B Decoherence and the Dust Particle

[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

 

[Feeble Wonk]

Basically - yes.

OK. Thanks Bill. I think I can make peace in my head with this general idea. If I'm understanding what you're saying, I should be able to envision decoherence as setting the allowed logical limits for parameters of state reduction, but I don't have to accept it as the "causative process" for that state reduction. I get the feeling that pursuing the point beyond that generality takes us into interpretational concepts that are not directly related to the formalism of theory, so I won't torture you with that discussion... today[emoji16].

Just an aside thought however... When I recognize that the state of the entire expanded system is reduced correspondingly as the dust particle becomes localized, it seems as though the logical ramifications could (should?) expand exponentially throughout large swaths of the universe. Yes?

 

[bhobba]

When I recognize that the state of the entire expanded system is reduced correspondingly as the dust particle becomes localized, it seems as though the logical ramifications could (should?) expand exponentially throughout large swaths of the universe. Yes?

No.

Thanks
Bill

 

[Feeble Wonk]

No.

Thanks
Bill

Is this because the information regarding the photon emission is so minimal (and potentially reversible) relative to the localization of the dust particle?

 

[Feeble Wonk]

No.

Thanks
Bill

...and yes I'm only asking in general terms. I strongly suspect that this is another one of those things that I'm not going to properly understand without the necessary command of the mathematics. I simply mean, is the reason that the state reduction not more expansive because the photon emission event is reversible in terms of the decoherence, or is it just because so little information is exchanged?

 

[bhobba]

...and yes I'm only asking in general terms. I strongly suspect that this is another one of those things that I'm not going to properly understand without the necessary command of the mathematics. I simply mean, is the reason that the state reduction not more expansive because the photon emission event is reversible in terms of the decoherence, or is it just because so little information is exchanged?

I gave the correct explanation. It mentions none of the things you mention. They have nothing to do with anything.

You are trying to reason linguistically and getting yourself very confused.

Please stop that because I will not respond any more.

Thanks
Bill

 

[Feeble Wonk]

Fair enough.

 

[cube137]

Fair enough.

Please note that Hobba and Neumaier are Ph.D. in mathematics so they don't have patience in dealing those below undergraduate in mathematics or physics. Advisers who are most patient are the rest like atyy or mfb. I guess the quantum physics forums have to be divided into two.. for undergraduates and for advanced laymen. We are advanced laymen who struggled for years reading many books. And because our professions are not mathematicians.. we want to ask direct question. In your case you asked: "When I recognize that the state of the entire expanded system is reduced correspondingly as the dust particle becomes localized, it seems as though the logical ramifications could (should?) expand exponentially throughout large swaths of the universe. Yes?". Only other advisers who are not Ph.D mathematicians can answer it. Also note Hobba and Neumaier hate the idea of wave functions as representing the objects in actual. They tend to think of the math only and really admit "They don't know" it's connection to reality.. hence both are Ensemblers.

Anyway. I'd like to know the answer to your questions too. So let's hope others ask it too. You are asking "is the reason that the state reduction not more expansive because the photon emission event is reversible in terms of the decoherence, or is it just because so little information is exchanged?" I think you are talking about the entanglement so complex that irreversibility is the norm.. but if wave function has ontology.. then indeed everything is reversible. In pure maths.. since you can't know or describe the environment because it's too complex.. then it's reversible. I think jilang has grasped this question and can comment. (I think it is a good idea that Hobba and Neumaier only deal with threads with Intermediate and Advanced and leave the B to the other Science Advisors with more patience. Thanks.

 

[bhobba]

Please note that Hobba and Neumaier are Ph.D. in mathematics

I don't have a Phd in math - I have the equivalent of an Honours degree in applied math and computer science. I have partially completed a masters but had to give it away for various reasons. I am self taught in physics so know exactly what is required to understand this stuff. A few weeks of an hour or so study each night is all that's required to learn enough to understand the technical explanation I gave.

If you don't want to do that you will be in a constant state of confusion going around in circles trying to understand what can't be understood without it. I gave the correct explanation - all that is needed is to understand it.

You may think its a mater of patience. IMHO it isn't. It's that this stuff can't be understood on the terms you want to understand it - it can't be done - wishful thinking that someone with more patience will do it simply will not work. This is not just my view eg have a look at the likes MFB gave my posts.

Also note Hobba and Neumaier hate the idea of wave functions as representing the objects in actual.

That's incorrect. But fits in with my observation you will not understand what's really being said if you don't know at least a smattering of the technicalities.

My ignorance ensemble interpretation is agnostic to such things.

Thanks
Bill

 

[cube137]

I don't have a Phd in math - I have the equivalent of an Honours degree in applied math and computer science. I have partially completed a masters but had to give it away for various reasons. I am self taught in physics so know exactly what is required to understand this stuff. A few weeks of an hour or so study each night is all that's required to learn enough to understand the technical explanation I gave.

If you don't want to do that you will be in a constant state of confusion going around in circles trying to understand what can't be understood without it. I gave the correct explanation - all that is needed is to understand it.

You may think its a mater of patience. IMHO it isn't. It's that this stuff can't be understood on the terms you want to understand it - it can't be done - wishful thinking that someone with more patience will do it simply will not work. This is not just my view eg have a look at the likes MFB gave my posts.
That's incorrect. But fits in with my observation you will not understand what's really being said if you don't know at least a smattering of the technicalities.

My ignorance ensemble interpretation is anostic to such things.

Thanks
Bill

What is funny is you don't understand Feeble question when he asked:

"When I recognize that the state of the entire expanded system is reduced correspondingly as the dust particle becomes localized, it seems as though the logical ramifications could (should?) expand exponentially throughout large swaths of the universe. Yes?"

Yet you answered "no". Later you mentioned the question kinda doesn't make even sense. So you should have answered "Feeble what you said doesn't make sense".

Anyway. I have read your every thread in this forums for more than a day and already get the gist of it. I know what you meant when you stated that

"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."

I understood it. Now I saw Feeble Wonk has been participating for more than 3 years in this thread. So I think he understood it too. Therefore I'd like him to ask the question using the above language.

Feeble. When you asked "When I recognize that the state of the entire expanded system is reduced correspondingly as the dust particle becomes localized, it seems as though the logical ramifications could (should?) expand exponentially throughout large swaths of the universe. Yes?" Can you rephrase it using Hobba language. I'll tried. Is it like asking:

"When you only have a few |a> representing the state of the photons, and |b> the state of the dust particle. And the simple combined state is u = |a>|b>. Due to interactions between the two described by a Hamiltonian and Schroedinger's equation that state changes. Does the state expand exponentially throughout large swaths of the universe?"

Feeble. I'm confused by your question. What do you mean "Does the state expand exponentially throughout large swaths of the universe?". Please use more accurate questions.

I'm interested in your interests in decoherence and have the same questions as you do.

 

[bhobba]

What is funny is you don't understand Feeble question when he asked:

Have you stopped to consider it actually doesn't make sense? Which it doesn't BTW eg exponential - where exactly that comes from beats me - actually it doesn't beat me - its a symptom of what I have been saying. This is my last comment in this thread - its serving no useful purpose and needs to be closed IMHO.

Thanks
Bill

 

[Feeble Wonk]

Have you stopped to consider it actually doesn't make sense? Which it doesn't BTW eg exponential - where exactly that comes from beats me - actually it doesn't beat me - its a symptom of what I have been saying.

I think we should just drop it. It seems to be getting personal, and I certainly had no intention of that. By "exponential", I simply meant expanding rapidly. As I've confessed previously, my mathematical terminology is sadly lacking. For that matter, the entire reference to expansion is likely a misconception as well. Your point is taken.

 

[vanhees71]

Please note that Hobba and Neumaier are Ph.D. in mathematics so they don't have patience in dealing those below undergraduate in mathematics or physics. Advisers who are most patient are the rest like atyy or mfb. I guess the quantum physics forums have to be divided into two.. for undergraduates and for advanced laymen. We are advanced laymen who struggled for years reading many books.

Well, then some tip: If you invest such a long time in reading "many books", why then don't you read the right books? It's fun to read one or two popular-science books. The problem is that most of them are very bad. It's very difficult to write a good popular-science book also for experts in the field (and you should sort out any popular-science book not written by an expert in the field, i.e., a scientist working in it). So if you are willing to spend several years in reading books, read good textbooks. You'll need to study a lot of math first, then classical mechanics and some classical electrodynamics to get used to the mathematical tools, but that's fun too!

 

[Feeble Wonk]

May I ask one basic question? Does a photon being emitted by a particle constitute a physical interaction (in terms of decoherence) in anyway comparable to a photon being absorbed by a particle?

 

[Feeble Wonk]

Never mind. I think it might be best to start a different thread with a different mind set, and let this one die a merciful death.

 

[mfb]

I agree.