How observation leads to wavefunction collapse?

[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

 

[gptejms]

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.

Schrodinger equation is the v/c<<1 limit of relativistic(KG or Dirac) equation.The latter describes a field(quantum field in fact)--so in that sense,Schrodinger equation also describes a field(i.e. a "real" wave)--it's just that this field also happens to satisfy the continuity equation, and hence may also be called a wavefunction(rather given the interpretation of a wavefunction).It is not just a mathematical entity.

 

[Demystifier]

Schrodinger equation is the v/c<<1 limit of relativistic(KG or Dirac) equation.The latter describes a field(quantum field in fact)--so in that sense,Schrodinger equation also describes a field(i.e. a "real" wave)--it's just that this field also happens to satisfy the continuity equation, and hence may also be called a wavefunction(rather given the interpretation of a wavefunction).It is not just a mathematical entity.

If Schrodinger equation describes a "real" field, then why its absolute value squared equals the probability density of pointlike particle positions? I think this is one of the greatest unsolved problems for those who think that nonrelativistic QM can be derived from relativistic QFT.

 

[gptejms]

If Schrodinger equation describes a "real" field, then why its absolute value squared equals the probability density of pointlike particle positions? I think this is one of the greatest unsolved problems for those who think that nonrelativistic QM can be derived from relativistic QFT.

By "real",I meant the real of cepheid's original post--this does not mean non-imaginary.Absolute value squared of (normalised)psi equals prob. density because continuity equation is satisfied.This psi is as much a field as the psi of KG equation.

 

[lightarrow]

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.

Ok.

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.

What does it mean? That we have come to the "Gods" territory? If something *really* exist in nature, how would you prove this fact, if you cannot reveal it?

 

[Demystifier]

Absolute value squared of (normalised)psi equals prob. density because continuity equation is satisfied.This psi is as much a field as the psi of KG equation.

My point is that if something satisfies a continuity equation, it does not yet imply that it describes probability. For example, a classical fluid, or a classical field, may also satisfy a continuity equation, but such a classical theory has nothing to do with probabilities. Instead, you must postulate probabilistic interpretation as an independent axiom. The problem is that the axioms of QFT, including those that refer to probabilities, do NOT imply the probabilistic interpretation of the Schrodinger field/wavefunction.

 

[Anonym]

You can say (together with Einstein) that QM is not a complete description of nature.

Please provide the reference including exact quotation.

Regards, Dany.

 

[meopemuk]

Ok.What does it mean? That we have come to the "Gods" territory? If something *really* exist in nature, how would you prove this fact, if you cannot reveal it?

Consider the following. Arrange a single slit experiment (as discussed by Mr Virtual in post #68, one even doesn't need two slits to see quantum "weirdness") and shoot electrons one-by-one. Notice that each electron lands at a different place on the screen. Recognize that there is absolutely no way to predict where each individual electron will land. Quantum mechanics can predict only the total probability distribution, but not the fate of each individual particle. So, we have a measurable physical fact (an electron hit a certain point on the screen), but we have no theoretical means to explain or predict this fact. Honestly, there could be only two conclusions from this observation:

1. Our present theory (quantum mechanics) is not a complete description of nature. There should be a deeper theory, which eventually will explain/predict the place of landing of each electron, or exact times of clicks of Geiger counters, or other events, which are currently described only probabilistically.

2. Events occurring with individual systems are fundamentally random. We will never know more than their probabilities. Quantum mechanics is the best possible (but not all-powerful) tool to describe nature.

There is no rational way to choose between these two conclusions. One should follow his/her intuition, philosophy, religion, etc.
Conclusion 1. is a path to "hidden variable" theories. This is a wrong path, in my humble opinion. I choose conclusion 2., which means that there are certain things about nature, that we will never understand.

 

[Mr Virtual]

2. Events occurring with individual systems are fundamentally random. We will never know more than their probabilities. Quantum mechanics is the best possible (but not all-powerful) tool to describe nature.

I think this conclusion is the correct one. Ther is no deeper theory. This is what nature is like.

Mr V

 

[meopemuk]

You can say (together with Einstein) that QM is not a complete description of nature.

Please provide the reference including exact quotation.

Isn't this the main idea of the famous paper?


A. Einstein, B. Podolsky, and N. Rosen, Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47 777 (1935).

 

[Anonym]

Isn't this the main idea of the famous paper?

A. Einstein, B. Podolsky, and N. Rosen, Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47 777 (1935).

Yes. However, A. Einstein as every other human being is allowed to make mistakes. The paper is wrong. I read in some place that it was not written by Einstein, only signed by him. You should consider things integrative and take into account later publications. Using the method of single isolated outcome you always will get random result with the probability to be correct close to 0.

Nevertheless, notice that the title is a question and not a statement.

Regards, Dany.

 

[meopemuk]

Yes. However, A. Einstein as every other human being is allowed to make mistakes.

I think it is well documented that Einstein didn't regard quantum mechanics as a complete description of nature. I think he was mistaken. However, I can also notice that Einstein's ideas about quantum mechanics were often much deeper than those of many of his contemporaries. For example, I was surprised to find that my own interpretation of quantum mechanics is best explained by Einstein's words (I don't think he personally subscribed to this particular interpretation):

I now imagine a quantum theoretician who may even admit that
the quantum-theoretical description refers to ensembles of systems
and not to individual systems, but who, nevertheless, clings to the
idea that the type of description of the statistical quantum theory
will, in its essential features, be retained in the future. He may
argue as follows: True, I admit that the quantum-theoretical
description is an incomplete description of the individual system. I
even admit that a complete theoretical description is, in principle,
thinkable. But I consider it proven that the search for such a
complete description would be aimless. For the lawfulness of nature
is thus constructed that the laws can be completely and suitably
formulated within the framework of our incomplete description. To
this I can only reply as follows: Your point of view - taken as
theoretical possibility - is incontestable.
A. Einstein, in "Albert Einstein: Philosopher-Scientist", (Open Court, 1949)

 

[olgranpappy]

If something *really* exist in nature, how would you prove this fact, if you cannot reveal it?

This is not exactly a question of physics, but rather of philosophy:

If I look at a small brown writing table, and if you look at the same table, we may both see a brown table. But if we were both to paint the table we would find that it is not exactly just brown; we would also need white for shine and black for shadow and we would put these colors in different places. The same goes for all of our other senses. We do not see the same exact table since our point of views are different.

So is there a *real* table?!

Of course, we can come up with a philosophy where there is no *real* table, but it will necessarily be quite a bit more contrived than the simple statement that, yes, there is a *real* table.

One can't *prove* that anything *really exists*, one simply accepts this fact as a a useful starting point.

 

[babelbusters]

One can't *prove* that anything *really exists*, one simply accepts this fact as a a useful starting point.

One can prove the existence of something. The opposite of something is nothing. Nothingness by definition is non-exisiting. It is a no-thing. Therefore, if nothing is not, then something necessarily is. What that necessary something is is a matter of debate, but to doubt the necessity of existence in general would appear to be illogical.

 

[olgranpappy]

One can prove the existence of something.

It should have been apparent from the context that by "anything" I meant "any particular thing" such as a table.

 

[olgranpappy]

P.S. I can prove anything I like--for example that santa claus exists.

Let P be that statement "santa claus exists" and let Q be defined as that statement which implys P; I.e., Q=Q \to P. The proof proceeds thusly:

1. Q \to Q (trivial)
2. Q\to Q \to P (def. of Q)
3. Q\to P (contraction)
4. Q (def. of Q)
5. P (modus ponens)

 

[olgranpappy]

P.P.S This is all quite tongue-in-cheek, btw.

 

[Fra]

Some _personal reflections_ again.

1. Our present theory (quantum mechanics) is not a complete description of nature. There should be a deeper theory, which eventually will explain/predict the place of landing of each electron, or exact times of clicks of Geiger counters, or other events, which are currently described only probabilistically.

2. Events occurring with individual systems are fundamentally random. We will never know more than their probabilities. Quantum mechanics is the best possible (but not all-powerful) tool to describe nature.

Some things are hard to grasp, but it isn't that hard. These discussions never end.

It seems some people are allergic to probabilities and that resorting to probabilites is somehow a defeat? Probability and bayesian logic is ultimately just a generalization boolean logic.

Sometimes one simply can't answer a question with a yes or a no. Sometimes the CORRECT answer is a maybe. And there are certain degrees of maybe. It really doesn't have to be more weird than that?

Does someone find this weird?

Does someone feel that yes or no, are the scientific answers, and maybe is not? Then go back to the scientific method and think again. I have a feeling that's where this confusion starts. I might even want som updates, improvements in the poppian ideals that ideas are falsified. The falsification should not be restricted to a boolan condition, it must be improved to degrees of belief, or nothing makes sense to me at least. Unlike what might seem the case, this is not only about human philosophy and irrelevant to physics.

> We will never know more than their probabilities.

I think even the probability we can't know exactly. You can't go out in a lab and make a simple measurement on a probability and get an exact value. The finite measurement have a deep implication IMO, if this is going to get near consistent.

There are also deep problems with the frequentist interpretation because the pictured ensmble is simply unreal. It can easily be imagined by a mathematician, but that's not the problem. We need interfaces with reality, and experimental contact.

I suspect that the further insight, may partly satisfy both sides. The fundamental fuzz is also a possibility! Meaning that catogoric statements as fundamental random, doesn't make complete sense.

/Fredrik

 

[masudr]

I think meopemuk was trying to express the idea that models of the universe can either, in principle,

(i) provide exact predictions for every event; or
(ii) provide predictions for ensembles only.

If you believe (i), then you will claim that there is more than QM; and if you believe (ii) then you will claim that there may be more than QM (as any model of the universe can be superseded by a new one that contains the old one in the limit of a parameter, or something), but we are stuck with probabilites forever.

Does someone find this weird?

Does someone feel that yes or no, are the scientific answers, and maybe is not?

It's not really about anyone finding anything weird. It's dependent on which of the two above you accept. A lot of people do believe (ii), in contrary to the assumptions in your post above.

 

[Fra]

I am not sure I can let the notion of "in principle" pass, I don't think it's not trivial. For example would "in principle" contain "we *might* - in the future"? or "we WILL in the future"?

/Fredrik

 

[meopemuk]

I think meopemuk was trying to express the idea that models of the universe can either, in principle,

(i) provide exact predictions for every event; or
(ii) provide predictions for ensembles only.

If you believe (i), then you will claim that there is more than QM; and if you believe (ii) then you will claim that there may be more than QM (as any model of the universe can be superseded by a new one that contains the old one in the limit of a parameter, or something), but we are stuck with probabilites forever.


It's not really about anyone finding anything weird. It's dependent on which of the two above you accept. A lot of people do believe (ii), in contrary to the assumptions in your post above.

Yes, this is exactly what I meant. And another important point was that if we accept (ii), then we also must accept that there is a limit to our knowledge. There are certain questions (at which point the next electron will hit the screen? when the Geiger counter will click next time?...) which simply don't have answers. One may consider it a sad news. I actually, think that this is a blessing. To me this means that we are possibly closer to a complete (within limits allowed by nature) physical "theory of everything" than we might think.

If there were no natural limits to our curiosity, we would keep asking why? why? why?... like 5-year old kids, always discovering deeper and deeper levels of reality without end in sight. This would be sad indeed.