High School Decoherence and the Dust Particle

[Feeble Wonk]

This question is a extremely logical & mathematical formulation is very challenging as long as causation and correlation issues are not resolved yet in this .

Which specific question are you referring to?

 

[Feeble Wonk]

Only if you perform a measurement that leads to decoherence.

But, does the "mixed" state describe the potential locations of the dust particle BEFORE decoherence?

 

[mfb]

No, that is the point of decoherence.

 

[Feeble Wonk]

No, that is the point of decoherence.

OK. I confess my ignorance on this topic. I'd appreciate the assistance in helping me understand how this works.
Prior to the interaction between dust particle and photon, what information regarding the dust particle is present in the quantum wave function describing the region of space-time? Or is that idea meaningless in and of itself?

 

[Feeble Wonk]

You need to understand the role of Hamiltonians in QM.

OK. Let's try this a different way. Can you tell me what physical parameters are described by information in the QM Hamiltonian?

 

[mfb]

A proper Hamiltonian is a full description of the physics of the system - at least in theory.

 

[Feeble Wonk]

A proper Hamiltonian is a full description of the physics of the system - at least in theory.

So... as well as location and spatial geometry, it would describe the dynamics of the electroweak forces, color, mass and gravitation?

 

[mfb]

A Hamiltonian in particle physics: sure. Usually the Lagrangian is used, and its fully expanded form is... well... let's go back to the compact version.

 

[Feeble Wonk]

LOL. I've seen the Lagrangian for the standard model in the past. I had to look away before my head ignited. I'm afraid that even the compact version is a little beyond me (I'm not even sure what the various symbols refer to).

Let's go back to the Hamiltonian for QM if you don't mind. Does it describe the "change" in the system, or the state of the system at any given time?

 

[mfb]

It allows you to find the state at any time in the future or the past if you know the state at a specific point in time.

 

[Feeble Wonk]

It allows you to find the state at any time in the future or the past if you know the state at a specific point in time.

Is there an layman level explanation as to how the Hamiltonian projects future states? My curiosity applies particularly to whether the degree of state reduction becomes less "refined" as the system moves forward in time. Demystifier suggested earlier (post #5) that decoherence is not irreversible... at least not in simple systems.

 

[mfb]

The Hamiltonian allows to calculate the time-evolution of a state. In nonrelativistic quantum mechanics, this is just the Schroedinger equation, for example. Note that no collapses or similar processes happen here. For systems of sufficient complexity, the time-evolution often leads to states that can be split into multiple pieces with practically no interaction between those pieces. That is decoherence. It is irreversible, as Demystifier said in post #5. An interaction that looks like a measurement can be reversible, but then it does not lead to decoherence.

You can now assume that (a) all but one piece magically disappear and the remaining piece gets a larger amplitude, (b) those pieces just stay independent and keep evolving according to the laws of quantum mechanics, (c) your initial state was not correct or didn't describe everything, (d) ... a few other things.
(a) leads to collapse-like interpretations, (b) to many worlds, (c) to de-Broglie-Bohm, and so on. Your description of the state after a while depends on the interpretation you choose. But all those things are interpretations, not measurement results, they are not necessary for making predictions.

 

[Feeble Wonk]

The Hamiltonian allows to calculate the time-evolution of a state. In nonrelativistic quantum mechanics, this is just the Schroedinger equation, for example. Note that no collapses or similar processes happen here. For systems of sufficient complexity, the time-evolution often leads to states that can be split into multiple pieces with practically no interaction between those pieces. That is decoherence. It is irreversible, as Demystifier said in post #5. An interaction that looks like a measurement can be reversible, but then it does not lead to decoherence.

You can now assume that (a) all but one piece magically disappear and the remaining piece gets a larger amplitude, (b) those pieces just stay independent and keep evolving according to the laws of quantum mechanics, (c) your initial state was not correct or didn't describe everything, (d) ... a few other things.
(a) leads to collapse-like interpretations, (b) to many worlds, (c) to de-Broglie-Bohm, and so on. Your description of the state after a while depends on the interpretation you choose. But all those things are interpretations, not measurement results, they are not necessary for making predictions.

Excellent. Thank you. Let me roll this around in my head for a bit.

 

[Feeble Wonk]

The Hamiltonian allows to calculate the time-evolution of a state. In nonrelativistic quantum mechanics, this is just the Schroedinger equation, for example. Note that no collapses or similar processes happen here. For systems of sufficient complexity, the time-evolution often leads to states that can be split into multiple pieces with practically no interaction between those pieces. That is decoherence. It is irreversible, as Demystifier said in post #5. An interaction that looks like a measurement can be reversible, but then it does not lead to decoherence.

I'm trying to imagine how the Hamiltonian changes if we expand the system being considered away from the locality of the dust particle to include the photon emitting events (assuming that "a few" photons are required) that might be countless light years away. Does the uncertainty in the possible path of the localizing photon have any bearing on anything?

 

[Feeble Wonk]

I've got to assume that the lack of response to my last question means that I, once again, phrased the idea in terms that are absurd and/or meaningless. So, I'd like to ask it in a different way.
You've patiently explained that the evolution of the quantum state of the system describing the dust particle evolves over time, and decoherence localizes the particle "after" interaction with one or more photons.
I believe it was further explained that in any system of sufficient complexity, the interactions are frequent enough that the decoherence is irreversible (such that the mixture of potential states will remain decohered forever as the separate Hamiltonians continue to evolve along different lines).
All of this makes sense to me. However, my confusion remains in regard to the assertion that the "potential" interaction with the photon(s) constitutes a measurement/observation. And this relates to my question regarding the "expanded" quantum system being considered.
When we consider the system to include not only the (potential) dust particle, but also the (potential) photon emitting event(s), it seems that the (potential) decohered states would be incalculably increased as a result. So yes, IF we stipulate that a dust particle in a specific location in space time interacts with one or more photons that have been emitted from any number of possible sources, then I suppose the location of the dust particle would be defined in one of those (incalculably various) potential states.
But how are we to say that such a logical limitation (of quantum state reduction) has "really" been observed/measured simply because the mathematics define the decohered state reduction IF that were the case?
Does that question make any more sense?

 

[cube137]

I've got to assume that the lack of response to my last question means that I, once again, phrased the idea in terms that are absurd and/or meaningless. So, I'd like to ask it in a different way.
You've patiently explained that the evolution of the quantum state of the system describing the dust particle evolves over time, and decoherence localizes the particle "after" interaction with one or more photons.
I believe it was further explained that in any system of sufficient complexity, the interactions are frequent enough that the decoherence is irreversible (such that the mixture of potential states will remain decohered forever as the separate Hamiltonians continue to evolve along different lines).
All of this makes sense to me. However, my confusion remains in regard to the assertion that the "potential" interaction with the photon(s) constitutes a measurement/observation. And this relates to my question regarding the "expanded" quantum system being considered.
When we consider the system to include not only the (potential) dust particle, but also the (potential) photon emitting event(s), it seems that the (potential) decohered states would be incalculably increased as a result. So yes, IF we stipulate that a dust particle in a specific location in space time interacts with one or more photons that have been emitted from any number of possible sources, then I suppose the location of the dust particle would be defined in one of those (incalculably various) potential states.
But how are we to say that such a logical limitation (of quantum state reduction) has "really" been observed/measured simply because the mathematics define the decohered state reduction IF that were the case?
Does that question make any more sense?

Your choice of words are kinda vague. Please rephrase the sentences such a way Bhohha, atyy or others can understand.. like what you mean logical limitation has been observed..

 

[Feeble Wonk]

Your choice of words are kinda vague. Please rephrase the sentences such a way Bhohha, atyy or others can understand.. like what you mean logical limitation has been observed..

I suppose you could just replace the words "logical limitation" with "realized state reduction", "collapse", or something like that.
I fully accept that the mathematics of decoherence limit the quantum states that CAN occur in such a way that macroscopic superposition will not be observed WHEN an observation is made. I have no qualms about that. Yet, particularly when we are considering a large system (as I've described earlier), it seems to me that the vast array of potential states would remain part of the Hamiltonian expression describing the "potential" locality of the "potential" dust particle.
So, yes, IF we stipulate that one or more photons from any of the countless potential photon emitting events interact with a dust particle at a given location, then I suppose you could say that the mathematics of decoherence would define the physical locality of the dust particle within the Hilbert space described by that expression. However, that seems (to me anyway) to be an arbitrary assumption in the absence of a "realized" observation of the photon(s)/dust particle interaction, if we are considering the larger system including the potential photon emission events.

 

[cube137]

I suppose you could just replace the words "logical limitation" with "realized state reduction", "collapse", or something like that.
I fully accept that the mathematics of decoherence limit the quantum states that CAN occur in such a way that macroscopic superposition will not be observed WHEN an observation is made. I have no qualms about that. Yet, particularly when we are considering a large system (as I've described earlier), it seems to me that the vast array of potential states would remain part of the Hamiltonian expression describing the "potential" locality of the "potential" dust particle.
So, yes, IF we stipulate that one or more photons from any of the countless potential photon emitting events interact with a dust particle at a given location, then I suppose you could say that the mathematics of decoherence would define the physical locality of the dust particle within the Hilbert described by that expression. However, that seems (to me anyway) to be an arbitrary assumption in the absence of a "realized" observation of the photon(s)/dust particle interaction, if we are considering the larger system including the potential photon emission events.

Ping any science advisor. Can you please respond the above as I'm interested in what he is saying. Thank you.

 

[Feeble Wonk]

Ping any science advisor. Can you please respond the above as I'm interested in what he is saying. Thank you.

I would appreciate a response as well. I might anticipate a statement that the photon/particle interaction IS the "observation" that produces the decoherence, but that feels very unsatisfying to me. That argument seems like a basic logical "if/then" statement of post-facto causation. IF the photon/dust particle interaction occurs at this point, THEN there must be a dust particle localized at that point and not in superposition over other potential points.
But from the larger system perspective, the dust particle might exist elsewhere as a quantum object, and potential photon emission might or might not occur, and the path of the photon might or might not intersect with the dust particle. So, it seems like the state reduction described by the mathematics of decoherence assumes the "interaction" that might or might not occur, and defines that as the "observation" that caused the decoherence, which then causes the state reduction. It all seems very circular to me.

 

[Jilang]

My take on this is one that comes down to the likelihood of reversibility. Quantum evolution is inherently time reversible. If a dust particle absorbs a photon is that reversible? Quite possibly, by re-emission of a photon. If said just particle absorbs said photon and encounters another one soon afterwards, the chances of the whole chain of events being reversed becomes very small indeed. Not zero, just very small. If the dust particle absorbs an re-emits just one photon which then interacts with a macroscopic object: no chance!

 

[bhobba]

it seems to me that the vast array of potential states would remain part of the Hamiltonian expression describing the "potential" locality of the "potential" dust particle.

It's hard to give a response because once you understand the technicalities statements like the above don't really make much sense - at least I can't make sense of them.

You are venturing into territory that's impossible, utterly impossible, to discuss linguistically. You must do the math.

I understand wanting to understand this stuff, I really do. But the correct way to proceed is to learn the real deal. How about going away and studying the basics:
https://www.amazon.com/dp/0465062903/?tag=pfamazon01-20

That way you will have what's needed to get a real explanation.

Thanks
Bill

 

[cube137]

I suppose you could just replace the words "logical limitation" with "realized state reduction", "collapse", or something like that.
I fully accept that the mathematics of decoherence limit the quantum states that CAN occur in such a way that macroscopic superposition will not be observed WHEN an observation is made. I have no qualms about that. Yet, particularly when we are considering a large system (as I've described earlier), it seems to me that the vast array of potential states would remain part of the Hamiltonian expression describing the "potential" locality of the "potential" dust particle.
So, yes, IF we stipulate that one or more photons from any of the countless potential photon emitting events interact with a dust particle at a given location, then I suppose you could say that the mathematics of decoherence would define the physical locality of the dust particle within the Hilbert space described by that expression. However, that seems (to me anyway) to be an arbitrary assumption in the absence of a "realized" observation of the photon(s)/dust particle interaction, if we are considering the larger system including the potential photon emission events.

Feeble Wonk. Before you spent 4 hours reading the book Bhobba suggested to you and perhaps spending 4 years taking physics course to even understand the book. Can you please explain in standard terms what you mean by the following:

"it seems to me that the vast array of potential states would remain part of the Hamiltonian expression describing the "potential" locality of the "potential" dust particle"

Bill can't understand the above words. What is the context or concept in conventional schroedinger equation did you mean by above? It's either the wave function collapses or it is under deterministic wave evolution. So what you mean by "potential"? Are you saying before collapse? Please explain it like explaining to laymen. Perhaps atyy or others can understand what you were saying. The first language of Bill and Neumaier are maths so they would have more difficulty trying to relate to people who are not dense in math. But people like atyy who have math as second language may be able to relate or adapt quickly.

 

[bhobba]

Before you spent 4 hours reading the book Bhobba suggested to you and perhaps spending 4 years taking physics course to even understand the book. Can you please explain in standard terms what you mean by the following:

It will take more than 4 hours - probably a few weeks spending an hour or so each day. But the pay-off is immense. I can quite easily explain what's going on with just a bit of technical background like that book provides - otherwise forget it. I remember similar discussions around the difference between a pure and mixed states. It went on and on and on. Post after post, and I am not sure after people were really any the wiser. However if you know the Bra-Ket notation it can be explained in a couple of lines. The same with the basic notion of superposition.

Thanks
Bill

 

[cube137]

It will take more than 4 hours - probably a few weeks spending an hour or so each day. But the pay-off is immense. I can quite easily explain what's going on with just a bit of technical background like that book provides - otherwise forget it. I remember similar discussions around the difference between a pure and mixed states. It went on and on and on. Post after post, and I am not sure after people were really any the wiser. However if you know the Bra-Ket notation it can be explained in a couple of lines. The same with the basic notion of superposition.

Thanks
Bill

What I meant was he spent 4 years taking course in physics first then spending 4 hours reading it (4 years later) . Because without any undergraduate course in physics.. even a few weeks is not enough. Anyway. For Brian Greene, they may be able to explain it at least the rough idea. I just want a rough idea what Feeble was talking about. Like I think maybe what he meant was that while they are not yet collapsed, the eigenstates are all there is.. maybe what he meant by "potential".. so Feeble.. please use the language of mixed state, pure state, eigenstates and other standard terms so at least I can understand what you are asking (it's ok if it would take 4 years later to have the answer).

 

[bhobba]

What I meant was he spent 4 years taking course in physics first then spending 4 hours reading it (4 years later)

That's not required.

A few hours reading Suskind's first book and Quick Calculus is all that's needed.

This idea learning the real deal needs years and years needs to be dispelled once and for all.

If you want to understand this stuff you MUST make the effort. Linguistically will simply not cut it. BTW Brian Green's stuff leaves a lot to be desired - but it's about the best you can do without the technicalities.

Like I think maybe what he meant was that while they are not yet collapsed, the eigenstates are all there is..

I can't make sense of that either. First QM does not have collapse - that is an interpretative thing. Any state is an eigenstate of some operator so 'the eigenstates are all there is'

Thanks
Bill

 

[cube137]

I suppose you could just replace the words "logical limitation" with "realized state reduction", "collapse", or something like that.
I fully accept that the mathematics of decoherence limit the quantum states that CAN occur in such a way that macroscopic superposition will not be observed WHEN an observation is made. I have no qualms about that. Yet, particularly when we are considering a large system (as I've described earlier), it seems to me that the vast array of potential states would remain part of the Hamiltonian expression describing the "potential" locality of the "potential" dust particle.
So, yes, IF we stipulate that one or more photons from any of the countless potential photon emitting events interact with a dust particle at a given location, then I suppose you could say that the mathematics of decoherence would define the physical locality of the dust particle within the Hilbert space described by that expression. However, that seems (to me anyway) to be an arbitrary assumption in the absence of a "realized" observation of the photon(s)/dust particle interaction, if we are considering the larger system including the potential photon emission events.

We have already read many times over Bill suggested decoherence paper like:

http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

we know the basic of decoherence already.. of course.. he suggested more books but I just want to know the context of the above for now. I wonder if it is the famous factorization problem or others? I think what Feeble was saying above (contemplating on it many hours) is that photon emission was probabilistic.. so how does it behave when it acts as the environment of the system (dust particle). Right? I hope atyy or others can comment (except Bill who I know would suggest for us to read dense textbooks... we would get to this but just want feedback from atyy or mfb who knows what Feeble was pointing out. Bill doesn't understand Feeble question so expect him to ask using Bra-ket notations)

 

[bhobba]

except Bill who I know would suggest for us to read dense textbooks

I am NOT suggesting that.

The books I have suggested are NOT dense. They will not take long to understand - a few weeks maybe.

What they will do is give the basics enough so you can understand a genuine explanation.

Thanks
Bill

 

[bhobba]

Here is the genuine explanation.

You have |a> representing the state of the photons, |b> the state of the dust particle. The combined state is u = |a>|b>. Due to interactions between the two described by a Hamiltonian and Schroedinger's equation that state changes. The equation is i∂u/∂t = Hu where H is the Hamiltonian. You solve it to get the state at any time t. Now what we find is this new state is no longer factorisable into the state of the photons and the state of the dust particle. They are entangled. However if we just observe the dust particle we find its in a mixed state of position ie |b> = Σpi |bi><bi| where each |bi><bi| is an eigenstate of position. This means it can be interpreted as having a definite position with probability pi. Note I have used the notation for a state |a> and |a><a| interchangeably. What a state is and what it means is explained in the references - that's one of the things you need to understand. You can't understand this without it.

Obviously its just an overview and tomes will give a LOT more detail. But its the correct explanation. You can't explain it linguistically.

Thanks
Bill

 

[Feeble Wonk]

.
I wonder if it is the famous factorization problem or others? I think what Feeble was saying above (contemplating on it many hours) is that photon emission was probabilistic.. so how does it behave when it acts as the environment of the system (dust particle). Right?

Yes. I think you've hit it pretty much on the head cube. Thank you.

You are venturing into territory that's impossible, utterly impossible, to discuss linguistically. You must do the math.

While I sincerely appreciate your support cube, I also sympathize with Bill's frustration. He's absolutely right about the difficult position I've put him in. My moniker was not chosen randomly. I'm painfully aware of my mathematical limitations, and how difficult that makes it for him (or others) to explain the mathematical aspects of the formalism to me. I obviously have a very poor grasp of even the appropriate parlance, let alone having the mathematical chops to actually run the numbers.

Yet, I continue to believe that the mathematics expressing the theory is actually describing "something", which I can only generally refer to as "Nature". I suppose that what I'm really asking about is what the theory is implying about the nature of "Nature", and my hope is that at least that much is describable with language.

One of my favorite Lee Smolin quotes is, "Math, in reality, comes after Nature. It has no generative power. Another way to say this is that in mathematics, conclusions are forced by logical implication. Whereas, in Nature, events are generated by causal processes acting in time. This is not the same thing."
I guess it's the same general idea that John Wheeler captured more humorously when, after drawing a complex mathematical formula on the chalk board, he joked "Now I'll clap my hands and a universe will spring into existence".

Here is the genuine explanation.

You have |a> representing the state of the photons, |b> the state of the dust particle. The combined state is u = |a>|b>. Due to interactions between the two described by a Hamiltonian and Schroedinger's equation that state changes. The equation is i∂u/∂t = Hu where H is the Hamiltonian. You solve it to get the state at any time t. Now what we find is this new state is no longer factorisable into the state of the photons and the state of the dust particle. They are entangled. However if we just observe the dust particle we find its in a mixed state of position ie |b> = Σpi |bi><bi| where each |bi><bi| is an eigenstate of position. This means it can be interpreted as having a definite position with probability pi. Note I have used the notation for a state |a> and |a><a| interchangeably. What a state is and what it means is explained in the references - that's one of the things you need to understand. You can't understand this without it.

This is helpful Bill. I'll try to digest it. Thank you. Is it accurate for me to conclude from this that I should think of the "potential" photon emission events and/or paths as being in an entangled state with the "potential" position of the dust particle? I apologize for the clumsy use of the word "potential" here, but I'm not sure how else to describe the concept.
If so, should I think of the photon/dust particle interaction event as being the "measurement" that determines the reduced state (differentiates between the potential reduced states) of the entangled system?
If so, should I simply think of decoherence as being the mathematical analysis revealing that the position eigenstate of the dust particle is defined precisely enough "within that reduced state" that no superposition will be (or can be) observed? Similarly, and perhaps more importantly, should I think of the quantum state(s) of the initial photon emission event(s) as being correspondingly reduced "within that reduced state" of the entangled system?

Again, I apologize for the clumsiness of the phrase, "within that reduced state", but I'm guessing that this an interpretational matter... in MW, they would be distinctly different branches... in CI, it would be a collapsed state... ect.

 

[bhobba]

If so, should I think of the photon/dust particle interaction event as being the "measurement" that determines the reduced state (differentiates between the potential reduced states) of the entangled system?

Basically - yes.

Thanks
Bill