Double slit experiment and Interaction

[bhobba]

As I see it wave function collapse is a bridge between wave function and particles.

The point is that wave function collapse is not part of QM - only interpretations. Quite a few interpretations don't have it.

Thanks
Bill

 

[craigi]

Well, let's say we want to try Bohmian Mechanics or Many Worlds. There is still no Bohmian Mechanics version of the standard model of particle physics, and it is unclear whether Many-Worlds really works, as even proponents like Deustch http://arxiv.org/abs/0712.0149 and Carroll http://www.preposterousuniverse.com...ion-of-quantum-mechanics-is-probably-correct/ agree. So I don't think it is true that we have at least one interpretation that solves the definite outcomes problem. That leaves us with Copenhagen which does have the problem, and the only way to solve it is to assert it is not a problem, which I think the consciousness ones do quite nicely :p

Also, Bohmian Mechanics is in principle testable, just as string theory is. Many-Worlds, if in fact the theory of everything, will not be falsified. But if it isn't, then it can be falsified. So the problem with BM or MWI for solving the definite outcomes problem is not experimentally deciding between them.

This is a good summary. The MWI is the simplest way to interpret QM, but as Einstein asserted, QM is incomplete. Consciousness can be used to complete other interpretations, but leaves with a subjective reality based upon a poorly defined concept, which is too difficult to reconcile

 

[Feeble Wonk]

It depends on the situation - specifically if the object or objects interact with what is being observed and the degree of interaction. You must analyse each situation in detail to determine if the decoherence (ie interaction) is enough to give a definite outcome in some observable.

Sorry for my ignorance, but it seems that I didn't express my question clearly enough. I'd like to return to the question of how decoherence locally determines the subsystem of "collapse" within the universal quantum state.
Again, I'm trying to conceptually avoid the "physics in a box" controls of a system-environment-apparatus relationship. The question is thus assuming that we are discussing the quantum state vector of the entire universe, such that the environment, system and even the "apparatus" are all part of the same state vector. So when we are considering the "potential" states of a few random photons emitted during decoupling more than 13 billion years ago, it is difficult to fathom that our handful of photons did not have the potential paths that would have interacted with potential dust particles at some previous point in time. Why does the decoherence determine that it occurs "now" rather than then.
I suppose a related question would be pertaining to the number of the potential photon paths required to produce the "collapsed" locality of the dust particle. If, as you say, one photon is not sufficient and it would require a "few" random photons from the CMBR, do all of these photons have to interact with the dust particle at a particular instantaneous moment, or is it a cumulative effect of sequential interactions over time?

 

[craigi]

Sorry for my ignorance, but it seems that I didn't express my question clearly enough. I'd like to return to the question of how decoherence locally determines the subsystem of "collapse" within the universal quantum state.
Again, I'm trying to conceptually avoid the "physics in a box" controls of a system-environment-apparatus relationship. The question is thus assuming that we are discussing the quantum state vector of the entire universe, such that the environment, system and even the "apparatus" are all part of the same state vector. So when we are considering the "potential" states of a few random photons emitted during decoupling more than 13 billion years ago, it is difficult to fathom that our handful of photons did not have the potential paths that would have interacted with potential dust particles at some previous point in time. Why does the decoherence determine that it occurs "now" rather than then.

The truth is, that radiation just didn't interact in any significant way in those 13 billion years. Space is very empty and enough radiation survives to be detected today.

I suppose a related question would be pertaining to the number of the potential photon paths required to produce the "collapsed" locality of the dust particle. If, as you say, one photon is not sufficient and it would require a "few" random photons from the CMBR, do all of these photons have to interact with the dust particle at a particular instantaneous moment, or is it a cumulative effect of sequential interactions over time?

Decoherence occurs at thermodynamically irreverisble events. An example of this would be photon absorption. Examples of reversible events are, the specular reflection of light at a mirror, and the refraction of light through lenses or lensing by gravitational fields.

What makes some interactions reversible and some irreversible? We don't need QM for that. It's just back to statistical mechanics.

 

[Feeble Wonk]

The truth is, that radiation just didn't interact in any significant way in those 13 billion years. Space is very empty and enough radiation survives to be detected today.

I guess I'm still not making the point that confuses me clear enough. Sadly, the embarrassing degree of my mathematical ineptitude makes it impossible for me to utilize the formalized calculations as a means of understanding this issue. That forces me to to try to wrap my head around the general idea in a purely conceptual manner, and the quantum state constraints imposed by decoherence is an idea that persistently eludes me. While I fully expect that this failure is largely the result of my utter ignorance, I'll try again...
My understanding is that the quantum wave (state vector?) of a single photon can be demonstrated to "spread out" sufficiently to pass through both slits of the dual slit experiment in the very limited time and distance involved as it travels from the emitting device through the screen. If I extrapolate that concept to the time and distance involved with a remnant photon of CMB radiation produced by a decoupling event more than 13 billion years ago, I would expect the potential path (and/or state vector?) to become increasingly "spread out".
In the dual slit experiment, by preparing the appropriate controls and measurement devices, you can reduce the quantum state of the photon to the path having passed through one or the other slit. This is generally understandable.
However, in a completely uncontrolled environment, when the quantum system being "observed" is the state vector of the entire universe... when the system "is" the environment... and the apparatus is simply part of that system... how does the process of decoherence determine where the Von Neumann cut is placed?

 

[Feeble Wonk]

I suppose I should clarify my previous question even more. I would think that the path of the photon(s) of CMB radiation would sufficiently uncertain that the entirety of the wave function would include paths that might or might not intersect with the potential location of the dust particle in question. If no specific observation is made, other than that by the photon itself, why does it need to decide if it interacted or not?

 

[StevieTNZ]

I suppose I should clarify my previous question even more. I would think that the path of the photon(s) of CMB radiation would sufficiently uncertain that the entirety of the wave function would include paths that might or might not intersect with the potential location of the dust particle in question. If no specific observation is made, other than that by the photon itself, why does it need to decide if it interacted or not?

Decoherence does not solve the measurement problem. It is merely that the photon is entangled with the dust particle, due to interacting by the wave function including paths that intersect with the potential location (yes, you are correct to say the dust particle is in a potential location) of the dust particle.

 

[bhobba]

I suppose I should clarify my previous question even more. I would think that the path of the photon(s) of CMB radiation would sufficiently uncertain that the entirety of the wave function would include paths that might or might not intersect with the potential location of the dust particle in question.

You are trying to understand something highly technical without math,

Its got nothing to do with wavefunctions spreading out etc etc.

What its got to with is if you write down the system of photons and dust particle, indeed any interacting systems, and you observe one part of the entangled system, it mathematically is exactly the same as a proper mixed state - because its only mathematically the same and not prepared the same way its called an improper mixed state. A proper mixed state consists of a number of states randomly presented for observation. That being the case there is no measurement problem, what you are observing is there before observation and everything is sweet. The reason it doesn't solve the measurement problem is its only mathematically the same - it wasn't prepared the same way. However observationally there is no difference.

Here is the detail:
http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

See section 1.2.3. The math is likely beyond you but unfortunately this is an area that can't be explained in English - you have to use the math.

Just as an example of where you are going wrong is that decoherence is a phenomena of entanglement - you can't consider the photons and particle having separate wave-functions until they stop interacting.

Unless you go and learn the math, specifically Linear Algebra and the Dirac notation, you must accept the word of those that have learned it.

Thanks
Bill

 

[Feeble Wonk]

Thanks Bill. You've actually given me that resource in the past. What I could decipher was interesting. But, yes, the math made my eyes roll back in my head a little bit.
Let me ask this then. Is there significant debate within the physics academia regarding how severely and how quickly the process of decoherence limits quantum states, or is it essentially accepted as fact across the board?

 

[bhobba]

Let me ask this then. Is there significant debate within the physics academia regarding how severely and how quickly the process of decoherence limits quantum states, or is it essentially accepted as fact across the board?

What do you mean by limits quantum states?

It generally happens so fast you can't observe it. The off-diagonal terms are way below detectability very quickly;y. It is an issue, as a matter of principle, that the models show while those off-diagonal elements go to zero very very quickly they never actually get to zero. FAPP they are zero - but the models do not generally have them as zero. Sometimes you find debate on that point. But the consensus is decoherence does explain apparent collapse - but not actual collapse - which is an entirely different matter. For that you need further interpretive assumptions such as BM or GRW.

Thanks
Bill

 

[rootone]

Please explain 'off diagonal', i don't know what that is.

 

[bhobba]

Please explain 'off diagonal', i don't know what that is.

A mixed state after decoherence is of the form ∑pi |bi><bi| where the |bi> are eigenvectors of what you are observing. If you write it as a matrix then it is a diagonal matrix. However the decoherence models actually have non zero off diagonal terms in the matrix that very quickly go to way below detectability and continue getting smaller - but never are exactly zero. Its like exponential decay - it very quickly goes to zero but never quite reaches it.

Unfortunately explaining this stuff without math is impossible - at least I can't do it.

Thanks
Bill

 

[rootone]

I'll see if I can get my head around that math then.

 

[craigi]

I'll see if I can get my head around that math then.

There are prerequistes to understanding the math. If you explain how far you've studied already we can certainly offer advice. Typically, QM is taught to physics undergrads. A requirement being a strong aptitude for mathematics and a complete understanding of high school mathematics.

The term "off-diagonal" pertains to matrices. Since it's unfamiliar to you, it's likely that there's a lot of groundwork that you should do first. In the meantime, I see no reason why you shouldn't pursue QM from a conceptual perspective.

 

[rootone]

I know what a matrix is, (not the movie version), I might pm you for more detailed advice.

 

[Rajkovic]

"Even the nucleus [of an atom], which we think of as so dense, pops in and out of existence just as readily as the electrons do"
- Dr. Jeffrey Satinover

Is is true?

 

[Dale]

Closed pending moderation.