Irreversibility vs reversibility

[Blue Scallop]

Decoherence is when the system is entangled with the environment irreversibile...

But when it is reversible.. is it still called Decoherence?

However, the universe is said to be a closed system. Does the irreversibility in decoherence means it is just our ignorance that we can't track it. For example. In the ocean. It is chaotic, when a big boat surfs it.. the wave disturbance it bestowed to the water is complex and our ignorance can't make us track all the wave interferences of the boat and the ocean. Is this also the case in Decoherence where we can't track all the massive degrees of freedom of the environment hence we call it irreversible? But like the ocean which in principle still has all the wave interferences there and in principle reversible.. is this also the case in environmental decoherence where the universe in principle still can keep tract of all degrees of freedom and hence in principle reversible?

 

[Demystifier]

Yes, like the ocean, it's reversible in principle but irreversible in practice.

 

[Blue Scallop]

Yes, like the ocean, it's reversible in principle but irreversible in practice.

But there must be a new degree of freedom. So my ballpoint can still be in superposition of left and right.. only the information is in the environment. So from Noether Theorem.. whenever something is conserved.. there is a new degree of freedom. What is that new degree of freedom in the environment? Or something along this line...

 

[Demystifier]

What is that new degree of freedom in the environment?

States of each atom of the environment. Many atoms means many degrees of freedom.

 

[Blue Scallop]

States of each atom of the environment. Many atoms means many degrees of freedom.

No relation to gauge invariance? Remember electromagnetic field came from U(1) local gauge invariance.. is there no corresponding symmetry in the quantum? And why is that? Thank you.

 

[hilbert2]

Yes, like the ocean, it's reversible in principle but irreversible in practice.

A good way to demonstrate why some processes are practically irreversible is to consider a simple heat conduction problem: suppose there's a thermally insulated 1D object between endpoints x=0 and x=L, and the temperature field T(x,t) on that interval obeys the heat equation

$\frac{\partial T}{\partial t} = c\frac{\partial^2 T}{\partial x^2}$.

If the initial temperature field is Gaussian: $T(x,0) = Ce^{-a(x-L/2)^2}$, it is possible to calculate the temperature distribution $T(x,t')$ at any later time $t'$, and the distribution approaches a constant: $T(x,t) \rightarrow C$, when $t \rightarrow \infty$. However, if you try to do that other way around, trying to calculate $T(x,0)$ from $T(x,t')$ where t' is very large, you'd have to know the function $T(x,t')$ as a function of x to a very large number of significant figures to even see that it deviates from a constant distribution at all, let alone deduce what the distribution has been at some much earlier time. So, here we see that the idea of irreversibility is that you'd need to know the state of a system with unrealistic accuracy to be able to calculate what the state was before the irreversible process.

 

[Demystifier]

No relation to gauge invariance? Remember electromagnetic field came from U(1) local gauge invariance.. is there no corresponding symmetry in the quantum? And why is that? Thank you.

There is gauge invariance in quantum theory, but I don't see how is that relevant to (ir)reversibility.

 

[Blue Scallop]

Demystifer stated that like the ocean, decoherence is reversible in principle but irreversible in practice

Although Decoherence is reversible in Bohmian Mechanics, MWI. Decoherence is Irreversible in Copenhagen... is this correct folks?

Now time is symmetric in quantum mechanics. Using MWI, can you time reverse the Universal Wave function and make the dead cat become alive again? Is this possible in principle but only In practice??

I think in Copenhagen it is not possible to bring dead cats back to life.. I'm not sure in Bohmian,, but in MWI.. is this possible since the Universal Wave Function is time symmetric?

Or what I'm asking is whether when branches in MWI have occurred.. whether you can initiate global time symmetric principle universally and reverse the universal wave function so the branches can revert back to original before they became two.

I think this is a question about MWI that Demystifier who is a Bohmian may not be able to answer so I'm inviting others to give their feedback. Thanks!

 

[Stephen Tashi]

The following two definitions of "reversible" appear to be different. Is there an argument that they are equivalent?

1)To say a process is reversible means that the previous states of the process can be deduced from the current state of the process.

2) To say a process is reversible means that it is physically possible to have another process whose states are those of the first process, but taking place in reverse order as time passes.

 

[Blue Scallop]

The following two definitions of "reversible" appear to be different. Is there an argument that they are equivalent?

1)To say a process is reversible means that the previous states of the process can be deduced from the current state of the process.

2) To say a process is reversible means that it is physically possible to have another process whose states are those of the first process, but taking place in reverse order as time passes.

You have made me think clearer. I was asking this.

After collapse (or branching in MWI). The wave function that starts evolving deterministically again after it is NOT the same as the wave function that evolved deterministically to the state just before the collapse (or branching). But they say time is symmetric in QM. Does this symmetric time means you can reverse the wave function from the state after the collapse (branching) to the stae prior the collapse (or branching). Or does QM time symmetry only work for the same wave function? But then in universal wave function.. can't we say the wave function that starts evolving deterministically again after the collapse (or branching) IS the same as the wave function that evolved deterministically to the state just before the collapse (or branching).

And what is the connection of time reversibility in QM to Demystifier statement that decoherence is not irreversible in principle? Thanks!

 

[stevendaryl]

The following two definitions of "reversible" appear to be different. Is there an argument that they are equivalent?

1)To say a process is reversible means that the previous states of the process can be deduced from the current state of the process.

2) To say a process is reversible means that it is physically possible to have another process whose states are those of the first process, but taking place in reverse order as time passes.

That's a good point. Certainly it's conceivable to have a physics where those two are not the same. For example, if there were a "time" variable that incremented by 1 each second, then that would be irreversible in the sense of 2) but not 1).

 

[PeterDonis]

But they say time is symmetric in QM.

More precisely, unitary evolution is time reversible in QM. So in a no collapse interpretation like the MWI, where it's all unitary evolution, yes, you can in principle reverse the branching. (Remember that all of the branches of the wave function are still there, so all you're doing is reversing the unitary operator that entangles the state of the measuring device with the state of the measured system.) Note that this is true even in the presence of decoherence; decoherence, as Demystifier said, is not irreversible in principle, because it's just more unitary evolution that entangles more things (degrees of freedom in the environment) with the measured system.

But in collapse interpretations, wave function collapse is not a unitary operation, so it can't be reversed. The problem is that, even though decoherence is reversible in principle, it isn't in practice because there are way too many degrees of freedom to keep track of in the environment. So there's no way for us to tell, experimentally, the difference between decoherence without collapse, and collapse.

 

[stevendaryl]

And what is the connection of time reversibility in QM to Demystifier statement that decoherence is not irreversible in principle? Thanks!

I think that they are very closely related, if not the same thing.

To illustrate classical irreversibility, imagine dropping a ball onto the floor in a closed room. The ball will bounce around but lose energy until eventually it comes to rest on the floor. That's irreversible in both of @Stephen Tashi's senses: (1) Seeing a ball on the floor, there is no way to figure out that it was once dropped at a particular location from a particular height. (2) The reverse transition never happens. It's never the case that a ball that is initially on the floor suddenly starts bouncing.

So why is that irreversible? The simple answer is that things tend to run down, and bouncing balls tend to lose energy. But that's an incomplete answer. The ball might be losing energy, but energy is conserved. So even though the ball is losing mechanical energy, that energy goes somewhere: into heating the ball or into heating the floor, or into vibrations in the floor. Why does energy tend to flow from the ball to the floor and into heat? The classical statistical mechanics answer is entropy: There is only one way for a ball to have kinetic energy, but there is an astronomical number of ways to distribute that energy among the vibrations of the molecules making up the ball and the floor. So the odds are enormously in favor of the energy finding its way into vibrations than it staying in the form of kinetic energy of the ball.

There is a similar irreversibility at work in quantum mechanics. If you start with a hydrogen atom with its electron in an excited state, the electron will tend to radiate away energy and fall into the ground state. But why? Why is there such a tendency? You can reason classically in this case, and say that the entropy of the electromagnetic field is vastly greater than the entropy of a hydrogen atom, so it's entropically favorable for the electron to give up its energy to the electromagnetic field (in other words, radiate). However, if you treat both the atom and the electromagnetic field quantum-mechanically, then what happens is that with time, the atom becomes entangled with the electromagnetic field. Which is what decoherence is about.

 

[Blue Scallop]

More precisely, unitary evolution is time reversible in QM. So in a no collapse interpretation like the MWI, where it's all unitary evolution, yes, you can in principle reverse the branching. (Remember that all of the branches of the wave function are still there, so all you're doing is reversing the unitary operator that entangles the state of the measuring device with the state of the measured system.) Note that this is true even in the presence of decoherence; decoherence, as Demystifier said, is not irreversible in principle, because it's just more unitary evolution that entangles more things (degrees of freedom in the environment) with the measured system.

Can you please give an example of reversing the branching in MWI? Is double slit or spin-1/2 particle better example of it? In the double slit, say the screen entangled with the electron giving the detection hit. So by reversing the branching. Can you make the hits disappeared and how do you do that??

But in collapse interpretations, wave function collapse is not a unitary operation, so it can't be reversed. The problem is that, even though decoherence is reversible in principle, it isn't in practice because there are way too many degrees of freedom to keep track of in the environment. So there's no way for us to tell, experimentally, the difference between decoherence without collapse, and collapse.

 

[PeterDonis]

Can you please give an example of reversing the branching in MWI?

In practice, the only operations we can actually reverse are the ones where decoherence has not happened; for example, qubit operations in quantum computing. But these are the ones where even collapse interpretations say there is no collapse--because collapse is not reversible.

So neither a standard spin-1/2 particle measurement nor the double slit experiment are practical examples of reversing branching in MWI, because they both involve decoherence, and therefore we cannot reverse them in practice.

 

[Blue Scallop]

In practice, the only operations we can actually reverse are the ones where decoherence has not happened; for example, qubit operations in quantum computing. But these are the ones where even collapse interpretations say there is no collapse--because collapse is not reversible.

So neither a standard spin-1/2 particle measurement nor the double slit experiment are practical examples of reversing branching in MWI, because they both involve decoherence, and therefore we cannot reverse them in practice.

In message #12, you wrote that:

More precisely, unitary evolution is time reversible in QM. So in a no collapse interpretation like the MWI, where it's all unitary evolution, yes, you can in principle reverse the branching. (Remember that all of the branches of the wave function are still there, so all you're doing is reversing the unitary operator that entangles the state of the measuring device with the state of the measured system.) Note that this is true even in the presence of decoherence; decoherence, as Demystifier said, is not irreversible in principle, because it's just more unitary evolution that entangles more things (degrees of freedom in the environment) with the measured system.

You wrote earlier that in MWI, where it's all unitary evolution, one can in principle reverse the branching.. even in the presence of decoherence as your emphasized. But in last message you have written that it can only happen if there is no decoherence.

However in principle you seemed to say it can happen. Can you give an example where you can reverse the unitary evolution even in presence of decoherence (in MWI) (in principle)?

 

[stevendaryl]

Can you please give an example of reversing the branching in MWI?

Decoherence reversing is almost exactly analogous to entropy reversing. If you have a tiny number of particles bouncing around inside a container, the entropy can go up and down, but if you have 10^{23} particles, you'll never see it go down. Decoherence basically is just entanglement involving an astronomical number of particles. For a small number of degrees of freedom, you can certainly witness entanglement reversing, but you'll never a macroscopic number of degrees of freedom disentangle itself.

 

[stevendaryl]

Okay, I realize that there is a bit of confusion about entanglement and decoherence. On the one hand, we say that it is irreversible. On the other hand, if it's really irreversible, then we shouldn't ever see any evidence of superpositions, at all, since everything should be maximally entangled by now.

So there is something to be explained, which is: How do we ever see unentangled systems?

If you assume wave function collapse, then that's sufficient to explain how things get unentangled:

You have an electron whose spin state is entangled with some other subsystem as follows

$|\Psi\rangle = \alpha |u\rangle |U\rangle + \beta |d\rangle |D\rangle$

where the electron's spin state is $|u\rangle$ or $|d\rangle$ and $|U\rangle$ and $|D\rangle$ are states of the rest of the other subsystem (maybe a measuring device).

You perform a measurement of the spin and find that it is spin-up. Then according to the collapse interpretation, the composite system is in the state

$|\Psi'\rangle = |u\rangle |U\rangle$

which is a disentangled state.

Without invoking collapse, you can get effective disentanglement by simply restricting your attention to the first component of the superposition. How can you get away with that? That's sort of a deep question.

 

[Stephen Tashi]

Decoherence reversing is almost exactly analogous to entropy reversing. If you have a tiny number of particles bouncing around inside a container, the entropy can go up and down, but if you have 10^{23} particles, you'll never see it go down.

The meaning of that, by the intuitive definition of entropy, is clear. However, technically, a specific number of particles with specific positions and velocities has no defined entropy - correct? Only "ensembles" of systems have a defined entropy and only ensembles of systems in equilibrium have a defined thermodynamic entropy. To have a Shannon type of entropy, we need to be talking about a probability distribution. So perhaps quantum mechanics can supply the probabilistic model for a specific set of particles (?)

 

[Blue Scallop]

Okay, I realize that there is a bit of confusion about entanglement and decoherence. On the one hand, we say that it is irreversible. On the other hand, if it's really irreversible, then we shouldn't ever see any evidence of superpositions, at all, since everything should be maximally entangled by now.

So there is something to be explained, which is: How do we ever see unentangled systems?

If you assume wave function collapse, then that's sufficient to explain how things get unentangled:

You have an electron whose spin state is entangled with some other subsystem as follows

$|\Psi\rangle = \alpha |u\rangle |U\rangle + \beta |d\rangle |D\rangle$

where the electron's spin state is $|u\rangle$ or $|d\rangle$ and $|U\rangle$ and $|D\rangle$ are states of the rest of the other subsystem (maybe a measuring device).

You perform a measurement of the spin and find that it is spin-up. Then according to the collapse interpretation, the composite system is in the state

$|\Psi'\rangle = |u\rangle |U\rangle$

which is a disentangled state.

Without invoking collapse, you can get effective disentanglement by simply restricting your attention to the first component of the superposition. How can you get away with that? That's sort of a deep question.

But restricting your attention to the first component of the superposition is using the concept of tracing out.. but tracing out automatically uses collapse, is it not.. so you invoke collapse by simply tracing out in the density matrix. So you can't say "without invoking collapse"..

 

[Blue Scallop]

Decoherence reversing is almost exactly analogous to entropy reversing. If you have a tiny number of particles bouncing around inside a container, the entropy can go up and down, but if you have 10^{23} particles, you'll never see it go down. Decoherence basically is just entanglement involving an astronomical number of particles. For a small number of degrees of freedom, you can certainly witness entanglement reversing, but you'll never a macroscopic number of degrees of freedom disentangle itself.

But if you can couple it to a negative entropy something.. you can reverse it. For example. in Biology.. our natural state is toward positive entropy.. but we have ATP in our cells that reverse the positive entropy. Now if the state vector is part of some kind of programming.. then you can reverse it by simply a program subroutine that can reverse the unitary operator and hence making macroscopic number of degrees of freedom disentangle itself. In other words. You can reverse the branching and rebranch it. You agree with this.. yes?

 

[PeterDonis]

in last message you have written that it can only happen if there is no decoherence

I said that in practice it can only happen if there is no decoherence.

Can you give an example where you can reverse the unitary evolution even in presence of decoherence

In principle any unitary evolution can be reversed. That is inherent in the definition of unitary evolution.

 

[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.

Ok. You haven't commented about the so called Preferred Basis problem in MWI yet.

It is mentioned that "In modern literature it is often claimed that the preferred basis is provided by decoherence.
However, decoherence requires a split of system into subsystems – the measured
system and the environment. On the other hand, if $|\Psi\rangle$ is all what exists, then such a
split is not unique. Therefore, MWI claiming that $|\Psi\rangle$ is all what exists cannot resolve
the basis problem, and thus cannot define separate worlds."

Can you please give an actual example of what this means? Thanks!

 

[PeterDonis]

You haven't commented about the so called Preferred Basis problem in MWI yet.

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.

It is mentioned that

Please give a link to what you are quoting from.

 

[Blue Scallop]

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.
Please give a link to what you are quoting from.

It's in section 3.3 of Demystifier's https://arxiv.org/abs/1703.08341

I'm trying to understand his point of view from that of Hobba. Demystifier belives it is a problem. While Hobba doesn't want to believe it. I'm wondering if it's because Hobba believes more in the Ensemble Interpretation where measuring devices are classical hence set the preferred basis. In MWI, nothing sets the preferred basis. Is the so called Factorization problem the same as preferred basis problem in MWI? Please comment on Demystifier punchline:

"In a nutshell, the argument is this:
To define separate worlds of MWI, one needs a preferred basis, which is an old well-known problem of MWI. In modern literature, one often finds the claim that the basis problem is solved by decoherence. What J-M Schwindt points out is that decoherence is not enough. Namely, decoherence solves the basis problem only if it is already known how to split the system into subsystems (typically, the measured system and the environment). But if the state in the Hilbert space is all what exists, then such a split is not unique. Therefore, MWI claiming that state in the Hilbert space is all what exists cannot resolve the basis problem, and thus cannot define separate worlds. Period! One needs some additional structure not present in the states of the Hilbert space themselves.

As reasonable possibilities for the additional structure, he mentions observers of the Copenhagen interpretation, particles of the Bohmian interpretation, and the possibility that quantum mechanics is not fundamental at all."

Why is it a problem how to split the system into subsystems (typically, the measured system and the environment) in MWI? In the thread https://www.physicsforums.com/threads/why-does-nothing-happen-in-mwi.822848/page-2 , you yourself stated: "The problem, according to Schwindt, is that the MWI doesn't have any states other than "the pure state of the entire universe". For example, when you say "cats decohere", you are assuming that there are "cats" picked out somewhere as identifiable quantum states. But if all we have is the pure state of the universe, there are no "cats"--or humans, or anything else. So you don't even have the structure needed to talk about "decoherence" at all."

Is this the Factorization problem or the Preferred Basis problem. You agreed there was a problem previously but contra it now by saying "I'm personally not sure it's actually a problem.". So I'm puzzled. Please elaborate the whole truth and don't worry about trying to make us comfortable by placating us that the universe is comprehensible. Thanks.

 

[PeterDonis]

It's in section 3.3 of Demystifier's https://arxiv.org/abs/1703.08341

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.

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>.

The problem, according to Schwindt, is that the MWI doesn't have any states other than "the pure state of the entire universe".

Remember that I said "according to Schwindt". I don't agree with him on this point.

Is this the Factorization problem or the Preferred Basis problem. You agreed there was a problem previously

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.

Please elaborate the whole truth

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.

 

[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.

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>.

In Kastner illustrated guide to it: see https://rekastner.files.wordpress.com/2014/07/decoherence-fail.pdf How does it relate to what you stated above when she mentioned there was obvious problem? I mean was she asking why the universe can even produce cats and humans enough for us to measure cats? Or please just state what she was talking about in reference to yours. Her punchline is:

"The basic problem is that we don’t have a clearly defined, force-based interaction
between the different components of our universe, because without collapse, there is ongoing
entanglement among all its components. What we need to be able to say is that we have a bunch
of separated pieces of the universe that have no quantum correlations amongst each other, but
that do have well-defined interactions that can be understood in terms of specific forces such as
gravitation or electromagnetism. But we cannot say this in the Many-Worlds picture, which has
no collapse that could truly distinguish the pieces from each other as independent objects that
only interact via well-defined forces."

Using your prevous example. How does it relate to it?

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]

What we need to be able to say is that we have a bunch
of separated pieces of the universe that have no quantum correlations amongst each other,

I think this is the key assumption that is driving Kastner's conclusions, and I don't agree with it. We don't know that this is what we need to be able to say. That's an open question. It might be that we can come up with an explanation of our everyday observations without having to say this.

In the case of the cat, what Kastner's claim amounts to is that we need to be able to say that the cat and its environment have no quantum correlations between each other; all their interactions can be formulated in terms of classical forces like gravity and electromagnetism. But decoherence doesn't work that way, at least not as we currently understand it: decoherence, as we currently understand it, requires there to be quantum correlations between the cat and its environment, since they are entangled, and that entanglement is what makes it the case that all observers in a given decohered branch will agree on the cat's state. 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).

 

[Blue Scallop]

I think this is the key assumption that is driving Kastner's conclusions, and I don't agree with it. We don't know that this is what we need to be able to say. That's an open question. It might be that we can come up with an explanation of our everyday observations without having to say this.

In the case of the cat, what Kastner's claim amounts to is that we need to be able to say that the cat and its environment have no quantum correlations between each other; all their interactions can be formulated in terms of classical forces like gravity and electromagnetism. But decoherence doesn't work that way, at least not as we currently understand it: decoherence, as we currently understand it, requires there to be quantum correlations between the cat and its environment, since they are entangled, and that entanglement is what makes it the case that all observers in a given decohered branch will agree on the cat's state. 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).

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.. this is what decohence was all about.. is this different concept to your "how the interaction--the quantum interaction--between the cat and its environment picks out the alive/dead basis as the one that gets decohered"? you mean in the unitary evolution in MWI.. not all basis is decohered.. because one can say that all basis is decohered. .and it includes the alive/dead basis as well, what is wrong with this reasoning?

 

[PeterDonis]

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

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 mean in the unitary evolution in MWI.. not all basis is decohered

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.

 

[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.

Thanks for the above. So you are saying that for simple systems. Demystifier and Kastners have no problem with it.. and the problem only occurs for macro objects like cats? and based on your previous statement "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).".. what is your analogy of this alive/dead cat basis and the spin 1/2 particle example above? What is the counterpart of the Stern-Gerlach device that "entangles the spin state of the particle with the momentum of the same particle".. or what device can entangle the alive/dead state of the cat wit the (counterpart of momentum) of the cat??

 

[PeterDonis]

So you are saying that for simple systems. Demystifier and Kastners have no problem with it

I don't know about Kastner, but Demystifier's objections to the MWI don't seem to be restricted to macroscopic systems.

What is the counterpart of the Stern-Gerlach device that "entangles the spin state of the particle with the momentum of the same particle".. or what device can entangle the alive/dead state of the cat wit the (counterpart of momentum) of the cat??

If the viewpoint I have been describing is correct, the cat itself is the "device": the interactions between its atoms are what pick out the "alive" and "dead" states (more precisely subspaces of the cat Hilbert space, since of course there are many, many quantum states of the cat that all would be described as "alive", and similarly for "dead"). But as I said before, nobody knows how to actually derive this mathematically for a system with as many degrees of freedom as a cat. We only know how to do it for very simple systems like the spin-1/2 particle and the Stern-Gerlach device.

 

[Blue Scallop]

I don't know about Kastner, but Demystifier's objections to the MWI don't seem to be restricted to macroscopic systems.
If the viewpoint I have been describing is correct, the cat itself is the "device": the interactions between its atoms are what pick out the "alive" and "dead" states (more precisely subspaces of the cat Hilbert space, since of course there are many, many quantum states of the cat that all would be described as "alive", and similarly for "dead"). But as I said before, nobody knows how to actually derive this mathematically for a system with as many degrees of freedom as a cat. We only know how to do it for very simple systems like the spin-1/2 particle and the Stern-Gerlach device.

In thread https://www.physicsforums.com/threads/why-does-nothing-happen-in-mwi.822848/page-3 message #45 you commented to Derek Potter words "The definition of a cat is up to the observer in the same factorization":

"This would help if you could show that "observers" only appear in certain factorizations--the ones with cats that are either dead or alive, but not the ones with cats in a superposition of dead and alive. But if you can't show that--if there are "observers" in every factorization--then this "definition" argument doesn't help, because there's nothing in the state vector that tells us what definition we should adopt.

Bear in mind, I am not arguing that the things you are suggesting can't be done; of course they can. Of course we define "objects" according to our own arbitrary criteria all the time. But the question is, if the only structure that physics gives you is the pure state vector of the entire universe, how can this thing we do all the time be explained? All your "explanations" amount to adding additional structure (picking a factorization), but that just concedes the point: the state vector itself doesn't contain the necessary structure, you have to add it in by hand."

What you mean you have to add it by hand. Doesn't the state vector contains cats and being alive and dead and all in between? why is this additional structure (factorization) not part of the pure unitary state vector of MWI? Is the consequence there are observers in all factorizations even those where cats are both alive and dead?

 

[PeterDonis]

Doesn't the state vector contains cats and being alive and dead and all in between?

This is an unsolved problem. Some people believe it does (I am one of them); other people believe it doesn't, so you have to add additional structure. But we don't have a proof either way, so it's an open question. I responded as I did to Derek Potter in that thread because he seemed to me to be claiming that the problem was solved: that we know how to pick out the cats and other objects in the state vector of a macroscopic system like the universe as a whole. We don't know how to do that. The belief that it is doable is, for the present, just a belief, which some people hold and others don't.

 

[Blue Scallop]

This is an unsolved problem. Some people believe it does (I am one of them); other people believe it doesn't, so you have to add additional structure. But we don't have a proof either way, so it's an open question. I responded as I did to Derek Potter in that thread because he seemed to me to be claiming that the problem was solved: that we know how to pick out the cats and other objects in the state vector of a macroscopic system like the universe as a whole. We don't know how to do that. The belief that it is doable is, for the present, just a belief, which some people hold and others don't.

In short you believe in a limbo world where cat can be dead and alive at the same time? (I have to re read Derek Potter thread to grasp the points more after learning from you the gist of what he is thinking.. thanks...)