and most other objects we can't measure or observe. We don't observe them yet they hold together. So what equations hold them together or the interactions?

 

[PeterDonis]

I mean those that we can't observe like 1 mile inside Pluto and most other objects we can't measure or observe.

We observe Pluto. That counts as a measurement that Pluto is holding together.

 

[jlcd]

We observe Pluto. That counts as a measurement that Pluto is holding together.

How about planetoids in stars millions of light years away that we can't observe or measure. What hold them together? We can see the stars though. So by act of observing the stars, each of the hidden planets exist?

Or before life existed on earth. What holds the forming star (or interactions) before it became our sun?

There should be equations irrespective of humans.

 

[andresB]

I'm not an expert on the topic, but these are my 2 cents:
Let's assume that there is indeed an objective wave function associated to a given quantum system. It seems to me that even in this case different people with different approaches to the system can disagree on the probabilities assigned to a given event, and be both "correct". The reasons is that they can't know the actual wave function for sure, so they will be using a density matrix.

On the other hand, there statement that all observers must agree on the outcome of an experiment has been questioned https://arxiv.org/abs/1902.05080