Quantum Decoherence: Understanding Contradictions

[faen]

I've been reading a bit about quantum decoherence today. But I'm stuck on the following contradictions:

I think I've read somewhere that after the wave function collapses, it will resume its normal superpositioned state soon after measurement. But according to quantum decoherence a superposition splitting into its sub states is thermodynamically irreversible. So how does the system resume to its "irreversible" state then? Does it somehow resume to its original state just by existing in its energy potential and then become a superposition of other similar substates?

Also some places i read that the substates of the particle are still in the same superposition of the particle even after measurement. At the same time i read that in order to be in a superposition, the sub states need to be in phase. But when the sub states of the particle entangle with the environment they change their phases. So how can they still constitute the superposition of the whole particle when they are out of phase?

Also, why isn't the "many worlds interpretation" useless when quantum decoherence predicts how the possibilities that were not measured still exist in our universe (entangled into the environment)?

I'd appreciate if anybody could clear out whatever i have missunderstood :)

 

[Antiphon]

It doesn't go back to it's original state, it begins a new evolution from the outcome of the collapse.

Your other questions are interesting. I'm not an expert in this area but I believe the collapse voids the existence of the wave functions' other states and they no longer exist. That's what it means to collapse rather than simply decohere. That they cease to exist is a disturbing thing and is what may have motivated the MWI. In that view there is no collapse.

 

[faen]

It doesn't go back to it's original state, it begins a new evolution from the outcome of the collapse.

Your other questions are interesting. I'm not an expert in this area but I believe the collapse voids the existence of the wave functions' other states and they no longer exist. That's what it means to collapse rather than simply decohere. That they cease to exist is a disturbing thing and is what may have motivated the MWI. In that view there is no collapse.

I see, so it evolves into a new superposition after measurement.. Thanks for answering.. When it comes to wave function collapse they won't disappear though. They will appear at random places in the universe since the universe is correlated as such due to entanglement. The energy eigenstates not measured will then be conserved and "collapse" in other wavefunctions it's entangled with..

 

[faen]

I think i'll give one last try to bump this thread since I am a bit curious on this topic

I'll try to repeat the question in case i can explain it better.. So the question is if a quantum superposition is measured on and entangled with the environment. Does it still remain the same superposition, or is it un entangled? Some places i read it is still the same super position. But at the same time i read that in order to be in a super position the phases of the wave needs to be the same. But the phase of the quantum states constituting the original superposition changes phase while being entangeled with the environment. How can they still be in the original superposition while out of phase? there's some kind of contradiction here..

 

[A. Neumaier]

I think i'll give one last try to bump this thread since I am a bit curious on this topic

I'll try to repeat the question in case i can explain it better.. So the question is if a quantum superposition is measured on and entangled with the environment. Does it still remain the same superposition, or is it un entangled? Some places i read it is still the same super position. But at the same time i read that in order to be in a super position the phases of the wave needs to be the same. But the phase of the quantum states constituting the original superposition changes phase while being entangeled with the environment. How can they still be in the original superposition while out of phase? there's some kind of contradiction here..

Yes, there is. Neither explanation is precise; neither is your question. So it is difficult to answer.

To get a fairly authoritative view on what decoherence is and does, you'd look not arbitrarily, but for example at the website http://www.decoherence.de/ !
It is maintained by one of the top people working in the field. Afterwards you'll be able to ask better questions. Only good questions can trigger good answers!

 

[Alfrez]

I think i'll give one last try to bump this thread since I am a bit curious on this topic

I'll try to repeat the question in case i can explain it better.. So the question is if a quantum superposition is measured on and entangled with the environment. Does it still remain the same superposition, or is it un entangled? Some places i read it is still the same super position. But at the same time i read that in order to be in a super position the phases of the wave needs to be the same. But the phase of the quantum states constituting the original superposition changes phase while being entangeled with the environment. How can they still be in the original superposition while out of phase? there's some kind of contradiction here..

I think this is where you got confused. Superposition can occur even when the phases are not the same. When they are the same, it is in "pure state". When not the same, it is in "mixed state". Before the system got entangled with the environment. It is in pure state. After entangling with the environment or decoherence, it is in mixed state. Superposition still exists even if the phase are not the same.

But I may be wrong. Right or wrong experts?

 

[faen]

Yes, there is. Neither explanation is precise; neither is your question. So it is difficult to answer.

To get a fairly authoritative view on what decoherence is and does, you'd look not arbitrarily, but for example at the website http://www.decoherence.de/ !
It is maintained by one of the top people working in the field. Afterwards you'll be able to ask better questions. Only good questions can trigger good answers!

I found some interresting papers from that link, thanks.

I think this is where you got confused. Superposition can occur even when the phases are not the same. When they are the same, it is in "pure state". When not the same, it is in "mixed state". Before the system got entangled with the environment. It is in pure state. After entangling with the environment or decoherence, it is in mixed state. Superposition still exists even if the phase are not the same.

But I may be wrong. Right or wrong experts?

I see, thanks for clearing that up :) Do u know how systems get unentangled by any chance?

 

[Alfrez]

I found some interresting papers from that link, thanks.



I see, thanks for clearing that up :) Do u know how systems get unentangled by any chance?

What do you mean by "unentangled"? If Decoherence is true. Everything is entangled. So no way to untangled it. If you mean entanglement as pure state, note entanglement can also occur in mixed state (where the phases are not the same). Since the components of the entire world is entangled with everything else, there is no sense to unentangled them).

 

[faen]

What do you mean by "unentangled"? If Decoherence is true. Everything is entangled. So no way to untangled it. If you mean entanglement as pure state, note entanglement can also occur in mixed state (where the phases are not the same). Since the components of the entire world is entangled with everything else, there is no sense to unentangled them).

Hm, i read about quantum decoherence from this link.. http://www.ipod.org.uk/reality/reality_decoherence.asp

It says the following things:

the question can also be asked as to why we never see these other states in macroscopic objects. For example, why is Schrödinger's cat never seen as being both alive and dead at the same time?

Now here is the absolutely key point: every component eigenstate has an associated phase (this was considered back in The Quantum Casino). It is this phase which gives the wavefunction its "wavelike" character (in complex space, remember). In order for the components to combine together correctly to produce a superposition state, they must be in the same phase (must be coherent). This is what happens in the double-slit experiment: interference components possessing the same phase combine to produce the interference effects.

 

[Alfrez]

Hm, i read about quantum decoherence from this link.. http://www.ipod.org.uk/reality/reality_decoherence.asp

It says the following things:

the question can also be asked as to why we never see these other states in macroscopic objects. For example, why is Schrödinger's cat never seen as being both alive and dead at the same time?

Now here is the absolutely key point: every component eigenstate has an associated phase (this was considered back in The Quantum Casino). It is this phase which gives the wavefunction its "wavelike" character (in complex space, remember). In order for the components to combine together correctly to produce a superposition state, they must be in the same phase (must be coherent). This is what happens in the double-slit experiment: interference components possessing the same phase combine to produce the interference effects.

In the same url you provided, it also said the following:

"What happens to a quantum particle in the real world is that each of its component states gets entangled (separately) with different aspects of its environment. As seen in the page on Quantum Entanglement, when particles become entangled you have to consider them as one single, entangled state (you use the tensor product to calculate the resultant state). So each component of our quantum particle forms separate entangled states. The phases of these states will be altered. This destroys the coherent phase relationships between the components. The components are said to decohere."

*********************

So in decoherence, the phase in the superposition are destroyed. But the superposition still remains, although in mixed state, meaning no interference, hence no double slit like effect. The superposition of the decoherence is in separate eigenstates... particle to particle with billions of this separate entanglement which disturbs the phase relationship so much no interference is possible

 

[faen]

In the same url you provided, it also said the following:

"What happens to a quantum particle in the real world is that each of its component states gets entangled (separately) with different aspects of its environment. As seen in the page on Quantum Entanglement, when particles become entangled you have to consider them as one single, entangled state (you use the tensor product to calculate the resultant state). So each component of our quantum particle forms separate entangled states. The phases of these states will be altered. This destroys the coherent phase relationships between the components. The components are said to decohere."

*********************

So in decoherence, the phase in the superposition are destroyed. But the superposition still remains, although in mixed state, meaning no interference, hence no double slit like effect. The superposition of the decoherence is in separate eigenstates... particle to particle with billions of this separate entanglement which disturbs the phase relationship so much no interference is possible

Yes that's the contradiction I wanted to point out.. But you are probably right, they still are in superposition... But what i don't understand then is why arent all quantum states one and the same, since every single superposition was entangled since the big bang? How can we then find a quantum state with just one particle, when this state is a superposition of the whole universe?

 

[faen]

By the way i just found this:

The mixed state, on the other hand, could not be described by a single state vector (because the particles were not all in the same state: some were green, some were blue).

So if it can't be described by a single vector, how can it be a superposition then?

 

[Alfrez]

By the way i just found this:

The mixed state, on the other hand, could not be described by a single state vector (because the particles were not all in the same state: some were green, some were blue).

So if it can't be described by a single vector, how can it be a superposition then?

Actually I've reading the website you shared for the past hour and analysing it. I got the idea that even mixed state is in superposition from a PF contributor here called Fredrik who wrote in another thread:

"In principle, if the Earth could be isolated from its environment (this could probably only happen in a universe without gravity), then from the point of view of an external observer, it could exist in a superposition of very different eigenstates of the observable that the external observer would measure when he breaks the isolation. Before that "measurement", those eigenstates would evolve completely independently of each other. It's possible that one of them involves people communicating over the internet, and that another one involves an Earth where everyone's dead."

 

[Alfrez]

By the way i just found this:

The mixed state, on the other hand, could not be described by a single state vector (because the particles were not all in the same state: some were green, some were blue).

So if it can't be described by a single vector, how can it be a superposition then?

Wait. It's possible you are right that mixed state is not in superposition (hope the experts can confirm). If that's the case, then it means decoherence occurs because there are billions of particles in pure state and you can't distinguish amonst them causing the macroscopic object to be in chaotic states? I thought about this because I found this message by Neumaier:

"Coherence has nothing at all to do with a symmetric arrangement of atoms.

It only means that you maintain the superposition (i.e., an approximately pure state rather than a mixture) long enough to be able to perform experiments with it. Decoherence means that the density matrix degenerates from a rank 1 matrix (corresponding to a pure state) to a diagonal matrix under the influence of noise from the environment. This degeneration is a continuous process that takes some time. If one can keep the interaction with the environment tiny, this time is very long, but it becomes smaller exponentially with the size of the system. This is a theoretically and experimentally very well established fact.

Nothing in quantum mechanics forbids an ensemble of cars to exist in a superposition. But decoherence would turn it in next to no time into a classical mixture. In practice, one cannot prepare such superpositions for large objects, because they degenerate even before they are created"

 

[Alfrez]

Yes that's the contradiction I wanted to point out.. But you are probably right, they still are in superposition... But what i don't understand then is why arent all quantum states one and the same, since every single superposition was entangled since the big bang? How can we then find a quantum state with just one particle, when this state is a superposition of the whole universe?

Maybe because when in mixed state, it's no longer in superposition. Anyway there is a passage in the website that confused me (now I'm in the same company as you confused as well):

"However, for all interference effects to disappear, the particle must have a macroscopic (rather than a microscopic) effect by forming entanglements with billions of particles in, say, a Geiger counter."

My question is. How can one particle form superposition with billions of particles??

 

[A. Neumaier]

So in decoherence, the phase in the superposition are destroyed. But the superposition still remains, although in mixed state

No. The superpositions turn into mixtures. Calling the latter superpositions is highly misleading. Mixtures are essentially classical, while superpositions are not.

 

[A. Neumaier]

"However, for all interference effects to disappear, the particle must have a macroscopic (rather than a microscopic) effect by forming entanglements with billions of particles in, say, a Geiger counter."

My question is. How can one particle form superposition with billions of particles??

In the tensor product space containing the billion plus 1 particles, this is the typical situation, just as in the tensor product space of two particles it is the norm that these two particles are in a superposition rather than in an eigenstate.

Decoherence is the effect that arises if one ignores the presence of all particles in the universe with exceptions of the few of current interest, and uses a reduced description in the few-particle space.

 

[Alfrez]

In the tensor product space containing the billion plus 1 particles, this is the typical situation, just as in the tensor product space of two particles it is the norm that these two particles are in a superposition rather than in an eigenstate.

Decoherence is the effect that arises if one ignores the presence of all particles in the universe with exceptions of the few of current interest, and uses a reduced description in the few-particle space.

I thought superposition only occurs for pure states where the phase are the same or in coherence, The 1 billion particles in the environment entangling with the same single particle can produce nearly a billion mixed states. So how they it still be a superposition??

 

[A. Neumaier]

I thought superposition only occurs for pure states where the phase are the same or in coherence, The 1 billion particles in the environment entangling with the same single particle can produce nearly a billion mixed states. So how they it still be a superposition??

A pure N particle state psi is unentangled only if it has the form
psi = psi_1(x_1) tensor psi_2(x_2) tensor ... tensor psi_N(x_N)
But the most general pure N particle state can be an arbitrary linear combination of states of this form - all these are called entangled. The Hamiltonian dynamics of a system generally (i.e., except under specially prepared conditions) turns an unentangled state immediately into an entangled state. Therefore in a pure state, N particles are almost always entangled.

 

[Alfrez]

A pure N particle state psi is unentangled only if it has the form
psi = psi_1(x_1) tensor psi_2(x_2) tensor ... tensor psi_N(x_N)
But the most general pure N particle state can be an arbitrary linear combination of states of this form - all these are called entangled. The Hamiltonian dynamics of a system generally (i.e., except under specially prepared conditions) turns an unentangled state immediately into an entangled state. Therefore in a pure state, N particles are almost always entangled.

Hope you can put this in english.

Say you have a one electron-at-a-time double slit experiment setup enclosed in a vacuum inside a container in the football field. Then you open the container and make the system exposed to the surrounding causing Decoherence. So the same electron is entangled to billions of photons coming from all directions. The phases of each electron-photon is different such that

electron-photon1 = 45 degrees
electron-photon2 = 32 degrees
electron-photon3 = 87 degrees
~~
electron-photon1 billion = 28 degrees

Are you saying that the above 1 billion photons to single electron coupling is in superposition because it has the common source in the 1 electron?? Pls. answer in english. Thanks :)

 

[A. Neumaier]

Hope you can put this in english.

Say you have a one electron-at-a-time double slit experiment setup enclosed in a vacuum inside a container in the football field. Then you open the container and make the system exposed to the surrounding causing Decoherence. So the same electron is entangled to billions of photons coming from all directions. The phases of each electron-photon is different such that

electron-photon1 = 45 degrees
electron-photon2 = 32 degrees
electron-photon3 = 87 degrees
~~
electron-photon1 billion = 28 degrees

Are you saying that the above 1 billion photons to single electron coupling is in superposition because it has the common source in the 1 electron?

No. I only said what appeared in my posting.

Superpositions have nothing at all to do with angles. You need to properly understand the definitions if you want to get a clearer picture of what is going on.

 

[Alfrez]

No. I only said what appeared in my posting.

Superpositions have nothing at all to do with angles. You need to properly understand the definitions if you want to get a clearer picture of what is going on.

Ok. After reading the site faen shared over and over again http://www.ipod.org.uk/reality/reality_decoherence.asp (best site about decoherence). I got many terms right. Superposition has to do with the phase as in "every component eigenstate has an associated phase. It is this phase which gives the wavefunction its "wavelike" character (in complex space, remember). In order for the components to combine together correctly to produce a superposition state, they must be in the same phase (must be coherent). This is what happens in the double-slit experiment: interference components possessing the same phase combine to produce the interference effects."

However, there is something that is unbelievable. It continues and mentions:

"What happens to a quantum particle in the real world is that each of its component states gets entangled (separately) with different aspects of its environment"

I thought the component states are just possibilities for the particle being in the state. But it actually happens real time? But there is no proof of it. When we send one electron at a time to a double slit and make it interfere. We don't see the entire interference patterns with just one electron. But only after numerous runs. In Einstein Ensemble Interpretation, only the ensemble matters. This means Einstein believes that the component states can't be active at once and get entangled separately with different aspects of its environment! What's the proof it does?? If it does, It's almost like the quantum particle literally *moves* thru all paths at once.

 

[A. Neumaier]

However, there is something that is unbelievable. It continues and mentions:

"What happens to a quantum particle in the real world is that each of its component states gets entangled (separately) with different aspects of its environment"

This statement is nonsense. If you really want to understand this stuff, you'd get your information from a serious source, not from a popular one.

www.decoherence.de/[/url] is maintained by Erich Joos, one of the leading experts in the field, who wrote books (cited on the web site) and articles (e.g., [url]http://xxx.lanl.gov/find/all/1/au:+Joos_E/0/1/0/all/0/1[/URL] ) about the topic on the expert level.
This site can be recommended for quality and reliability.

[PLAIN]http://www.ipod.org.uk/reality/reality_decoherence.asp is written by Andrew Thomas, a scientific nobody with a Ph.D. in electrical engineering
(see http://tetrahedral.blogspot.com/2010/02/unsolved-problems-in-physics.html), and freely mixes superficial science with art and music.
This site is for people who don't bother about consistency and believability, and can be recoomended only for entertainment value.

 

[Alfrez]

This statement is nonsense. If you really want to understand this stuff, you'd get your information from a serious source, not from a popular one.

But you agreed with him when he mentioned:

"However, for all interference effects to disappear, the particle must have a macroscopic (rather than a microscopic) effect by forming entanglements with billions of particles in, say, a Geiger counter.""

You even gave details of how for decoherence to occur, it must form entanglement with billions of particles. How else can the billion particles get entangled but with the component states of the quantum particle. Why is he wrong? Let me know and I'll tell him. Or maybe you misunderstood him. The following is the complete passage to get the idea of the context of what he is saying (let me know where he got it wrong and I'll tell him so he can correct it):

"What happens to a quantum particle in the real world is that each of its component states gets entangled (separately) with different aspects of its environment. As seen in the page on Quantum Entanglement, when particles become entangled you have to consider them as one single, entangled state (you use the tensor product to calculate the resultant state). So each component of our quantum particle forms separate entangled states. The phases of these states will be altered. This destroys the coherent phase relationships between the components. The components are said to decohere.

If a particle interacts with just a single photon, for example, then the two particles will enter an entangled state and that will be enough to trigger the onset of decoherence (for example a single photon entering the double-slit experiment will be enough to destroy the interference pattern). However, for all interference effects to disappear, the particle must have a macroscopic (rather than a microscopic) effect by forming entanglements with billions of particles in, say, a Geiger counter. This is described in the book Quantum Enigma: "Whenever any property of a microscopic object affects a macroscopic object, that property is 'observed' and becomes a physical reality" (this idea of "decoherence=observation" is considered in greater detail in the next page on Quantum Reality). In that case, if there are no longer any interference terms then to all intents and purposes the particle is now in a single, quantum state - one of the component eigenstates"

--------------------------

What is wrong in what he is saying? What is the correct way to put it. Let me know so I can tell him where he made the wrong assumptions. Thanks.

 

[A. Neumaier]

But you agreed with him when he mentioned:

"However, for all interference effects to disappear, the particle must have a macroscopic (rather than a microscopic) effect by forming entanglements with billions of particles in, say, a Geiger counter.""

You even gave details of how for decoherence to occur, it must form entanglement with billions of particles.

One correct statement doesn't imply that everything is correct, and agreeing to one statement is no agreement to everything.

How else can the billion particles get entangled but with the component states of the quantum particle. Why is he wrong?

There are no well-defined components, and decoherence has nothing to do with components.There is no entanglement with components of a state (this concept is meaningless), but only entanglement between complete substates of a composite system.

There is just one big state for one million plus one particles (the system), and it is entangled w.r.to the particle once this state is not of the extremely special form of a tensor product of a one million particle state (the substate of the detector) and a single particle state (the substate of the particle).
This is essentially always the case once there is interaction between the million particles and the additional particle. The interaction causes the entanglement.

"when particles become entangled you have to consider them as one single, entangled state (you use the tensor product to calculate the resultant state).
---AN: this makes sense ---
So each component of our quantum particle forms separate entangled states.
--- AN: this is nonsense and does not follow. It flatly contradicts the previous sentence.
The notion of separate entangled states of a single particle cannot even be translated into something meaningful on the formal level. ---
"Whenever any property of a microscopic object affects a macroscopic object, that property is 'observed'"
---AN: this makes sense ---
In that case, if there are no longer any interference terms then to all intents and purposes the particle is now in a single, quantum state - one of the component eigenstates"
--- AN: this is a gross simplification ---

What is wrong in what he is saying? What is the correct way to put it.

I interspersed some comments.

The final statement of those I quoted is in fact at the borderline of what decoherence can explain. It is a frequently found misunderstanding of what decoherence achieves. What decoherence proves (under appropriate conditions that must be assumed) is only that the particle state becomes a mixture (rather than a superposition) of the eigenstates. This is enough to eliminate all interference effects.

But nothing in the theory of decoherence says that the particle state becomes an eigenstate. This is the collapse of the Copenhagen interpretation, and is _not_ explained by decoherence. Read Schlosshauer's paper cited on www.decoherence.de (under Literature/Articles), where this is made quite clear.

 

[Alfrez]

One correct statement doesn't imply that everything is correct, and agreeing to one statement is no agreement to everything.



There are no well-defined components, and decoherence has nothing to do with components.There is no entanglement with components of a state (this concept is meaningless), but only entanglement between complete substates of a composite system.

There is just one big state for one million plus one particles (the system), and it is entangled w.r.to the particle once this state is not of the extremely special form of a tensor product of a one million particle state (the substate of the detector) and a single particle state (the substate of the particle).
This is essentially always the case once there is interaction between the million particles and the additional particle. The interaction causes the entanglement.



I interspersed some comments.

The final statement of those I quoted is in fact at the borderline of what decoherence can explain. It is a frequently found misunderstanding of what decoherence achieves. What decoherence proves (under appropriate conditions that must be assumed) is only that the particle state becomes a mixture (rather than a superposition) of the eigenstates. This is enough to eliminate all interference effects.

But nothing in the theory of decoherence says that the particle state becomes an eigenstate. This is the collapse of the Copenhagen interpretation, and is _not_ explained by decoherence. Read Schlosshauer's paper cited on www.decoherence.de (under Literature/Articles), where this is made quite clear.

I've been analysing this for 5 hours even reading Schlosshauer book "Decoherence and the Quantum-to-Classical Transition" and I'm quite confused of your position. Let's standardize our definitions as I think you are using non-standard terms or just messing up my mind. Let's start about Hilbert Space and initiate semantic normalization.

Brief relevant passages from http://www.ipod.org.uk/reality/reality_quantum_casino.asp . Let me know any terms or concepts you don't believe so I can know how you see it.

"Wavefunction state can be a single point vector in a state space in Hilbert space."

"Any wavefunction state of the system can be generated from linear combinations of the eigenstates (this is what is known as quantum superposition).
We can represent the eigenstates by orthogonal vectors called eigenvectors"

"Whatever the state the system is in, can be represented as being a sum (superposition) of varying amounts of the eigenstates. The amount that each eigenstate contributes to the overall sum is called a component."

"Hence any wavefunction state of the system can be generated from linear combinations of the eigenstates (this is what is known as quantum superposition). Rather remarkably, before the measurement is taken, a quantum system can exist in a mix of all of its allowed states simultaneously."

"An analogy can be made with the superposition of waves. It can be shown that a complicated composite wave (representing the state vector) is composed of varying quantities of simple harmonic waves (representing the eigenstates)."

--------------------
Now fastforward to Decoherence.

Let's agree that "Component" means the amount that each eigenstate contributes to whatever state the system is in which can be represented as being a sum (superposition) of varying amounts of the eigenstates.

So far are all of the above standard terms accepted by physicists?

Now what is the wrong with the Component making entanglement with the photon in the environment as in "each of its component states gets entangled (separately) with different aspects of its environment" (like photons in surrounding)?? Why is it meaningless? Are you only the one who don't believe it? Meaning, Is this because of your unique interpretation of Quantum Mechanics or is this "component making entanglement" thing also not believed by the mainstream??

 

[Alfrez]

To continue with the above statements. Decoherence has to do with the phases of the states being altered "which destroys the coherent phase relationships between the components. The components are said to decohere." as the author put it. I think this is believed by the mainstream. So I can't undertand why you said decoherence doesn't have anything to do with component (see my definition of *component* in the message right before this). If you are giving your own concept, pls.emphasize it's yours alone and not the mainstream so as not to confuse. Thanks.

 

[Alfrez]

Hmm.. unless you meant this. I mean.. let's take the example of plain superposition and the composites Fourierwise as in:

"An analogy can be made with the superposition of waves. It can be shown that a complicated composite wave (representing the state vector) is composed of varying quantities of simple harmonic waves (representing the eigenstates):"

Now in a superposition of waves such as water. Are you saying it is impossible to pick out the simple harmonic waves by some kind of gadget or method? Analogy is each photon in the environment picking out the component states of the state vector??

But then what if Hilbert Space has some real correlate somewhere. It is easy then to invade it and find the Eigenstates (or composite wave analogywise) as well as components. We can treat photons as having natural affinity to navigate the Hilbert Space and seek out those component states and entangle with them. What is this impossible?? This is even more logical than Many Worlds. Maybe you just want to treat everything as pure mathematical without physical correlate. What if Hilbert Space being complex space has real locality in complex spacetime. Then it is possible.

 

[A. Neumaier]

Hmm.. unless you meant this. I mean.. let's take the example of plain superposition and the composites Fourierwise as in:

"An analogy can be made with the superposition of waves. It can be shown that a complicated composite wave (representing the state vector) is composed of varying quantities of simple harmonic waves (representing the eigenstates):


Now in a superposition of waves such as water. Are you saying it is impossible to pick out the simple harmonic waves by some kind of gadget or method?

Try to pick out a harmonic wave from the wave you get when throwing a stone into water.

But then what if Hilbert Space has some real correlate somewhere. It is easy then to invade it and find the Eigenstates (or composite wave analogywise) as well as components. We can treat photons as having natural affinity to navigate the Hilbert Space and seek out those component states and entangle with them. What is this impossible?? This is even more logical than Many Worlds. Maybe you just want to treat everything as pure mathematical without physical correlate. What if Hilbert Space being complex space has real locality in complex spacetime. Then it is possible.

You are using the words without assigning to them the right meaning. Most of what you write here is incomprehensible to me. Do you know what a Hilbert space is, an eigenstate, or complex spacetime? What is meant by a component state?

It doesn't make sense to ask for clear answers to fuzzy questions? The first thing you need to get wright is that you learn the standard meaning of standard notions - otherwise communication is next to impossible.

 

[A. Neumaier]

reading Schlosshauer book "Decoherence and the Quantum-to-Classical Transition" and I'm quite confused of your position. Let's standardize our definitions as I think you are using non-standard terms or just messing up my mind.

You seem to believe that the terms in a layman's version of physics are standard, while those used by physicists themselves are not... It's your favorite decoherence site that is messing up your mind!

Let's agree that "Component" means the amount that each eigenstate contributes to whatever state the system is in which can be represented as being a sum (superposition) of varying amounts of the eigenstates.

Please express this in terms of formulas, so that I can see whether it is something I can agree to.

So far are all of the above standard terms accepted by physicists?

No. They are a diluted version for lay people who cannot think in terms of precise formulas. They contain small errors that make a difference.

But I am not willing to discuss http://www.ipod.org.uk/reality/ which is far too superficial; the author doesn't even distinguish between a superposition and a mixture! (at least, according to your quote, he uses 'mix' for a superposition)

Please quote instead from Schlosshauer. Once you understand him you can find the errors in the above statements yourself.

 

[Alfrez]

Try to pick out a harmonic wave from the wave you get when throwing a stone into water.



You are using the words without assigning to them the right meaning. Most of what you write here is incomprehensible to me. Do you know what a Hilbert space is, an eigenstate, or complex spacetime? What is meant by a component state?

It doesn't make sense to ask for clear answers to fuzzy questions? The first thing you need to get wright is that you learn the standard meaning of standard notions - otherwise communication is next to impossible.

Isn't there any device or gadget that can home in the harmonic wave from the wave when one throw a stone into water?

Anyway.

Hilbert Space = complex vector space
Eigenstate = allowed states
Complex spacetime = a special kind of spacetime that holds complex numbers

The third is the key, what if Hilbert Space were real and located in a netherland region of spacetime. That is. What if Complex Numbers have its own physical space and not just a mathematical expression. Then the photons from the environment can navigate Hilbert Space and lock on to the components of the Eigenstates. Right?? I wonder if this is what the author of the website thinks. I'll contact him anyway and tell him what you told me.

 

[A. Neumaier]

Hilbert Space = complex vector space
Eigenstate = allowed states
Complex spacetime = a special kind of spacetime that holds complex numbers

You need to be much more precise if you ever want to understand decoherence in a better than just entertainment fashion.

Please look up these terms in Wikipedia, compare, and correct your concepts.

 

[Alfrez]

A pure N particle state psi is unentangled only if it has the form
psi = psi_1(x_1) tensor psi_2(x_2) tensor ... tensor psi_N(x_N)
But the most general pure N particle state can be an arbitrary linear combination of states of this form - all these are called entangled. The Hamiltonian dynamics of a system generally (i.e., except under specially prepared conditions) turns an unentangled state immediately into an entangled state. Therefore in a pure state, N particles are almost always entangled.

Ok. So Andrew Thomas with Ph.D. in Electrical Engineering is wrong. His incorrect stuff sidetracked me for a while. Now going back to 100 photons in the environment and how it entangled with the one single electron in the double slit experiment causing decoherence. You said above that the entire 100 photon + 1 electron is in pure state. I have difficulty with this concept.

A pure state is when there is quantum coherence, meaning there are interferences amongst the phase relationships such that in the double slit, there are interferences, so pure state automatically means there is interference in the quantum state, agree?

Also I presume entanglement automatically means being in pure state. In other words, Superposition, entanglement, and pure state are always together.

When the 100 photons in the surrounding got entangled with the single electron, Schlosshauer described the the coherence being "carried" away to the environment, or the coherence being delocalized from the system. Now you described it as still being in pure state.

But pure state means there is interference. However, this wikipedia article says "Decoherence occurs when a system interacts with its environment in a thermodynamically irreversible way. This prevents different elements in the quantum superposition of the system+environment's wavefunction from interfering with each other."

Now since there is no more interference, then it can't be pure state. But you said it's still pure state. There's the contradiction.

Unless you mean that in pure state, it is possible the interference can be hidden amongst the many degrees of freedom and still call it pure state? This means pure state doesn't automatically means there is interference that can be measured, is this it?

 

[Alfrez]

I think you will agree (see post above) that in pure state, interference can be hidden amonst many degrees of freedom in the environment and beyond the realm of measurement, right?

If so, Next inquiry. Since the 100 photons + 1 electron system-environment stuff is in contact with other particles in the surrounding. In fact, since everything is connected to everything in say your living room. Can you say the entire living room is in pure state?
If not, what prevents the 100photons + 1 electron from being entangled with other objects in the environment? What's the dividing line?

 

[A. Neumaier]

Your statements are too vague to allow them to be properly discussed.

You said above that the entire 100 photon + 1 electron is in pure state.

It may or may not be in a pure state. My assumption was just for simplicity.

A pure state is when there is quantum coherence, meaning there are interferences amongst the phase relationships such that in the double slit, there are interferences, so pure state automatically means there is interference in the quantum state, agree?

A pure state means that the system can be described by a wave function psi, while mixed states must be described by a density matrix rho. (The density matrix can also describe pure states, namely when it is of the form rho = psi psi^*.)

This is completely independent of a discussion of phase relationships or interference.
In particular, you can observe interference only for a small system, not for a system and its environment together.

Also I presume entanglement automatically means being in pure state. In other words, Superposition, entanglement, and pure state are always together.

One usually assumes a system to be in a pure state when discussing superpositions and entanglement. But pure states neither need to be entangled nor be in a superposition.

When the 100 photons in the surrounding got entangled with the single electron, Schlosshauer described the the coherence being "carried" away to the environment, or the coherence being delocalized from the system. Now you described it as still being in pure state.

Yes. A unitary dynamics preserves the pureness of a state.

But pure state means there is interference.

No. pure state means not mixed, and nothing else.