Does MWI Adequately Explain Observer Branching in Quantum Mechanics?

[Blue Scallop]

It seems many people even experts don't understand the basic of MWI. In the double slit.. what is wrong with the statement that "that observer will "split" as well--one version of him for each way the double slit experiment came out.". Peterdonis wrote it. And I included it in a thread as reference. But Nugatory stated whether it is based on a solid premise. And I'm getting confused. The environment doesn't split, only the system, yes? So the observer should "split". No? Other synonyms for "split"?

How do you use more accurate phrases to describe what happen to the observers in the double slit in MWI?

 

[bhobba]

See:
http://www.anthropic-principle.com/preprints/manyworlds.html

Forget the double slit - its a red herring here.

Thanks
Bill

 

[Blue Scallop]

See:
http://www.anthropic-principle.com/preprints/manyworlds.html

Forget the double slit - its a red herring here.

Thanks
Bill

In Q8 in your article. It's written:

"The cat splits when the device is triggered, irreversibly. The
investigator splits when they open the box. The alive cat has no idea
that investigator has split, any more than it is aware that there is a
dead cat in the neighbouring split-off world. The investigator can
deduce, after the event, by examining the cyanide mechanism, or the
cat's memory, that the cat split prior to opening the box."

Why is this not a red herring and why is the double slit a red herring?

 

[PeterDonis]

Nugatory stated whether it is based on a solid premise

The problem with the thread that got closed wasn't your statement (referring to mine) about "splitting". It was your statement that "MWI assumes the brain is classical". It doesn't.

Nor is it really correct to view the different "worlds" that get split off in the MWI as classical. The MWI is an interpretation of quantum mechanics, not classical mechanics. It assumes that everything is quantum, including you and me.

The environment doesn't split, only the system, yes?

No. See below.

How do you use more accurate phrases to describe what happen to the observers in the double slit in MWI?

You don't. You use math.

The double slit is a bad example to use because there are not two distinct "results" of the experiment when it is run the same way multiple times. To change the result you have to change the experimental setup (close one of the slits, put measuring devices at the slits, etc.). That's not what the MWI is talking about.

A better example is a measurement of the spin of a spin-1/2 particle about a fixed axis. Such a measurement, when run the same way multiple times, will yield one of two results each time, which we can call "up" and "down" and denote by the symbols $+$ and $-$. For each run, the measuring device starts out in a state we can call "ready" and denote by the symbol $R$, and ends up in either the "measured spin up" state or the "measured spin down" state, which we can denote by the symbols $U$ and $D$. Mathematically, we write this evolution of states during the measurement as follows:

$$
\vert \Psi \rangle \vert R \rangle = \left( a \vert + \rangle + b \vert - \rangle \right) \vert R \rangle \rightarrow \vert \Psi' \rangle = a \vert + \rangle \vert U \rangle + b \vert - \rangle \vert D \rangle
$$

Here $a$ and $b$ are complex numbers that satisfy $\vert a \vert^2 + \vert b \vert^2 = 1$.

The best ordinary language term to describe the above evolution is not "splitting" but "entanglement": the state of the measuring device gets entangled with the state of the measured system. The term "splitting" comes from focusing on the fact that the measuring device starts out in the state $R$, but ends up in a superposition of states (more precisely, as factors in two terms of a superposition: the measuring device in the entangled state after the measurement does not have a state that is separable from the state of the measured system). But that is focusing on just a piece of the wave function instead of the whole wave function. And notice that the other piece, the state of the measured system, does not change at all; there are $+$ and $-$ terms in $\Psi$ and there are $+$ and $-$ terms in $\Psi'$, with the same coefficients.

Also, the above evolution applies just as well if the "measuring device" is an observer like you or me: it just says that our state becomes entangled with the state of the measured system, so the states $U$ and $D$ are something like "I observed the spin to be up" and "I observed the spin to be down". So we ourselves, if we take the QM math at face value, end up in states that are not separable from the states of the things we observe.

The two main types of QM interpretations are identical up to this point; where they differ is in what happens next. In no collapse interpretations like the MWI, nothing happens next; the wave function $\Psi'$ just keeps on undergoing unitary evolution, just as the process that goes from $\Psi$ to $\Psi'$ is unitary evolution. In collapse interpretations like Copenhagen, the state "collapses" from $\Psi'$ to one of the two terms in it; the probability of collapsing to each term is given by the squared modulus of its coefficient ($a$ or $b$).

 

[bhobba]

The double slit is a bad example to use because there are not two distinct "results" of the experiment when it is run the same way multiple times. To change the result you have to change the experimental setup (close one of the slits, put measuring devices at the slits, etc.). That's not what the MWI is talking about.

That's exactly what I meant - in discussing MW it's not a good example.

Thanks
Bill

 

[Blue Scallop]

The problem with the thread that got closed wasn't your statement (referring to mine) about "splitting". It was your statement that "MWI assumes the brain is classical". It doesn't.

Nor is it really correct to view the different "worlds" that get split off in the MWI as classical. The MWI is an interpretation of quantum mechanics, not classical mechanics. It assumes that everything is quantum, including you and me.

I mentioned the brain was classical because I thought each world of MWI was collapsed. When you see airplanes and roads.. they definitely looked collapsed. But in Everett times. there was not any concept of Decoherence. So did Everett think each world/branch of MWI is collapsed or not? Even now. Decoherence concept says each world of MWI forms because of decoherence. But within a world/branch.. it's also sustained by internal decoherence (our automobile is not in two places at once because the environment measures each atoms of the automobile putting it in classical state) and so each world/branch is not really collapsed? Did Everett think of this originally? Or did he think automobile are collapsed because each world/branch is collapsed? But in Everett times, where concept of decoherence didn't exist. How could he think of world as not collapsed and how was it sustained (if not by decoherence processes inside each world/branch)?

Thanks for all below. I understood what you meant how spin was better example of two distinct results than double slit. 5 stars.

No. See below.
You don't. You use math.

The double slit is a bad example to use because there are not two distinct "results" of the experiment when it is run the same way multiple times. To change the result you have to change the experimental setup (close one of the slits, put measuring devices at the slits, etc.). That's not what the MWI is talking about.

A better example is a measurement of the spin of a spin-1/2 particle about a fixed axis. Such a measurement, when run the same way multiple times, will yield one of two results each time, which we can call "up" and "down" and denote by the symbols $+$ and $-$. For each run, the measuring device starts out in a state we can call "ready" and denote by the symbol $R$, and ends up in either the "measured spin up" state or the "measured spin down" state, which we can denote by the symbols $U$ and $D$. Mathematically, we write this evolution of states during the measurement as follows:

$$
\vert \Psi \rangle \vert R \rangle = \left( a \vert + \rangle + b \vert - \rangle \right) \vert R \rangle \rightarrow \vert \Psi' \rangle = a \vert + \rangle \vert U \rangle + b \vert - \rangle \vert D \rangle
$$

Here $a$ and $b$ are complex numbers that satisfy $\vert a \vert^2 + \vert b \vert^2 = 1$.

The best ordinary language term to describe the above evolution is not "splitting" but "entanglement": the state of the measuring device gets entangled with the state of the measured system. The term "splitting" comes from focusing on the fact that the measuring device starts out in the state $R$, but ends up in a superposition of states (more precisely, as factors in two terms of a superposition: the measuring device in the entangled state after the measurement does not have a state that is separable from the state of the measured system). But that is focusing on just a piece of the wave function instead of the whole wave function. And notice that the other piece, the state of the measured system, does not change at all; there are $+$ and $-$ terms in $\Psi$ and there are $+$ and $-$ terms in $\Psi'$, with the same coefficients.

Also, the above evolution applies just as well if the "measuring device" is an observer like you or me: it just says that our state becomes entangled with the state of the measured system, so the states $U$ and $D$ are something like "I observed the spin to be up" and "I observed the spin to be down". So we ourselves, if we take the QM math at face value, end up in states that are not separable from the states of the things we observe.

The two main types of QM interpretations are identical up to this point; where they differ is in what happens next. In no collapse interpretations like the MWI, nothing happens next; the wave function $\Psi'$ just keeps on undergoing unitary evolution, just as the process that goes from $\Psi$ to $\Psi'$ is unitary evolution. In collapse interpretations like Copenhagen, the state "collapses" from $\Psi'$ to one of the two terms in it; the probability of collapsing to each term is given by the squared modulus of its coefficient ($a$ or $b$).

 

[LeandroMdO]

The double slit is a bad example to use because there are not two distinct "results" of the experiment when it is run the same way multiple times. To change the result you have to change the experimental setup (close one of the slits, put measuring devices at the slits, etc.). That's not what the MWI is talking about.

Once the particle gets detected at position x_i on the screen (I'm keeping it discrete for convenience and because ultimately the screen is made of atoms anyway), there is some kind of signal that is the detected by the observer. Result: you get states of the form |particle detected at x_i>|observer saw light coming from position x_i>, so MWI does assert that the worlds do split, once for each detection event. So I don't think this example is misleading, or a "bad question", or anything like that.

 

[PeterDonis]

I mentioned the brain was classical because I thought each world of MWI was collapsed.

There is no collapse in the MWI. So evidently you were thinking of the MWI wrong.

When you see airplanes and roads.. they definitely looked collapsed.

They look the way they look, according to the MWI, because your state is entangled with their states. No collapse required.

Decoherence concept says each world of MWI forms because of decoherence.

No. Decoherence explains why each "world" (branch of the wave function) remains self-consistent. It is not needed to explain how each branch forms: that's just simple unitary evolution.

our automobile is not in two places at once because the environment measures each atoms of the automobile putting it in classical state

This is ok except for the last part: "putting in classical state". You should banish the word "classical" and anything connected with it from your thinking if you are trying to use the MWI. You should also banish the word "collapse", and banish the idea that decoherence has anything to do with collapse. It doesn't.

 

[Blue Scallop]

There is no collapse in the MWI. So evidently you were thinking of the MWI wrong.
They look the way they look, according to the MWI, because your state is entangled with their states. No collapse required.
No. Decoherence explains why each "world" (branch of the wave function) remains self-consistent. It is not needed to explain how each branch forms: that's just simple unitary evolution.

In your spin example. You mean even if we don't observe it (and entangling with it) or there is no measuring device.. the spin up and spin down still form a branch?

Does the Universal Wave Function has information on everything in the universe like the Higgs vacuum expectation values and all constant of nature? Or is the Universal Wave function just ignorant of them and separate from these information?

This is ok except for the last part: "putting in classical state". You should banish the word "classical" and anything connected with it from your thinking if you are trying to use the MWI. You should also banish the word "collapse", and banish the idea that decoherence has anything to do with collapse. It doesn't.

 

[PeterDonis]

You mean even if we don't observe it (and entangling with it) or there is no measuring device.. the spin up and spin down still form a branch?

No.

Does the Universal Wave Function has information on everything in the universe like the Higgs vacuum expectation values and all constant of nature?

The Higgs VEV is a property of quantum field interactions, so the wave function would include information about it. A constant like the fine structure constant--the coupling constant for electromagnetic interactions--isn't really a property of the wave function, it's a property of the Lagrangian.

 

[Blue Scallop]

No.

But you just mentioned that "No. Decoherence explains why each "world" (branch of the wave function) remains self-consistent. It is not needed to explain how each branch forms: that's just simple unitary evolution."

You said decoherence not needed to explain how each branch forms. So I thought the branch already there even without decoherence. So you are saying that indeed decoherence is really needed to explain how each branch forms? What you mean "self-consistent". Please clarify your statements. Thank you.

The Higgs VEV is a property of quantum field interactions, so the wave function would include information about it. A constant like the fine structure constant--the coupling constant for electromagnetic interactions--isn't really a property of the wave function, it's a property of the Lagrangian.

 

[Nugatory]

I mentioned the brain was classical because I thought each world of MWI was collapsed.

Not at all... There is no collapse in MWI, and that is its biggest selling point.

 

[PeterDonis]

You said decoherence not needed to explain how each branch forms. So I thought the branch already there even without decoherence.

Yes, but that just means branches form some other way. That other way is by entanglement via interactions and unitary evolution. When you have two subsystems that interact, unitary evolution entangles them. I showed how in post #4.

 

[Blue Scallop]

The problem with the thread that got closed wasn't your statement (referring to mine) about "splitting". It was your statement that "MWI assumes the brain is classical". It doesn't.

Nor is it really correct to view the different "worlds" that get split off in the MWI as classical. The MWI is an interpretation of quantum mechanics, not classical mechanics. It assumes that everything is quantum, including you and me.
No. See below.
You don't. You use math.

The double slit is a bad example to use because there are not two distinct "results" of the experiment when it is run the same way multiple times. To change the result you have to change the experimental setup (close one of the slits, put measuring devices at the slits, etc.). That's not what the MWI is talking about.

A better example is a measurement of the spin of a spin-1/2 particle about a fixed axis. Such a measurement, when run the same way multiple times, will yield one of two results each time, which we can call "up" and "down" and denote by the symbols $+$ and $-$. For each run, the measuring device starts out in a state we can call "ready" and denote by the symbol $R$, and ends up in either the "measured spin up" state or the "measured spin down" state, which we can denote by the symbols $U$ and $D$. Mathematically, we write this evolution of states during the measurement as follows:

$$
\vert \Psi \rangle \vert R \rangle = \left( a \vert + \rangle + b \vert - \rangle \right) \vert R \rangle \rightarrow \vert \Psi' \rangle = a \vert + \rangle \vert U \rangle + b \vert - \rangle \vert D \rangle
$$

Here $a$ and $b$ are complex numbers that satisfy $\vert a \vert^2 + \vert b \vert^2 = 1$.

The best ordinary language term to describe the above evolution is not "splitting" but "entanglement": the state of the measuring device gets entangled with the state of the measured system. The term "splitting" comes from focusing on the fact that the measuring device starts out in the state $R$, but ends up in a superposition of states (more precisely, as factors in two terms of a superposition: the measuring device in the entangled state after the measurement does not have a state that is separable from the state of the measured system). But that is focusing on just a piece of the wave function instead of the whole wave function. And notice that the other piece, the state of the measured system, does not change at all; there are $+$ and $-$ terms in $\Psi$ and there are $+$ and $-$ terms in $\Psi'$, with the same coefficients.

Above you emphasized that even without measuring device or observer that entangled with the measured system, there is still + and - or spin up and spin down in the superposition, why can't these spin up or spin down be called world/branches?

Also, the above evolution applies just as well if the "measuring device" is an observer like you or me: it just says that our state becomes entangled with the state of the measured system, so the states $U$ and $D$ are something like "I observed the spin to be up" and "I observed the spin to be down". So we ourselves, if we take the QM math at face value, end up in states that are not separable from the states of the things we observe.

The two main types of QM interpretations are identical up to this point; where they differ is in what happens next. In no collapse interpretations like the MWI, nothing happens next; the wave function $\Psi'$ just keeps on undergoing unitary evolution, just as the process that goes from $\Psi$ to $\Psi'$ is unitary evolution. In collapse interpretations like Copenhagen, the state "collapses" from $\Psi'$ to one of the two terms in it; the probability of collapsing to each term is given by the squared modulus of its coefficient ($a$ or $b$).

 

[PeterDonis]

Above you emphasized that even without measuring device or observer that entangled with the measured system, there is still + and - or spin up and spin down in the superposition

It's only a superposition because of the basis we picked. But without an actual measurement in that basis--i.e., without an interaction that entangles the system's state with that of a measuring device--there is no physical reason to choose that basis over any other. That basis is only picked out because of the measurement that gets made. So without a measurement being made, we can't say whether the state is a superposition or not.

why can't these spin up or spin down be called world/branches?

Because in the absence of a measurement, there is no entanglement of the system's state with the state of a measuring device. It's the entanglement that creates "branching", to the extent that term is applicable at all. See my post #4.

 

[Blue Scallop]

It's only a superposition because of the basis we picked. But without an actual measurement in that basis--i.e., without an interaction that entangles the system's state with that of a measuring device--there is no physical reason to choose that basis over any other. That basis is only picked out because of the measurement that gets made. So without a measurement being made, we can't say whether the state is a superposition or not.

There is no word "basis" in your post #4. How do you use the example of spin + and - in this superposition and basis connection? Or how do you insert this basis business in your post#4? You are incredible helpful, thanks a lot!

Because in the absence of a measurement, there is no entanglement of the system's state with the state of a measuring device. It's the entanglement that creates "branching", to the extent that term is applicable at all. See my post #4.

 

[PeterDonis]

There is no word "basis" in your post #4.

A basis is any set of mutually orthogonal vectors that span the space of all possible states of the system. In the case of spin for a spin-1/2 particle, the "up" and "down" states for any axis form a basis. So the states I called $+$ and $-$ in post #4 are a basis. But the only thing that picks out that particular basis is our choice of a particular axis about which to measure the spin; and that only has physical meaning if we actually make the measurement.

 

[Blue Scallop]

A basis is any set of mutually orthogonal vectors that span the space of all possible states of the system. In the case of spin for a spin-1/2 particle, the "up" and "down" states for any axis form a basis. So the states I called $+$ and $-$ in post #4 are a basis. But the only thing that picks out that particular basis is our choice of a particular axis about which to measure the spin; and that only has physical meaning if we actually make the measurement.

Oh, going back to your "It's only a superposition because of the basis we picked". Can you give an example of basis we picked that won't make it a superposition?

 

[PeterDonis]

Can you give an example of basis we picked that won't make it a superposition?

Sure, just pick the basis in which the state $a \vert + \rangle + b \vert - \rangle$, which is the state that the system starts out in in post #4, is one of the basis states. The other basis state will then be $b \vert + \rangle - a \vert - \rangle$. It's easy to show that these two states are orthogonal, just as the $+$ and $-$ states are orthogonal.

 

[Blue Scallop]

I wrote earlier: "You said decoherence not needed to explain how each branch forms. So I thought the branch already there even without decoherence."

Yes, but that just means branches form some other way. That other way is by entanglement via interactions and unitary evolution. When you have two subsystems that interact, unitary evolution entangles them. I showed how in post #4.

So Decoherence is not in Unitary Evolution and not having "entanglement via interactions"? Because you said branches could form some other way. But Decoherence is entanglement of environment and subsystem so why can't it is referred as "entanglement via interactions"? And Decoherence is entanglement of environment and subsystem which is not dissimilar to two subsystems so like you mentioned above.. "unitary evolution entangles" them. So decoherence also obeys unitary evolution and it is intanglement via interactions. Yet you seemed to state Decoherence is neither of the two. Please clarify your statements. I greatly appreciated all the amount of help.

 

[PeterDonis]

So Decoherence is not in Unitary Evolution

No.

and not having "entanglement via interactions"?

No.

This issue is really not a "B" level issue. You really need to spend some time working through a recent QM textbook. But even in this thread, in my post #4, which I have now referred to repeatedly, I explained how unitary evolution + entangement via interactions forms branches. There is no decoherence anywhere in that post. So decoherence is not required to form branches.

Heuristically, decoherence comes in when we ask what happens next to the state we ended up with in post #4. For example, what prevents us from simply applying the reverse interaction to the one I described in post #4? Unitary evolution is always reversible, so such an interaction must exist. And that interaction would "undo" the entanglement that formed due to measurement (just reverse the arrow I gave in post #4).

If we are dealing only with microscopic quantum systems and devices, like electrons and photons and beam splitters and so forth, we can actually do this in some cases. But in most real cases, we can't. Why not? Because the state we ended up with in post #4 interacts with the environment, which contains huge numbers of degrees of freedom that we can't keep individual track of. And because we can't keep individual track of all the environment degrees of freedom, we can't reverse the interaction any more, because it would not just be a matter of reversing the microscopic interaction I described in post #4, but of reversing all of the huge numbers of interactions (and entanglements) that take place between the system and the measuring device and the environment. And that process--the process of interactions becoming effectively irreversible due to interactions and entangments with a huge number of degrees of freedom in the environment--is decoherence.

Note, btw, that the "environment" here can actually be part of what, in ordinary language, we would consider to be the measuring device. For example, in many photon experiments we use a device called a photomultiplier to detect photons at the end of an experiment. From the standpoint of post #4 and the above, the photomultiplier is an "environment": by the time you observe an output from the photomultiplier, the photon that was detected has already interacted with and been entangled with a huge number of degrees of freedom, i.e., with an "environment" in the sense I was using the term above. The "environment" in this case is all of the atoms inside the photomultiplier, the electrons inside the circuit that amplifies the photon detection, etc. The "measuring device" in the sense of post #4, the thing whose state goes from $R$ to $U$ or $D$, is more like the first atom inside the photomultiplier that interacts with the photon, and whose state gets entangled with it. But it is only a very small fraction of a second before that atom's interaction with the photon has cascaded into a huge number of interactions inside the photomultiplier, so that the overall interaction is irreversible and decoherence has occurred.

 

[LeandroMdO]

So decoherence is not required to form branches.

Decoherence is necessary, together with locality, for solving the basis selection problem, which is crucial to "branching".

 

[Blue Scallop]

I asked "Can you give an example of basis we picked that won't make it a superposition?
You answered:

Sure, just pick the basis in which the state $a \vert + \rangle + b \vert - \rangle$, which is the state that the system starts out in in post #4, is one of the basis states. The other basis state will then be $b \vert + \rangle - a \vert - \rangle$. It's easy to show that these two states are orthogonal, just as the $+$ and $-$ states are orthogonal.

Can you give an example of basis we picked that WILL make it a superposition? This is just to make your statements complete and make sure I understood it right. Thanks.

And oh, how come a measuring device can't entangled with both spin up and spin down at same time? so if the states
$U$ = "I observed the spin to be up"
$D$ = "I observed the spin to be down".

why is "I observed the spin to be up and down" forbidden?

 

[PeterDonis]

Can you give an example of basis we picked that WILL make it a superposition?

The basis I originally wrote the state down in, where $+$ and $-$ are the basis states.

how come a measuring device can't entangled with both spin up and spin down at same time?

Because of the physical nature of the device. More precisely, the name "spin measuring device" is a label we put on a device whose physical nature we have determined, by experiments, to be such that it always gives "up" or "down" as a result, never both. We have not found any physical device that gives a result "both up and down". And our current understanding of QM says that no such device should be possible.

Mathematically, the operation of a measuring device is modeled as a Hermitian operator that describes the device. Applying that operator to the initial state, before the measurement, is how you mathematically compute the state after the measurement; that's how you would derive the time evolution I gave in post #4. There is no Hermitian operator that gives a time evolution where "I observed the spin to be both up and down" is a possible result.

 

[Blue Scallop]

The basis I originally wrote the state down in, where $+$ and $-$ are the basis states.
Because of the physical nature of the device. More precisely, the name "spin measuring device" is a label we put on a device whose physical nature we have determined, by experiments, to be such that it always gives "up" or "down" as a result, never both. We have not found any physical device that gives a result "both up and down". And our current understanding of QM says that no such device should be possible.

Mathematically, the operation of a measuring device is modeled as a Hermitian operator that describes the device. Applying that operator to the initial state, before the measurement, is how you mathematically compute the state after the measurement; that's how you would derive the time evolution I gave in post #4. There is no Hermitian operator that gives a time evolution where "I observed the spin to be both up and down" is a possible result.

Thanks for the clarifications. Let's say the spin up and down is exposed to the environmental heat bath (or decoherence) so a photon is entangled to spin up, another photon is entangled to spin down.. and another one to spin up and down and so on. If we view the system, would we see spin up or spin down?

 

[PeterDonis]

Let's say the spin up and down is exposed to the environmental heat bath (or decoherence) so a photon is entangled to spin up, another photon is entangled to spin down.. and another one to spin up and down and so on. If we view the system, would we see spin up or spin down?

What state did the system (the original system, not the heat bath) start out in? And what measurement was made on it?

Those questions have to be answered before you even try to analyze what decoherence does.

 

[Blue Scallop]

What state did the system (the original system, not the heat bath) start out in? And what measurement was made on it?

Those questions have to be answered before you even try to analyze what decoherence does.

Lets take your example in post #4 with the particle in superposition of spin up and spin down then it is subjected to environmental heat bath or decoherence. If you try to measure it. Would you see spin up or spin down?

 

[PeterDonis]

Lets take your example in post #4 with the particle in superposition of spin up and spin down then it is subjected to environmental heat bath or decoherence. If you try to measure it.

You're missing the point of what I said before. Measurement happens before decoherence. So asking what happens if you try to measure the particle after it's been subjected to decoherence doesn't make sense.

 

[Blue Scallop]

You're missing the point of what I said before. Measurement happens before decoherence. So asking what happens if you try to measure the particle after it's been subjected to decoherence doesn't make sense.

If you want to "look" at the system after decoherence, what word do you use then instead of "measurement"?

Let's say you want to look if the spin-1/2 particle is spin up or spin down after decoherence.. maybe you can see random (say spin up).. so the other spin down is in another world/branch, yes?

 

[PeterDonis]

If you want to "look" at the system after decoherence, what word do you use then instead of "measurement"?

I'm not sure what you mean by "looking" at the system, other than what has already been discussed. The "environment" we talked about in reference to decoherence includes the states of conscious observers that have "looked at" the results of the measurement. There is no separate "looking" process.

 

[Blue Scallop]

I'm not sure what you mean by "looking" at the system, other than what has already been discussed. The "environment" we talked about in reference to decoherence includes the states of conscious observers that have "looked at" the results of the measurement. There is no separate "looking" process.

Our bicycles are decohered objects. And we can look at them. So officially what language should one use to describe looking at bicycles (or decohered spin-1/2 particles?

 

[PeterDonis]

Our bicycles are decohered objects.

Why?

And we can look at them.

What happens when we look at them? Is there any quantum uncertainty involved?

 

[Blue Scallop]

Why?

Because Bicycles are exposed to the environment like sun rays, CMBR, thermal photons, etc.

What happens when we look at them? Is there any quantum uncertainty involved?

I'm just asking what language to use to refer to observe decohered objects like bicycles or spin-1/2 particles. If "measurements" are reserved for that occur before decoherence. What language to use just to observe the one after decoherence. And if "observation" is more appropriate term. Let's say you want to observe if the spin-1/2 particle is spin up or spin down after decoherence.. maybe you can observe random (say spin up).. so the other spin down is in another world/branch, yes? If your answer if we can't observed decohered objects.. but we can observe bicycles.. don't we.

 

[PeterDonis]

Because Bicycles are exposed to the environment like sun rays, CMBR, thermal photons, etc.

You're missing the point. What quantum measurement do bicycles undergo after which they then become decohered? What is the analogue, in the case of the bicycle, to the spin measurement, which results in either up or down, in the case we were discussing?

I'm just asking what language to use to refer to observe decohered objects like bicycles or spin-1/2 particles.

And I'm trying to get at what physical process you are talking about when you say "observe decohered objects".

 

[Blue Scallop]

You're missing the point. What quantum measurement do bicycles undergo after which they then become decohered? What is the analogue, in the case of the bicycle, to the spin measurement, which results in either up or down, in the case we were discussing?
And I'm trying to get at what physical process you are talking about when you say "observe decohered objects".

We observe decohered bicycles by photons reflecting of it. I was just inquiring whether we would observe spin up or spin down in the decohered spin-1/2 particle. I put this question yesterday because I was wondering if during superposition of the spin-1/2 particle. Does the spin up and spin down really can separately entangled to different photons in the environment.. it's as if there are really different copies of the spin 1/2 particle being up or down. And if is. Then after decoherence. When we observe the particle as spin up.. does it mean it has separate spin down in another branch or world. If my language are rough. Please correct the language I should use as I don't understand why you can't get what I mean by simply observing the bicycles or spin-1/2 particle after decoherence. Former physical process is photon reflecting it. The latter physical process is instrument to detect spin up or spin down.

 

[PeterDonis]

Does the spin up and spin down really can separately entangled to different photons in the environment

No, that's not how it works. Go back to post #4; remember we ended up with the state

$$
\vert \Psi' \rangle = a \vert + \rangle \vert U \rangle + b \vert - \rangle \vert D \rangle
$$

However, if we're now going to talk about the environment, this state is incomplete. We need to include the environment's state and how it's entangled with the state of the system and the measuring device (which, remember, is something microscopic like the first atom that interacts with the measured system). So we need something like this:

$$
\vert \Psi' \rangle \vert E \rangle = \left( a \vert + \rangle \vert U \rangle + b \vert - \rangle \vert D \rangle \right) \vert E \rangle
\rightarrow
a \vert + \rangle \vert U \rangle \vert E_U \rangle + b \vert - \rangle \vert D \rangle \vert E_D \rangle
$$

In other words, from the standpoint of unitary evolution/entanglement, the interaction with the environment is just more of the same: where in post #4, the state of the measuring device branched, here the state of the environment branches. But the difference is that the measuring device was microscopic, or at least it was such that we were able to keep track of its detailed microstate, so that we could in principle reverse the measurement. But the environment, by hypothesis, is something whose detailed microstate we cannot keep track of, so the $\rightarrow$ above is irreversible: once the entanglement with the environment happens, there is no way to reverse it.

So the states $E$, $E_U$, and $E_D$ are not microscopic quantum states like the states $+$, $-$, $U$, $D$; they are really huge subspaces of the environment's Hilbert space, and we can't keep track which individual microstate inside each subspace the environment is actually in. But in each subspace, the environment is composed of the same microscopic constituents--the same photons that bounced off the measured system/measuring device, the same atoms that interacted with it, the same molecules in your retinal cells that received the photons, etc., etc. The only difference is which subspace of the environment Hilbert space all those interactions ended up in.

 

[Jilang]

You're missing the point of what I said before. Measurement happens before decoherence. So asking what happens if you try to measure the particle after it's been subjected to decoherence doesn't make sense.

Peter, I'm having a real problem with this. I have always understood the opposite. Interactions (as a result of the setup for the measurement) cause the decoherence and the final measurement result is following the decoherence. If my understanding of measurement as a two stage process is flawed I would like to know as I would have been labouring under a serious misapprehension for many years!

 

[PeterDonis]

I have always understood the opposite.

Based on what sources?

Interactions (as a result of the setup for the measurement) cause the decoherence

If this were always true, there would be no such thing as reversible interactions. But in the quantum computing world they do reversible interactions on qubits all the time. They entangle them and then un-entangle them, swap entanglements from one qubit to another, etc., etc., all reversibly.

What makes all these interactions reversible, as I said, is that we can keep precise track of the exact microstates of all of the systems involved. (Actually, that's not quite true: some of the devices that are used to implement qubit operations, like beam splitters, are macroscopic devices and we can't keep track of their precise microstates. But the precise microstates of those devices--the ones that implement the operations on qubits, rather than the qubits themselves--turn out not to matter, because no information is stored in them; their states don't get entangled with the states of the qubits. A full discussion of that would take us way beyond the "B" level.)

So "interactions cause decoherence" can't be right, because we can do all kinds of interactions in the lab that don't cause decoherence. What causes decoherence is interactions with the environment, i.e., with stuff outside the lab, or at least outside the precisely designed, calibrated, etc. lab equipment that we know we can manipulated without causing decoherence (like the beam splitters that act on qubits). In other words, interactions with systems that (a) have a lot of degrees of freedom, that (b) we can't keep precise track of, that (c) store information, via entanglement, about the state of the system we are interested in.

What I have been describing, in posts #4 and #36, is a highly idealized measurement where we can cleanly separate the initial "measurement interaction", where we entangle the state of the system with the state of some idealized "measuring device" whose state we can keep precise track of (so we can potentially reverse the measurement), from the subsequent decoherence, where the entanglement spreads to the environment, we can't keep precise track of it any more, and the whole process becomes irreversible. In most real situations, there is no such clean separation. When you see a bicycle (to use the example brought up earlier in this thread), there is no analogue to the initial idealized "measuring device", or even the initial "system" being measured. (I was hoping to get that point across by asking the question rhetorically.) The bicycle itself has a huge number of degrees of freedom, and those degrees of freedom are constantly interacting with each other and with an even huger number of degrees of freedom in the environment, like photons bouncing off the bicycle and then entering your eyes. There is no single "measurement" going on; it's just continuous interaction. And there isn't really decoherence going on in the bicycle case either, because there is no initial "coherence" (the analogue of the process I described in post #4) going on to be decohered from. The bicycle, and the photons bouncing off it, and your eyes, and your brain, body, etc., are never "coherent" in the first place (in the sense in which "decoherence" uses the term).

the final measurement result is following the decoherence

More precisely: knowledge of the final measurement result is following the decoherence. Or, to put it another way (the way an MWI theorist might put it): the final measurement result is only "final" after decoherence has occurred, because that is what makes that final measurement result constitute a separate "world". Once decoherence has taken place, that final measurement result is fixed, in that "world"--all observers will agree on it, further checks on what the result was will all agree, etc. The measurement can't be "undone" at that point. Whereas, as I said above, it might be that the measurement can be undone if all that has happened is an interaction, because the interaction might be between systems like qubits whose state we can keep precise track of.

 

[stevendaryl]

Peter, I'm having a real problem with this. I have always understood the opposite. Interactions (as a result of the setup for the measurement) cause the decoherence and the final measurement result is following the decoherence. If my understanding of measurement as a two stage process is flawed I would like to know as I would have been labouring under a serious misapprehension for many years!

Here's the way I understand measurement:

You have a macroscopic system that is in a metastable state. What that means is that it is stable, but it only takes a tiny push to send it into a drastically different state. For example, imagine a coin balanced on its edge. It's neither "heads" nor "tails". But give it a tiny push and it will fall into a more stable state: heads up or tails up.

Then you couple the metastable macroscopic system with the microscopic system that you are measuring. I don't know how you would do this, but suppose you make it so that if an electron is spin-up, it will give the coin a tiny push to make it fall heads-up, and if it is spin-down, it will make it fall tails-up.

So that's a crude measuring device for spin.

However, there is a hidden assumption here that is so deeply ingrained in our reasoning about cause and effect that we typically don't think about it: Why does the coin "prefer" to be on its side (heads or tails) instead of on its edge? The glib answer is that systems always try to minimize their energy, and the coin on its edge is a higher-energy state than the coin on its side. But that is not really a complete answer. Energy is conserved, so the total energy is the same, whether or not the coin is on its edge or on its side. The real story is that if the coin is on its edge, the energy is stored in the coin, while if the coin topples onto its side, the energy radiates away in the form of vibrations in the floor. So it's really not about energy, it's about entropy: having energy in the form of vibrations in the floor is a much higher entropy state than having energy in the form of a coin on its edge.

The above paragraph is speaking classically, but there is an quantum analogy: the coin falling onto its edge means coupling the state of the coin with the vibrational state of the floor; it means the coin's state becoming entangled with the states of the particles in the floor.

I think that classically, you haven't performed a measurement until an irreversible, entropy-increasing change to a more stable state. Quantum mechanically, you haven't performed a measurement until the measuring device becomes irreversibly entangled with the rest of the universe. So to me, measurement requires entanglement.

It's not true the other way around, though. You can have entanglement without anything that would count as a measurement.

 

[Blue Scallop]

No, that's not how it works. Go back to post #4; remember we ended up with the state

$$
\vert \Psi' \rangle = a \vert + \rangle \vert U \rangle + b \vert - \rangle \vert D \rangle
$$

However, if we're now going to talk about the environment, this state is incomplete. We need to include the environment's state and how it's entangled with the state of the system and the measuring device (which, remember, is something microscopic like the first atom that interacts with the measured system). So we need something like this:

$$
\vert \Psi' \rangle \vert E \rangle = \left( a \vert + \rangle \vert U \rangle + b \vert - \rangle \vert D \rangle \right) \vert E \rangle
\rightarrow
a \vert + \rangle \vert U \rangle \vert E_U \rangle + b \vert - \rangle \vert D \rangle \vert E_D \rangle
$$

In other words, from the standpoint of unitary evolution/entanglement, the interaction with the environment is just more of the same: where in post #4, the state of the measuring device branched, here the state of the environment branches. But the difference is that the measuring device was microscopic, or at least it was such that we were able to keep track of its detailed microstate, so that we could in principle reverse the measurement. But the environment, by hypothesis, is something whose detailed microstate we cannot keep track of, so the $\rightarrow$ above is irreversible: once the entanglement with the environment happens, there is no way to reverse it.

So the states $E$, $E_U$, and $E_D$ are not microscopic quantum states like the states $+$, $-$, $U$, $D$; they are really huge subspaces of the environment's Hilbert space, and we can't keep track which individual microstate inside each subspace the environment is actually in. But in each subspace, the environment is composed of the same microscopic constituents--the same photons that bounced off the measured system/measuring device, the same atoms that interacted with it, the same molecules in your retinal cells that received the photons, etc., etc. The only difference is which subspace of the environment Hilbert space all those interactions ended up in.

What do you mean in each subspace, the environment is composed of the same microscopic constituents? Do you mean
$E_U$ = same subspace, same microscopic constituents as $E_D$
$E_D$ = same subspace, same microscopic constituents as $E_U$

If this is so. Then Spin Up is entangled with the $E_U$, Spin Down is entangled with the $E_D$, and since $E_U$=$E_D$, then spin up and spin down is still in superposition. This is because according to Wikipedia:

"Decoherence happens when different portions of the system's wavefunction become entangled in different ways with the measuring device. For two einselected elements of the entangled system's state to interfere, both the original system and the measuring in both elements device must significantly overlap, in the scalar product sense. If the measuring device has many degrees of freedom, it is very unlikely for this to happen."

But you are claiming that different portions of the system's wavefunction become entangled in SAME ways with the measuring device. Here "both the original system and the measuring in both elements device HAS significantly overlap, in the scalar product sense". Therefore there is still quantum coherence (between spin up and spin down) because you have the exact environment.. so what if we can't keep tract of the environment and can't reverse it.. the spin up and spin down has identical environment, therefore they should still interfere (or the left and right slit of the double slit should still interfere if they can exposed to the same huge subspace of the environment), ain't it?

(I wonder if spin up and spin down is good example of this being able to interfere.. in the spin 1/2 particle, can we say the spin up and spin down is interfering? maybe this is the case where the double slit experiment left and right slit path is better example or spin up and down is still the prime example of it?)

 

[PeterDonis]

Do you mean

$E_U$ = same subspace, same microscopic constituents as $E_D$

$E_D$ = same subspace, same microscopic constituents as $E_U$

Same microscopic constituents, yes. Same subspace, no; $E_U$ and $E_D$ are different, disjoint subspaces of the Hilbert space of the environment. The difference is not in the microscopic constituents, but in the microstates of those constituents.

But you are claiming that different portions of the system's wavefunction become entangled in SAME ways with the measuring device.

No, I'm not. See above.

 

[Blue Scallop]

Same microscopic constituents, yes. Same subspace, no; $E_U$ and $E_D$ are different, disjoint subspaces of the Hilbert space of the environment. The difference is not in the microscopic constituents, but in the microstates of those constituents.
No, I'm not. See above.

But in the double slit experiment, in the single at a time emission of a photon or electron which goes to left or right slit, it can't be the same photons (microscopic constituents) that hit each slit because there is a difference in position (of left and right slit). But in the spin-1/2 particle, it has same position (spin up and spin down) so it can get entangled with the same photons (but in different microstates or subspaces as you said). Yes?

 

[PeterDonis]

in the double slit experiment, in the single at a time emission of a photon or electron which goes to left or right slit, it can't be the same photons (microscopic constituents) that hit each slit

You don't detect the result of a double slit experiment by looking at the slits. You detect it by looking at the interference pattern on the screen that gets built up over time as each photon or electron goes through the experiment. The screen doesn't move.

 

[Blue Scallop]

You don't detect the result of a double slit experiment by looking at the slits. You detect it by looking at the interference pattern on the screen that gets built up over time as each photon or electron goes through the experiment. The screen doesn't move.

But decoherence occurs halfway.. in the C60 fullucume experiment, thermal baths can change the interference patterns by the path of the atoms being affected by thermal photons (which is halfway).

Anyway. In spin-1/2 particles. How do you know whether it is in superposition of spin up and spin down or it has already suffered decoherence.. how do you check? maybe if the measuring device sees spin up and spin down randomly.. it is in superposition.. if it always see spin up or always see spin down.. it is already decohered?

 

[PeterDonis]

in the C60 fullucume experiment, thermal baths can change the interference patterns by the path of the atoms being affected by thermal photons (which is halfway)

I don't understand what you mean by "halfway". Do you have a reference?

How do you know whether it is in superposition of spin up and spin down or it has already suffered decoherence.. how do you check?

Look again at what I wrote mathematically to describe the process. Superposition never disappears anywhere in the process. You start with a system, like an electron, in a superposition of eigenstates of some measurement operator. The measurement operator gets applied to the system and entangles it with a microscopic measuring device, which puts that device into a superposition (as I posted in post #4). Then the microscopic measuring device gets entangled with the environment (decoherence), which puts the environment into a superposition (as I posted in post #36). No superposition ever gets removed.

Now if we were talking about a collapse interpretation, then at some point the superposition would collapse onto one of its terms (and to be consistent with our observations, this would have to happen after decoherence). But we are talking about the MWI, where there is no collapse; the superposition just stays there (and keeps spreading, as parts of the environment interact and get entangled with other parts of the environment). The only difference decoherence makes is to make this process irreversible, because we can no longer keep track of the detailed microstate of the superposition, since it involves so many degrees of freedom in the environment. So if your observation is irreversible, then it occurs after decoherence.

 

[Blue Scallop]

I don't understand what you mean by "halfway". Do you have a reference?

It's very popular setup:

http://www.univie.ac.at/qfp/research/matterwave/c60/

the decoherence occurs halfway .see:

"It is intriguing that C60 can almost be considered to be a body obeying classical physics in view of its many excited internal degrees of freedom. Leaving the source, it has as much as 7 eV of internal energy stored in 174 vibrational modes, and highly excited rotational states with quantum numbers greater than 100. Fullerenes can emit and absorb blackbody radiation very much like a solid and they can no longer be treated as a simple few level system.
Quantum interference experiments with large molecules, of the kind first reported here, open up many novel possibilities among them decoherence studies and nanolithography experiments."

Look again at what I wrote mathematically to describe the process. Superposition never disappears anywhere in the process. You start with a system, like an electron, in a superposition of eigenstates of some measurement operator. The measurement operator gets applied to the system and entangles it with a microscopic measuring device, which puts that device into a superposition (as I posted in post #4). Then the microscopic measuring device gets entangled with the environment (decoherence), which puts the environment into a superposition (as I posted in post #36). No superposition ever gets removed.

Now if we were talking about a collapse interpretation, then at some point the superposition would collapse onto one of its terms (and to be consistent with our observations, this would have to happen after decoherence). But we are talking about the MWI, where there is no collapse; the superposition just stays there (and keeps spreading, as parts of the environment interact and get entangled with other parts of the environment). The only difference decoherence makes is to make this process irreversible, because we can no longer keep track of the detailed microstate of the superposition, since it involves so many degrees of freedom in the environment. So if your observation is irreversible, then it occurs after decoherence.

 

[PeterDonis]

the decoherence occurs halfway

I still don't understand what you mean by "halfway". Please explain in more detail.

 

[Blue Scallop]

I still don't understand what you mean by "halfway". Please explain in more detail.

Simple. As the C60 atom emits from source.. it can enter either the left or right slit.. but decoherence can make the path known before it even reaches the slit (destroying any interference in the screen).. the effect is like the left or right slit being covered. Why, how do you understand the c60 buckyball thermal experiment? where does decoherence occur there?

 

[PeterDonis]

decoherence can make the path known before it even reaches the slit

In which case you do not get interference fringes. But the page you linked to says interference fringes were detected. That means they did not do anything to make the path known in the middle of the experiment.

where does decoherence occur

It depends on what experiment you are running. If you run the experiment where you are detecting which slit the particle goes through, that is a different experiment from the experiment where you don't detect which slit the particle goes through. So you can't draw deductions about where decoherence occurs in the second experiment from the results of the first one. That's true whether the "particle" in the experiment is a photon, an electron, or a buckyball.

As for the general question of where decoherence occurs, I've already answered it, several times. Decoherence occurs when the process of interaction becomes irreversible because it has spread over a large enough number of degrees of freedom that we can't track the precise microstate any more.

 

[Blue Scallop]

Sure, just pick the basis in which the state $a \vert + \rangle + b \vert - \rangle$, which is the state that the system starts out in in post #4, is one of the basis states. The other basis state will then be $b \vert + \rangle - a \vert - \rangle$. It's easy to show that these two states are orthogonal, just as the $+$ and $-$ states are orthogonal.

$+$ and $-$ are orthogonal and yet they are in superposition.
$a \vert + \rangle + b \vert - \rangle$ and $b \vert + \rangle - a \vert - \rangle$ are orthogonal and yet they are not in superposition.
Why is the latter not in superposition? I think this is related to what Sabine wrote in http://backreaction.blogspot.com/2016/03/dear-dr-b-what-is-difference-between.html:

"All this is just to say that whether a particle is or isn’t in a superposition is ambiguous. You can always make its superposition go away by just wanting it to go away and changing the notation. Or, slightly more technical, you can always remove a superposition of basis states just by defining the superposition as a new basis state. It is for this reason somewhat unfortunate that superpositions – the cat being both dead and alive – often serve as examples for quantum-ness. You could equally well say the cat is in one state of dead-and-aliveness, not in a superposition of two states one of which is dead and one alive."

So let's say one basis is the cat is in state of dead-and-aliveness and another basis is in state of dead-minus-alive (or others). Why are these basis not in superposition?