A Is the wavefunction subjective? How?

[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.

 

[jlcd]

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.
What "orthodox interpretation" are you talking about?

Orthodox in the sense he mentioned psi(x) had no physical meaning and only probability and squaring it stuff.

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.
No, it doesn't. See above.
Anything relativistic. The Schrodinger Equation (either version) is a non-relativistic approximation.
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.

Focusing on the subject of this thread which is how the wave function is subjective. During the time of Bohr. How did he model entangled particles which didn't have wave function? How did he make entangled particles subjective too?

 

[PeterDonis]

During the time of Bohr. How did he model entangled particles which didn't have wave function?

A quantum system consisting of entangled particles does have a wave function. The particles taken individually don't, but that doesn't stop Bohr or anyone else from modeling the system using its wave function.

 

[jlcd]

A quantum system consisting of entangled particles does have a wave function. The particles taken individually don't, but that doesn't stop Bohr or anyone else from modeling the system using its wave function.

I mean in decoherence, entangled particles are not in superposition.In your Insight Article where you mentioned about more complete description (hidden variables?) if the state was subjective. Quoting it::

"For #1, the obviously true part is that we can never directly observe the state, and we can never make deterministic predictions about the results of quantum experiments. That makes it seem obvious that the state can’t be the physically real state of the system; if it were, we ought to be able to pin it down and not have to settle for merely probabilistic descriptions. But if we take that idea to its logical conclusion, it implies that QM must be an incomplete theory; there ought to be some more complete description of the system that fills in the gaps and allows us to do better than merely probabilistic predictions. And yet nobody has ever found such a more complete description, and all indications from experiments (at least so far) are that no such description exists; the probabilistic predictions that QM gives us really are the best we can do."

Reference https://www.physicsforums.com/insights/fundamental-difference-interpretations-quantum-mechanics/

Is the complete description the same as Hidden Variables? Or separate concept. If they are synonyms. Is the complete description or hidden variable describable by quantum field theory, or would it still be QM?

 

[PeterDonis]

in decoherence, entangled particles are not in superposition

Huh? I can't even make sense of this.

Is the complete description the same as Hidden Variables?

Hidden variables would be one kind of more complete description. But they would have to be nonlocal hidden variables because of Bell's Theorem.

 

[jlcd]

Huh? I can't even make sense of this.

I mean broken entangled particles are no longer in superposition. For example, in EPR, if you have entangled particles - as soon as one is observed it becomes entangled with the observational apparatus and is no longer entangled with the particle.

The math of which as Bhobba repeated many times throughout the years:

"There are standard definitions of superposition and entanglement in QM. I suggest you stick to those.
They are:

1. Superposition reflects the vector space structure of so called pure states. That is if you have a system that can be in state state |a> and state |b> then it can be in a superposition of those states ie c1*|a> + c2*|b> where c1 and c2 are complex numbers. This is called the principle of superposition and is a fundamental principle of QM. It is not an axiom because it follows from something else - but no need to go into that here.

2. Entanglement applies the principle of superposition to separate systems. Suppose you have a system that can be in state |a> or |b> and another system that also can be in state |a> or |b>. If system 1 is in state |a> and system 2 in state |b> that is written as |a>|b>. Conversely if system 1 is in state |b> and system 2 on state |a> that is written as state |b>|a>. But we can apply the principle of superposition to give a state c1*|a>|b> + c2*|b>|a>. The two systems are then said to be entangled. It is a peculiar non classical situation - system 1 is no longer in state |a> or |b> and the same with system 2 - they are entangled with each other. If you observe system 1 and find it in state |a> by the principles of QM the combined system is in state |a>|b> - so system 2 is in state |b> and conversely. Observing one system immediately has told you about another due to entanglement."

Reference https://www.physicsforums.com/threads/bells-inequality.791592/page-2#post-4975266

Hidden variables would be one kind of more complete description. But they would have to be nonlocal hidden variables because of Bell's Theorem.

I was inquiring earlier about the other equations based on your Insight Article. I was asking what kind of equations the more complete description may take. If Schroedinger Equation is only for tool for probability and subjective. So I thought your complete description mean more objective equations. It can involve Hidden Variables as you say but won't it need QFT on majority since there may be some exotic fields involved or must one focus on QM to solve for this complete equations. What do you think?

 

[PeterDonis]

Entanglement applies the principle of superposition to separate systems.

I'm not sure I would put it this way, but I see now what you meant.

 

[PeterDonis]

I was asking what kind of equations the more complete description may take.

Nobody has such a more complete description, so this question is not answerable.

 

[jlcd]

Nobody has such a more complete description, so this question is not answerable.

If someone can demonstrate that low energy physics like water and salt is enough to produce new physics. Is QM description enough or must one need QFT for water and salt? I know QFT is needed in the Large Hadron Collider, but still water and salt have electrons and electromagnetic interaction. So QFT is needed? This is the last (and critical) question as I don't want to hijack the thread, lol. So others can discuss the topics of the OP. Thanks.

 

[PeterDonis]

must one need QFT for water and salt?

Neither one involves any relativistic effects, so no.

 

[Stephen Tashi]

I see a measurement device (or any interacting part) as a kind of "information processing" object.

If we consider Nature to exist independently of human opinions about it then whether something is measuring device is subjective. For example, there can be a local phenomena that human beings agree to call a voltmeter. Sitting on a table beside it can be a local phenomena that human beings agree to call a coffee cup. Both the voltmeter and the coffee cup presumbably have inputs and outputs in the sense that humans can declare some phenomena to be external to these objects and declare other phenomena to be the objects' reactions to external pheomena.

This is one way to view the "cut" between classical and quantum systems. Is it more or less what the originators of the "cut" concept had in mind?

 

[jlcd]

I: "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.

Let's focus on this odd situation where QM does not necessary rule the object dynamics and what it meant.

Before the interpretation of the wave function as probability wave. Schrodinger's theory gave a complete description of the spectral lines in the hydrogen atom, reproducing touchstone Balmer formula. In addition, the splitting in electric and magnetic fields also popped right out of the wave equation.

Schrödinger was thus able to observe that the integers (number of nodes) derived from a three-dimensional wave solution precisely correspond to the three quantum numbers n, k and m from the old quantum theory.

Schrodinger actually initially thought it was literal matter waves before Henrik Lorentz made him realized key points like the fact wave packets will spread with time and the idea of representing particles completely in terms of the superposition of waves is invalid.

But can't the success of reproducing the Balmer formula tell something about the Schrodinger Equation able to describe the dynamics of objects?

Let's the case of the hydrogen atom. The interaction of the electron to the nucleus is via coulomb, and this can be described by QM. Can you give some examples showing that the Schrodinger equation doesn't necessarily describe the dynamics of objects?

I always read about Quantum Mechanics giving us so many discoveries like integrated circuits, processors, iphones, etc. So it's odd it can't even describe or rule the dynamics of objects.

And for those who take the wave function as real. Do they also say the Schrodinger Equation doesn't really rule or describe the dynamics of objects? Then why aren't any of the camps try to figure out the laws governing the real dynamics of objects instead of just this subjective thing?

 

[PeterDonis]

And for those who take the wave function as real. Do they also say the Schrodinger Equation doesn't really rule or describe the dynamics of objects?

Of course not. Those who take the wave function as real have no reason to say any such thing. But what they mean by "objects" might not be what you're thinking. See my next post.

 

[PeterDonis]

I always read about Quantum Mechanics giving us so many discoveries like integrated circuits, processors, iphones, etc. So it's odd it can't even describe or rule the dynamics of objects.

Ok, so it's odd. So are all interpretations of QM. Taking the wave function as real might fit in better with your intuitions about describing the dynamics of objects, but on that interpretation, the "objects" in question are wave functions, which if we take the Schrodinger Equation as always describing the dynamics, bear no resemblance whatever to the actual objects we observe. What you get when you just say there's the wave function evolving by the Schrodinger Equation and nothing else is the Many Worlds interpretation, which is certainly "odd" by any reasonable criterion of oddness.

 

[jlcd]

Ok, so it's odd. So are all interpretations of QM. Taking the wave function as real might fit in better with your intuitions about describing the dynamics of objects, but on that interpretation, the "objects" in question are wave functions, which if we take the Schrodinger Equation as always describing the dynamics, bear no resemblance whatever to the actual objects we observe. What you get when you just say there's the wave function evolving by the Schrodinger Equation and nothing else is the Many Worlds interpretation, which is certainly "odd" by any reasonable criterion of oddness.

I know Many world was the consequence of taking wave function as real as you emphasized in your Insight Article (i almost memorized every word of it).

But Many worlds can be tamed by simple altering unitarity. I know this needs new math and physics. But then by altering it too much. Won't it be as complex as not taking wave function as real like Bohr and just cooking up the complete descriptions?

Both need real hard work.. altering unitarity in many worlds is as Zurek put it :

"Repeatability leads to branch-like states, Eq. (13), suggesting Everettian ‘relative states’ [19]. There is no need to attribute reality to all the branches. Quantum states are part information. As we have seen, objective reality is an emergent property. Unobserved branches can be regarded as events potentially consistent with the initially available information that did not happen. Information we gather can be used to advantage—it can lead to actions conditioned on measurement outcomes [5]."

By going to Bohr and treating wave function as subjective one needs to develope more complete description. No problem as data is not lacking. But what is more elegant. Zurek idea of othe branches as information or the whole wave function as subjective and one has to cook up the complete description. But would the complete description retain some part of Zurek idea of the other branches as part information? What is the constrains for the more complete description if case 1 was true. Like in addition to discover any hidden variables. Must one produce new way of interaction that even involve spacetime. This is why I see case 1 as more elegant because there are more degrees of freedom in cooking up the new physics that involves spacetime. With wave function as real, it is not integrated to spacetime and looks a bit boring to compare to the potentiality in case 1.

Where did I go wrong in the analysis above?

Any references by say Perimeter Institute researchers about this so I can explore it further? Anyone?

 

[PeterDonis]

Many worlds can be tamed by simple altering unitarity. I know this needs new math and physics.

Yep. Which makes it out of scope for discussion unless you can give a specific reference.

as Zurek put it

Please give a reference.