Does the environment cause wave function collapse

[Fiziqs]

Einstein once asked Bohr is the Moon there when you are not looking, and in answer to that and similar questions, Bohr said - stop telling God what to do. The jokes on both of them though - we now know the moon is being observed all the time by its environment, and that in fact is how this classical commonsense world emerges.

I came across this statement by bhobba in another thread and it got me to thinking, if the "environment" itself is capable of collapsing the wave function, then how is it possible to produce an interference pattern in a double slit experiment? After all, the particle isn't traveling through a vacuum. It's traveling through, and doubtlessly interacting with, a vast multitude of air molecules on its path from the emitter to the screen, yet none of these interactions seem to be capable of collapsing the wave function. So why doesn't the environment collapse the wave function in a double slit experiment?

Why is the environment capable of collapsing the wave function in some cases, but not in others?

 

[naima]

I think that it is because the information about which path on air molecules are erased by further scatterings with other molecules. When light decoheres a dust particules you can read the photons. they keep the information.
If a double screen set up was in a wire chamber interference of electrons would not occur.

 

[bhobba]

I came across this statement by bhobba in another thread and it got me to thinking, if the "environment" itself is capable of collapsing the wave function, then how is it possible to produce an interference pattern in a double slit experiment?

It doesn't collapse anything - it decoheres it - which causes 'apparent' collapse:
http://www.ipod.org.uk/reality/reality_decoherence.asp
'So why does the electron in the double-slit experiment still show interference effects? Why does it not decohere? The answer is because it is not a macroscopic object, it is an isolated microscopic object. While decoherence happens extraordinarily fast for macroscopic objects, for an electron the decoherence time (the so-called coefficient fluctuation time) is about 107 seconds, or about a year - plenty of time to perform the double-slit experiment and see interference effects.'

Thanks
Bill

 

[Fiziqs]

The answer is because it is not a macroscopic object, it is an isolated microscopic object.

Bill, thanks for the link. I found it quite informative and bookmarked it so that I could go back and read the other linked articles. But it did raise a couple of further questions. In what way is the particle "isolated". Isn't it almost constantly interacting with the air molecules? Let's say that we performed the double slit experiment in water, instead of in air. Would the increased density of the water molecules cause a quicker decoherence than we see when we do the experiment in air? What about still denser mediums? Is there a correlation between the "density" of the environment and speed of decoherence? I ask these questions because it is part of my nature to ask questions, so no offense intended.

Also, in the double slit experiment it seems that no matter how subtle we try to be in measuring the path of the particle, the act of measuring it will cause it to decohere. So one seemingly insignificant interaction will cause the particle to decohere, while the millions of interactions with the air molecules won't. It would seem that it's not just the quantity of the interactions, but the quality of the interactions, the type of interactions, that matter. So if one interaction can cause decoherence where millions of others can't, what is the nature of that specific interaction that causes it to have such a disproportionate effect? What is it about some interactions that cause them to have a greater effect than others? This would seem to show that interaction alone is not sufficient to cause decoherence, but some other characteristic is responsible for decoherence.


Thanks

 

[atyy]

http://arxiv.org/abs/0712.3703 section IV.B summarizes a bunch of decoherence experiments. Fig. 35 shows there's more decoherence if there is more uncontrolled environment.

 

[naima]

So one seemingly insignificant interaction will cause the particle to decohere, while the millions of interactions with the air molecules won't.

Where did you read that?

 

[naima]

If you have the photon in mind, Emitting just one photon is not enough to watch the electron.

 

[StevieTNZ]

It doesn't collapse anything - it decoheres it - which causes 'apparent' collapse:

Keyword: apparent.

Whether decoherence actually causes collapse or not is a question not answered yet.

 

[audioloop]

Keyword: apparent.

Whether decoherence actually causes collapse or not is a question not answered yet.

fully concur.


.

 

[Len M]

Isn't it almost constantly interacting with the air molecules? Let's say that we performed the double slit experiment in water, instead of in air. Would the increased density of the water molecules cause a quicker decoherence than we see when we do the experiment in air? What about still denser mediums? Is there a correlation between the "density" of the environment and speed of decoherence?

This may be of interest:

P264 of the book “Decoherence and the Quantum to Classical Transition” by Maximilian Schlosshauer describes the effect of differing densities of background gas on “double slit experiments” using C70 molecules. The C70 molecule is not a microscopic particle (but neither is it a macroscopic object) so it doesn’t fully address your question concerning electrons, but the principle of the medium affecting the interference fringes perhaps applies to electrons as well, as discussed by d’Espagnant below.

….Here, the amount of collisional decoherence can be precisely tuned by changing the density of the background gas.

….As the background gas is increased, the interference fringes become less pronounced

From “On Physics and Philosophy” by Bernard d’Espagnat.

Note that for the fringes to appear it is necessary that, on their way, the particles should undergo no appreciable interactions. If, for example, some dense gas were blown between the diaphragm and the screen, with the consequence that very many particles would hit molecules of gas, the fringes would fade. At high density, that is, if such interactions became the rule, it is expected that the observed behaviour of the particles would simulate the one they would have if they obeyed classical physics. Their impacts on the screen would gather within two blobs.

Up to now the “with gas” scheme is but a thought experiment. It serves to describe observational predictions that unambiguously follow from the quantum predictive rules when the particle is assumed to interact with the environment, here symbolised by the gas. For more details and references to actually performed experiments (with neurons, etc.) see for example, Giulini et al (1996), p.67

 

[Jilang]

I came across this statement by bhobba in another thread and it got me to thinking, if the "environment" itself is capable of collapsing the wave function, then how is it possible to produce an interference pattern in a double slit experiment? After all, the particle isn't traveling through a vacuum. It's traveling through, and doubtlessly interacting with, a vast multitude of air molecules on its path from the emitter to the screen, yet none of these interactions seem to be capable of collapsing the wave function. So why doesn't the environment collapse the wave function in a double slit experiment?

Why is the environment capable of collapsing the wave function in some cases, but not in others?

I thought that this experiment needed to be performed in a pretty robust vacuum or you would see nothing. Perhaps this was a false assumption!

 

[Fiziqs]

This may be of interest:

P264 of the book “Decoherence and the Quantum to Classical Transition” by Maximilian Schlosshauer

Thank you Len M, this is indeed helpful, and what atyy was perhaps alluding to in his/her linked article, but I was having trouble deciphering. However I'm not sure as to whether this is evidence of decoherence, or diffraction, or some other phenomena. Is it evidence that the environment induced decoherence, or that the environment altered the wave function so as to eliminate interference? In other words, does the particle still take both paths, but the effect of the medium on the paths is such as to obscure the interference pattern? I would assume that a careful examination of the resulting interference pattern would shed some light on this question, but I lack the information and intelligence to reach a definite conclusion. Maybe I just need to give it some more thought, or perhaps someone else can shed some further light on this subject.

Thanks for the input everyone.

 

[audioloop]

Thank you Len M, this is indeed helpful, and what atyy was perhaps alluding to in his/her linked article, but I was having trouble deciphering. However I'm not sure as to whether this is evidence of decoherence, or diffraction, or some other phenomena. Is it evidence that the environment induced decoherence, or that the environment altered the wave function so as to eliminate interference? In other words, does the particle still take both paths, but the effect of the medium on the paths is such as to obscure the interference pattern? I would assume that a careful examination of the resulting interference pattern would shed some light on this question, but I lack the information and intelligence to reach a definite conclusion. Maybe I just need to give it some more thought, or perhaps someone else can shed some further light on this subject.

Thanks for the input everyone.

another big problem, at the begginig of the universe, which environment ?



.

 

[atyy]

Thank you Len M, this is indeed helpful, and what atyy was perhaps alluding to in his/her linked article, but I was having trouble deciphering. However I'm not sure as to whether this is evidence of decoherence, or diffraction, or some other phenomena. Is it evidence that the environment induced decoherence, or that the environment altered the wave function so as to eliminate interference? In other words, does the particle still take both paths, but the effect of the medium on the paths is such as to obscure the interference pattern? I would assume that a careful examination of the resulting interference pattern would shed some light on this question, but I lack the information and intelligence to reach a definite conclusion. Maybe I just need to give it some more thought, or perhaps someone else can shed some further light on this subject.

Yes, Len M's referring to the same stuff I was alluding to.

The rough idea of uncertainty/complementarity is that the particle does not have definite position and wavelength and that position and wavelength cannot be simultaneously measured with complete precision. Decoherence takes the environment and the apparatus and particles, and the interaction with the environment causes information about the path to be in the environment. Since someone could (in principle) measure the environment perfectly to find out the path, decoherence causes the interference to disappear. The more precise way of calculating it is by taking the state of the environment and system, and tracing out the environment (which you are in practice ignorant about) leaving the effective state or "reduced density matrix" of the system - which is no longer pure, but mixed, so that when a measurement is made on the system, the results are the same as if the environment had made a "measurement" on the system.

One way to test the idea that it's the uncontrolled environment that is causing the loss of coherence is to see whether there is more decoherence when there is more uncontrolled environment. Here is an experiment that shows the degree to which the interference disappears depends on how much "uncontrolled environment" there is. Take a look at Fig. 3 of http://www.physics.arizona.edu/~cronin/Research/Publications/multi-photonPRL.pdf

 

[bhobba]

Whether decoherence actually causes collapse or not is a question not answered yet.

Its been answered - it doesn't.

That's not, nor ever has been, the issue.

The issue is, is APPARENT collapse good enough - that's the key point, that's where the argument lies.

Different interpretations have different takes.

As I have posted many times I will not get into a discussion about it. I will simply point people to a paper I think presents the issue fairly and people can make up their own mind:
http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

If anything that paper is slighly pessimistic in my view - but I rather like that because people are not getting what I think, and will not be 'contaminated' by that.

Thanks
Bill

 

[bhobba]

P264 of the book “Decoherence and the Quantum to Classical Transition” by Maximilian Schlosshauer describes the effect of differing densities of background gas on “double slit experiments” using C70 molecules. The C70 molecule is not a microscopic particle (but neither is it a macroscopic object) so it doesn’t fully address your question concerning electrons, but the principle of the medium affecting the interference fringes perhaps applies to electrons as well, as discussed by d’Espagnant below.

Glad others are reading that book - it my go-to book on such things.

I like the essay I link to on decoherence, but that book is a few steps above in comprehensiveness, and careful explaining.

Thanks
Bill

 

[bhobba]

another big problem, at the begginig of the universe, which environment ?

Well, as far as I am aware, no one is claiming any kind of observation then, so its a total non issue.

Thanks
Bill

 

[bhobba]

In other words, does the particle still take both paths, but the effect of the medium on the paths is such as to obscure the interference pattern?

One thing you need to understand about Feynman's sum over histories approach is viewing particles as actually taking all the paths is really a hidden variable theory of a rather non trivial type.

Mathematically that the wave function behaves LIKE that is beyond question, but if it really does is an interpretive assumption. Nice in understanding certain problems like the double slit experiment - but still its not strictly implied by the formalism.

In this context its important to realize that while the double slit experiment is usually discussed as an aid, and motivation for, discussing quantum principles, it in fact can be analysed the other way around.

A link that does just that has been posted in the past and its probably worthwhile those interested in the issue seeing if they can dig it up, or those that know it post it in this thread.

Regarding why photons in the double slit experiment have very long decoherence times, its like many things in physics, for the details you need to consult the technical tomes. I don't know a reference off hand for that, but again if anyone is interested I am sure a bit of investigation at a university library will yield the details.

Thanks
Bill

 

[bhobba]

I thought that this experiment needed to be performed in a pretty robust vacuum or you would see nothing. Perhaps this was a false assumption!

For objects other than photons - yes - for photons its probably related to they travel so quickly and there is so many of them, since their decoherence time is so long, very few interact with objects on the way through enough to decohere them - although it may decohere other objects. Of course those that are decohered and given an actual position will not participate in the interference effect.

Thanks
Bill

 

[audioloop]

Well, as far as I am aware, no one is claiming any kind of observation then, so its a total non issue.

Thanks
Bill

who said observation ?


.

 

[Fiziqs]

One thing you need to understand about Feynman's sum over histories approach is viewing particles as actually taking all the paths is really a hidden variable theory of a rather non trivial type.

Mathematically that the wave function behaves LIKE that is beyond question, but if it really does is an interpretive assumption. Nice in understanding certain problems like the double slit experiment - but still its not strictly implied by the formalism.

In this context its important to realize that while the double slit experiment is usually discussed as an aid, and motivation for, discussing quantum principles, it in fact can be analysed the other way around.

I freely admit that my understanding of the quantum world is strongly influenced by Feynman's sum over histories approach, but in some sense it's the only tool available to me. I only have a ninth grade education, so fancy mathematical models or seemingly cryptic experimental explanations are apt to just go right over my head. But Feynman's sum of the paths approach is simple and elegant and easy for me to visualize, and so it is a method that I have come to rely upon. I don't remember if it was the early eighties or even before that, when I first encountered Feynman's explanation of why light travels in a straight line, as being understandable as simply the sum of all of a photon's possible paths. But ever since then, that's how I have tried to visualize the fundamental nature of the world, and QM. I just love waves!

Sometimes this simple method works quite well, for example, earlier in this thread Len M and atyy cited experiments that seemed to show that the rate of decoherence may be relative to the density of the medium through which a particle passes. This is something that is quite easy to visualize, and would seem to intuitively indicate that the increased interactions in a denser medium do indeed cause accelerated decoherence. But when I try to visualize this in my head, a problem arises. Namely, that the path of the wave can be influenced by variations in the density of the medium, and that the denser the medium, the more pronounced this effect might be. So it may not be that there is an actual increased rate of decoherence, but simply an increasing influence of the lack of uniformity within the medium. So whereas some people may look at the experiments and think that it's obvious that the rate of decoherence is relative to density, I have to question it. At least based upon the information that I have. Give me more information, and I can give you a better answer. From my own point of view though, I would tend to believe that density does indeed relate to the rate of decoherence.

But doubts such as these are one of the reasons why in another thread, I expressed an interest in setting up my own double slit apparatus. So that I can attempt to answer questions like this one on my own. As with Feynman's sum over histories approach, the double slit experiment is simple, and easy to visualize, for people like me with no formal education. It may lead to erroneous conclusions at times, but I have found such errors to be the result of my own ignorance, not a consequence of the method. The sum over histories method may be simple, but I have found it to be reliable, when correctly applied.

As for decoherence, I'm a firm believer in collapse, because visualizing things as waves leads inexorably to that conclusion. If you have one wave, then you have a certain degree of uncertainty within that wave, and it can be quite broad. If you allow this wave to interact with another wave, then you tend to have a limiting influence on the possible states of the two combined waves. Not always, but generally. The larger the system, the more pronounced the limiting influence, until the state of each individual wave falls to within a very small degree of uncertainty. Sometimes the limiting influence is gradual, depending upon the number, and types of waves that you're interacting with, and sometimes the influence is immediate, leading to instantaneous collapse.

I realize that this is all just my own point of view, based upon the sum of histories approach that I have basically been forced to adopt, due to my lack of formal education. I do appreciate opposing points of view, because I'm a glutton for information. Unfortunately on this forum, most of the exchanges of ideas go right over my head, but I try to glean as much information as possible from them. And so I appreciate any and all, ideas, links, citations, and references. The simpler the better, because us simple minded folk require simple explanations. But then on the other hand, as Archimedes said, "Give me a lever long enough, and a fulcrum on which to place it, and I shall move the world."

Posts like this one are what you get when I have too much free time. I tend to babble. Sorry.

 

[Jilang]

Fiziqs, have you watched any on-line lectures? I would recommend
http://theoreticalminimum.com/courses
If the maths is too tricky the words are still good to listen too.

 

[Maui]

Why is the environment capable of collapsing the wave function in some cases, but not in others?

The environment is part of the wavefunction so you are essentially asking how can the wavefunction collapse the wavefunction? Beware that the collapse event is not part of the formalism so the odds of you getting genuine snake oil are quite high.

 

[atyy]

It's completely fine to work in a framework in which collapse exists. In this framework, we divide the universe into two parts. A classical world which we are part of, and a quantum world which we are studying. Collapse is what happens when a classical measurement occurs - ie. when a classical apparatus interacts with a quantum system, and a definite classical result is left on the classical observer and apparatus. In this framework, quantum mechanics does not describe the whole universe, because it does not describe the classical apparatus. However, it does also acknowledge that different classical observers can divide up the universe into classical and quantum parts, so that what is classical to one observer may be quantum to another observer. It seems puzzling but it works, so this is usually called shut-up-and-calculate.

There are frameworks without collapse, such as de Broglie Bohm and Many-Worlds (I'm not really sure Many-Worlds works, but many - including Aharonov and Rohrlich https://www.amazon.com/dp/3527403914/?tag=pfamazon01-20 - believe it does).

Decoherence is common to all frameworks, as it only assumes that the wave function of the environment, apparatus, and system, evolves according to the Schroedinger equation without collapse. In a framework with collapse, this would describe what happens up to the point of measurement.

 

[bhobba]

another big problem, at the begginig of the universe, which environment

who said observation ?

Then your point about environment is?

Thanks
Bill

 

[Fiziqs]

Fiziqs, have you watched any on-line lectures? I would recommend
http://theoreticalminimum.com/courses
If the maths is too tricky the words are still good to listen too.

Jilang, yes I have watched most of these lectures, although I have never actually watched any of them all the way through. I still find them to be very helpful to a point. What inevitably happens though, is that I will start out with a very good grasp of what Prof. Susskind is talking about. I will understand it perfectly. But then he begins to use terminology with which I am unfamiliar. At first I can deduce what many of the terms are, and what they are referring to, and I can disregard others, but eventually I get to the point where I really have no idea what he's talking about. He's using terms that I don't understand based on earlier terms that I didn't understand. Until I finally get to the point where I go, I can't follow this anymore, I'm lost. I'm getting bits and pieces, but for the most part he's lost me.

It's not the concepts that are confusing me, it's the terminology. I'm sure that if I could ask him to clarify certain things, and he had the patience to explain them, that I would find the vast majority of what he teaches to be perfectly simple and understandable. The parts that I do get, I understand and agree with. Still I watch them every now and again, and hopefully I understand a little bit more each time. One of these days I may even get all the way through one of them.

 

[Fiziqs]

The environment is part of the wavefunction so you are essentially asking how can the wavefunction collapse the wavefunction?

I agree to a point. What many argue, and logically so, is that the environment causes decoherence, yet in the double slit experiment we have a complex environment that does not seem to be causing decoherence. The question then is, why? How can the particle be a part of this complex environment, this wave function as you call it, and not experience decoherence?

I could postulate a number of explanations on my own. It could be that the particle rarely interacts with anything during the very brief amount of time between the slits and the screen. Thus there is little opportunity for interaction, and for decoherence to be introduced. In which case, the particle's wave function, and the environment's wave function essentially remain separate. But if you introduce something into the environment, like a measuring device specifically designed to interact with the particle, then the likelihood of interaction with the environment increases to the point where the interference pattern disappears. Decoherence becomes likely. In this case the environment fails to eliminate interference because the particle never actually interacts with the environment. It's only when you increase the likelihood of interaction by adding a measuring device, that the interference pattern disappears. I find this argument to be somewhat counter-intuitive. How does a wave pass through an environment without interacting with the objects within that environment? Still, not understanding the mechanisms involved with such interactions, makes this argument difficult to rule out.

But there are other possibilities. It could be that the particle does indeed interact with the environment on its way from the slits to the screen, but that none of these interactions result in the obtaining of "which path" information, and it is only when you introduce something into the environment specifically designed to measure "which path" the particle took, that the interference pattern disappears. In this case the particle and the environment can indeed be modeled as one wave function, but the interference pattern remains because the environment doesn't obtain "which path" information, until something is present within the environment to do so.

But there are still further possible explanations, and I was hoping that someone would have some evidence to support a specific hypothesis. Thus the reason behind my initial question, why doesn't the environment collapse the wave function in a double slit experiment, even though it is claimed by many that the environment is indeed responsible for decoherence?

It may be erroneous of me to refer to the particle and the environment as separate wave functions, but hopefully you can overlook the poor terminology, and understand the question that I was attempting to ask.

Beware that the collapse event is not part of the formalism so the odds of you getting genuine snake oil are quite high.

I am quite aware that the odds of my looking like a complete idiot are indeed very high, but it wouldn't be the first time. I have a history of such things. There is no harm in you pointing it out however, and your input is appreciated.

 

[atyy]

I agree to a point. What many argue, and logically so, is that the environment causes decoherence, yet in the double slit experiment we have a complex environment that does not seem to be causing decoherence. The question then is, why? How can the particle be a part of this complex environment, this wave function as you call it, and not experience decoherence?

Because there is no complex environment, or it does not interact with it. In these experiments, there is a loss of interference as a complex environment is introduced with which the particle interacts.

But there are other possibilities. It could be that the particle does indeed interact with the environment on its way from the slits to the screen, but that none of these interactions result in the obtaining of "which path" information, and it is only when you introduce something into the environment specifically designed to measure "which path" the particle took, that the interference pattern disappears. In this case the particle and the environment can indeed be modeled as one wave function, but the interference pattern remains because the environment doesn't obtain "which path" information, until something is present within the environment to do so.

More or less, yes. There's a famous experiment discussed by Bohr and Einstein.

"Einstein proposed the famous recoiling-slit experiment to gently measure which path the particle took through a two-path interferometer. In reply Bohr pointed out that the slit itself must also obey the laws of quantum mechanics and therefore is subject to the Heisenberg uncertainty principle. He showed quantitatively that if the initial momentum of the slit-assembly is known well enough to permit the recoil measurement of which path the particle took, then the initial position of the slit must have been so uncertain that fringes would be unobservable." http://arxiv.org/abs/0712.3703 (p34)

A version of this experiment was performed by Bertet and Haroche. They say "Recoil of the quantum slit causes it to become entangled with the particle, resulting in a kind of Einstein-Podolsky–Rosen pair. As the motion of the slit can be observed, the ambiguity of the particle's trajectory is lifted, suppressing interference effects. In contrast, the state of a sufficiently massive slit does not depend on the particle's path; hence, interference fringes are visible." http://www.nature.com/nature/journal/v411/n6834/abs/411166a0.html

 

[Fiziqs]

Because there is no complex environment, or it does not interact with it. In these experiments, there is a loss of interference as a complex environment is introduced with which the particle interacts.

Now this is an interesting question. What actually constitutes a complex environment? Is there a specific scientific definition for it? If not, I could venture a really off-the-cuff guess, that a complex system is one in which the relationship between the components of the system are such, that it imposes restrictions upon the possible states of the individual components of the system, or a subset of those components.

In other words, in the case of the double slit experiment, if we have a detector at the slits, then the state of the detector imposes a restriction upon the state of the particle. Specifically, it limits the possibilities as to which slit the particle came through. But in the case of an environment made up solely of air molecules, due to the nature of the slits the state of any single, or group of molecules, does not restrict the possibilities as to which slit the particle came through. So long as the particle was capable of interacting with that molecule regardless of which slit it came through, then such interactions impose no restrictions upon the path of the particle.

But this definition raises a problem, because the density of the medium within the double slit experiment should then have no effect upon the rate of decoherence. It wouldn't matter how many interactions the particle had between the slits and the screen, if none of those interactions could provide a restriction as to which slit the particle came through. But the experiments cited by Len M and atyy seem to indicate that there is indeed a correlation between the density of the medium, and the rate of decoherence. (Although as I stated in a previous post, I'm not sure that that effect wasn't due to some other factor) But this would seem to indicate that my definition of what constitutes a complex system is inadequate, incomplete, or incorrect.

As everyone can no doubt tell, I'm blathering again. This stuff is coming right off the top of my head. But does anyone else have a more formal definition as to what constitutes a complex environment?

 

[Maui]

Because there is no complex environment, or it does not interact with it. In these experiments, there is a loss of interference as a complex environment is introduced with which the particle interacts.

This assumes that there is a classical environment consisting of ball-like particles but so far there is no evidence for the existence of such particles. We have to introduce them for the hypothesis to work, right?