Irreversibility vs reversibility

[Demystifier]

I'm personally not sure it's actually a problem. The usual way the problem is stated is that the wave function for the universe has no natural basis built into it. But different measurements correspond to physically different configurations, which means physically different wave functions (because under the MWI everything, including measuring devices, is included in the wave function). It's the difference between the wave functions that tells you which measurement is being made. You can then use that difference to pick out a basis of eigenstates for the measurement. At least, that's my personal take. But I know there is a lot of discussion of this in the literature.

Take one-particle state for example. By "wave function" do you mean $|\psi\rangle$, or do you mean $\psi(x)=\langle x|\psi\rangle$? If you mean the latter, then you have already picked one preferred basis - the position basis. If you mean the former, I will explain you the problem in the next step.

 

[Demystifier]

His equation (2) in that section leaves out the rest of the universe; his kets |live cat> and |dead cat> only describe the cat, not everything else. But if we observe the cat to be alive or dead, then our state is entangled with the cat's state (and so is the state of everything else we interact with--if not all of the universe, certainly our surrounding environment which includes a lot of stuff). So the actual pair of possible kets would be more like

|live cat>|cat observed to be alive, including everything in the environment entangled with that>

and

|dead cat>|cat observed to be dead, including everything in the environment entangled with that>

Here is the second step that I promised in the post above. Let me introduce the notation
$$|LIVE\rangle = |live\;\; cat\rangle |cat\;\; observed\;\; to\;\; be\;\; alive,\;\; including\;\; everything\;\; in\;\; the\;\; environment\;\; entangled\;\; with\;\; that\rangle$$
and similarly for $|DEAD\rangle$. Then the whole state of universe/multiverse can be written as
$$|\Psi\rangle = |LIVE\rangle + |DEAD\rangle$$
But when written in that form, one can see no entanglement. To see entanglement, one must decompose $|LIVE\rangle +|DEAD\rangle$ into a sum of factors. But mathematically, the decomposition into a sum of factors is not unique. It depends on the choice of basis. See e.g. https://arxiv.org/abs/1210.8447 Eqs. (29)-(31).

 

[PeterDonis]

In short you believe in a limbo world where cat can be dead and alive at the same time?

No. I believe (but cannot demonstrate) that the necessary "additional structure", that allows you to pick out the alive/dead basis as the one that is physically relevant, is already present in the universal wave function; it doesn't have to be added in "by hand".

 

[PeterDonis]

By "wave function" do you mean $|\psi\rangle$,

Yes, I was being somewhat sloppy in terminology (or perhaps the notion of "wave function" is somewhat sloppy as to whether it requires choosing a particular basis).

To see entanglement, one must decompose $|LIVE\rangle +|DEAD\rangle$ into a sum of factors. But mathematically, the decomposition into a sum of factors is not unique. It depends on the choice of basis.

Yes, agreed. We don't know how to extract the "additional structure" that let's us pick a basis from the wave function (or whether that's even possible at all). But we also don't know how to explain why we observe things/things get decohered in a particular basis (for cats, the alive/dead basis) if that "additional structure" is not there in the wave function. This is why I said there is an unsolved problem.

(One point that I have not raised is that the wave function is not the only "structure" present in QM; there is also the Hamiltonian, or Lagrangian if you are doing QFT. So one possibility that we have not discussed is that the "additional structure" is in the Hamiltonian, not the wave function; that the Hamiltonian of the cat, or the cat/environment system, is what picks out the alive/dead basis as the one that gets decohered.)

 

[Demystifier]

Yes, I was being somewhat sloppy in terminology (or perhaps the notion of "wave function" is somewhat sloppy as to whether it requires choosing a particular basis).

Yes, agreed. We don't know how to extract the "additional structure" that let's us pick a basis from the wave function (or whether that's even possible at all). But we also don't know how to explain why we observe things/things get decohered in a particular basis (for cats, the alive/dead basis) if that "additional structure" is not there in the wave function. This is why I said there is an unsolved problem.

(One point that I have not raised is that the wave function is not the only "structure" present in QM; there is also the Hamiltonian, or Lagrangian if you are doing QFT. So one possibility that we have not discussed is that the "additional structure" is in the Hamiltonian, not the wave function; that the Hamiltonian of the cat, or the cat/environment system, is what picks out the alive/dead basis as the one that gets decohered.)

Fine, so we agree on that. But advertisers of MWI usually point out that MWI is the best because, unlike other interpretations, it does not require any additional structure. So if it does require additional structure, just like other interpretations, then what is the true advantage of MWI over other interpretations?

 

[Blue Scallop]

His equation (2) in that section leaves out the rest of the universe; his kets |live cat> and |dead cat> only describe the cat, not everything else. But if we observe the cat to be alive or dead, then our state is entangled with the cat's state (and so is the state of everything else we interact with--if not all of the universe, certainly our surrounding environment which includes a lot of stuff). So the actual pair of possible kets would be more like

|live cat>|cat observed to be alive, including everything in the environment entangled with that>

and

|dead cat>|cat observed to be dead, including everything in the environment entangled with that>

It's the second part of each of these kets--the observer's state and the environment state including all of the other stuff that gets entangled--that picks out the basis: the observer's interaction with the cat, and the environment's interaction with them, is such that |live cat> and |dead cat> are the orthogonal states that get picked out by decoherence, just as when we measure an electron's spin about the z axis, |z spin up> and |z spin down> are the orthogonal states that get picked out by decoherence.

concering the above.. Demystifier (who is few in words) states:

Then the whole state of universe/multiverse can be written as
$$|\Psi\rangle = |LIVE\rangle + |DEAD\rangle$$
But when written in that form, one can see no entanglement. To see entanglement, one must decompose $|LIVE\rangle +|DEAD\rangle$ into a sum of factors. But mathematically, the decomposition into a sum of factors is not unique. It depends on the choice of basis. See e.g. https://arxiv.org/abs/1210.8447 Eqs. (29)-(31).

When written in $$|\Psi\rangle = |LIVE\rangle + |DEAD\rangle$$, why is there no entanglement? And to see entanglement.. what does it mean to decompose $|LIVE\rangle +|DEAD\rangle$ into a sum of factors?? Can you please give an example? Thank you!

The only difference with the cat, on the MWI view I am describing, is that in the case of the spin of an electron, we know how to make measurements in a different basis, such as spin about the x axis, in which our original eigenstates, |z spin up> and |z spin down>, become superpositions. But we don't know how to measure a cat in any basis in which the eigenstates are superpositions of |live cat> and |dead cat>; and there might not even be any such basis, because the cat is a macroscopic object containing something like $10^{25}$ atoms, and even if nobody observes the cat, all those atoms are interacting with each other all the time, and those interactions, as far as we can tell, already pick out |live cat> and |dead cat> as the basis of states which get decohered. So it might not even be possible to make a measurement of a cat that would pick out a basis of superpositions of |live cat> and |dead cat>.
Remember that I said "according to Schwindt". I don't agree with him on this point.
No, I didn't; I only said that some other author claimed it was a problem. See above.

As far as which problem it is, I don't think it's that important to try to make fine distinctions in this regard. The "factorization problem" and the "preferred basis problem" are just aspects of the same thing. Figuring out how to pick out subsystems like cats in the overall wave function of the universe requires you to do basically the same thing as figuring out which basis decoherence will actually occur in.
We don't know "the whole truth". That's why I said I was giving my own personal take. This is an unsolved problem and an open area of research. The best overall description of it might be figuring out how to apply QM on a macroscopic scale.

 

[PeterDonis]

When written in
$$
|\Psi\rangle = |LIVE\rangle + |DEAD\rangle
$$,

why is there no entanglement?

Because this formulation just looks at two different possible states of the whole system, the $LIVE$ state and the $DEAD$ state, without saying anything about how (or whether) the whole system can be decomposed into subsystems. And as a whole system, there is no entanglement; there is just a superposition of two different states. The entanglement is only present if we decompose the system into subsystems.

what does it mean to decompose $|LIVE\rangle +|DEAD\rangle$ into a sum of factors??

Just rewrite it using the definitions of $|LIVE\rangle$ and $|DEAD\rangle$ that Demystifier gave, which express those states 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.

 

[Blue Scallop]

I originally inquired: "I thought the answer was known.. that because the dead cat and live cat has entangled wit the environment subspaces in different ways.. the dead and live cat can no longer form superposition" and you answered:

This is not "known" in the sense that we have proven it mathematically for systems like cats. We can only do that in the case of very simple systems.

You said we can only do it for very simple systems like spin 1/2 particles. Of course a cat with 10^25 microscopic degree of freedom is complex. What is the simplest system where we can still do it? like maybe 10 atom particles?

You wrote: "What we would like to be able to show, but don't know how to, is how the interaction--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)."

Of course we must not start with cats. But with simplest system that you can call macroscopic, then we can perhaps know how the quantum interaction, between the object (that is in the boundary of very simple and complex) and its environment picks out the alive/dead basis as the one that gets decohered. What object could that be? that we can still track in labs or even mathematically?

Not quite. The decoherence happens regardless of which basis we choose to describe things in. But how the decoherence happens depends on how the process is physically set up.

Let's go back to the simple spin measurement of a spin-1/2 particle. Suppose we are using a Stern-Gerlach device, which is basically an inhomogeneous magnetic field that causes the two spin eigenstates to move in opposite directions. If we orient the field in the z direction, then we are measuring spin about the z axis, and the two eigenstates will move up or down, respectively. So this device entangles the spin state of the particle with the momentum of the same particle (the momentum is then the "measuring device" in terms of our previous formulations). Mathematically, we end up with a state like

$$
a \vert z+ \rangle \vert \uparrow \rangle + b \vert z- \rangle \vert \downarrow \rangle
$$

where the $+$ and #-## signs are the spin eigenstates and the arrows are the directions of the particle's momentum after it comes out of the device.

Now, what is this device actually doing? Well, it entangles a particular pair of spin eigenstates with a particular pair of momentum eigenstates. But which spin eigenstates and which momentum eigenstates get entangled depends on the direction in which the device is oriented: the key is that it entangles spin eigenstates and momentum eigenstates that are pointed in the same directions (in the sense of the spin axis and the momentum directions being aligned). And that entanglement determines how things get decohered.

So it isn't really that the device itself "picks out a particular basis"; it's that it picks out a particular entanglement process: a particular way of entangling the spin and momentum of a particle. We "pick out a particular basis" by choosing to orient the device in a particular direction. Once that choice is made, everything else follows.

 

[PeterDonis]

What is the simplest system where we can still do it?

I don't know. I'm not familiar enough with the literature to know what specific models have been tried and what size quantum systems they have been tried on.

 

[Blue Scallop]

This is not "known" in the sense that we have proven it mathematically for systems like cats. We can only do that in the case of very simple systems.
Not quite. The decoherence happens regardless of which basis we choose to describe things in. But how the decoherence happens depends on how the process is physically set up.

Let's go back to the simple spin measurement of a spin-1/2 particle. Suppose we are using a Stern-Gerlach device, which is basically an inhomogeneous magnetic field that causes the two spin eigenstates to move in opposite directions. If we orient the field in the z direction, then we are measuring spin about the z axis, and the two eigenstates will move up or down, respectively. So this device entangles the spin state of the particle with the momentum of the same particle (the momentum is then the "measuring device" in terms of our previous formulations). Mathematically, we end up with a state like

$$
a \vert z+ \rangle \vert \uparrow \rangle + b \vert z- \rangle \vert \downarrow \rangle
$$

where the $+$ and #-## signs are the spin eigenstates and the arrows are the directions of the particle's momentum after it comes out of the device.

Now, what is this device actually doing? Well, it entangles a particular pair of spin eigenstates with a particular pair of momentum eigenstates. But which spin eigenstates and which momentum eigenstates get entangled depends on the direction in which the device is oriented: the key is that it entangles spin eigenstates and momentum eigenstates that are pointed in the same directions (in the sense of the spin axis and the momentum directions being aligned). And that entanglement determines how things get decohered.

So it isn't really that the device itself "picks out a particular basis"; it's that it picks out a particular entanglement process: a particular way of entangling the spin and momentum of a particle. We "pick out a particular basis" by choosing to orient the device in a particular direction. Once that choice is made, everything else follows.

In the above.. is your Stern-Gerlach device the system or apparatus? How does your example work when there is system, apparatus and environment? It seems you are using system (Stern-Gerlach device) and environment only so I'm thinking how to relate system, apparatus and environment. In most example of solution to preferred basis problem like Einselection, it uses example of environment, system and apparatus. For example in the original 1981 Physical Review D article "Pointer basis of quantum apparatus: Into what mixture does the wave packet collapse", Zurek talked:

"In real-world apparatuses the role of the "additional apparatus a" or, equivalently, the role of the "environment S" is usually played by part of the physical setup of the apparatus itself. For, what we have called "the apparatus a" is just a small part of the complete setup, which can be fully described by a state vector in nondegenerate Hilbert space spanned by a set of basis vectors {|Ap>}. In contrast to this simplified model, setups of real-world apparatuses are much more complicated and demand extensive product spaces to allow for a complete description. Out of this vast product Hilbert space we have singled out just one subspace, claiming it describes the "pointer," and hence epitomizes the apparatus itself. The rest of the apparatus setup described by the remaining parts of the product space - by far larger than the subspace used to represent the apparatus proper - describes then a natural immediate environment S. As long as the coupling between the apparatus a and it's "built-in" environment allows for the existence of the pointer basis, the apparatus will be able to record the corresponding relative states of the to-be-measured quantum system S. Therefore, part of the apparatus setup, the built-in environment, can be said to act as an interface between the apparatus proper a and the rest of the world".

 

[Blue Scallop]

by the way.. the abstract of the paper above is: " The form of the interaction Hamiltonian between the apparatus and its environment is sufficient to determine which observable of the measured quantum system can be considered "recorded" by the apparatus. The basis that contains this record—the pointer basis of the apparatus—consists of the eigenvectors of the operator which commutes with the apparatus-environment interaction Hamiltonian. Thus the environment can be said to perform a nondemolition measurement of an observable diagonal in the pointer basis."

I thought the apparatus was enough to choose the preferred basis.. but why is the environment involved.. any example? Thanks!

 

[PeterDonis]

is your Stern-Gerlach device the system or apparatus?

It's actually neither. The "system" in this case is the spin of the electron, and the "apparatus" (which gets entangled with the system by the measurement process) is the momentum of the electron. The Stern-Gerlach device is really just a way of physically realizing the unitary operator that entangles the system with the apparatus; the "state" of the device itself is not even modeled. (In a more complete model, you could view the device's state as part of the environment, but since nothing in the device gets entangled in any significant way with either the system or the apparatus, it doesn't really matter.)

How does your example work when there is system, apparatus and environment?

You would add to the model the different states of the environment that, when entangled with the system and the apparatus, show which measurement result the apparatus is displaying. In the case of the Stern-Gerlach device, these would be states of, for example, air molecules, photons, neurons in people's brains, etc., all showing which direction (up or down) the electron's momentum was pointing.

 

[Blue Scallop]

It's actually neither. The "system" in this case is the spin of the electron, and the "apparatus" (which gets entangled with the system by the measurement process) is the momentum of the electron. The Stern-Gerlach device is really just a way of physically realizing the unitary operator that entangles the system with the apparatus; the "state" of the device itself is not even modeled. (In a more complete model, you could view the device's state as part of the environment, but since nothing in the device gets entangled in any significant way with either the system or the apparatus, it doesn't really matter.)
You would add to the model the different states of the environment that, when entangled with the system and the apparatus, show which measurement result the apparatus is displaying. In the case of the Stern-Gerlach device, these would be states of, for example, air molecules, photons, neurons in people's brains, etc., all showing which direction (up or down) the electron's momentum was pointing.

In Zurek article mentioned above it is said "Moreover, everyday experience convinces us that the choice of "what has this apparatus measured" cannot be made arbitrarily, long after the apparatus-system interaction has taken place, as Eqs (1.1) - (1.3) would seem to imply. The "real-world" apparatuses constructed to measure momentum do measure momentum and not the conjugate observable, position.
A question can then be raised: What does, in the real-world apparatuses, determine this apparently unique pointer basis {|Ap>}, which records the corresponding relative states {|p>} of the system?
Interaction with the environment is the key feature that distinguishes the here-proposed model of the apparatus from the manifestly quantum systems. We argue that the apparatus cannot be observed in a superposition of the pointer-basis states because its state vector is continuously collapsed. It is the "monitoring" of the apparatus by the environment which results in the apparent reduction of the wave packet. Correlations between states of the pointer basis and corresponding relative states of the system are nevertheless preserved... "

Something quite confused me. Was Zurek referring to Everett unitary wave functions where the environment is entangled with the apparatus so the for example spin 1/2 particles have the Up and Down separately form entangled wit the apparatuses and environments (causing the Everett split as you mentioned in related thread) or was Zurek referring to single world where apparatus is classical? In the double slit, the system is the electron emitted from source, and the apparatus is the physical slits right? But the double slits are sufficient to dictate how the electron behaves. Zurek has to include the environment and it is more complex than what you described as simply "In the case of the Stern-Gerlach device, these would be states of, for example, air molecules, photons, neurons in people's brains, etc., all showing which direction (up or down) the electron's momentum was pointing". Zurek was not talking about this. Was he basically saying the physical slits splitted to each electron as well as the environment splitted (or form separate entangled with each branch of the physical slits and electron?

 

[PeterDonis]

Was Zurek referring to Everett unitary wave functions where the environment is entangled with the apparatus so the for example spin 1/2 particles have the Up and Down separately form entangled wit the apparatuses and environments (causing the Everett split as you mentioned in related thread) or was Zurek referring to single world where apparatus is classical?

Zurek's analysis is compatible with both interpretations (i.e., no collapse interpretations like MWI and collapse interpretations). He's not always clear about that, and I think he actually prefers collapse interpretations, but nothing in his actual math precludes no collapse interpretations, as far as I can see.

In the double slit, the system is the electron emitted from source, and the apparatus is the physical slits right?

No, the "apparatus" in Zurek's terminology is the screen that records where each electron lands after passing through the slits. The slits are what determine the Hamiltonian that gets applied to the electron's starting state vector to give the state vector that gets entangled with that of the apparatus (with each term in the entangled state being a product of the electron being in a particular position on the screen and the screen recording an electron landing at that same position).

the double slits are sufficient to dictate how the electron behaves

But not to dictate how the electron gets entangled with the apparatus (the screen), or how the apparatus then gets entangled with the environment. The slits have nothing to do with any of that.

Zurek has to include the environment and it is more complex than what you described as simply "In the case of the Stern-Gerlach device, these would be states of, for example, air molecules, photons, neurons in people's brains, etc., all showing which direction (up or down) the electron's momentum was pointing". Zurek was not talking about this.

He doesn't explicitly describe what is contained in the environment, but what he's referring to as the "environment" is basically what I described.

 

[Blue Scallop]

Zurek's analysis is compatible with both interpretations (i.e., no collapse interpretations like MWI and collapse interpretations). He's not always clear about that, and I think he actually prefers collapse interpretations, but nothing in his actual math precludes no collapse interpretations, as far as I can see.
No, the "apparatus" in Zurek's terminology is the screen that records where each electron lands after passing through the slits. The slits are what determine the Hamiltonian that gets applied to the electron's starting state vector to give the state vector that gets entangled with that of the apparatus (with each term in the entangled state being a product of the electron being in a particular position on the screen and the screen recording an electron landing at that same position).
But not to dictate how the electron gets entangled with the apparatus (the screen), or how the apparatus then gets entangled with the environment. The slits have nothing to do with any of that.
He doesn't explicitly describe what is contained in the environment, but what he's referring to as the "environment" is basically what I described.

Zurek said: "We argue that the apparatus cannot be observed in a superposition of the pointer-basis states because its state vector is continuously collapsed. It is the "monitoring" of the apparatus by the environment which results in the apparent reduction of the wave packet."

What does he mean it is the "monitoring" of the apparatus by the environment which results in the apparent reduction of the wave packet??

 

[Blue Scallop]

No. I believe (but cannot demonstrate) that the necessary "additional structure", that allows you to pick out the alive/dead basis as the one that is physically relevant, is already present in the universal wave function; it doesn't have to be added in "by hand".

Einselection (https://en.wikipedia.org/wiki/Einselection) is supposed to be the "additional structure" already present in the universal wave function that doesn't need to be added by hand (which Demystifier hasn't seemed to address) and the most powerful counter-Einselectioner is Kastner. She argued Einselection is not even enough and can't take off. Do you have any critical reasoning or argument that can counter Kastner?

http://philsci-archive.pitt.edu/10757/1/Einselection_and_HThm_Final.pdf

When I'd share about Einselection in a hall telling how it can select the Preferred Basis that doesn't have to by added by hand. And there is someone who would mention Kastner arguments. I want to be ready what to say.

 

[PeterDonis]

What does he mean it is the "monitoring" of the apparatus by the environment which results in the apparent reduction of the wave packet??

He means the constant interaction of the apparatus with the environment which entangles the states of the two.

Do you have any critical reasoning or argument that can counter Kastner?

No. This is an unsolved problem. Kastner does not prove that something like Zurek's scheme is impossible; she only proves that he has not proven it is possible. In other words, it's still an open question.

 

[Blue Scallop]

I said that in practice it can only happen if there is no decoherence.
In principle any unitary evolution can be reversed. That is inherent in the definition of unitary evolution.

Going back to this reversibility thing. When glass falls to floor.. it can't go up by itself and reform because of entropy. In quantum, stevendaryl mentioned about this Entropy angle yet Tashi countered in message #19 there was no entropy in quantum system... and the two haven't followed up their discussions.

I seemed unable to disentangle Born Rule from this reversibility thing.

But first thing first. You said in principle unitary evolution can be reversed. Did you mean in practice it can't happen due to Entropy? And broken glasses can't reform being the same reason unitary evolution can't be reversed in pactice? But in principle broken glasses can reform if you can reverse entropy in the same way unitary evolution can be reversed by reversing entropy?

Or is the reason unitary evolution can't be reversed in practice because you can't tract the many degrees of freedom in the environment and disentangled the wave function? Here we assume the particle is not destroyed. I assume this reasoning doesn't work if the electron is destroyed like in the double slit detection event where it is destroyed (same situation of Entropy unable to reverse burned paper back to normal)

Or in practice unitary evolution can't be reserved due to the former case of not able to reverse entropy or in the latter case simply not able to tract the environment and find where the two entangled pairs is located (and simply disentangling each one manually without taking into account entropy)?

Now connecting this to Born rule. It is random where the electron will hit the detector or in situation where the particle is not destroyed. So even if you can track the particles in the environment and reverse all the entanglement.. how do you know which branch is entangled to which branch or how do you reverse the Born rule (reversing random thing you still get random)?

 

[PeterDonis]

You said in principle unitary evolution can be reversed. Did you mean in practice it can't happen due to Entropy?

In practice it can't happen for large systems because we can't keep exact track of all of the degrees of freedom. That is generally taken to be related to entropy, yes: there is information about the exact microstate of the system that we do not have.

However, we have to be careful about what "reversing" actually means in this context. Consider the broken glass. What would it mean to "reverse" that process? We would have to be able to take every single little piece of glass and give it exactly the reverse of the motion it had while falling to the floor, so the pieces would come together in exactly the right way: and then we would have to take each of the individual atoms in each of the broken surfaces and re-attach them in exactly the right way. In other words, we would have to be able to exert a kind of detailed control over each individual atom that we simply do not know how to exert, at least not with our current technology. So even if we did know the exact microstate of the broken glass, it wouldn't help because we don't know how to control all the pieces and all the atoms the right way to "unbreak" it.

Trying to reverse the unitary evolution of any large system will be the same sort of thing: even knowing the exact final microstate of system plus apparatus plus environment (for example, cat plus everything else) won't help because we won't be able to control all the individual quantum degrees of freedom in the right way. So it's not just a matter of not knowing the exact state. The concept of "entropy" doesn't really include all that, at least not as it's usually defined.

 

[Blue Scallop]

d

In practice it can't happen for large systems because we can't keep exact track of all of the degrees of freedom. That is generally taken to be related to entropy, yes: there is information about the exact microstate of the system that we do not have.

However, we have to be careful about what "reversing" actually means in this context. Consider the broken glass. What would it mean to "reverse" that process? We would have to be able to take every single little piece of glass and give it exactly the reverse of the motion it had while falling to the floor, so the pieces would come together in exactly the right way: and then we would have to take each of the individual atoms in each of the broken surfaces and re-attach them in exactly the right way. In other words, we would have to be able to exert a kind of detailed control over each individual atom that we simply do not know how to exert, at least not with our current technology. So even if we did know the exact microstate of the broken glass, it wouldn't help because we don't know how to control all the pieces and all the atoms the right way to "unbreak" it.

Trying to reverse the unitary evolution of any large system will be the same sort of thing: even knowing the exact final microstate of system plus apparatus plus environment (for example, cat plus everything else) won't help because we won't be able to control all the individual quantum degrees of freedom in the right way. So it's not just a matter of not knowing the exact state. The concept of "entropy" doesn't really include all that, at least not as it's usually defined.

Ok. Thanks.. the above is very clear. To make my questions complete. Whenever you hear they say decoherence can be reversed in principle in MWI or unitary evolution. Does it mean all branches need to be reversed at same time. For example. Supposed there is another branch where Clinton won the election and in this branch it was Trump. To reverse the unitary evolution.. can we just reverse Trump branch without affecting Clinton branch or do all branches have to be reversed at same time when they are talking about reversing is possible in principle?

 

[PeterDonis]

Whenever you hear they say decoherence can be reversed in principle in MWI or unitary evolution. Does it mean all branches need to be reversed at same time.

Obviously, since they were all produced by unitary evolution, reversing the unitary evolution will reverse all of them.

 

[Blue Scallop]

Obviously, since they were all produced by unitary evolution, reversing the unitary evolution will reverse all of them.

Ok. Let me ask this critical question here instead of making another thread as don't want to belabor it (and want to rest next week from sleepless nights thinking about this all). Zurek mentions that:

"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"

My inquiry is, if other branches are just information and not really there.. are they all still called Unitary?? And can you still reverse all branches (that includes the real one and even those Unobserved branches that "can be regarded as events potentially consistent with the initially available information that did not happen"?

 

[PeterDonis]

if other branches are just information and not really there

Then we are not talking about unitary evolution. Unitary evolution requires that all of the branches are really there. Any interpretation where they are not all really there requires unitary evolution to be violated at some point in the process.