# I Classicality and the Correspondence Principle

#### charters

The detector is not "exit ports", it's a screen of some kind (in the original SG experiment it was photographic film) that shows spots when electrons (or whatever particles you're using; in the original SG experiment it was silver atoms with one unpaired electron) hit it. The screen has a large number of degrees of freedom that can't be kept track of, which is why it produces decoherence. Just exiting the magnetic field area, whether it's through "exit ports" or just traveling through empty space, does not, as you point out, decohere anything or even constitute a measurement.
Ok, when I said exit ports I was picturing them having two little screens that capture the electron like in the image I just linked, so I think we agree and this is just semantics. I can see what you mean from other images.

#### jlcd

Peterdonis. Neumaier and i sent replies at exactly the same time so you might have missed my reply. It happened to me. This is a question of vital import.

Right now. In the case of the cat, we don't know what pick out the alive/dead basis as the one that is physically relevant. We don't know how the quantum interaction between the cat and its environment picks out the alive/dead basis as the one that gets decohered, so that all observers will agree that the cat is either alive (in one branch) or dead (in the other branch). But in the case of spin up and down in the Stern Gerlach experiment. Why do we know how to do it?

#### A. Neumaier

In the case of the cat, we don't know what pick out the alive/dead basis as the one that is physically relevant [...] But in the case of spin up and down in the Stern Gerlach experiment. Why do we know how to do it?
In both cases, Nature picks and we describe the statistics of what it picks. Nobody knows how.

#### PeterDonis

Mentor
We don't know how the quantum interaction between the cat and its environment picks out the alive/dead basis as the one that gets decohered
There doesn't even have to be any interaction between the cat and its environment; the cat is its own "environment". The cat, all by itself, has a huge number of degrees of freedom which will decohere each other. So the cat's own internal structure is what picks out the alive/dead basis. We can't write down in detail how that works because there are way too many degrees of freedom.

In fact, even stating the cat's "preferred basis" as alive/dead is misleading. The cat's state at the classical level, i.e., after decoherence, can be specified much more precisely than just "alive" or "dead", and whether it is in fact alive or dead is assessed based on observations of multiple pieces of information at the classical level. Otherwise nobody would have been able to tell whether a cat was alive or dead until QM was discovered. In other words, "alive" and "dead" are not really orthogonal quantum states of the cat; they're names for two disjoint subspaces of the set of classical cat states, where the classical state space has many more than two degrees of freedom (but many fewer than the quantum state space).

in the case of spin up and down in the Stern Gerlach experiment. Why do we know how to do it?
We only know how to do part of it for the SG experiment, because for that part of it the number of degrees of freedom is so small. The SG magnetic field entangles spin with momentum; it's easy to write down and easy to understand. But if you ask why the detector (photographic film or whatever) decoheres in the position basis, we don't have a good answer, because, just as with the cat above, the detector has way too many degrees of freedom and we can't write down in detail how it works.

#### jlcd

There doesn't even have to be any interaction between the cat and its environment; the cat is its own "environment". The cat, all by itself, has a huge number of degrees of freedom which will decohere each other. So the cat's own internal structure is what picks out the alive/dead basis. We can't write down in detail how that works because there are way too many degrees of freedom.

In fact, even stating the cat's "preferred basis" as alive/dead is misleading. The cat's state at the classical level, i.e., after decoherence, can be specified much more precisely than just "alive" or "dead", and whether it is in fact alive or dead is assessed based on observations of multiple pieces of information at the classical level. Otherwise nobody would have been able to tell whether a cat was alive or dead until QM was discovered. In other words, "alive" and "dead" are not really orthogonal quantum states of the cat; they're names for two disjoint subspaces of the set of classical cat states, where the classical state space has many more than two degrees of freedom (but many fewer than the quantum state space).

We only know how to do part of it for the SG experiment, because for that part of it the number of degrees of freedom is so small. The SG magnetic field entangles spin with momentum; it's easy to write down and easy to understand. But if you ask why the detector (photographic film or whatever) decoheres in the position basis, we don't have a good answer, because, just as with the cat above, the detector has way too many degrees of freedom and we can't write down in detail how it works.
But 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.
But those definitions depend on being able to separate the system into the two disjoint subsystems "cat" and "cat's environment". 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.

By the arguements above. Isn't "alive" and "dead" really orthogonal quantum states of the cat. And not as you described "they're names for two disjoint subspaces of the set of classical cat states, where the classical state space has many more than two degrees of freedom (but many fewer than the quantum state space)."

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?

#### PeterDonis

Mentor
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

Mentor
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

Mentor
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

Mentor
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

"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

Mentor
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

Gold Member
2018 Award
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

Mentor
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

Mentor
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

Mentor
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

Mentor
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.

"Classicality and the Correspondence Principle"

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