How observation leads to wavefunction collapse?

[Gza]

For a somewhat wider context, some sections of
http://xxx.lanl.gov/abs/quant-ph/0609163
may also be useful, e.g. Sec. 2 and especially Sec. 4.2.

I just KNEW you were going to find a way to get your paper mentioned in this thread

 

[Demystifier]

I just KNEW you were going to find a way to get your paper mentioned in this thread

Actually, I have many papers, but I mentioned this one because I honestly believe that it may be helpful to him.
Of course, it does not make me more modest, as it is certainly not modest to think that my papers are more useful than those of others. But I can't help it, I admit that I think so. In fact, if I was not thinking that (at least in one aspect) my paper would be better than others, I would not write it. Would you?

Now seriously, I can list several introductions to the Bohmian interpretation that (even to me) seem much better than those I mentioned, but the problem is that they are not available online.

 

[Doc Al]

Now seriously, I can list several introductions to the Bohmian interpretation that (even to me) seem much better than those I mentioned, but the problem is that they are not available online.

I'd be very interested in those references if you would be kind enough to provide them. (I want to learn more about the Bohmian interpretation.)

 

[Demystifier]

I'd be very interested in those references if you would be kind enough to provide them. (I want to learn more about the Bohmian interpretation.)

In that case, I suggest you to read the following, in that order:
1. D. Bohm, Phys. Rev. 85 (1952) 166.
2. D. Bohm, Phys. Rev. 85 (1952) 180.
3. D. Bohm and B.J. Hiley, Phys. Rep. 144 (1987) 323.
4. D. Bohm, B.J. Hiley, and P.N. Kaloyerou, Phys. Rep. 144 (1987) 349.
5. P.R. Holland, Phys. Rep. 224 (1993) 95.
6. P.R. Holland, The Quantum Theory of Motion (Cambridge University Press, Cambridge, 1993).
This, in fact, is enough to become an expert.

 

[Doc Al]

Thanks! I actually have several of those references in my "someday I should study these" pile.

 

[rewebster]

Thanks! I actually have several of those references in my "someday I should study these" pile.

huh---I've got several of those 'piles' in several rooms around the house (and the basement)---(and the garage)

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

If you only have one ---I really need to get going!

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

but, it has to do with 'relative' framework of the size of the pile(s), too

 

[Doc Al]

My entire apartment is one huge pile--impossible to tell where one ends and another begins. Thousands of books and papers...everywhere.

 

[rewebster]

My entire apartment is one huge pile--impossible to tell where one ends and another begins. Thousands of books and papers...everywhere.

Well, if yours is that way I don't feel quite so guilty/embarrassed then

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

do you issue 'Doc Al's Library' cards?

 

[Gza]

Actually, I have many papers, but I mentioned this one because I honestly believe that it may be helpful to him.
Of course, it does not make me more modest, as it is certainly not modest to think that my papers are more useful than those of others. But I can't help it, I admit that I think so. In fact, if I was not thinking that (at least in one aspect) my paper would be better than others, I would not write it. Would you?

Now seriously, I can list several introductions to the Bohmian interpretation that (even to me) seem much better than those I mentioned, but the problem is that they are not available online.

In all honesty your paper: "QM myths and facts"; was extremely well written and an enjoyable read. If you can maybe expand the section on the Bohmian interpretation into another paper, I'm sure a lot of people who post in QP will be eternally greatful; and i'll be the first one to link it in other threads when the topic arises

 

[Demystifier]

In all honesty your paper: "QM myths and facts"; was extremely well written and an enjoyable read. If you can maybe expand the section on the Bohmian interpretation into another paper, I'm sure a lot of people who post in QP will be eternally greatful; and i'll be the first one to link it in other threads when the topic arises

Thanks!
The reason I have not (yet) written a pedagogic review of the Bohmian interpretation is because it seems to me that it would not contain something that is not already written somewhere else. Good pedagogic reviews of the Bohmian interpretation already exist, I have already listed several of them. Their problem is that most physicists do not read them as they are not interested in the Bohmian interpretation, mainly because they think that the standard interpretation is fine. One of the main motivations for my "Myths and facts" paper is to show them that the standard interpretation is not fine, which then may motivate them to learn about the Bohmian interpretation more, from some of those good already existing papers (and books).

 

[jostpuur]

I skimmed through the thread, and didn't notice any remarks about decoherence. Isn't this explanation among the most standard ones: The electron gets coupled with the photon (that is used to measure it's position or path), and when the photon gets coupled with a macroscopic measuring device, the electron is coupled with this macroscopic device also and interference patterns will be gone then. In effect, the electron's wave function has collapsed where it encountered the photon, but not really in the original copenhagenian sense.

 

[Demystifier]

Decoherence does NOT explain the collapse. It only explains why quantum statistics can be approximated by classical statistics. It does not explain how an observable picks one particular value. For example, it does not explain how a cat chooses whether it will be dead or alive.

 

[jostpuur]

Decoherence does NOT explain the collapse. It only explains why quantum statistics can be approximated by classical statistics. It does not explain how an observable picks one particular value. For example, it does not explain how a cat chooses whether it will be dead or alive.

The OP wasn't a clearest possible, but I assumed it was about the experiment, where photons are used to measure which slit electrons pass through, and about the known result that the interference pattern is destroyed by this measurement. Altough the first question is "how and why did the wave function collapse at the slit?", to more precise, it is the lack of interference pattern that requires explanation and not an assumed copenhagenian collapse at the slit.

btw, I'm also frustrated with the claims that the decoherence would solve the Shrodinger's cat paradox, but that is a different matter.

 

[jostpuur]

Ouh, I should have used term "entangled" and not "coupled". The edit button time could be a bit larger than 24h.

 

[mgelfan]

Hi all
So, in the double slit experiment, if a photon observes an electron, the interference pattern vanishes. Why is this so?

In order to observe (to use the term somewhat loosely) whatever it is that's transmitted through slit 1, then something has to interact with it. The net effect of this is that whatever it is that was originally transmitted through slit 1 is either completely blocked or altered to the extent that it no longer (apparently) interacts with whatever it is that's transmitted through slit 2 -- at least not in the way that it apparently would have if no measurement was done at either slit.

In other words, measuring at slit 1 or slit 2 effectively closes the slit where the measurement operation is done. So, you calculate as if only one slit were open and you get the correct data distribution.

Also, can anybody explain to me as to how a single electron creates an interference pattern in reality?
I am completely at sea as far as understanding this phenomenon is concerned. I know that in theory we have wavefunctions, but how can all the paths that can be followed by the electron, consist of one in which it passes through both the slits?

Everybody is in the same sea of not understanding this phenomenon as you. It's the archetypal quantum mystery.

It's just that if you don't do any measurement operation at slit 1 or slit 2 then you can calculate in terms of both slits being open, and you get the correct data distribution (eg., a banded interference pattern in a typical single quantum two-slit experiment registering sequences of detections of individual quanta).

What's actually, physically happening at the slits and the detectors is anybody's guess. And, if the principles of quantum theory are correct, then whatever is going on in reality (regarding emitters and filters and detectors of quantum phenomena) will remain a matter of metaphysical speculation.

 

[neu]

I'm not trying to get around the problem here, I just want to clarify something.

What about enclosing the whole thing in a ionisation chamber and looking at the paths of the charged electron throught the system. Presumably one would observe straight lines through one slit or the other and no interferrence pattern?

apologies for my ignorance

 

[Fra]

Not sure I got the orignal question but IMO if you take the information theoretic view, the collapse is seen as a revision of the expectations in response to further information (observation).

If you have a box containing a cat, and you know that either it's dead or alive. Then after you check it and see it's dead, you obviously update your opinion. You no longer think it's 50/50.

The key might be that all other observers, and particles interacting with this box, will act upon the possibility that it's dead or alive. Like a poker player, he acts upon not what is the truth, but what the information he has about the truth, and he updates his opinion each time he observes new cards.

/Fredrik

 

[akhmeteli]

I was impressed by the following article answering the question in the thread title:
http://www.arxiv.org/abs/quant-ph/0702135
"The measurement of a spin-$\half$ is modeled by coupling it to an apparatus, that consists of an Ising magnetic dot coupled to a phonon bath. Features of quantum measurements are derived from the dynamical solution of the measurement, regarded as a process of quantum statistical mechanics. Schr\"odinger cat terms involving both the system and the apparatus, die out very quickly, while the registration is a process taking the apparatus from its initially metastable state to one of its stable final states. The occurrence of Born probabilities can be inferred at the macroscopic level, by looking at the pointer alone. Apparent non-unitary behavior of the measurement process is explained by the arisal of small many particle correlations, that characterize relaxation."

 

[meopemuk]

I agree. But my question is that why this distribution on the screen resembles to a wave interference pattern, instead of the usual pattern observed when bullets are hit through two slits? This interference pattern can result only when some of the electrons are passing through both the slits at the same time, which is impossible to be done by a particle. If, then, an electron is a wave, then what is the nature of this wave? A wave consists of quanta, but electron itself is a fundamental particle. Then what type of quanta does this electron-wave consist of, and does it actually consists of any quanta at all or not? How is mass distributed in this wave? Why does a photon collapse this wave? As far as I know, waves normally do not collapse into particles on interaction with other waves.

thanks
Mr V

These are very good questions, but I am afraid, they don't have good answers. One important thing is that the role of theory is to explain/predict results of experiments. If a theoretical concept cannot be verified by a measurement, then there is a good chance that this is an empty or irrelevant concept.

Think about how the double-slit experiment is performed. You make an electron source, erect a screen with two holes, and put a scintillating screen behind it. Then you turn on the source and start recording points where electrons hit the scintillating screen. A good theory (quantum mechanics) does, basically the same thing. It describes the initial state of electrons (by their wave function at t=0), it describes the physical environment in which these electrons move (two holes), and it gives you a rule (Schroedinger equation) by which you can predict the (probabilities of the) results of your measurements, i.e., where the electrons will hit the scintillating screen. Quantum mechanics performs this task extremely well. If you completely specified the experimental conditions, QM would give you precise probabilities of measurements. That's all that is required from a good theory.

Now, you are asking for a lot more:
1. is electron a wave or a particle?
2. how electron's wave function collapses.
3. is electron passing through one hole or through two holes simultaneously?

Questions 1. and 2. probably don't have answers, because one cannot build any measuring apparatus to answer them experimentally. So, I won't even try to answer them. Actually, it is better to say that these questions have many different answers, as QM has many different "interpretations". But these answers, in my opinion, have nothing to do with physics. They belong to philosophy. And it is important to separate physics from someone's philosophical preferences.

Question 3. makes more sense, because one *can* try to answer it experimentally. To do that, one can shoot photons near the holes and try to decide which hole the electron passed through by looking at photon's scattering. Surely, this can be done. But then you have changed your experimental setup. In addition to the electron source, the screen with two holes, and the scintillating screen you added a photon source and a photon detector.

So, the Scroedinger equation that you used for theoretical description of the first setup is not valid anymore. You need to write a new initial wavefunction (now it should describe states of both electrons and photons). And you need to write a new Schroedinger equation that takes into account photons as well. If you carefully do all of this, you'll be able to accurately describe/predict results of your measurements again. Certainly, in these new conditions the electron interference pattern would change due to electron-photon interactions. However, you should realize that the new interference pattern and photon scattering data don't give you any useful information about the experiment you began with. Even if you can determine which electron passed through which hole in the second experiment, this doesn't tell you what happened in the original experiment.

So, in my opinion, the most important lesson of quantum mechanics is that we should not ask about things, which are not measured or observed. Asking such questions may lead to strange paradoxes, but these paradoxes are irrelevant for physics. The only important thing is that our theory should be able to describe/predict results of actual measurements. Everything else is bull... philosophy.

 

[Fra]

More philosophical reflections.. which I don't think is bad as such.

> 1. is electron a wave or a particle?
> 2. how electron's wave function collapses.

If we're talking about one datapoints, it could be argued that the wave is the question, and the set of expected answers, and the particle detection is the answer that updates our wave into a new question.

There is one possible analogy in my thinking. The response of the answer is an updated question. The response to a particle detection is an updated wavefunction. Now if you model the measureing device as well, then you aren't asking the same question. This is like bayesian updates. New data updates your prior probability distribution. I think the way to go is to unify interaction and observation, because it's ultimately the same thing, just taking place at different complexity levels.

This way of thinking, is IMO very nice and powerful. But of course like has been said we have different preferences.

/Fredrik

 

[Demystifier]

Questions 1. and 2. probably don't have answers, because one cannot build any measuring apparatus to answer them experimentally. So, I won't even try to answer them. Actually, it is better to say that these questions have many different answers, as QM has many different "interpretations". But these answers, in my opinion, have nothing to do with physics. They belong to philosophy. And it is important to separate physics from someone's philosophical preferences.

I disagree. In fact, I think that pure experiments cannot answer ANY question beginning with "How ... ?" or "Why ... ?". Instead, it is theory that answers such questions. But a good theory gives also some numbers, which allows to test the numerical aspect of the theory by experiments. This is how we "test" theories. The problem occurs when two or more different theories give the same measurable numbers. In this case, it is common to say that such theories belong to philosophy, rather than physics. Nevertheless, I do not see why two theories with same numbers would be more philosophical and less physical than one theory with numbers. (For example, if we knew only about one interpretation of QM, would you still call it "philosophy", or would you then call it "physics"?) Therefore, it is not a good strategy to reject thinking about different theories (or interpretations, if you like) just because they seem to give the same numbers. Instead, it is more constructive to think how to extend the applicability of these theories into a regime in which they may give different numbers. For example, different interpretations of nonrelativistic QM may give different numbers when extended to a relativistic regime.

 

[Mr Virtual]

Thanks again for all your replies. I am learning a lot from all of you.

Mr V

 

[Fra]

I think the "why X" questions should really be interpreted as request for a better question which can be valid. Ie. the response to the question is more sensible question.

However I think that care should be taken when beeing too categorical, rejecting seemingly fuzzy questions, because it can even be argued that the only "sensible" and well defined, questions are the close to trivial questions, which there is not point in answering because it's trivial and there is no gain. Real life problems are often composed of this kind of fuzzy questions, where we make incremental progress, part answers + refined questions.

I think a physicists must not be afraid to attack fuzzy questions, because they are often the interesting ones. But part of the quest is to refine the questions. This may seem ambigous to some, but who said nature is unambigous?

/Fredirk

 

[Fra]

I think the phenomenon of trying to improve your own questions, almost before they are fired can be considered as a kind of self interaction. I think humans do it, but also particles, in a crude sense.

/Fredrik

 

[meopemuk]

I disagree. In fact, I think that pure experiments cannot answer ANY question beginning with "How ... ?" or "Why ... ?". Instead, it is theory that answers such questions. But a good theory gives also some numbers, which allows to test the numerical aspect of the theory by experiments. This is how we "test" theories. The problem occurs when two or more different theories give the same measurable numbers. In this case, it is common to say that such theories belong to philosophy, rather than physics. Nevertheless, I do not see why two theories with same numbers would be more philosophical and less physical than one theory with numbers. (For example, if we knew only about one interpretation of QM, would you still call it "philosophy", or would you then call it "physics"?) Therefore, it is not a good strategy to reject thinking about different theories (or interpretations, if you like) just because they seem to give the same numbers. Instead, it is more constructive to think how to extend the applicability of these theories into a regime in which they may give different numbers. For example, different interpretations of nonrelativistic QM may give different numbers when extended to a relativistic regime.

Vanilla quantum mechanics (with Hilbert spaces, state vectors, and operators) doesn't answer questions "how...?" and "why...?" It is a "cooking recipe" which answers quantitative questions like "how much...?" and "when...?" pretty well. It is designed to answer well-posed questions like (1) "what would we see if we looked?" However, our curious minds are demanding more thant that: they are demanding answers to ill-posed questions like (2) "what is going on while we are not looking?"

My only point was that type (2) questions may not have good answers. Even if our philosophy provides some answer, we can never verify this answer experimentally. Because in order to verify we need to look, and by looking at the system we can answer question (1), but not (2). If a theory cannot be verified by experiment, it is an empty theory, in my opinion.

 

[Demystifier]

Vanilla quantum mechanics (with Hilbert spaces, state vectors, and operators) doesn't answer questions "how...?" and "why...?" It is a "cooking recipe" which answers quantitative questions like "how much...?" and "when...?" pretty well.

Again, I disagree. Even such "cooking recipe" formulation of QM gives some answers to questions "How ...?" and "Why ...?".
Here is an example:
How 2 electrons in an atom know about the spins of each other?
They know it by sharing the same wave function in the configuration space having the property of entanglement.
Why this wave function is entangled?
Because the wave function must be antisymmetric with respect to exchanges of the particles.

Of course, one may not find these answers sufficiently intuitive, but intuition is a matter of practice.

By the way, why is it called "vanilla" QM?

 

[masudr]

By the way, why is it called "vanilla" QM?

Anything that is standard or plain can be colloquially given the adjective vanilla, simply because that is the flavour of plain ice cream (i.e. the most unflavoured type of ice cream is vanilla ice cream).

 

[Demystifier]

Anything that is standard or plain can be colloquially given the adjective vanilla, simply because that is the flavour of plain ice cream (i.e. the most unflavoured type of ice cream is vanilla ice cream).

Excellent explanation, thanks!

 

[rewebster]

Anything that is standard or plain can be colloquially given the adjective vanilla, simply because that is the flavour of plain ice cream (i.e. the most unflavoured type of ice cream is vanilla ice cream).

WHAT?!

Vanilla is my most favorite flavor!

unflavoured!


(yeah, I know... I get the 'gest' of it, but it--vanilla-- IS one of the most powerful taste and smell products/natural flavors around)
-----------------------------
(hmmm-----vanilla(QM?)=one of the tastiest versions!?)

 

[meopemuk]

How 2 electrons in an atom know about the spins of each other?
They know it by sharing the same wave function in the configuration space having the property of entanglement.

But electrons cannot "know" or "share" anything. They are not intelligent beings. This kind of language could be useful as a mnemonic tool. But I think it is dangerous to imagine that we know about electrons more than there is written in the Schroedinger equation.

 

[cepheid]

*Sigh*. You guys are going to kill me because I haven't read the ALL of the discussion in this thread and am asking one of those dreaded "why" questions. But I feel that the following is perhaps one of the issues raised by the OP. If you let a large number of electrons loose upon the slits one at a time, statisically they will land at various points on the screen such that the overall pattern is the familar interference pattern of bright and dark bands. In other words:

statistically, the impact points suggest that each electron is governed by a wavefunction that has been "shaped" by the slits into areas of minimum and maximum probability density in much the same way as a physical wave passing through would be shaped by the slits through the mechanism of interference.

If that is the case, then what the heck is the wavefunction? If it is just a mathematical entity, why is it modified by the slits in the manner of a "real" wave? I'm sure this question has been asked many times, but I'm new to QM, so bear with me. I've only taken the "vanilla" undergraduate variety described above. As Griffiths puts it in his preface, he has taught the basics of how to DO quantum mechanics, nothing more.

 

[meopemuk]

If you let a large number of electrons loose upon the slits one at a time, statisically they will land at various points on the screen such that the overall pattern is the familar interference pattern of bright and dark bands.

This is the most mysterious puzzle of nature. You prepare many electrons (to the best of your abilities) in exactly the same state. And they still land at different point on the screen. Quantum mechanics cannot explain that. No theory known to man can explain that. Quantum mechanics simply accepts this statistical character of nature as a given fact and builds a mathematical theory around this fact. This mathematical theory can only predict probabilities. It cannot tell, even approximately, where each individual particle will hit the screen. You can say (together with Einstein) that QM is not a complete description of nature. However, I think, it is more fair to say that nature doesn't allow a complete description of itself. There is always a certain degree of randomness. One just needs to accept this fact and move on.

 

[Mr Virtual]

Does this wavefunction of an electron traveling through the slits depend upon Heisenberg's uncertainty principle?
I say this because suppose, you have a single slit instead of a double slit, and you fire electrons at this slit, one at a time. Initially each electron has been provided with momentum only in the x-axis, and zero momentum in the y-axis. If the width of slit is not too small, then we don't have a clear idea about where exactly the electron is when it passes through the slit. But if the slit's width is made extremely small, the electron forms a wave-like pattern on the screen, which means that it gains a momentum in y-axis too, which was surely not there at the time of firing the electron. This is because as the slit's width decreases, the uncertainty about its position also decreases. As such, the uncertainty in momentum increases. This uncertainty in momentum manifests itself in the form of uncertainty in momentum in y-axis. As the slit's width goes on decreasing, the uncertainty in p(y) increases, and wave-function spreads more, resulting in a more spread wave-like pattern. Thus, the wave function of electron is directly related to width of the slit. Lesser the width, more spread is the wavefunction.

Is it the same case with the double-slit??

regards
Mr V

 

[Fra]

Set aside vanilla stuff... this is what it should be IMHO:

> If that is the case, then what the heck is the wavefunction?

The wavefunction is supposedly a representation of your information about the system, thus rendering it relative to you. The interesting thing is what A knows about B. Then A writes down the a wavefunction of B. Ask C to write down the wavefunction of B and it will generally differ unless A=C. OR EVEN, you can't just compare the two like that, because in the comparasion process you have to transform A to C. Just like you need to parallelltransform vectors from different tangentspaces before the notion of comparing them makes sense. It's the same with information, but it may be more abstract and harder to picture in terms of visualisations.

Them, the _evolution of the wave function for B_ is your *estimated* change of your own information about B. NOTE that also the information about change is also bound relative - kind of meaning that hamiltonian is relative if you think of it in the classical way, or the whole construction isn't logically consistent IMO.

Note that consistency and observer invariance of laws of nature, must not make any fundamental difference between a human scientist and a particle. Perhaps a bit bold to some, but not to me. This suggest that consistent laws governing the interaction between particles should be in terms of relative information. To take the view of a particle, you should ask how the wavefunction of particle B would be written *relative* particle A (unlike, relative a human scientist that are separated by many orders of magnitudes in complexity.)

However, in this spirit, ordinary QM is seen to be incomplete. So I wouldn't get too hung up on trying to understand the classical QM, because if you find it weird, that's a good sign. Because something aint right. I would suggest try to understand the problems QM solves, maybe learn howto make some basic calculations, but then appreciate the problems, and focus on solving them instead of wasting your youth to "understand" what is most probably incomplete anyway :)

I think this thing about "what A knows about it's environmen" should ultimately be understood in the larger context of life.

Anyway, I remember asking exactly the same questions long time ago. I went through different phases, the first obstacle was to go from analytical classical mechanics to QM. Once you learned the beauty of classical analytical mechanics, you are told that it just ain't right. That took me some years to get over. Then I thought I understood QM. But then I realized that while it works (ie it's a successful theory) something is just plain wrong, or missing. But that took some more time.

If my current self would try to explain this to my self (13 years ago) I think I would have had a hard time convinving myself. I'm not sure, but perhaps it's a process. My change involved widening the views, looking a biological system as well, and the human brain. Physics can't be isolated from the rest of science without tradeoffs. Since them I don't care to put names of things. If I do physics or whatever. I'm trying to answers my questions, regardless of classification.

/Fredrik

 

[Fra]

A valid question is to question the notion of "information". And if you do this, progress is made by many new interesting questions. I don't think it's completely settled yet, but for me personally at least the general direction of research is reasonably clear. I'm just trying to convey my thinking, but as you immediately see on a forum like this... people think differently and when they think too differently, they even run into communication problems.

I think the best starting point is that of subjective probabilities. And then consider a learning problem. One can make the association of learning ~ equilibration, which I find interesting. To learn about something, is closely analogous to reach equilibrium with something.

/Fredrik