# I Do macro objects get entangled?

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1. May 8, 2018

### 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?

2. May 8, 2018

### Staff: Mentor

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

3. May 8, 2018

### entropy1

Ok, thanks for getting me on my way

4. May 8, 2018

### DrChinese

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.

5. May 8, 2018

### 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?

Last edited: May 8, 2018
6. May 8, 2018

### Staff: Mentor

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.
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?

7. May 11, 2018

### stevendaryl

Staff Emeritus
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.

8. May 11, 2018

### stevendaryl

Staff Emeritus
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.

9. May 11, 2018

### entropy1

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

10. May 11, 2018

### stevendaryl

Staff Emeritus
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.

11. May 11, 2018

### 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?

12. May 11, 2018

### Owen Loh

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 havent 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 im wrong tho.

13. May 11, 2018

### stevendaryl

Staff Emeritus
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.

14. May 11, 2018

### StevieTNZ

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

15. May 11, 2018

### Staff: Mentor

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.
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".

16. May 11, 2018

### StevieTNZ

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

17. May 11, 2018

### entropy1

I will order it right away.

18. May 11, 2018

### StevieTNZ

19. May 13, 2018

### entropy1

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?

20. May 13, 2018

### stevendaryl

Staff Emeritus
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.