I Do macro objects get entangled?

[entropy1]

If we consider the Unitary evolution of the wavefunction, and interpret measurements as becoming in superposition, taking it that the measurement device gets in a superposition of spin up and spin down, do two measurement devices that each measure one particle of an entangled pair become entangled, as macro-objects?

 

[Nugatory]

Decoherence kills the superposition in any physically realistic macroscopic measuring devices.

 

[entropy1]

Ok, thanks for getting me on my way

 

[DrChinese]

If we consider the Unitary evolution of the wavefunction, and interpret measurements as becoming in superposition, taking it that the measurement device gets in a superposition of spin up and spin down, do two measurement devices that each measure one particle of an entangled pair become entangled, as macro-objects?

I think you are asking: Do observers/measuring apparati Alice and Bob become entangled after measuring each of a pair of entangled particles? I would say the answer is no if that is your question.

 

[entropy1]

@DrChinese: Yes, that is what I mean.

If we adopt the MWI, does decoherence occur in both world branches?

Does Unitary evolution come with the MWI?

 

[Nugatory]

Does Unitary evolution come with the MWI?

Not only does unitary evolution "come with" the MWI, but that is a big piece of its appeal - MWI uses just unitary evolution and does not make additional ad hoc assumptions about the non-unitary wave function reduction that some other interpretations require.

If we adopt the MWI, does decoherence occur in both world branches?

Yes. In fact, decoherence goes a long ways towards resolving one of the difficulties of MWI, the "preferred basis" problem - informally, why do the various branches correspond to plausible macroscopic outcomes and not something else altogether?

 

[stevendaryl]

There are two seemingly contradictory answers to the question of whether macroscopic objects can be entangled, and it's probably worth saying in more detail why they aren't really contradictory.

We can define entanglement negatively, by first defining two systems $A$ and $B$ to be "disentangled" if the composite state $|\Psi\rangle$ can be written as a product state: $|\Psi\rangle = |\psi\rangle |\phi\rangle$ where $\psi$ only involves system $A$, and $\psi$ only involves system $B$. Then the two systems are entangled if their composite state can't be written as such a product state.

So an entangled state is a superposition of two or more product states:

$|\Psi\rangle = \alpha |\psi_1\rangle |\phi_1\rangle + \beta |\psi_2\rangle |\phi_2\rangle$

Here's the reason for the contradictory answers about entanglement. If system $A$ is some big system, like a cat, and system $B$ is an even bigger system, the rest of the universe, then if initially you have a superposition of macroscopically different states of $A$ (say, a dead cat and a live cat) then the state of the cat will very rapidly become "entangled" with the rest of the universe:

$(\alpha |\psi_{dead}\rangle + \beta |\psi_{alive}\rangle) |\phi_0\rangle \Rightarrow \alpha |\psi_{dead}\rangle |\phi_{dead}\rangle + \beta |\psi_{alive}\rangle |\phi_{alive}\rangle$

So entanglement is the norm for macroscopic objects. However, for practical purposes, macroscopic superpositions don't interfere with each other. So when we observe the cat is alive, then for all practical purposes, we can forget about the other term in the superposition, and act as though the new state is:

$|\psi_{alive}\rangle |\phi_{alive}\rangle$

which is not entangled.

Von Neumann described the two types of processes (whether or not you take them literally, they definitely act as a rough and ready rule of thumb for applying QM):

1. Smooth unitary evolution according to Schrodinger's equation
2. "Collapse" of a superposition to an eigenstate of an observable when a measurement is performed.

Process 1 tends to make things more entangled, while process 2 tends to make them less entangled. Of course, there is a sense in which entanglement and the unobservability of macroscopic superpositions is an explanation for process 2.

 

[stevendaryl]

In fact, decoherence goes a long ways towards resolving one of the difficulties of MWI, the "preferred basis" problem - informally, why do the various branches correspond to plausible macroscopic outcomes and not something else altogether?

I'm not 100% sure that I would say that decoherence solves the preferred basis problem. What I think is true is this (when I say "you do this" I mean, in principle you could do it)

1. You have a state for the universe, $|\psi\rangle$
2. You form the corresponding density matrix, $\rho = |\psi\rangle \langle \psi|$
3. You trace out the "environmental" degrees of freedom to get a new, reduced matrix: $\rho_{red}$.
4. You diagonalize this to find the "branch" structure: $\rho_{red} = \sum_j p_j |\phi_j\rangle \langle \phi_j|$. This can be interpreted as meaning: "The system of interest is in one of the states $|\phi_j\rangle$ with probability $p_j$"

That sort of solves the preferred basis problem, but it pushes subjectivity into the choice for how to split the universe into system of interest + environment.

 

[entropy1]

However, for practical purposes, macroscopic superpositions don't interfere with each other. So when we observe the cat is alive, then for all practical purposes, we can forget about the other term in the superposition

Could you shed some light on what these practical purposes may be? And what would such interference look like?

 

[stevendaryl]

Could you shed some light on what these practical purposes may be? And what would such interference look like?

At time $t$, you measure an electron's spin. It is spin-up. From that point on, all your future observations will be consistent with the electron being in a definite spin-up state at time $t$. If immediately before the measurement, the electron was in a superposition of spin-up and spin-down, the spin-down part is for practical purposes gone forever, never again to affect anything you can observe.

 

[entropy1]

So I guess macro-objects can then be regarded as in superposition until they are measured/observed?

I don't understand the contribution of decoherence in preventing superposition. Is that easy to explain?

 

[Owen Loh]

So I guess macro-objects can then be regarded as in superposition until they are measured/observed?

I don't understand the contribution of decoherence in preventing superposition. Is that easy to explain?

Imagine a big system.It has a
1.superposition of both spin up and down(micro)
2. Human Alice(macro)
3. Human Bob(macro)
4.Human Charlie(macro)

The particle before being observed by the humans is itself in a superposition.

When Alice observes and the others dont, the spin to her has collapsed into only one state, the superposition is gone in Alices perspective.
But to both Bob and Charlie, they haven't observed Alice or the particle so they think that both of them are entangled, both of them are in a superposition

When Bob observes Alice, he collapses the superposition of the the Alice-spin system
To Charlie , Bob and Alice and spin is in an entangled state, or the bob-alice-spin system is in an entangled state, until he observes it , the charlie-bob-alice-spin system is entangled to someone else.

Decoherence is when every thing is so entangled that we have collapsed all superpositions.Sorry i duno why u i used 'human', it sounds weird.
Pls correct if I am wrong tho.

 

[stevendaryl]

So I guess macro-objects can then be regarded as in superposition until they are measured/observed?

I don't understand the contribution of decoherence in preventing superposition. Is that easy to explain?

No, they can’t be regarded as in a superposition, precisely because of decoherence. A microscopic system can be in a superposition. The entire universe can be in a superposition. But a macroscopic part of the universe cannot be in a superposition of macroscopically different states.

 

[StevieTNZ]

But a macroscopic part of the universe cannot be in a superposition of macroscopically different states.

For example, only taking into account certain macroscopic objects and not everything in the universe?

 

[Nugatory]

So I guess macro-objects can then be regarded as in superposition until they are measured/observed?

That is pretty much exactly the situation of Schrodinger's thought experiment with the cat in a box . The cat is a macroscopic object; if you do not consider the effects of decoherence you will conclude that the cat could be in a superposition of dead and alive until the box is opened. Of course (for reasons endlessly discussed in some of our many interpretation threads) this conclusion is hard to swallow, and the Wigner's Friend variant makes it even less palatable. If you do pay attention to the effects of decoherence, you come to a different conclusion: although the line between macroscopic and microscopic is a bit blurry and heroic experimental measures can keep surprisingly large objects in superposition for a while, macroscopic objects like cats are not in superposition, even long before they are measured.

I don't understand the contribution of decoherence in preventing superposition. Is that easy to explain?

Surely you've seen Lindley's book "Where does the weirdness go?" recommended here before? It's a good layman's starting point on this question.

Very informally: Decoherence says that even if you were able to prepare a cat in a state that is a quantum superposition of dead and alive, that state would very quickly evolve into the classical state "the cat is definitely either dead or alive; we won't know which unless we look, but it as surely one way or the other as a tossed coin on the floor is either heads-up or heads-down whether it's observed or not".

 

[StevieTNZ]

Very informally: Decoherence says that even if you were able to prepare a cat in a state that is a quantum superposition of dead and alive, that state would very quickly evolve into the classical state "the cat is definitely either dead or alive; we won't know which unless we look, but it as surely one way or the other as a tossed coin on the floor is either heads-up or heads-down whether it's observed or not".

Remember that is FAPP. If you consider the cat + whole environment, in principle it remains in a superposition.

 

[entropy1]

Surely you've seen Lindley's book "Where does the weirdness go?" recommended here before? It's a good layman's starting point on this question.

I will order it right away.

 

[StevieTNZ]

Another book, recently published, is 'Quantum Sense and Nonsense' by Jean Bricmont. My copy of the book arrived yesterday.
https://www.springer.com/gp/book/9783319652702

 

[entropy1]

Very informally: Decoherence says that even if you were able to prepare a cat in a state that is a quantum superposition of dead and alive, that state would very quickly evolve into the classical state "the cat is definitely either dead or alive; we won't know which unless we look, but it as surely one way or the other as a tossed coin on the floor is either heads-up or heads-down whether it's observed or not".

So a (macro-)object either evolves to one or the other value, or it is (still) in superposition, right? And a decision has to be made somewhere. If it can't be told where this decision has to occur, how can we claim it is made?

 

[stevendaryl]

So a (macro-)object either evolves to one or the other value, or it is (still) in superposition, right? And a decision has to be made somewhere. If it can't be told where this decision has to occur, how can we claim it is made?

I'm not exactly sure where the problem is, but let me try again to explain the situation mathematically.

If you assume that there is such a thing as wave functions for big things like cats and the universe, then the situation can be described this way:

Initially, suppose we have the cat in a superposition of two states, $|\psi_{cat}\rangle = \alpha|D\rangle + \beta |A\rangle$, where $|A\rangle$ is the alive state, and $|D\rangle$ is the dead state. Let $|\psi_{environment}\rangle$ be the state of the rest of the universe. So the total state can be written as:

$|\Psi_i\rangle = (\alpha |D\rangle + \beta |A\rangle) |\psi_{environment}\rangle$

Now we let the universe evolve, and eventually it evolves into the state:

$|\Psi_f\rangle = \alpha |D\rangle |\psi_{environment, D} + \beta |A\rangle |\psi_{environment, A}\rangle$

So that's not a case of the cat being in a superposition of states. It's a case of the entire universe being in a superposition of states, one in which the cat is alive, and another in which the cat is dead. Using the Born probabilities, we would say, rather than the cat having a probability $|\alpha|^2$ of being dead and probability $|\beta|^2$ of being alive, the entire universe has probability $|\alpha|^2$ of being a universe with a dead cat and probability $|\beta|^2$ of being a universe with a live cat. That state of affairs can best be described as "The cat is alive or dead, we just don't know which".

This is different from the case of a microscopic superposition of a spin-up and spin-down electron. In that case, until the electron's spin is measured, there is presumably no influence of the electron on the rest of the universe. The rest of the universe doesn't evolve into a superposition of a spin-up universe and a spin-down universe. Only when you measure the spin does the rest of the universe become "infected" by the superposition.

 

[entropy1]

$|\Psi_f\rangle = \alpha |D\rangle |\psi_{environment, D} + \beta |A\rangle |\psi_{environment, A}\rangle$

Thank you. Did the universe evolve differently in both cases? Could you say that in either case, the history of the universe could differ?

 

[stevendaryl]

Thank you. Did the universe evolve differently in both cases? Could you say that in either case, the history of the universe could differ?

Which two cases? If the cat is alive, the universe evolves into one state. If the cat is dead, it evolves into a different state. Even if you don't actually observe the cat, dead cats are different from live cats, and the electromagnetic and gravitational fields are very subtly different in those two cases.

 

[entropy1]

Which two cases? If the cat is alive, the universe evolves into one state. If the cat is dead, it evolves into a different state. Even if you don't actually observe the cat, dead cats are different from live cats, and the electromagnetic and gravitational fields are very subtly different in those two cases.

I ment where the histories of the universa (dead/alive cat) start to differ, that is: if you were to calculate backwards in time from the hypothetical observation of the cat, dead in case one and alive in case two, would the calculation of both possibilities converge to a common history?

(This is a digression - I realize)

 

[Nugatory]

So a (macro-)object either evolves to one or the other value, or it is (still) in superposition, right?

It is not still in superposition (at least if we're glossing over the complexities behind @StevieTNZ's #16 above, and if we aren't glossing over those complexities your question is not well-formed). The quantum state "superposition of A and B" is a different quantum state than "either A or B, but we haven't looked to see which"; the difference is clear when you write the density matrix in the A/B basis.

 

[stevendaryl]

I ment where the histories of the universa (dead/alive cat) start to differ, that is: if you were to calculate backwards in time from the hypothetical observation of the cat, dead in case one and alive in case two, would the calculation of both possibilities converge to a common history?

(This is a digression - I realize)

If I understand what you're asking, the two histories---live cat versus a dead cat--will start to diverge in microscopic details from almost the beginning.

 

[entropy1]

If I understand you're asking, the two histories---live cat versus a dead cat--will start to diverge in microscopic details from almost the beginning.

So one could pinpoint the moment where a 'decision' has gotten upcomming?

I don't know if QM is deterministic, at least in the MWI, but who is to say that if the outcome is "dead cat", that hasn't been established at the beginning of time? That is, the history of "dead cat" is not (necessarily) the same as the history of "live cat"?

 

[stevendaryl]

So could one pinpoint the moment where a 'decision' has gotten upcomming?

I don't know if QM is deterministic, at least in the MWI, but who is to say that if the outcome is "dead cat", that hasn't been established at the beginning of time? That is, the history of "dead cat" is not (necessarily) the same as the history of "live cat"?

Well, it's too complicated to analyze for something like a cat, but in microscopic cases, where the choice is an electron being spin-up or spin-down, rather than a cat being alive or dead, Bell's theorem gives a good reason not to believe that the result is established from the beginning of time. And you can use the spin-up, spin-down electron to determine whether or not to kill the cat. So if the electron spins are not predetermined, then neither is the cat's fate.

 

[entropy1]

[..] Bell's theorem gives a good reason not to believe that the result is established from the beginning of time.

Could you elucidate that a little?

 

[stevendaryl]

Could you elucidate that a little?

You know EPR, right? In the spin-1/2 case, you have some source of electron/positron pairs. Alice measures the spin of one of them along the z-axis, and finds the result +1/2. Bob measures the spin of the other along the z-axis, and finds the result -1/2. If they both measure the spin along the same direction, then they always get opposite answers. So you might think that a good explanation for this certainty is that it is predetermined whether a measurement will result in +1/2 or -1/2.

However, you can measure spin along any axis you like. Instead of measuring along the z-axis, maybe Alice measures along the y-axis. Same result: If Bob happens to measure his particle's spin along the y-axis, he will get the opposite of whatever Alice got.

So to explain this, you can extend your hypothesis about predetermined values, and assume that every time an electron/positron pair is created, there is an associated deterministic function $F(\vec{a})$, which always returns +1/2 or -1/2 for every possible direction $\vec{a}$. If you measure the electron along axis $\vec{a}$ you get $+F(\vec{a})$. If you measure the positron, you get $-F(\vec{a})$.

Bell proved that there is no function that agrees with the predictions of quantum mechanics.

 

[entropy1]

Thank you all for taking the effort to respond to my questions. In particular this topic. I have some light shed on things I don't understand so well. I think I can proceed from here. I will ponder the things you wrote. Maybe if allowed I have some more questions later. Thanks!

 

[entropy1]

Decoherence kills the superposition in any physically realistic macroscopic measuring devices.

I think you are asking: Do observers/measuring apparati Alice and Bob become entangled after measuring each of a pair of entangled particles? I would say the answer is no if that is your question.

If Wigner's friend can be considered in superposition because the object is in superposition, then the object (+friend) can be considered in superposition, right?

 

[stevendaryl]

If Wigner's friend can be considered in superposition because the object is in superposition, then the object (+friend) can be considered in superposition, right?

The lesson of decoherence is that superpositions of subystems tend to "infect" the rest of the universe. So it makes sense to talk about a microscopic system (a single atom, maybe) as being in a superposition of different possibilities. And it makes sense to talk about the entire universe being in a superposition of different possibilities. But it doesn't make sense to talk about a macroscopic system that is smaller than the whole universe being in a superposition.

 

[entropy1]

Surely you've seen Lindley's book "Where does the weirdness go?" recommended here before? It's a good layman's starting point on this question.

Is in the pipeline

Very informally: Decoherence says that even if you were able to prepare a cat in a state that is a quantum superposition of dead and alive, that state would very quickly evolve into the classical state "the cat is definitely either dead or alive; we won't know which unless we look, but it as surely one way or the other as a tossed coin on the floor is either heads-up or heads-down whether it's observed or not".

So if I understand correctly, we, observers, as inhabitants of the universe, become part of the WF of the cat, being in superposition of $|A \rangle |measure A \rangle$ and $|B \rangle |measure B \rangle$, and therefore part of only one of the two possible outcomes?

(If this is correct, it is really fun! )

Could we speak of: "As the measured value tends to A, the measurement outcome tends to A", and: "As the measurement outcome tends to B, say, the measured value tends to B"?

 

[entropy1]

$|\Psi_f\rangle = \alpha |D\rangle |\psi_{environment, D}\rangle + \beta |A\rangle |\psi_{environment, A}\rangle$

Is this a pure state?

 

[stevendaryl]

Is this a pure state?

Yes. However, it becomes a mixed state when the unobservable environmental degrees of freedom are traced out.

 

[stevendaryl]

Could we speak of: "As the measured value tends to A, the measurement outcome tends to A", and: "As the measurement outcome tends to B, say, the measured value tends to B"?

I'm not sure what you mean by that.

 

[Lord Jestocost]

Yes. However, it becomes a mixed state when the unobservable environmental degrees of freedom are traced out.

No! Physics should at least be precise when discussing fundamental and essential questions.

“Decoherence is, formally, never complete. There always remain exponentially small non-diagonal terms in the reduced density matrix, reminding us that an initial pure state remains pure according to basic quantum mechanics.” (Roland Omnes, “Results and Problems in Decoherence Theory“)

 

[stevendaryl]

No! Physics should at least be precise when discussing fundamental and essential questions.

“Decoherence is, formally, never complete. There always remain exponentially small non-diagonal terms in the reduced density matrix, reminding us that an initial pure state remains pure according to basic quantum mechanics.” (Roland Omnes, “Results and Problems in Decoherence Theory“)

I don't think I deserved an exclamation point, because what I said was right. When you start with a pure state, form the density matrix, and trace out some of the degrees of freedom, the result is a mixed state.

 

[entropy1]

I'm not sure what you mean by that.

I mean that the WF evolves to
$|A \rangle|measured A \rangle + |B \rangle|measured B \rangle$
rather than
$|A \rangle|measured B \rangle + |B \rangle|measured A \rangle$
?

 

[stevendaryl]

I mean that the WF evolves to
$|A \rangle|measured A \rangle + |B \rangle|measured B \rangle$
rather than
$|A \rangle|measured B \rangle + |B \rangle|measured A \rangle$
?

Oh. Yeah, I think that there probably would be a tiny amplitude for having the "wrong" measurement result. The way I think of a measurement is in terms of an unstable equilibrium, where a tiny (microscopic) shove in one direction or another makes a big (macroscopic) difference in the outcome. For example, if you carefully balance a telephone pole on one end, a small push can make it fall in one direction or the other. Getting the "wrong" measurement result would be comparable to pushing on a telephone pole and having it fall toward you, instead of away from you. That's certainly possible (if it's not perfectly balanced, or if there are other forces pushing it toward you).

 

[entropy1]

Oh. Yeah, I think that there probably would be a tiny amplitude for having the "wrong" measurement result. The way I think of a measurement is in terms of an unstable equilibrium, where a tiny (microscopic) shove in one direction or another makes a big (macroscopic) difference in the outcome. For example, if you carefully balance a telephone pole on one end, a small push can make it fall in one direction or the other. Getting the "wrong" measurement result would be comparable to pushing on a telephone pole and having it fall toward you, instead of away from you. That's certainly possible (if it's not perfectly balanced, or if there are other forces pushing it toward you).

So the measured value (the cat) is fixed according to you? We have the resulting WF $|A \rangle|measured A \rangle + |B \rangle|measured B \rangle$. So wouldn't that suggest the measured value is not fixed?

 

[stevendaryl]

So the measured value (the cat) is fixed according to you? We have the resulting WF $|A \rangle|measured A \rangle + |B \rangle|measured B \rangle$. So wouldn't that suggest the measured value is not fixed?

I'm not sure what you mean by "fixed". With the analogy of the telephone pole balanced on one end, we know:

• If there is some tiny force that shoves the pole to the left, then the pole will almost certainly fall to the left.
• If there is some tiny force that shoves the pole to the right, then the pole will almost certainly fall to the right.
• Therefore, to the extent that everything is describable using quantum mechanics, which uses linear evolution equations, if you start in a state that is a superposition of a force shoving to the left and a force shoving to the right, then you will end up in a state that is a superposition of a state in which the pole fell to the left and a state in which the pole fell to the right.

 

[entropy1]

I'm not sure what you mean by "fixed". With the analogy of the telephone pole balanced on one end, we know:

• If there is some tiny force that shoves the pole to the left, then the pole will almost certainly fall to the left.
• If there is some tiny force that shoves the pole to the right, then the pole will almost certainly fall to the right.
• Therefore, to the extent that everything is describable using quantum mechanics, which uses linear evolution equations, if you start in a state that is a superposition of a force shoving to the left and a force shoving to the right, then you will end up in a state that is a superposition of a state in which the pole fell to the left and a state in which the pole fell to the right.

So do you mean the amplitude of one of the terms in the WF goes to zero during decoherence?

 

[stevendaryl]

So do you mean the amplitude of one of the terms in the WF goes to zero during decoherence?

No. I am definitely not saying that. It seems to me that the information has been presented again and again in this thread, but the same questions about it keep getting asked.

The terms in a superposition evolve independently. If an amplitude starts off nonzero, then it will always be nonzero.

 

[stevendaryl]

There seems to be misunderstandings that are just not getting cleared up.

Decoherence does not make one branch of the wave function go to zero. What it does is destroy interference between branches. The interference terms are what go to zero. If there is no interference between branches, then for all intents and purposes, you can reason as if we're in one branch or the other. The existence of the other branch has no effect on anything in this branch.

 

[stevendaryl]

I don't know how to make this clearer: If there are two systems, the observer and the cat, there is a distinction between:

$|Me\rangle (|Dead\rangle + |Live\rangle)$

and

$|Me_{dead}\rangle |Dead\rangle + |Me_{live}\rangle |Live\rangle$

In the former case, it would be correct for me to say that "The cat is in a superposition". In the latter case, there are two different "me"s, and for each of them, the cat is in a definite state.

 

[entropy1]

@stevendaryl So in which branch we end up is still a mystery? (measurement problem)

Or is the state of the cat fixed but only unknown? Or is the cat also in two distinct branches?

 

[stevendaryl]

@stevendaryl So in which branch we end up is still a mystery? (measurement problem)

We're venturing into the philosophy of many-worlds here, but in MW, both branches happen. There is a branch in which I see a dead cat, and there is a branch in which I see a live cat. The two branches have no effect on each other, so in each branch, I'm free to act as if it's the only branch.

 

[entropy1]

@stevendaryl Ok, so if you are in the branch in which the cat is dead, you are not going to change that anymore when the interference is gone?

Does that have to do with entropy or with decoherence?

(I hope it is not a too stupid question )

 

[stevendaryl]

@stevendaryl Ok, so if you are in a universe in which the cat is dead, you are not going to change that anymore?

Does that have to do with entropy or with decoherence?

(I hope it is not a too stupid question )

I'm not sure what you mean. The world keeps evolving, and both you and the cat can change with time.