How observation leads to wavefunction collapse?

[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.

 

[Fra]

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.

Ok, I read it more carefully. That makes it look a bit better, I was too quick to comment. My apologees.

But I still think that the two options overlap.

(I)

If you believe (i), then you will claim that there is more than QM

(II)

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.

I'm not trying to silly or play games, I do understand what you probably suggest the difference is, but I am still of the opinion that the distincion is more fuzzy than what the first impression suggests. This was my point.

This suggest that (as I also suggested) that the two views is not necessarily (unless we can refine the notions here) _fundamentally_ incompatible after all.

So both approaches seem to think there is more than QM as we currently know it? The question seems to be what this extension is like?

/Fredrik

 

[Fra]

even the limits themselves are evolving. I think that there are somehow limits of the rate of change as well, but even this limit is changing.

In conclusion this is where the standard QM makes no sense to me. So wether this "there more to QM" makes me (i) or (ii) seems a matter of definition, I'd probably say (ii), but it depends on how the question is posed.

One implication is that things that are banned in standard QM shouldn't be banned. Unitarity is at stake here. If someone can come up with a reasonable proper evolutionary framework and still cling onto some unitary ideals, I'd be interested, but I have yet to see it.

Some people try to make a bigger model, that encapsulates the old one, and still preserves unitarity. But that's not true evolution. It's replacing the old theory with a new one. A proper evolutionary strategy should explain exactly how a new models grows out of the old one. This should not be theorist magic!

/Fredrik

 

[Fra]

Look at master nature. Mammals don't evolve new spieces by starting over from microbiological evolution, it would be a highly unsuccessful strategy. The evolve smoothly. The problem I have with some methods is that this isn't appreciated. It's too much ad hoc still, if not in the models - in the method.

So when looking at theories, it's not just a matter of if they make correct predictions in a snapshot of time. It's a matter of how these theories can live and adapt to REALITY.

/Fredrik

 

[masudr]

So both approaches seem to think there is more than QM as we currently know it?

No; the second approach is accepting that we may not have a complete description of nature (as per the Laplacian dream). I only added that QM may not be the best model, since any current model can be superseded by a later one. I cannot suggest that QM is the final word -- none of us can. This is not a comment about QM in particular, but to any model of the universe.

 

[Fra]

Ok. I guess we could leave it here as it's not that much to discuss but a final comment.

I agree with you completely that this discussion is indeed not specifically about QM, it's about modelling in general. And that was what I tried to say, becuase I had the impression that the discussion had a confusing focus.

IMO, if we are talking about different theories and strategies, and which one makes more sense, I suggest it should be done in the larger context of general modelling or scientific method, otherwise the mere comparasion is unclear. Without a connection whatsoever the comparastion easily gets ambigous.

I suggest that any specific model of reality can not be separated completely from the scientific method that generated it, and the various abstractions used.

/Fredrik

 

[lightarrow]

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.

I don't agree on the fact only hidden-variables theory could account of it. We are not considering the possibility that {electron/first screen with slit/last screen} form a unique system, the behaviour of which gives the location of the flash on the last screen.

Let's say, to give the idea, that the last screen is completely absorbing, and that I place a tiny photodetector in a specific point of it. I have changed the properties of the screen only, but now I see "flashes" in that point and not in others. Should I imagine "hidden properties" of the electron to account of this new behaviour?

And what if I put many tiny photodetectors tuned so that it will flash only the one that will receive, in that moment, the maximum amplitude of the electron field? Maybe the electron wavefunction's amplitude, which has been modified by the first screen with the slit, can have just little amplitude variations from a point to another, that could give rise to a flash in a point instead of another (where a "standard" computation would tell us that instead the amplitude is the same); or it could be little amplitude variations from point to point in the screen's wavefunction or, in general, both. This is really obvious to me. Is not the same for you? Don't you see the analogy between the hypothetical case I made and the real one?

 

[meopemuk]

And what if I put many tiny photodetectors tuned so that it will flash only the one that will receive, in that moment, the maximum amplitude of the electron field? Maybe the electron wavefunction's amplitude, which has been modified by the first screen with the slit, can have just little amplitude variations from a point to another, that could give rise to a flash in a point instead of another (where a "standard" computation would tell us that instead the amplitude is the same); or it could be little amplitude variations from point to point in the screen's wavefunction or, in general, both. This is really obvious to me. Is not the same for you? Don't you see the analogy between the hypothetical case I made and the real one?

What you are describing looks like a "hidden variable" theory to me. You suggest that the point of the next flash is, in principle, calculable. You talk about some "little amplitude variations" which are responsible for the location of the flash. Logically, I accept such a possibility. I just don't believe that nature works that way.

 

[gptejms]

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.

Yes, of course.But once you give it a probability interpretation, it does not cease to be a field.

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.

Schrodinger equation is anyway an approximate(i.e. non-relativistic) description of reality--why worry about it all when relativistic formalism is available.I think we stick to the Schrodinger equation because it's (mathematically)easier to deal with.

 

[meopemuk]

No; the second approach is accepting that we may not have a complete description of nature (as per the Laplacian dream). I only added that QM may not be the best model, since any current model can be superseded by a later one. I cannot suggest that QM is the final word -- none of us can. This is not a comment about QM in particular, but to any model of the universe.

I can easily believe that QM (quantum logic, Hilbert spaces, state vectors, Hermitian operators, etc.) IS the final word. In my view, QM is a perfect physical theory, and it is virtually impossible to add or remove anything from it. I know that I should never say "never", but I am tempted to say that QM will be never superseded by any more general theory.

 

[Fra]

QM is a perfect physical theory, and it is virtually impossible to add or remove anything from it. I know that I should never say "never", but I am tempted to say that QM will be never superseded by any more general theory.

/Fredrik

 

[Anonym]

I can easily believe that QM (quantum logic, Hilbert spaces, state vectors, Hermitian operators, etc.) IS the final word. In my view, QM is a perfect physical theory, and it is virtually impossible to add or remove anything from it. I know that I should never say "never", but I am tempted to say that QM will be never superseded by any more general theory.

Sorry, I did not follow the discussion in this session. I hope QM you mean the non-relativistic limit. I do not think even within non-relativistic QM the “quantum logic” is the final word. The approach has his roots in J. von Neumann, Mathematische Grundlagen der Quantenmechanik, Berlin, (1931) Ch3, par. 5; definition of “eigenschaften”. I think it may be corrected by more adequate consideration. And non-Hermitian operators are still terra incognita.

Regards, Dany.

 

[lightarrow]

What you are describing looks like a "hidden variable" theory to me. You suggest that the point of the next flash is, in principle, calculable. You talk about some "little amplitude variations" which are responsible for the location of the flash. Logically, I accept such a possibility. I just don't believe that nature works that way.

A hidden variable shoud be an objective property of the electron only, not of the entire system.

 

[meopemuk]

I hope QM you mean the non-relativistic limit.

Not at all. Relativistic quantum mechanics is fine as well. Being relativistic or non-relativistic does not change the fundamental structure of QM. It simply changes the invariance group (Galilei or Poincare).

 

[Ariste]

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.

I'm no expert in physics, but conceptually it's difficult for me to accept (ii), and beyond that, option (ii) is just disheartening.

Conceptually, it seems to me that (ii) defies causality. The theory behind physics is that the behavior of nature is governed by certain laws, and that we can predict the behavior of nature according to these laws. To say that we cannot, under any circumstances, accurately predict the behavior of an electron is to say either that a) the behavior of an electron is not governed by natural laws or that b) our models and/or equipment are inadequte to accurately derive these laws. To me, the second option seems much more logical and likely.

 

[masudr]

The theory behind physics is that the behavior of nature is governed by certain laws, and that we can predict the behavior of nature according to these laws. To say that we cannot, under any circumstances, accurately predict the behavior of an electron is to say either that a) the behavior of an electron is not governed by natural laws or that b) our models and/or equipment are inadequte to accurately derive these laws. To me, the second option seems much more logical and likely.

Note that these are your opinions and musings on nature. There's no reason why nature should (nor is there a reason why nature shouldn't) conform to your opinions.