I Classicality and the Correspondence Principle

[PeterDonis]

if you express|LIVE⟩ and |DEAD⟩ as products of a state of the cat ("live" or "dead") and a state of the cat's environment ("observed to be live, etc." or "observed to be dead, etc."). So now the state of the overall system is a sum of products of states of two subsystems, i.e., an entangled state.

You don't even need the environment; that's the point. The cat has so many degrees of freedom all by itself, which can't possibly remain coherent with each other, that the cat states "alive" and "dead" are already decohered. Or, to put it another way, the parts of the cat are already entangled with each other in a way that separates the "alive" and "dead" states--each of them is really one of two terms in an incredibly complicated entangled state involving all of the cat's degrees of freedom.

And given all that, any extra entanglement with degrees of freedom in an "environment" outside the cat is trivial, and thinking of the cat as only being decohered into "alive" or "dead" states by becoming entangled with an "environment" outside the cat is wrong. All of the decoherence has already happened long before any degrees of freedom outside the cat become involved.

those definitions depend on being able to separate the system into the two disjoint subsystems "cat" and "cat's environment".

Yes, that's true.

That is what we don't know how to do in the general case using just the information in the overall system's wave function.

Yes, that's true in the general case. But I think it's quite possible that in any special case of actual practical interest--like a cat or a human or even a table or a rock--separating out the objects of interest as systems can be done to a good enough approximation. The cases where the split is not sufficiently clear might just be edge cases that don't need to be dealt with in practice.

Isn't "alive" and "dead" really orthogonal quantum states of the cat.

No. They are orthogonal subspaces of the state space of the cat, as I said. Neither one is a single state or anything close to it, since the cat has so many degrees of freedom that there are a huge number of microstates it can have that are equivalent from the standpoint of it being alive or dead.

Or is the truth we really don't know if alive and dead are orthogonal quantum states of the cat or classical state space due to lack of information?

The "classical state space" is just a coarse-graining of the quantum state space--basically you ignore interference between decohered alternatives. It's not something separate. So the distinction you are trying to make here doesn't really exist.

 

[jlcd]

You don't even need the environment; that's the point. The cat has so many degrees of freedom all by itself, which can't possibly remain coherent with each other, that the cat states "alive" and "dead" are already decohered. Or, to put it another way, the parts of the cat are already entangled with each other in a way that separates the "alive" and "dead" states--each of them is really one of two terms in an incredibly complicated entangled state involving all of the cat's degrees of freedom.

But the argument is still valid even if the cat is its own environment. If |psi> is all there is. What created or produced the cat own decoherence in the first place? This was my context.

And given all that, any extra entanglement with degrees of freedom in an "environment" outside the cat is trivial, and thinking of the cat as only being decohered into "alive" or "dead" states by becoming entangled with an "environment" outside the cat is wrong. All of the decoherence has already happened long before any degrees of freedom outside the cat become involved.
Yes, that's true.
Yes, that's true in the general case. But I think it's quite possible that in any special case of actual practical interest--like a cat or a human or even a table or a rock--separating out the objects of interest as systems can be done to a good enough approximation. The cases where the split is not sufficiently clear might just be edge cases that don't need to be dealt with in practice.
No. They are orthogonal subspaces of the state space of the cat, as I said. Neither one is a single state or anything close to it, since the cat has so many degrees of freedom that there are a huge number of microstates it can have that are equivalent from the standpoint of it being alive or dead.
The "classical state space" is just a coarse-graining of the quantum state space--basically you ignore interference between decohered alternatives. It's not something separate. So the distinction you are trying to make here doesn't really exist.

 

[PeterDonis]

If |psi> is all there is. What created or produced the cat own decoherence in the first place?

This is still an open question. But it's just as much of an open question for the SG experiment as for a cat, because we can't observe the result of an SG experiment without a detector, and the detector raises all of the same questions.

 

[jlcd]

This is still an open question. But it's just as much of an open question for the SG experiment as for a cat, because we can't observe the result of an SG experiment without a detector, and the detector raises all of the same questions.

In this argument that |psi> is all there is. Is the dead and alive the orthogonal subspaces of the classical state space of the cat, or quantum states of the cat?

 

[PeterDonis]

In this argument that |psi> is all there is. Is the dead and alive the orthogonal subspaces of the classical state space of the cat, or quantum states of the cat?

There is only one state space, the quantum state space. Dead and alive are orthogonal subspaces of it. The "classical state space", as I said, is just a coarse-graining of the quantum state space; "dead" and "alive" would belong to different classical states, i.e., different sets of quantum states in the coarse-graining.

 

[jlcd]

There is only one state space, the quantum state space. Dead and alive are orthogonal subspaces of it. The "classical state space", as I said, is just a coarse-graining of the quantum state space; "dead" and "alive" would belong to different classical states, i.e., different sets of quantum states in the coarse-graining.

Oh. So the mere fact there is even a cat means |psi> is not all there is. Fine.

Say, Is it possible to mention in for example a book or article that quantum mechanics is about the |psi> and it's still a great mystery how the position, energy basis even existed? Like I want to not mention the entire Copenhagen interpretation at all .. which is simply accepting there is result and doesn't even offer a mechanism and telling the generations to just "shut up and calculate". Or explaining one has alternative way to think of the quantum without Copenhagen interpretation?

I will mention the math and state "then the wand is waved and the position, momentum, spin basis appeared"? This is a good alternative way to present the quantum without mentioning Copenhagen right? Just theoretically asking. Of course serious students will be introduced to all. But just asking if it can be presented the way I described above?

 

[PeterDonis]

the mere fact there is even a cat means |psi> is not all there is.

I'm not sure how you're reaching that conclusion. Nothing I have said picks out any particular interpretation of QM; it is all consistent with, for example, the MWI, which says that psi is all there is. (Well, strictly speaking, psi plus the Hilbert space plus the Hamiltonian, which determines the time evolution of psi.) Unless I'm misunderstanding what you mean by "psi is all there is".

But just asking if it can be presented the way I described above?

I would not undertake to write a book or article at all on this subject without spending a lot of time reading the literature--textbooks and peer-reviewed papers--making sure to cover as wide a selection as possible in order to get presentations of many different QM interpretations. Once you've taken the time to do that, you will be able to make up your own mind about presentation.

 

[jlcd]

I'm not sure how you're reaching that conclusion. Nothing I have said picks out any particular interpretation of QM; it is all consistent with, for example, the MWI, which says that psi is all there is. (Well, strictly speaking, psi plus the Hilbert space plus the Hamiltonian, which determines the time evolution of psi.) Unless I'm misunderstanding what you mean by "psi is all there is".

Oh, i just referring to the nothing happens in many worlds thread. I understood it.

I would not undertake to write a book or article at all on this subject without spending a lot of time reading the literature--textbooks and peer-reviewed papers--making sure to cover as wide a selection as possible in order to get presentations of many different QM interpretations. Once you've taken the time to do that, you will be able to make up your own mind about presentation.

I spent a lot of time reading the literature - textbooks and peer-reviewed papers and wil do so for decades to come. I have some query with regards to Zurek's paper

https://arxiv.org/pdf/1412.5206.pdf
"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]."

Some anti-realists believe that the properties we ascribe to atoms and elementary particles are not inherent in those objects, but are created only by our interactions with them, and exist only at the time when we measure them.

While realists believe that matter have a stable set of properties in and of itself, without regard to our perceptions and knowledge.

In Zurek's view that the quantum states are part information and "There is no need to attribute reality to all the branches". Is it anti-realist or realist viewpoints? What do you think?

 

[PeterDonis]

Is it anti-realist or realist viewpoints?

I'm not sure. Zurek's position seems to me to be a mixture of pointing out particular aspects of the basic math of QM, which are independent of any particular interpretation, and trying to construct a new interpretation of QM.

Personally, I don't think "realist" or "anti-realist" are very useful terms, because they don't have precise definitions and their function in discussions ends up being nothing more than labels for the two sides.

 

[Lord Jestocost]

Some anti-realists believe that the properties we ascribe to atoms and elementary particles are not inherent in those objects, but are created only by our interactions with them, and exist only at the time when we measure them.

While realists believe that matter have a stable set of properties in and of itself, without regard to our perceptions and knowledge.

Realism and anti-realism in the philosophy of science are merely different approaches regarding the meaning of physical theories. As Massimo Pigliucci puts it on http://rationallyspeaking.blogspot.com/2012/08/surprise-naturalistic-metaphysics.html:

“To put it very briefly, a realist is someone who thinks that scientific theories aim at describing the world as it is (of course, within the limits of human epistemic access to reality), while an anti-realist is someone who takes scientific theories to aim at empirical adequacy, not truth. So, for instance, for a realist there truly are electrons out there, while for an anti-realist “electrons” are a convenient theoretical construct to make sense of certain kinds of data from fundamental physics, but the term need not refer to actual “particles.” It goes without saying that most scientists are realists, but not all. Interestingly, some physicists working on quantum mechanics belong to what is informally known as the “shut up and calculate” school, which eschews “interpretations” of quantum mechanics in favor of a pragmatic deployment of the theory to solve computational problems.”

 

[jlcd]

I'm not sure. Zurek's position seems to me to be a mixture of pointing out particular aspects of the basic math of QM, which are independent of any particular interpretation, and trying to construct a new interpretation of QM.

Personally, I don't think "realist" or "anti-realist" are very useful terms, because they don't have precise definitions and their function in discussions ends up being nothing more than labels for the two sides.

Now to connect classicality, correspondence principle and decoherence. The latter says macroscopic superposition is not possible due to decoherence, the correspondence principle is classical physics is restored for large quantum numbers or degrees of freedom.

But is the above a solid rule or can be written in a formal proof or theorem that say the human body being macroscopic doesn't have quantum effects?

However what would happen if quantum mechanics or even QFT is just emergent. Then the formal proof instantly vaporized?

It's like the von Neumann impossible proof of No Hidden Variables that Bohm challenged.

 

[PeterDonis]

is the above a solid rule or can be written in a formal proof or theorem that say the human body being macroscopic doesn't have quantum effects?

No. Nobody has any formal proofs or theorems that show this.

 

[jlcd]

No. Nobody has any formal proofs or theorems that show this.

All look at any coherence but because decoherent time scale is so fast. Biology is said to be ruled by classical mechanics. Maybe the fact decoherent time is so fast as computed is the formal proof itself? Why can't it be made a theorem?

Do you know of other mechanisms they explore for any quantum effects?

About the predictibility sieve where the hilbert space is sorted for pointer states that are most classical. It can't help too because at the end of the day we were dealing with only one pointer state or branch for our classical object. Right?

I'm exploring beyond Zurek. Do you know (or anyone else) who are other good researchers like Zurek besides Smolin researching the same lines in quantum foundations and has good results?

 

[jlcd]

I'm not sure. Zurek's position seems to me to be a mixture of pointing out particular aspects of the basic math of QM, which are independent of any particular interpretation, and trying to construct a new interpretation of QM.

Just a clarification about the pointer states. When one pointer state of the cat classicality was chosen (by the predictivity sieve which sorts the hilbert space for the most classical state). How long the pointer state remains that way before it reprepares again? Or is the pointer state permanent? Remember Decoherence doesn't choose one of the outcomes. So how the outcome of one of the pointer states was chosen depends on interpretation. But speaking of the math. Collapse or being in eigenstate doesn't mean it remains that way forever. It can reprepare. So how long before the pointer state of the cat reprepares? In micro seconds? or 1 sec?

 

[PeterDonis]

How long the pointer state remains that way before it reprepares again? Or is the pointer state permanent?

If the pointer state is "cat alive", it will stay that way until the cat dies. If the pointer state is "cat dead", as far as we know, that's permanent.

Of course, this just reflects the fact that "cat alive"and "cat dead" are not single quantum states of the cat; they are huge subspaces of the cat's state space. This will be true for any "pointer state" since any such state will involve a macroscopic object and any macroscopically distinguishable state of a macroscopic object (which is pretty much what "pointer state" means) will be some subspace of the object's full state space that contains a huge number of microstates. And the pointer states behave classically to a very, very good approximation, so the way to answer your question is to look at classical-type dynamics of typical macroscopic objects. And such objects don't "re-prepare" themselves.

 

[jlcd]

If the pointer state is "cat alive", it will stay that way until the cat dies. If the pointer state is "cat dead", as far as we know, that's permanent.

Of course, this just reflects the fact that "cat alive"and "cat dead" are not single quantum states of the cat; they are huge subspaces of the cat's state space. This will be true for any "pointer state" since any such state will involve a macroscopic object and any macroscopically distinguishable state of a macroscopic object (which is pretty much what "pointer state" means) will be some subspace of the object's full state space that contains a huge number of microstates. And the pointer states behave classically to a very, very good approximation, so the way to answer your question is to look at classical-type dynamics of typical macroscopic objects. And such objects don't "re-prepare" themselves.

Let's distinguish between microscopic and macroscopic cat-states. Macroscopic cat-states are in principle pointer states, however, they describe a higher level of organisation than the pointer-states of individual cat cells or dna or even lower levels.

So if the microstates (micro pointer states) can be influenced. It can affect the microstates (the main pointer state)?

It may not be possible to raise the dead cat because the microstates were already so altered. But for an alive cat. Different microstates can be realized that can affect the macro pointer state, right?

So seconds by seconds, the macro pointer state can be altered by different possibiities or outcome in the cat microstates pointer states causing sick cat, healthy cat, etc, right?

 

[SFXMan]

It may not be possible to raise the dead cat because the microstates were already so altered. But for an alive cat. Different microstates can be realized that can affect the macro pointer state, right?

Insofar as the quantum time-evolution of the microstate is a more complete description than the approximately classical time-evolution of the macrostate, yes.

 

[PeterDonis]

Let's distinguish between microscopic and macroscopic cat-states.

That's not the right distinction. The right distinction is between individual microstates of the cat, which we can't possibly measure since there are way too many degrees of freedom, and huge sets of microstates that all have certain macroscopic properties in common (for example, the macroscopic property that the cat is alive). The sets of microstates are what we have been calling "macroscopic cat states" or "pointer states".

So if the microstates (micro pointer states) can be influenced.

There is no such thing as "micro pointer states". Pointer states (which is really a misnomer, these are huge sets of states, not single states) are macroscopically distinguishable.

It can affect the microstates (the main pointer state)?

You mean affect the macrostates. The vast majority of changes in the microstate do not change the main pointer state, because they don't change whether the cat is alive or dead. Only a very, very small fraction of changes in the microstate will change whether the cat is alive or dead and thereby change the main pointer state.

It may not be possible to raise the dead cat because the microstates were already so altered. But for an alive cat. Different microstates can be realized that can affect the macro pointer state, right?

What I said just above is true regardless of whether the cat is currently alive or dead. From the standpoint of the microstate and its time evolution there is no difference between these two main pointer states. The fact that we don't know how to raise dead cats whereas we do know how to kill live cats is not because it's "easier" for a microstate to evolve one way vs. the other. It's just due to our vast ignorance about the details of how cats and other living things actually work.

 

[jlcd]

That's not the right distinction. The right distinction is between individual microstates of the cat, which we can't possibly measure since there are way too many degrees of freedom, and huge sets of microstates that all have certain macroscopic properties in common (for example, the macroscopic property that the cat is alive). The sets of microstates are what we have been calling "macroscopic cat states" or "pointer states".
There is no such thing as "micro pointer states". Pointer states (which is really a misnomer, these are huge sets of states, not single states) are macroscopically distinguishable.
You mean affect the macrostates. The vast majority of changes in the microstate do not change the main pointer state, because they don't change whether the cat is alive or dead. Only a very, very small fraction of changes in the microstate will change whether the cat is alive or dead and thereby change the main pointer state.
What I said just above is true regardless of whether the cat is currently alive or dead. From the standpoint of the microstate and its time evolution there is no difference between these two main pointer states. The fact that we don't know how to raise dead cats whereas we do know how to kill live cats is not because it's "easier" for a microstate to evolve one way vs. the other. It's just due to our vast ignorance about the details of how cats and other living things actually work.

I wrote: "If |psi> is all there is. What created or produced the cat own decoherence in the first place?" Your reply was:

This is still an open question. But it's just as much of an open question for the SG experiment as for a cat, because we can't observe the result of an SG experiment without a detector, and the detector raises all of the same questions.

In this paper https://arxiv.org/pdf/quant-ph/0509174.pdf

Concept for predictability sieves and pointer states were used for simple systems such as an underdamped harmonic oscillator, for which coherent states are unanimously chosen by all criteria, and a free particle undergoing quantum Brownian motion.

The environment-induced super selection (einselection) are quantified using four different criteria:

1. predictability sieve (which selects states that produce least entropy),
2. purification time (which looks for states that are the easiest to find out from the imprint they leave on the environment),
3. efficiency threshold (which finds states that can be deduced from measurements on a smallest fraction of the environment), and
4. purity loss time (that looks for states for which it takes the longest to lose a set fraction of their initial purity)

These are only used for pure quantum systems and not the cat. The reason is i think because the cat has already decohered. Now for sake of discussion. If |psi> is all there is (in second type of MWI interpretation where there are no inherent position basis). And the cat has no inherent positions.. meaning it doesn't reflect light.. has no shape. Not yet decohered. This "inherent cat" state vector can have the predictability sieves, purification time applied to it? Or even with intact cat with position basis, the predictability sieves can likewise apply to it? Zurek only not using it because of the complexity of cat, hence using just simple example of underdamped harmonic oscillator or free particle undergoing quantum Brownian motion?

 

[PeterDonis]

the cat has no inherent positions.. meaning it doesn't reflect light.. has no shape. Not yet decohered.

A cat that has not yet decohered is an impossibility in any practical sense. A cat has so many degrees of freedom that there is no way to keep it from decohering on a timescale much, much shorter than any timescale we can work with in experiments now or in the foreseeable future.

What that means is that we have no experimental basis for assuming that we can model something like a cat using a non-decohered pure quantum state at all. It could be that, on a short enough time scale, we can model cats that way, and if we were ever able to do, say, a double slit experiment on a time scale of $10^{-40}$ seconds or something like that, we might be able to see quantum interference effects in a cat. Or it could be that, long before we get to that short a time scale, we find that there is other physics coming into play--for example, a time scale that short corresponds to an energy per particle close to the Planck scale, which means that quantum gravity effects might be significant, and might completely change the dynamics on that scale.

Or even with intact cat with position basis, the predictability sieves can likewise apply to it?

I am not familiar enough with Zurek's argument to say whether it could be applied to a real, decohered cat. Given the examples he uses, it certainly doesn't seem like anyone has tried to do so.

 

[jlcd]

If the pointer state is "cat alive", it will stay that way until the cat dies. If the pointer state is "cat dead", as far as we know, that's permanent.

Ok. If the pointer state is "cat alive", it will stay that way until the cat dies. If the pointer state is "cat dead", as far as we know, that's permanent. No problem.

But how about the pointer state of your mood (related to brain dynamics). Now since it varies hour to hour or even minute to minute (for very moody people). Then it is right to say the pointer states of mood in brain can change hour to hour, minute to minute?

Of course, this just reflects the fact that "cat alive"and "cat dead" are not single quantum states of the cat; they are huge subspaces of the cat's state space. This will be true for any "pointer state" since any such state will involve a macroscopic object and any macroscopically distinguishable state of a macroscopic object (which is pretty much what "pointer state" means) will be some subspace of the object's full state space that contains a huge number of microstates. And the pointer states behave classically to a very, very good approximation, so the way to answer your question is to look at classical-type dynamics of typical macroscopic objects. And such objects don't "re-prepare" themselves.

 

[PeterDonis]

Then it is right to say the pointer states of mood in brain can change hour to hour, minute to minute?

Yes. Obviously there are various kinds of "pointer states" (states of macroscopic objects) that behave in various ways. We didn't need quantum mechanics to tell us that.

Nor did we need it to tell us that we can partition the states of macroscopic objects in various ways at various levels of detail. For example, cats have moods too; saying that a cat is "alive" is a very, very coarse way of specifying its "pointer state". It could be happy, sad, hungry, thirsty, etc., etc., and its mood can change hour to hour, minute to minute. All of these are just ways of partitioning the "cat alive" subspace of all cat states into finer-grained distinctions. All of this is obvious, and none of it has anything to do with QM, as far as I can see.

I think you're making this much harder than it needs to be, and I'm not sure why.

 

[Mentz114]

...

I found that the Ehrenfest approach (dynamics) helps a lot to get rid of the confusion caused by introducing the wave function without any context.

There does not appear to be a much literature but there is a chapter in Ballentine and it is used in the thermal interpretation arXiv:1902.10779v2 [quant-ph] 24 Apr 2019 and possibly made rigorous in this arXiv:0907.1877v1 [math-ph] 10 Jul 2009.

The wiki article is also informative https://en.wikipedia.org/wiki/Ehrenfest_theorem

 

[jlcd]

Yes. Obviously there are various kinds of "pointer states" (states of macroscopic objects) that behave in various ways. We didn't need quantum mechanics to tell us that.

Nor did we need it to tell us that we can partition the states of macroscopic objects in various ways at various levels of detail. For example, cats have moods too; saying that a cat is "alive" is a very, very coarse way of specifying its "pointer state". It could be happy, sad, hungry, thirsty, etc., etc., and its mood can change hour to hour, minute to minute. All of these are just ways of partitioning the "cat alive" subspace of all cat states into finer-grained distinctions. All of this is obvious, and none of it has anything to do with QM, as far as I can see.

I think you're making this much harder than it needs to be, and I'm not sure why.

When I mentioned "pointer states" and macroscopic object. I was using the context of Zurek quantum darwinism where he didn't use the born rule and states are the primitive (versus copenhagen where observations are the primitive). I understood a lot about fragments and how objectivity is derived. No problem about that. I just want to know whether using quantum darwinism without born rule can give macroscopic object more degrees of freedom (meaning is the dynamics using quantum darwinism without born rule and orthodox using born rule exactly identical or does the former has more degrees of freedom in some aspects?).

Another issue. We humans use born rule so we can get eigenstates and see the results with our eyes or the via the instruments.

But let's take an object like iron bar. When a molecule inside it is "measuring" other molecules inside it. Does the latter have to be in eigenstates before the molecule can interact with it? Or can molecules interact with one another within being in any eigenstates? And can molecules interact with one another without using any born rule? Let's not use MWI or BM analysis. Point is. Only we humans need born rule in measurement (where we need to see the eigenstates)? Can molecules self measure each other without using any born rule or doesn't need to be in any eigenstates? I'm thinking they may not because they have the wave function to see through each other while we are not wave function aware so need to see the particles via detector using born rule (?).

 

[PeterDonis]

We humans use born rule so we can get eigenstates

We humans don't directly observe any quantum system that is simple enough that we can even write down a specific operator and its eigenstates. By the time we observe anything, a huge number of degrees of freedom are involved and a lot of decoherence has occurred. So this statement is not correct as a statement about what we humans actually do.

In some very special cases, we can ignore the above and treat our observation as if we were directly observing eigenstates of some simple operator of some simple quantum system. But that's a convenient simplification that has practical uses. It is not in any way a claim about how things "really are".

let's take an object like iron bar.

What I said above applies to any macroscopic object.

When a molecule inside it is "measuring" other molecules inside it.

This is not a useful way of viewing what is going on. The iron bar has something like $10^{25}$ atoms in it. All of them are continually interacting; the bar as a whole is continually decohering. This is not a "measurement" in any useful sense. It's just part of being a macroscopic object.

Does the latter have to be in eigenstates before the molecule can interact with it?

Individual atoms can interact with each other regardless of what states they are in.

Also, you keep saying "eigenstates" as though they were properties of the atom. They're not. They're properties of an operator, i.e., some measurement you can make on a quantum object. For example, if you measure an electron's spin in the $z$ direction, there are two states of the electron that are eigenstates of that measurement. But if you measure the spin in the $x$ direction, there are two different states of the electron that are eigenstates of that measurement.

But even the above, as I said before, assumes that you have a quantum system and a measurement that are simple enough that you can write them down. We can't do that for macroscopic objects.

(Also, saying that we "measure" the electron's spin, if all that's involved is the electron's spin degree of freedom, is really a misnomer. We pass the electron through a magnetic field that entangles its spin with its linear momentum. This is a unitary interaction and does not require anything to be observed at all. When we say we "measure" the spin, what we mean is that we have a detector, such as a piece of photographic film--a macroscopic object--placed so that we will see a spot at one of two points on the detector: which point depends on which direction the electron was moving when it came out of the magnetic field, i.e., what its linear momentum was, which the magnetic field entangled with the spin. The "result" of the measurement is actually the position of the spot--that's what we observe. We infer from that observation that the electron's spin was up or down, because we follow the chain of reasoning backwards from the spot position to the electron's momentum coming out of the magnetic field to the electron's spin that got entangled with the momentum.)

 

[jlcd]

We humans don't directly observe any quantum system that is simple enough that we can even write down a specific operator and its eigenstates. By the time we observe anything, a huge number of degrees of freedom are involved and a lot of decoherence has occurred. So this statement is not correct as a statement about what we humans actually do.

In some very special cases, we can ignore the above and treat our observation as if we were directly observing eigenstates of some simple operator of some simple quantum system. But that's a convenient simplification that has practical uses. It is not in any way a claim about how things "really are".
What I said above applies to any macroscopic object.
This is not a useful way of viewing what is going on. The iron bar has something like $10^{25}$ atoms in it. All of them are continually interacting; the bar as a whole is continually decohering. This is not a "measurement" in any useful sense. It's just part of being a macroscopic object.
Individual atoms can interact with each other regardless of what states they are in.

I kept saying "eigenstates" as though they were properties of the atom because of position. We tried to measure positions as in the spots in the double slit. Position is the most common preferred basis. Even without any measurements by humans. Objects naturally have positions, although one can say the environment is continuously doing measurement causing decoherence. Yet still postion basis is singled out. This is why I seemed to be saying eigenstates are properties of the atom because of the self decoherence of objects.
Now refer to this.

Why do you think Einstein mean?

Since atoms don't have to form position eigenstates first before they can interact. And as you say "Individual atoms can interact with each other regardless of what states they are in.". This means they can even interact without position basis? So it's like the position basis is so we can see them? If there were no position basis, as Einstein was contemplating, does it mean atoms and molecules can still exist? They can become shapeless and not visible? This is in context to Einsteins reflections and not personal speculations.

Also, you keep saying "eigenstates" as though they were properties of the atom. They're not. They're properties of an operator, i.e., some measurement you can make on a quantum object. For example, if you measure an electron's spin in the $z$ direction, there are two states of the electron that are eigenstates of that measurement. But if you measure the spin in the $x$ direction, there are two different states of the electron that are eigenstates of that measurement.

But even the above, as I said before, assumes that you have a quantum system and a measurement that are simple enough that you can write them down. We can't do that for macroscopic objects.

(Also, saying that we "measure" the electron's spin, if all that's involved is the electron's spin degree of freedom, is really a misnomer. We pass the electron through a magnetic field that entangles its spin with its linear momentum. This is a unitary interaction and does not require anything to be observed at all. When we say we "measure" the spin, what we mean is that we have a detector, such as a piece of photographic film--a macroscopic object--placed so that we will see a spot at one of two points on the detector: which point depends on which direction the electron was moving when it came out of the magnetic field, i.e., what its linear momentum was, which the magnetic field entangled with the spin. The "result" of the measurement is actually the position of the spot--that's what we observe. We infer from that observation that the electron's spin was up or down, because we follow the chain of reasoning backwards from the spot position to the electron's momentum coming out of the magnetic field to the electron's spin that got entangled with the momentum.)

 

[PeterDonis]

Position is the most common preferred basis.

That has everything to do with human convenience, and nothing to do with the physics (as far as we know).

Objects naturally have positions

Macroscopic objects have such a small uncertainty in position that we can treat their positions classically to a very good approximation. But this does not mean your statement is true.

postion basis is singled out

No, as above, we treat macroscopic objects as having classical positions and behaving classically to a good approximation. But this has nothing to do with the "position basis" at the quantum level.

People seem to have a strong desire to interpret wave functions in the position basis, i.e., as functions on ordinary 3-dimensional space, even though, as soon as you have more than one particle, this interpretation is no longer valid. The wave function of a two-particle system is not a function on ordinary 3-dimensional space; it's a function on a 6-dimensional space, and there is no "position operator" on this space. (There are operators for "position of the first particle" and "position of the second particle", but those aren't the same thing, and even they are problematic.) The wave function on a $10^{25}$ particle system is a function on a $3 \times 10^{25}$ dimensional space.

Why do you think Einstein mean?

I would have to see the entire letter to know. Anyway, it was a letter, not a peer-reviewed paper, so I would be very careful in putting any weight on what it says.

This means they can even interact without position basis?

Interactions between atoms have nothing whatever to do with a human's choice of basis. The choice of basis is a human convenience for doing the math. The atoms don't know what basis the humans have chosen, and don't care because the basis is not there in the physics, it's only there in the math the humans do to model the physics. Don't confuse the map with the territory.

 

[PeterDonis]

If there were no position basis, as Einstein was contemplating

I don't see how what Einstein was saying in what you quoted has anything to do with the position basis, or indeed any basis.

 

[jlcd]

No, as above, we treat macroscopic objects as having classical positions and behaving classically to a good approximation. But this has nothing to do with the "position basis" at the quantum level.

Is the above statement colored by intepretation?

I have thought for that puzzling statement the whole day even when in the mall at starbucks or at midnight when waking up.

I then consulted a Ph.D. physicist about it. He thought of classical physics as an approximation derived from quantum physics. This means if for sake of discussion an object had no position basis, objects won't have any position or invisible. In your case, he thought you answered differently because you thnk of classical physics as independent of quantum physics, is this right?

Interactions between atoms have nothing whatever to do with a human's choice of basis. The choice of basis is a human convenience for doing the math. The atoms don't know what basis the humans have chosen, and don't care because the basis is not there in the physics, it's only there in the math the humans do to model the physics. Don't confuse the map with the territory.

I searched for "map territory" under your name in PF to get more details of it and I came up with the following passage in the thread "Hawking believes "God confuses us throwing dice...", why? started by someone called mario rossi. You wrote:

The reason the map-territory distinction is made is to make it clear that our physical models are distinct from the things they are trying to model. That let's us take a step back, so to speak, and keep ourselves from making commitments based on our models that might be too broad. For example, quantum physics is a model--a map: it can be used to make very accurate predictions about the results of experiments. But there are multiple, mutually inconsistent interpretations of QM, which amount to multiple, mutually inconsistent claims about exactly what kind of territory the map is modeling. Those claims can't be resolved by experiment (because all of the interpretations make the same predictions for all experimental results)

So for those who think the wave function or state vectors are the objects themselves such as Many worlders, quantum physics is both map and territory? Territory in the sense that objects are really wave functions and state vector themselves (where they are models of).

For Bohr Copenhagen who think the wave functions or state vectors are just tools to make statistical predictions. quantum physics is only map and not the territory? Here the territory is something unknown.

So when you believe positon basis has nothing to do with classical positions of objects. You were thinking in terms of the latter or Copenhagen context. While the Ph.D. expert was thinking of the former where the state vectors are the objects themselves hence the classical positions are the actual position basis themselves?

 

[Mentz114]

Is the above statement colored by intepretation?

[..]
He thought of classical physics as an approximation derived from quantum physics. This means if for sake of discussion an object had no position basis, objects won't have any position or invisible. In your case, he thought you answered differently because you thnk of classical physics as independent of quantum physics, is this right?

I don't know what your current interlocutor thinks but the extent to which classical mechanics is an approximation of quantum mechanics is fruitfully addressed by the Ehrenfest formalism. Interpretaions which adopt it assume that CM is an approximation of QM.