Revisiting the Completeness of Quantum Theory: A Scientist's Perspective

[computerphys]

If nature is that way(electrons not having a definite position and momentum at the same time), then qm is complete.

If you want to posit some hidden variables theory about an underlying hidden reality, make it a non-local one(i.e. a pilot wave that instructs/directs the particle).

No, I don't need any hidden variables to get the conclusion that QM is incomplete. As I said before, I do believe in the uncertainty as a fundamental feature of the nature, and I know they are debunked due to Bell and Aspect, so forget hidden variables.

I still don't see why you say QM is complete while you agree with the empirical fact that the outcome of a measurement is a single eigenvalue, and at the same time knowing that QM is not capable of render/predict such a single eigenvalue, but a bunch of them.

Einstein's point in short words:

How can we say that QM is complete when it cannot render accurately experimental outcomes?

Thanks!

 

[computerphys]

It is possible, computerphys, that you're confusing chaotic, nonlinear, or stochastic processes with non-determinism.

Thanks for the hints, but no. Independently of these uncertainty sources, there is a fact we cannot avoid: the nature renders a single eigenvalue but QM renders a lot of them. So, nature is not completely described by QM. QM is incomplete.

By the way, chaotic or nonlinear cases belong to the Hidden Variables scheme, if I am not wrong. So, we should avoid them.

And models don't really have any purpose outside of determinism

I agree with you, but it does not change Einstein's point:

QM is incomplete because it cannot renders accurately eigenvalues as nature does.

 

[GeorgCantor]

No, I don't need any hidden variables to get the conclusion that QM is incomplete. As I said before, I do believe in the uncertainty as a fundamental feature of the nature, and I know they are debunked due to Bell and Aspect, so forget hidden variables.

I still don't see why you say QM is complete while you agree with the empirical fact that the outcome of a measurement is a single eigenvalue, and at the same time knowing that QM is not capable of render/predict such a single eigenvalue, but a bunch of them.

I didn't say qm was complete, look at my first post. In order for me to know this, i would have to know if there exist at the fundamental level such a thing as an electron with a defnite momentum and definite position at the same time. I don't know if this is true, hence i am not taking a side.

Einstein's point in short words:

How can we say that QM is complete when it cannot render accurately experimental outcomes?

Thanks!

Einstein didn't know that lhv would be refuted so any underlying model has to either be non-realistic(counterfactual), non-local or the observers have no free will.

You seem to insist that fundamental particles must have a definite position and momentum at the same time, but what is the justification for this, except a classical mindset?

 

[computerphys]

Just for the sake of clarity, when I say that QM is incomplete, I am not implying that it should exist a deeper theory that would "fix" QM. In fact, I believe that deeper theory cannot exist.

What I mean by incomplete is fairly simple: nature is given us more information in the experimental outcomes than QM can render/predict. Just that.

The key concept in this thread should be the completeness, its meaning and its applicability to QM. I hope that clarifies my point which I think it is the same that Einstein's.

Thanks again!

 

[computerphys]

I didn't say qm was complete, look at my first post. In order for me to know this, i would have to know if there exist at the fundamental level such a thing as an electron with a defnite momentum and definite position at the same time. I don't know if this is true, hence i am not taking a side.

I apologize for my misunderstanding. I respect you taking no side.

Einstein didn't know that lhv would be refuted so any underlying model has to either be non-realistic(counterfactual), non-local or the observers have no free will.

Yes, Einstein believed in hidden variables as a solution to the incompleteness of QM. But I don't share that point with him. Nevertheless it seems to me that Einstein was right when telling Bohr that QM is not complete due to the lack of accuracy in QM predictions as opposed to the accuracy nature give us in the measurement process.

You seem to insist that fundamental particles must have a definite position and momentum at the same time, but what is the justification for this, except a classical mindset?

I don't know where I have said that, but I don't think that fundamental particles must have a definite position and momentum at the same time.

What I say is just that what you measure in the laboratory cannot be rendered by QM.

I think that is equivalent to say that QM is not complete, but not meaning there should exist another alternative, deeper and more complete theory.

Just would like to know if this point could be a sound argument under a scientific and philosophical basis.

Thanks!

 

[computerphys]

"non-deterministic correction" is a bit of an oxymoron isn't it?

Yes, you are right. Call it instead "quantum uncertainty". Then, the sentence would be:

Quantum uncertainty is out of NM scope. So, NM is effectively complete.

 

[GeorgCantor]

I don't know where I have said that, but I don't think that fundamental particles must have a definite position and momentum at the same time.

What I say is just that what you measure in the laboratory cannot be rendered by QM.

Hundreds of experiments confirm the validity of the uncertainty principle. There is no experiment to my knowledge that doesn't agree with the mathematical formalism to date. In fact, qm and qft are the most 'complete' theories we currently have and present a much fuller and more valid picture of what it is that is actually going on.

 

[computerphys]

Hundreds of experiments confirm the validity of the uncertainty principle. There is no experiment to my knowledge that doesn't agree with the mathematical formalism to date. In fact, qm and qft are the most 'complete' theories we currently have and present a much fuller and more valid picture of what it is that is actually going on.

I agree with you. The point is that "the most 'complete' theories we currently have" are not fully complete. I have heard a lot of times that QM is complete, and Einstein was wrong. That is the problem. There is no way to justify that QM is complete. As a matter of fact, I think that when we compare nature's outcome with QM's outcome, it becomes evident that QM is not complete. So, saying QM is not complete is justifiable, but saying the contrary is not.

We can say that QM is our most complete theory, yes, but we cannot say QM is complete or fully complete, because it is false, with all my respects. (If I am wrong, please tell me why, where is the flaw in this argument).

To say that QM is not complete is not an aggression toward the QM mathematical formalism, nor any experiment. It is just to establish the limits of QM and be conscious that nature is more than QM (at the very QM scope). There is not an "homomorphical" or "bijective" relation between nature and QM. This is another way to express that QM is not complete.

We cannot say seriously that a theory is complete if nature's outcome does not correspond (*) to theory's prediction.

* Through a relation of homomorphism/bijection.

Thanks!

 

[computerphys]

MWI, for example, is complete and deterministic

I have followed your advice and read a little bit about MWI. My conclusion seems to be that the predictive power of MWI is the same as QM plain formalism. Well, actually that is not a surprise due to MWI being just an interpretation of QM. Tell me if I am wrong:

1.- MWI cannot predict the position of a free electron, just only a set of eigenvalues.

2.- QM plain formalism, exactly the same.

3.- Nature gives us the exact position of the free electron.

So, comparing the information got from the outcomes of the 3 of them we may say that:

MWI = QM < Nature

Nature renders more information, so nature is complete, but QM is incomplete and MWI as well.

MWI cannot tell us where exactly we are going to find the electron, but nature can.

Other equivalent way to understand the word "complete" is defining it roughly as "that where nothing is left". In QM, somebody telling us which eigenvalue will be the outcome of the experiment is the part that is left (and I say it is left because we expect a theory like QM to be a model for the nature, rendering the same values for every measurement). In Nature, nothing is left, because nature give us only one eigenvalue as the result of the measurement.

I am not telling we need an additional theory for the part that is left (the man telling us which eigenvalue is the outcome). I know (according to Bell and Aspect) that an additional theory cannot exist. I accept Heisenberg principle as something unavoidable.

I am just telling that something (not necessarily a theory) is left because nature has it, but neither MWI nor QM has it. Suppose that QM had that "thing", then and only then we could say QM is complete.

It seems to me that substituting wavefunction collapse (non-determinist process) for world branching (also a non-determinist process, if I am not wrong ...) doesn't change the fact that QM cannot render outcomes as accurately as nature does.

If nature does a thing that the theory doesn't (under its own scope), I think the correct word to describe that situation is "incomplete".

Thanks!

 

[computerphys]

I have just run into something interesting at:

http://en.wikipedia.org/wiki/Incompleteness_of_quantum_physics

Incompleteness, it seems, is here to stay: The theory prescribes that no matter how much we know about a quantum system—even when we have maximal information about it—there will always be a statistical residue. There will always be questions that we can ask of a system for which we cannot predict the outcomes. In quantum theory, maximal information is simply not complete information [Caves and Fuchs 1996]. But neither can it be completed.

 

[ThomasT]

By your definitions, if nature happens to be nondeterministic, then I think every scientific theory must be incomplete by your definition.

Even if nature happens to be deterministic, or maybe especially so, then I agree that every current scientific theory is incomplete.

 

[ConradDJ]

I have just run into something interesting at:

http://en.wikipedia.org/wiki/Incompleteness_of_quantum_physics

"Incompleteness, it seems, is here to stay: The theory prescribes that no matter how much we know about a quantum system—even when we have maximal information about it—there will always be a statistical residue. There will always be questions that we can ask of a system for which we cannot predict the outcomes. In quantum theory, maximal information is simply not complete information [Caves and Fuchs 1996]. But neither can it be completed."

I wanted to mention Carlo Rovelli's attempt ("Relational Quantum Mechanics") to derive the formalism of QM from these two postulates:

> There is a maximum amount of information that can be obtained about a system.

> Having obtained the maximum information, one can always interact with a system in a way that produces new information about it.

These may sound contradictory, but essentially the idea is that reality itself is not "complete" -- it's an interactive information system that's always creating new answers to new questions in new situations. The idea of "completeness" seems to assume a notion of reality in which all the answers are already there, whether or not any question is asked.

 

[computerphys]

... reality itself is not "complete" -- it's an interactive information system that's always creating new answers to new questions in new situations. The idea of "completeness" seems to assume a notion of reality in which all the answers are already there, whether or not any question is asked.

That "interactive information system" is a nature's process.

The description of this process, by which this new information is added to the system, is unknown and unknowable (according to Bell and Aspect).

So, the process exists in nature, but the theory that describes it will never exist. So, again, theory doesn't reach nature and won't ever.

* I admit QM is "scientifically complete" in the sense that science cannot create a more complete theory that would predict accurate eigenvalues.

* But I also think is quite obvious that QM is "naturally incomplete" in the sense that QM cannot successfully describe nature (the how) when rendering eigenvalues.

Am I wrong concluding that ...?: Einstein was right: Nature can do it, QM cannot.

 

[Dickfore]

> There is a maximum amount of information that can be obtained about a system.

> Having obtained the maximum information, one can always interact with a system in a way that produces new information about it.

In Shannon's Information Theory, concepts of information and entropy are defined for random variables. What is the meaning of information about a system?

 

[GeorgCantor]

Am I wrong concluding that ...?: Einstein was right: Nature can do it, QM cannot.

Aha, i now see the point you were making from the beginning.

Yes, Einstein was right imo that Nature can do it but qm cannot, but for a different reason - the reason being that Nature(whatever it is) is hollistic. I guess this isn't news in any way to those involved the foundational issues of physics(think about it in terms of background-independence and space and time being emergent).

Outcomes are sellected for in a way to preserve a kind of determinism that is explicit on the macro scale. Nature is definitely more than the sum of its parts.

And if you think about it, so are we, regardless of what compatibilists(i am told they exist ) might say.


Perhaps, that's Nature's way of observing itself(if i start sounding like Wheeler, that's a coincidence).

 

[computerphys]

Nature(whatever it is) is hollistic ...
Nature is definitely more than the sum of its parts.

Sorry, but I don't get the point about the relation between holism, "non-reductionism" and QM completeness.

Are you meaning that holism and "non-reductionism" must fill the gap left by QM incompleteness?

Sorry in advance if I understood wrong

 

[GeorgCantor]

Sorry, but I don't get the point about the relation between holism, "non-reductionism" and QM completeness.

Reality simply is, it can't be reduced from the fundamental interactions. Look at the interpretations - none of them solve the problem of outcomes, namely why we get the outcomes we observe. Reality is holistic(more than the sum of its parts) and a case can be made that it strives towards observers, hence why the fundamental constants seem fine tuned for life(silly idea but what do we know?). The "gap" is filled with what you might wish to call "self-organization at different levels" or alternatively "mind of god", "a universe that's alive in some sense", etc. The theory of everything is a mirage, a naive human invention.

 

[computerphys]

Reality simply is, it can't be reduced from the fundamental interactions. Look at the interpretations - none of them solve the problem of outcomes, namely why we get the outcomes we observe. Reality is holistic(more than the sum of its parts) and a case can be made that it strives towards observers, hence why the fundamental constants seem fine tuned for life(silly idea but what do we know?). The "gap" is filled with what you might wish to call "self-organization at different levels" or alternatively "mind of god", "a universe that's alive in some sense", etc. The theory of everything is a mirage, a naive human invention.

I am very glad to hear that. I agree with you 100%.

Thanks for sharing your point of view!

 

[imiyakawa]

Reality simply is, it can't be reduced from the fundamental interactions. Look at the interpretations - none of them solve the problem of outcomes, namely why we get the outcomes we observe. Reality is holistic(more than the sum of its parts) and a case can be made that it strives towards observers, hence why the fundamental constants seem fine tuned for life(silly idea but what do we know?). The "gap" is filled with what you might wish to call "self-organization at different levels".

If materialism, how do we know that the whole is greater than the sum of its parts? Who are we to say that ostensible self-organization at the "higher" levels isn't run by strict laws at the base of reality? Even if something like Navier-Stokes fluid dynamics can't be deduced from our current host of 'base' formalisms, do we really have to infer "greater than the sum of its parts"? It would just mean that either we don't have all the base laws figured out yet, or there's laws that 'kick in' at the higher levels, perhaps interference of self-gravitation onto the system that isn't seen on the singular wavefunction level.. Maybe I'm being tripped up on what you mean by "whole is greater than sum of its parts".

I know apeiron will step in here - I wait to be educated!

And, assuming a non-local hidden variable interp. is false, why does random collapse to discrete-state give credence to the notion that the whole is > the sum of its parts? Sure, we could engage in a debate of whether this entails acausality or not, and the consequences of this..[a debate I don't wish to have :D]

When a theory predicts an experiment outcome under its scope, we should say it is complete, as for example, Newtonian Mechanics. Of course, NM gets out of its scope when relativistic corrections are needed. So, at least we have a complete theory of something here.

Prediction vs. Explanation.

In contrast, my point is that QM seems to me to be a theory that cannot predict an experiment outcome under its own scope, as for example the position of a free electron (after measuring its momentum).

Doesn't mean that it's an incomplete theory. The very failure of the measurement could be a confirmation of the theory.

 

[computerphys]

Doesn't mean that it's an incomplete theory. The very failure of the measurement could be a confirmation of the theory.

We are not doubting about the validity of QM, so another "confirmation of the theory" is not necessary.

We are discussing the completeness of QM. QM can be a very good theory, but at the same time an incomplete one.

The fact that QM cannot yield accurate measurement predictions is the proof of QM incompleteness. Incompleteness doesn't mean a new theory is left. It only means that QM cannot explain/predict the nature we observe. It can explain part of it, but not the whole of it. So, it is logical to say that it is incomplete.

Heisenberg principle is telling us what is the empirical part that nature can render but QM cannot. Accepting Heisenberg principle is accepting that QM is incomplete.

How do we fill that gap, is another question.

 

[imiyakawa]

The fact that QM cannot yield accurate measurement predictions is the proof of QM incompleteness. Incompleteness doesn't mean a new theory is left. It only means that QM cannot explain/predict the nature we observe. It can explain part of it, but not the whole of it. So, it is logical to say that it is incomplete.

Heisenberg principle is telling us what is the empirical part that nature can render but QM cannot. Accepting Heisenberg principle is accepting that QM is incomplete..

The automatic corollary isn't incompleteness. Ceteris paribus, forgetting future discoveries, and assuming a random interpretation;
A. acausality, then QM is complete.
B. not-acausality, QM is incomplete if universe has causal closure.

 

[ConradDJ]

The description of this process, by which this new information is added to the system, is unknown and unknowable (according to Bell and Aspect).

So, the process exists in nature, but the theory that describes it will never exist. So, again, theory doesn't reach nature and won't ever...

Am I wrong concluding that ...?: Einstein was right: Nature can do it, QM cannot.

Well, even apart from QM, in classical physics -- three massive bodies can move under the influence of their mutual gravitation, but Newton's equations only describe the motion of two gravitating bodies. There is no equation that can (without approximation) predict the motion of three bodies. I'm not sure that means the theory is incomplete or in any way inadequate. Certainly nature can do a hell of a lot that mathematics can't.

 

[ConradDJ]

In Shannon's Information Theory, concepts of information and entropy are defined for random variables. What is the meaning of information about a system?

Rovelli does build directly on Shannon's theory. He thinks of "information about a system" as a series of yes-no questions that can be "put to the system" by another observing system. What that means exactly raises the complex question about all the different parameters that physical systems have and all the ways each of them can be measured... which he specifically avoids.

Here's the link if you're interested --
http://arxiv.org/abs/quant-ph/9609002v2"

 

[GeorgCantor]

If materialism, how do we know that the whole is greater than the sum of its parts? Who are we to say that ostensible self-organization at the "higher" levels isn't run by strict laws at the base of reality?

What is the base of reality you speak of? Me, you, bits, hologram, god, relations, master equation, fields,...? There is not much left for a base of reality after GR. Do you hope to deduce everything we observe from there? Are you going to deduce "the base of reality" from some other more basic laws, and the laws from other laws, that in turn would come from other laws...?

Even if something like Navier-Stokes fluid dynamics can't be deduced from our current host of 'base' formalisms, do we really have to infer "greater than the sum of its parts"?

What i implied was not a specific case of unexplained behavior, but the impossibility to tell why intrinsic quantum randomness manifests as seemingly deterministic patterns on the macro scale(this is concerning the whole of reality, the entire universe, not a specific phenomenon).
Can you answer why intrinsic quantum randomness translates into outcomes that preserve determinism and causality within the same FOR? I.e. why doesn't the HIV virus materialize into my bloodstream if i sit close to a HIV-sick person(an unmeasured HIV virus isn't well localized)? Or if you believe in decoherence, why doesn't it decohere in the blood of a person sitting somewhere close by? QM's indeterminancy says it's possible but it's never been observed to my knowledge and lhv models are refuted. There is either a non-local(and very possibly non-realistic) underlying reality(what you refer to as "base of reality") or reality is simply hollistic. As a side note, non-local and non-real underlying reality is the other name for mind(information).

It would just mean that either we don't have all the base laws figured out yet, or there's laws that 'kick in' at the higher levels, perhaps interference of self-gravitation onto the system that isn't seen on the singular wavefunction level.. Maybe I'm being tripped up on what you mean by "whole is greater than sum of its parts".

The laws that "kick in at higher levels" is exactly what i was talking about. This is a good description of what a hollistic reality is about.

And, assuming a non-local hidden variable interp. is false, why does random collapse to discrete-state give credence to the notion that the whole is > the sum of its parts?

Where do the determinism and causality on the macro level come from? Or are you one of those guys that believe that electrons have a well defined position and momentum at the same time and it's guided by a non-local pilot wave to a deterministic picture of laptops, TV's, chairs and tables?

 

[imiyakawa]

The laws that "kick in at higher levels" is exactly what i was talking about. This is a good description of what a hollistic reality is about.

Good, we are in conceptual agreement. We are in agreement that this type of reality is possible. We aren't in agreement about the level of a priori certainty that should be invested in this reality.

Are you going to deduce "the base of reality" from some other more basic laws, and the laws from other laws, that in turn would come from other laws...?

My position is "I don't know". This may be the case, it may not be. We don't know.

I just had trouble with the saying "whole greater than sum of its parts". If you define this saying as your "hollistic" reality, then we are in agreement that the preceding saying may or may not be correct. I was operating under a different definition of that saying than you were.

My second concerd was with the certainty of your exposition.

Where do the determinism and causality on the macro level come from?

I don't know.

Your main premise was "Reality simply is, it can't be reduced from the fundamental interactions" which is what I had trouble with; I just don't see how you can be certain.

Where is your certainty sourced from? The quantum/classical threshold? The potential for an infinite regress down the rabbit hole of finding laws that govern smaller and smaller units? Hmm

My friend is a physicist and he holds a completely opposed view. Is he wrong and you correct?

I'm going to remain ambivalent on something we cannot know.

There is either a non-local(and very possibly non-realistic) underlying reality(what you refer to as "base of reality") or reality is simply hollistic.

Precisely. We are in utter agreement of the two possibilities. My questioning of your post was simply me expressing anxiety at how you could be so sure the latter was true (also, if you define "whole > sum of parts" as a hollistic reality, then I'm NOT debating against you, we're talking about different definitions). I never said it wasn't. I'm saying we don't know at present.

why doesn't the HIV virus materialize into my bloodstream if i sit close to a HIV-sick person(an unmeasured HIV virus isn't well localized)? Or if you believe in decoherence, why doesn't it decohere in the blood of a person sitting somewhere close by? QM's indeterminancy says it's possible but it's never been observed to my knowledge and lhv models are refuted.

Are you asking why their blood doesn't collapse into your body? I see why you brought this up.

Apeiron's global constraints!

This doesn't suggest the whole being greater than the sum of its parts. Are you saying something other than:

a non-local underlying reality

is governing this system [i.e. the reality is "hollistic"]? How do you know?

If you're not saying this, then you can shift from the laws governing the system and say a complex system is greater than the sum of its parts through its interactions. I'm not debating this. I was assuming that when you said "whole > sum of parts" you meant reality IS hollistic and isn't a slew of "base" laws that interact to produce complex systems.
---------------------------------

All in all, I was debating:
- the definition of "the whole being greater than the sum of its parts" as what you call a hollistic reality. My position is it's too early to know whether or not higher level interactions can be predicted solely from NL base laws - assuming they even exist.
- the assertion that "it can't be reduced from the fundamental interactions".

I wasn't debating:
- "the whole being greater than the sum of its parts" under the definition of the parts + interactions, which is what your HIV scenario supports.

 

[GeorgCantor]

All in all, I was debating:
- the definition of "the whole being greater than the sum of its parts" as what you call a hollistic reality. My position is it's too early to know whether or not higher level interactions can be predicted solely from NL base laws - assuming they even exist.
- the assertion that "it can't be reduced from the fundamental interactions".

I wasn't debating:
- "the whole being greater than the sum of its parts" under the definition of the parts + interactions, which is what your scenario supports - however it doesn't yet support hollistic vs. litany of NL fundamental laws (if they exist), which is the only thing I had trouble with.

Then let's word it differently - "The whole is definitely more than the sum of its parts(as we know them now)".

I have very severe conceptual difficulties believing that ALL of our observations(incl. mind) will be explained within the framework of causal interactions in a "universe" where spacetime is not a fundamental concept and where the "stuff" is a non-local energy-wave 'thing' that doesn't have fixed properties across different inertial frames.The uncertainty principle, which i take to be a fundamental postulate of qm, is a very grave obstacle as well.
But since this is the philosophy forum and a deeper perspective is sought, you are right, my opinion is a reflection of the current knowledge so it could be wrong in the very long run. It does seem to me like a very well motivated and argumented opinion(as of NOW!) and it would be a good idea to ask your friend why he believes what he does. Perhaps he has a vision(interpretation) of reality that is very different from anything i have met, read or thought about so far.

 

[computerphys]

The automatic corollary isn't incompleteness. Ceteris paribus, forgetting future discoveries, and assuming a random interpretation;
A. acausality, then QM is complete.
B. not-acausality, QM is incomplete if universe has causal closure.

Assuming option A, I don't get how you reach at the conclusion that QM is complete.

(Of course, I discard option B due to debunked hidden variables.)

Filling the gap left by uncertainty principle with acausality doesn't change the fact that there is a gap and it is not filled with QM.

If we have a glass of water with a leak at the upper side, it becomes impossible to fill it completely (at equilibrium). Can we say it is completely filled when there is air instead of water in the upper part of the glass due to the leak?

I think correct expression for that case is saying that the glass is not completely full of water and it cannot be completed in any way. I don't know if I am expressing correctly this simile.

 

[GeorgCantor]

My position is "I don't know". This may be the case, it may not be. We don't know.

Something tells me you don't believe it will one day be possible to recover your "self"(the "I") somewhere among the non-local energy-wave manifestations whose actualities appear to be dependent on the environment and the observations you take on them.

As far as i can tell, it's a self-referential loop and it'd be naive and ignorant of me if i were hopeful that we'd one day explain everything.

It's too late where i am, i will come up with examples tomorrow where Nature appears as if it tries to 'hide' its secrets.

 

[computerphys]

Well, even apart from QM, in classical physics -- three massive bodies can move under the influence of their mutual gravitation, but Newton's equations only describe the motion of two gravitating bodies. There is no equation that can (without approximation) predict the motion of three bodies. I'm not sure that means the theory is incomplete or in any way inadequate. Certainly nature can do a hell of a lot that mathematics can't.

1.- N-body lack of integrability is a limit of mathematics.
2.- Heisenberg principle is a limit of physics.

I think it would be right to say that case #1 implies that integral calculus is incomplete, and correspondingly, case #2 implies that QM is incomplete.

 

[computerphys]

I have just found out that there are 3 possible senses about the concept of completeness:

A complete theory describes:

1.- all there is to say about nature (Shimony)
2.- all elements of reality (Einstein's EPR)
3.- all outcomes of experiments (Ballentine and Jarretts, "predictive completeness")

A complete glass of water is:

1.- that full of water up to the highest place you can
2.- that full of water up to the top of your concept of glass
3.- that full of water up to the top of the glass you can observe

Is that simile correct?