Is the wavefunction subjective? How?

[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

 

[PeterDonis]

How about planetoids in stars millions of light years away that we can't observe or measure. What hold them together?

If we can't observe or measure them, how do you even know they're there?

We do observe galaxies very far away, which counts as a measurement.

There should be equations irrespective of humans.

No, there is a universe irrespective of humans. But equations are human constructs. Nature doesn't solve equations. It just is.

 

[jlcd]

If we can't observe or measure them, how do you even know they're there?

We do observe galaxies very far away, which counts as a measurement.
No, there is a universe irrespective of humans. But equations are human constructs. Nature doesn't solve equations. It just is.

So the above is the belief or thinking system of those Bohrians who treated the quantum state as just tool that we use to predict the probabilities of different results for measurements we might choose to make of the system. Their arguments why unobservable planets in galaxies far far away exist is because we can observe those galaxies even as mere dots in photos? Right?

So these folks treat the entire Schroedinger Equation as only a tool used by humans and not necessariy ruling the objects dynamics? But then I read this in Deep Down Things:

"So, if we look at the factors that multiply the wave function in the Schrodinger equation, we find that to the left of the equals sign we have the sum of the kinetic plus potential energies at the point x, while to the right of the equals sign, we have the total energy. Thus, the Schrodinger equation is just the wave-mechanical statement that the sum of the kinetic and
potential energies at any given point is just equal to the total energy—the Schrodinger equation is simply the quantum-mechanical version of the notion of energy conservation. From this quantum-mechanical formulation of energy conservation arises the full set of constraints that prescribe the possible
quantum mechanical wave functions for the object. This again illustrates the central importance of the idea of energy conservation (note 3.11)."

Can't it be like the 3 vectors describing an actual object in Newtonian physics? Although the wave function lives in higher dimensional configuration space with 3N times the particles. So if there are 5 particles, it's in 15 dimensional space. But still it is possible to convert the 15 dimensions to a spot in 3 dimensions let's saying we were talking of the position observable (roughly speaking). By the way, what is the conversion formula to locate to one 3D position the 15 dimensional configuration space.

Bottom line is. Wave function can be like the 3 vectors in Newtonian physics.

Or at least the arguments the particles were obeying law of conservation of energy in that the Schrodinger equation is just the wave-mechanical statement that the sum of the kinetic and potential energies at any given point is just equal to the total energy.

If the Bohrians don't think the particles even exist to take part in the Schrodinger Equations before they were measurements. Then what are particles to them? In one of your Insight Articles. It's missing the more complete description or Hidden Variable.

So can we say the non-local Hidden Variables is the more complete equations where the Schroedinger Equations were just low limit and valid only for very few particles. It can't even described entangled particles which needs the density matrix approach. By the way, what is Bohr equations for entangled particles. I know the density matrix (used in decoherence) was discovered after Bohr died.

 

[PeterDonis]

So these folks treat the entire Schroedinger Equation as only a tool used by humans and not necessariy ruling the objects dynamics?

For that particular interpretation, yes, that's basically it.

then I read this in Deep Down Things

Which appears to be using a different interpretation.

still it is possible to convert the 15 dimensions to a spot in 3 dimensions

No, it isn't.

what is the conversion formula to locate to one 3D position the 15 dimensional configuration space.

There isn't one. It's not possible to reduce a point in a 15 dimensional space to a point in 3 dimensional space.

 

[jlcd]

For that particular interpretation, yes, that's basically it.
Which appears to be using a different interpretation.
No, it isn't.
There isn't one. It's not possible to reduce a point in a 15 dimensional space to a point in 3 dimensional space.

Why did you say it's using another interpretation? What statements in the above makes you think so? Deep Down Thing is using the orthodox interpretation when it stated this:

"Although psi(x) has no physical meaning, any physical property of the object can be determined once psi (x) is known. If you want to know the probability of finding the object at any point in space, you simply perform a specific procedure on psi (x)—in this case, just squaring (multiplying it by itself once) the value of psi(x) at that particular point in space. If you want to know the object’s kinetic energy, you perform a different procedure (in this case, involving taking some derivatives, that is, performing a little calculus). If you want to know the object’s speed and direction of motion (to the accuracy permitted by the uncertainty principle), there’s a procedure for finding that and so forth."

If the Schrodinger equation is just the wave-mechanical statement that the sum of the kinetic and potential energies at any given point is just equal to the total energy. Then it completely captures the state of the physical system except fields. What else it can't capture or describe? I'm pondering what possible reasons the wave function as subjective is not complete description.

 

[PeterDonis]

Why did you say it's using another interpretation?

I don't have the book so I can only go on the quotes you give. The quote you gave before says the Schrodinger Equation (presumably he means the time-independent Schrodinger Equation, the one describing energy eigenstates, since his description does not fit the time-dependent Schrodinger Equation) is the quantum version of energy conservation. That sounds like he's saying it's describing something real, not just something subjective. Energy conservation is not subjective.

Deep Down Thing is using the orthodox interpretation when it stated this:

What "orthodox interpretation" are you talking about?

the Schrodinger equation is just the wave-mechanical statement that the sum of the kinetic and potential energies at any given point is just equal to the total energy.

This is, as above, the time independent Schrodinger Equation, the one whose solutions describe energy eigenstates. It is not the time dependent Schrodinger Equation, the one whose solutions describe general states.

Then it completely captures the state of the physical system except fields.

No, it doesn't. See above.

What else it can't capture or describe?

Anything relativistic. The Schrodinger Equation (either version) is a non-relativistic approximation.

I'm pondering what possible reasons the wave function as subjective is not complete description.

It can't be because it's non-relativistic. In quantum field theory, the combination of QM with relativity, there are no wave functions except in very special cases. Quantum fields are a whole different kind of thing.