Measurements and The Copenhagen Interpretation

[jambaugh]

I started this thread to continue the following discussion from the thread:
https://www.physicsforums.com/showthread.php?p=2203566#post2203566"

The 'collapse' of the wave-function is just a weird Copenhagen-interpretation way of looking at things that makes the false assumption that a measurement is performed independently of the system being measured.

In reality two interacting systems cannot be separated, so I see no reason to believe wave functions ever truly 'collapse' in the Copenhagen sense.

I believe you are misinterpreting the CI. In CI the wave functions collapse is not qualitatively different from the classical analogue of updating a classical probability distribution given new information about the system. For example prior to the drawing the distribution for all tickets in a simple lottery is uniform. After the drawing it "collapses" to 100% for the winning ticket and 0 for the rest.

It is unfortunate that the term "collapse" is used. If you replace "collapse of the wavefunction" with "update of the wavefunction" in all texts you then get the correct application of the CI.

Now you are welcome to disagree with CI but please don't misrepresent it.

I understand what you're saying, but I don't see how this contradicts anything I said.

You're repeating the same underlying assumption, phrased differently. The point was: You can't have information about the system independently of the system. Say you have a system that's a superposition of two states: $$|\psi>_{measured} = |0>_{measured} + |1>_{measured}$$. You're saying that you perform a 'measurement' and the state becomes either |0> or |1>. How do you measure a system? By interacting with it.

The result of such an interaction, when you model it entirely quantum-mechanically is an entangled state between the 'measuring' and 'measured' systems. You don't really gain any information from interacting at the quantum level. Which is why the Copenhagen Interpretation assumes classical measurement. That assumption is obviously false. In which case you have to ask where this 'collapse' supposedly comes from. That isn't to say it doesn't work, I already said it does. I'm saying it's simply not possible for it to be a true picture of what's going on, since the assumption it's based on is known to be false.

What I'm talking about is essentially what Stephen Weinberg is talking about in the http://en.wikipedia.org/wiki/Copenhagen_interpretation" [Broken] on WP's "Copenhagen interpretation" page.

But you and Weinberg are both making a mistake in assuming ontological status to both the collapse of the wave function and to entanglement within the Copenhagen interpretation (CI). It is a subtle mistake but is there in the distinction being made between a classical and quantum mechanical description of the measuring device.

Yes the measuring device and observer are fundamentally more accurately described quantum mechanically but there is no physical barrier between quantum and classical description across which information must traverse.

Yes the act of measurement is an interaction and creates entanglement between measuring device and measured system. But entanglement itself is not a physical property of a system but rather a property of the system's description, in particular how the system is subdivided into component subsystems.

This is not to say entanglement is an illusion, it has real physical consequences but these are again no different qualitatively from classical correlation.

Now as to Weinberg's critique of CI, the quote cited:

Steven Weinberg in "Einstein's Mistakes", Physics Today, November 2005, page 31, said:

All this familiar story is true, but it leaves out an irony. Bohr's version of quantum mechanics was deeply flawed, but not for the reason Einstein thought. The Copenhagen interpretation describes what happens when an observer makes a measurement, but the observer and the act of measurement are themselves treated classically. This is surely wrong: Physicists and their apparatus must be governed by the same quantum mechanical rules that govern everything else in the universe. But these rules are expressed in terms of a wave function (or, more precisely, a state vector) that evolves in a perfectly deterministic way. So where do the probabilistic rules of the Copenhagen interpretation come from?
Considerable progress has been made in recent years toward the resolution of the problem, which I cannot go into here. It is enough to say that neither Bohr nor Einstein had focused on the real problem with quantum mechanics. The Copenhagen rules clearly work, so they have to be accepted. But this leaves the task of explaining them by applying the deterministic equation for the evolution of the wave function, the Schrödinger equation, to observers and their apparatus.

The problem of thinking in terms of classical measurements of a quantum system becomes particularly acute in the field of quantum cosmology, where the quantum system is the universe.

Where he says "this is surely wrong..." he makes the mistake of identifying the laws governing the behavior of the physical system with the choice of the description of the system. The classical description of the Moon is not "wrong" because it fundamentally obeys quantum mechanical rules. It is rather less than maximal. However the critical issues is that we desire to speak in absolute terms about a specific outcome of a measurement. This dictates a classical description of the record of this measurement. There must be a classical/quantum cut between the piece of paper on which one writes down the result and the actual system for which this measurement is recorded.

Where you and He state that the act of measurement is treated classically in CI "which is obviously false" the statement itself is false. It is the record of the measurement which is treated classically. (Or at worst the gross variables of the position and velocity of the measuring device where applicable). The act (those variables of the measuring device which interact with the system) is left without detailed description except that it must obey the rules predicted by QM, i.e. one must be able to re-measure the system immediately and obtain the same result for the act to be called a "measurement".

When he speaks of the wave-function evolving in a perfectly deterministic way and asks from where the quantum probabilities come, he is again confusing subtly the wave-function with the physical system. The probabilities were there from the beginning. They are what the wave-function is modeling. It is not qualitatively different from a classical deterministic evolution of a classical probability distribution in phase space. One obviously doesn't puzzle over whence those probabilities arise. Why should one in the QM case?

As to his problem with CI in quantum cosmology, I assert that it is the problem with quantum cosmology not CI in that it is meaningless to describe a wave-function for the "universe as a whole" beyond a very trivial one of a 1 dimensional mode space "it exists!". All other measurements must be comparitive and thus applied to a part of the universe w.r.t. the rest of the universe. But that's a whole other thread in itself.

Finally as to a quantum treatment of the measurement process. First remember that measurement is a dissipative process. It is fundamentally an act of amplification and requires an entropy dump (heat sink) The meta-system of system+measuring device must then be described within QM using density operators wherein both classical and quantum probabilities may be expressed. You also must describe the coupling to the entropy dump but you fundamentally cannot describe the entropy dump itself. It is by definition beyond observation. One at best introduces a noisy component to the Hamiltonian of the system to model such a coupling.

So you set up your act of measurement... the meta-system evolves and quickly decoheres into a composite system with classical correlation between the measuring device with the appropriate record of possible outcomes in a classical set of probabilities, which are correlated with the various "collapsed" wave-functions for the measured system. All that entanglement gets shifted into the entropy dump.

If you wish you can model the entropy dump in part but when you do the partial trace over it to get the reduced density operator for meta-system you get the same situation.

At this point you choose one outcome in exactly the same sense as a classical outcome of a classical random variable. The result is the choice of one measurement with the corresponding "collapsed" wave function to describe future behavior of the system. The CI prescription just skips the busywork since we only care about our description of the system in hand.

This is the measurement process and you can't alter it significantly without invalidating the device as a measuring device.

Within CI there is no measurement problem. It only becomes a problem when you reify the wave function in one of the alternative interpretations.

[PS: I ought to write all this up in formal terms with proof or citations to proof of the assertions I am making. I have the summer off and that sounds like a good project! I can never find all the pieces in one place.]

 

[meopemuk]

Hi James,

I would like to disagree with the statement that in quantum mechanics the measuring device is treated as a classical object.

In fact, the measuring device has a purely quantum description - it is represented by the Hermitian operator of the observable measured by it. Yes, it seems strange that different descriptions are used in QM for the physical system (wave function) and for the measuring apparatus (Hermitian operator). However, this separation would become completely understandable if you accept that quantum mechanics is just a tool for the theoretical description of experiments. In each particular experimental setup, the separation between the (measured) physical system and the measuring device is always clear. So, quantum mechanics just faithfully reproduces this separation.

Of course, if our goal is to describe the universe as a whole, then the separation between the physical system and the measuring apparatus becomes troublesome. But I suspect that this ambitious goal is simply non-achievable, so QM should be OK as it stands.

 

[Count Iblis]

Finally as to a quantum treatment of the measurement process. First remember that measurement is a dissipative process. It is fundamentally an act of amplification and requires an entropy dump (heat sink) The meta-system of system+measuring device must then be described within QM using density operators wherein both classical and quantum probabilities may be expressed. You also must describe the coupling to the entropy dump but you fundamentally cannot describe the entropy dump itself. It is by definition beyond observation. One at best introduces a noisy component to the Hamiltonian of the system to model such a coupling.

Dissipative processes do not exist at the fundamental level. So, this can only be an approximate description of reality. The fact that we cannot imagine practical situations where CI will fail is not a good excuse to dismiss thought experiments where it will fail.

One can construct thought experiments were observers are implemented by quantum computers. An observer can observe a qubit in some basis, but then if he forgets the result of the observation, but not that he has observed it, he can dump the information back on the qubit and then the observation has been undone. According to CI the qubit's state will have collapsed and thus the qubit's state will be different than what it was before the observation. But this then contradicts unitary time evolution.


The conclusion has to be that without postulating new physics, the CI is self contradictory, but this inherent contradiction is wept under the big carpet of the large and effectively dissipative classical world. This new physics which you need to make the CI correct would have to show how a pure state can evolve into a mixed state.

 

[jambaugh]

Hi James,

I would like to disagree with the statement that in quantum mechanics the measuring device is treated as a classical object.

In fact, the measuring device has a purely quantum description - it is represented by the Hermitian operator of the observable measured by it. Yes, it seems strange that different descriptions are used in QM for the physical system (wave function) and for the measuring apparatus (Hermitian operator). However, this separation would become completely understandable if you accept that quantum mechanics is just a tool for the theoretical description of experiments. In each particular experimental setup, the separation between the (measured) physical system and the measuring device is always clear. So, quantum mechanics just faithfully reproduces this separation.

Of course, if our goal is to describe the universe as a whole, then the separation between the physical system and the measuring apparatus becomes troublesome. But I suspect that this ambitious goal is simply non-achievable, so QM should be OK as it stands.

Firstly the hermitian operator represents the action of the measuring device on the system not the description of the actual measuring device itself. Note the hermitian operator is unchanged by the measuring process while the measuring device necessarily changes as it registers the measured quantity.

I see no point in describing "the universe as a whole" as a single physical system as that is to my thinking an undefined concept. Being "physical" in the sense of being well define by physics implies external observability.

None-the-less it is a worthwhile and achievable goal to describe how system descriptions extend and how we may move the dividing line between measured system and measuring device. But most attempts I've seen (particularly those trying to invalidate CI) make the gross mistake of starting with a wave-function or Hilbert space vector representing the combined system and measuring device. This ignores the thermodynamic nature of the act of measurement and one should begin with the more general density operator formalism.

This having been said it is not too difficult to imagine how one goes about describing the process of measurement within this language. The measurement process can be understood in this context in terms of decoherence of the composite system. The entropy dump of which I spoke earlier is the source of the decoherence and a necessary part of the measurement process.

 

[jambaugh]

Dissipative processes do not exist at the fundamental level.

But they do exist. What determines what is "the fundamental level"? I think you are making the mistake here of confusing the deterministic evolution of the wave function with a deterministic evolution of the system. If you want to get "fundamental" in the most appropriate way then remember that the fundamental root of the physics is the operational meaning of the formal language and that begins with the act of measurement which via CI is fundamentally dissipative/non-reversible. You are introducing from the beginning a bias towards ontological description when you begin with this statement.

So, this can only be an approximate description of reality.

Again the mistake that one is describing "reality". One is describing behavior, especially within CI. Placing value on "description of reality" is assuming your hypothesis (invalidity of CI) and so you can't use it to argue against CI.

The fact that we cannot imagine practical situations where CI will fail is not a good excuse to dismiss thought experiments where it will fail.

I challenge you to formulate a well defined thought experiment where CI fails.

One can construct thought experiments were observers are implemented by quantum computers. An observer can observe a qubit in some basis, but then if he forgets the result of the observation, but not that he has observed it, he can dump the information back on the qubit and then the observation has been undone. According to CI the qubit's state will have collapsed and thus the qubit's state will be different than what it was before the observation. But this then contradicts unitary time evolution.

Your coherent "observer" is not performing a measurement within CI. A measurement has occurred when a record of the event has been stored in such a way that it can be read repeatedly without destroying that information. The information must be classically observable. This invalidates the "reversible measurement". Again CI does not assert that the measurement process is classical but rather the registration of the measured quantity is classically stored.

You may feel this is too limiting a restriction on the definition of "measurement". Fine but this is the necessary property of any measurement one can communicate (while retaining a copy) so that multiple observers can compare notes and ultimately publish findings. Without this restriction it would be hard to give measurement operational meaning.

I see your example as simply the act of reversibly entangling and then disentangling two systems. Calling one an "observer" doesn't make it one.

The conclusion has to be that without postulating new physics, the CI is self contradictory, but this inherent contradiction is wept under the big carpet of the large and effectively dissipative classical world. This new physics which you need to make the CI correct would have to show how a pure state can evolve into a mixed state.

You can't invalidate CI by a priori assuming its antithesis, that the mode vector reflects a physical state of the system. There is no "state" in CI-QM you can have pure and mixed descriptions base on what you know about the system. (At the same time you must always define "what you know about the system" in terms of physical acts of observation.) The qualities of "pure" vs "mixed" are not properties of the system but of our information about the system, e.g. that it came from a particular mode of preparation.

Of course you come to only one conclusion if you are assuming it prior to applying logic. You are not observing CI as self contradictory but rather in contradiction to your implicit assumption of an alternative interpretation.

You are getting bogged down in ontological issues, "the quantum nature of reality" and all that. First understand the epistemological self consistency of QM and CI. Then if you feel the need to go beyond that fine. If you feel unfulfilled with CI because it is agnostic about ontological reality then feel free to reject CI. Invoke many worlds, invoke god if you like but your "disproof" of CI is circular reasoning and indicates you still do not fully understand CI.

 

[Dmitry67]

Hi, jambaugh!
I was missing you, because for several month there were no CI believers here. Here is a proof:
https://www.physicsforums.com/showthread.php?t=309717
Looks like you are the very last one. :)
May be you could reply my unreplied question there in this thread or in my thread.
Thank you

 

[Hurkyl]

But they do exist. What determines what is "the fundamental level"?

"More fundamental" is the direction you go when you analyze. "Less fundamental" is the direction you go when you synthesize. For example think of the classical kinetic theory of gas: "particles bouncing around and interacting with each other" is the fundamental level.

(I'm pretty sure this is what he means)

I think you are making the mistake here of confusing the deterministic evolution of the wave function with a deterministic evolution of the system.

Is QM complete or incomplete? If it's complete, then it's not "confusion".

The information must be classically observable.
...
You may feel this is too limiting a restriction on the definition of "measurement".
...
Without this restriction it would be hard to give measurement operational meaning.

I do think it's too limiting. You may have given up on trying to understand measurement and settled for something 'easy' -- but I really don't understand how you can justify criticizing people who haven't given up.

Also, I notice your word choice suggests your understanding of measurement isn't even an a priori one -- it was derived from classical mechanics. So that begs yet another question: given that we know quantum mechanics is more accurate than classical mechanics, how can you justify using the less accurate theory as the one upon which we should base our understanding of such an important aspect of science?

There is no "state" in CI-QM you can have pure and mixed descriptions base on what you know about the system.
...
The qualities of "pure" vs "mixed" are not properties of the system but of our information about the system

Calling it "not a state" doesn't make it not one. There is no meaningful difference between "X" and "all information about X".

P.S. how is "our information about the system" not one of its properties? :tongue:

 

[jambaugh]

"More fundamental" is the direction you go when you analyze. "Less fundamental" is the direction you go when you synthesize. For example think of the classical kinetic theory of gas: "particles bouncing around and interacting with each other" is the fundamental level.

(I'm pretty sure this is what he means)

Yes but there are different contexts of analysis/synthesis. In mathematics the postulates are most fundamental. In an ontological context the most basic (atomic) level of reality is most fundamental. However in the context of science and especially physics you must go back to the epistemological roots there is what is most fundamental. The operational definition of the terms used in a theory. As Einstein found: time is what a clock measures, distance is what a measuring rod measures. In quantum theory the foundation is the act of measurement corresponding to an observable, and the act of system preparation corresponding to a particular mode vector and/or density operator.

Is QM complete or incomplete? If it's complete, then it's not "confusion".

It is epistemologically complete predicting all that can be predicted about say arbitrary sequences of spin measurements.

Seeing as it is ontologically agnostic in the CI interpretation then it is beyond incomplete in that context. But then science is "incomplete" in that it doesn't address the existence/absence of God in that very same context.

I do think it's too limiting. You may have given up on trying to understand measurement and settled for something 'easy' -- but I really don't understand how you can justify criticizing people who haven't given up.

Firstly my criticism is not of the dismissal of CI but rather of the mistake in asserting CI is self contradictory or inconsistent. Do you understand the logical fallacy of the circular argument? It is especially easy to make in a RAA argument. My criticism of the individual is in their not understanding CI rather than their not adopting CI. (That's for another debate once the individual understands it.)

Now as to understanding measurement, that's all well and noble but before one goes about trying to break down the measurement process in QM make sure you understand QM properly. You have to know if you are predicting from the theory ore inventing a new theory or speculating all together outside of physics and into metaphysics.

As for my part, I am fascinated by the subject and would like to push it as far as I can. I really seek to understand how the uncertainty relations arise from the act of measurement. But you can't do this by creating thought experiments wherein you are changing the definition of a measurement unless you are explicit in that change and provide a new more general definition. You certainly must be careful about redefining terms if you are trying to find a inconsistency in the interpretation which is based on the original definition.

Also, I notice your word choice suggests your understanding of measurement isn't even an a priori one -- it was derived from classical mechanics. So that begs yet another question: given that we know quantum mechanics is more accurate than classical mechanics, how can you justify using the less accurate theory as the one upon which we should base our understanding of such an important aspect of science?

I don't know where to begin. You better quote the word choice in context so I can address it directly. But first let me ask you for a single example of where QM is more accurate than CM... (not to challenge your claim but rather to make a point...)

Now in this example explain what you mean by more accurate. I.e. give me the measured value. Finally do so without using my definition of measurement (a recorded value which can be copied and transmitted).

It is not about being accurate. It is about communicating knowledge about a system as knowledge. We can't have this discussion without the letters appearing on screen/printer being classically readable.

Calling it "not a state" doesn't make it not one.

Nor, of course, does calling it a state vector make it a representation of a state. The question is answered in how one operationally interprets the mathematical object in terms of laboratory actions. When one refers to a "vertically polarized photon" one is referring to a photon which has emerged from a vertical polarizer. It is a mode of preparation not an objective state. What we know about this photon is that it will again pass through a vertical polarizer and not be absorbed... what the mode vector is is a description of how the system behaves.

There is no meaningful difference between "X" and "all information about X".

You just go on thinking that and see were it takes you. I'll be happy to sell you all the information about a Ferrari for one tenth the sticker price of a Ferrari and you just see how far you get down the highway.

I suppose you also believe that the needs of a group outweigh the needs of an individual?

P.S. how is "our information about the system" not one of its properties? :tongue:

It is, but when describing properties of the information one is then describing a property of a property and not a property of the original system.

The fact that apples are red and red is a color does not make apples colors. The fact that an electron has a wave-function and that wave-function evolves deterministically does not mean the electron evolves deterministically. (It doesn't mean it doesn't either but...) The wavefunction represent probabilistic information about how the electron will behave and not the electron itself. The wave-function is a classical object (conceptual not physical) the electron a quantum. We can write down and copy the wave function describe it exactly in every detail.

 

[Count Iblis]

I agree with Hurkyl's comments. Let me focus on the following points:

I challenge you to formulate a well defined thought experiment where CI fails.

And:

Your coherent "observer" is not performing a measurement within CI. A measurement has occurred when a record of the event has been stored in such a way that it can be read repeatedly without destroying that information. The information must be classically observable. This invalidates the "reversible measurement". Again CI does not assert that the measurement process is classical but rather the registration of the measured quantity is classically stored.

I think that "classically observable" can only be an approximate concept. Ultimately everything is reversible, in the sense that the time evolution of two different initial states of a isolated system cannot evolve to the same final state. If this were not true, then one could get rid of information in a truly irreversible way, leading to problems (e.g. you would have found a way around Landauer's argument of why Maxwell's demon cannot work).

But if one accepts that informaton cannot be destroyed, then the notion of the classical observation (in the sense of records being kept that can be read in a classical way), requires an infinite universe in which you can copy information without limit.

Strictly speaking, an observer in a finite universe, or hypothetically in a finite isolated box, does not exactly satisfy the CI criteria that an observer should satisfy, or at least the observations made by the observer should satisfy. We, as real observers in this universe, may be very far removed from the regime where we could perform David Deutsch's thought experiment, but we are not precisely at the classical limit either.

Anyway, to come back to your first point about an experiment where CI fails, one can argue that it wouldn't matter for us if we would live in a closed and perfectly isolated box with a radius of many lightyears. We could still measure the spin the z-component of an electron that is initially polarized in the x-direction. Then, while strictly speaking the CI definition of observation is not exactly valid here, if one wants to object on that ground here, one disqualifies CI as being relevant to real observations.

To an external observer outside this box of lightyears across, the quantum state of the box after the measurement is of the form

1/sqrt(2) [|box_1>|+> + |box_2> |->]

where |+> and |-> are spin up and spin down in the z-direction, respectively. This state is, in principle, not the same as the mixed state: 1/2 [|+><+| + |-><-|] for the external observer. To see the difference, it may well be the case that the external oberver needs to resort to extremely complicated coherent masurements involving every atom in the box.

But the laws of physics do not forbid such measurements. And the results of such measurements would be effectively classically accessible just like measurements done by the people in the box are.

Now, if we think about this, we see that the number of degrees of reedom accessible to the external observer for his measurements must be (much) larger than the degrees of freedom inside the box (otherwise one could not perform a coherent measurement of every degree of freedom that exists in the box).

So, one can say that the external observer and his measurement apparatus is even more classical. If we let the system tend to the classical limit by letting the box become larger and larger, we can let the external system to become larger and larger as well, in such a way that the inherent quantum nature of the physics inside the box is always visible to the external observer.

 

[jambaugh]

I think that "classically observable" can only be an approximate concept.

Yes but to a degree which is controllable to whatever level one chooses. We can paint the results of a two outcome experiment in mile high letters on the moon and you can still quibble about the googlth power of infinitesimal chance that those letters reconfigure spontaneously to represent the opposite outcome.

Ultimately everything is reversible, in the sense that the time evolution of two different initial states of a isolated system cannot evolve to the same final state.
If this were not true, then one could get rid of information in a truly irreversible way, leading to problems (e.g. you would have found a way around Landauer's argument of why Maxwell's demon cannot work).

Your argument is not self consistent. The point of Maxwell's demon is to show a way to reverse a process which by virtue of its being irreversible must exclude said demon. You then say all processes are reversible by virtue of an argument which relies on the exclusion of said demon and thus the relies on the irreversibility of some processes.

In summary you're saying "All processes are reversible because some processes are irreversible."

I also don't agree with your definition of "reversible". Remember you can have processes which are reversible in principle, i.e. one can set up in a lab with sufficient time and trials a time reversed version of the process. And thus one can set up an instance of that class of process in such a way that it reverses. But this doesn't mean that a given instance of a process is reversible.
(Well then only for certain classes of processes e.g. deterministic ones.)
(And again unitarity of the evolution of the wave function is not the same as unitarity of the evolution of the physical system. Don't keep confusing the wave function with the system for which it gives a probabilistic description.)

But if one accepts that informaton cannot be destroyed,

Which fact I do agree with but this is not the same as thermodynamic reversibility. Whether the information exists out there somewhere is not the same as that information being accessible. One can cast the information to the winds so to speak by coupling the system variable to a black body radiating into space. That information hasn't been destroyed but one cannot chase it down as it expands at the edge of one's future light-cone.

then the notion of the classical observation (in the sense of records being kept that can be read in a classical way), requires an infinite universe in which you can copy information without limit.

Don't confuse the ability to make a third and fourth copy with the requirement that there exist an infinite number of copies.

Strictly speaking, an observer in a finite universe, or hypothetically in a finite isolated box, does not exactly satisfy the CI criteria that an observer should satisfy, or at least the observations made by the observer should satisfy. We, as real observers in this universe, may be very far removed from the regime where we could perform David Deutsch's thought experiment, but we are not precisely at the classical limit either.

Anyway, to come back to your first point about an experiment where CI fails, one can argue that it wouldn't matter for us if we would live in a closed and perfectly isolated box with a radius of many lightyears. We could still measure the spin the z-component of an electron that is initially polarized in the x-direction. Then, while strictly speaking the CI definition of observation is not exactly valid here, if one wants to object on that ground here, one disqualifies CI as being relevant to real observations.

To an external observer outside this box of lightyears across, the quantum state of the box after the measurement is of the form

1/sqrt(2) [|box_1>|+> + |box_2> |->]

Let me stop you right here although the remaining arguments are well thought out and quite sensible. You see from the beginning this is counterfactual. The assumption "we live inside the box" or simply that some form of measuring device is inside the box precludes it being described in a sharp mode via a single vector in Hilbert space. The box must have a non-zero entropy given both life and measuring devices are themodynamic systems. It is not sufficent for the thought experiment for you to speak of a spatial box but rather a spatial box plus its past and future history.

Again you are confusing the mode vector for a state of the box. You can't just take a system assert that it has a state and write down an arbitrary hilbert-space vector. This is the most grating of errors in people who speak of "the wave function of the universe". The operational meaning of a mode vector e.g. { PSI= |box_1>|+> + |box_2>|-> } is a source or mode of preparation for said boxes+spin-1/2 particles. If you cannot at least in principle create such a system of mode preparations (which is in principle calibratable and thus repeatible) then you can't properly say the mode vector has any meaning.

In order to describe the box in a sharp ("coherent" as you use the word) mode you must remove any entanglement of the box with its environment prior to the act of measurement. You must in essence refrigerate the box down to zero entropy. Using the idea of conservation of information you can view entropy as entanglement with the external environment. This act of refrigeration is not compatible with the assumption that a measuring device within the box recorded a measurement in even a gross approximation to the CI definition.

Again: measurement is a thermodynamic process.

If you want to dissect the measurement process that is a noble task but please begin with density operators and an accounting of the entropy changes as the measurement is made.

 

[Dmitry67]

Again: measurement is a thermodynamic process.

Wait, wait. AFAIK, in 'classical' CI measurement is not a physical process at all, but a change of an observer's knowledge about an object. Like wavefunction itself, measurement and collapse in CI is subjective, not objective

Are you talking about a different flavor of CI - some modern CI merged with Quantum Decoherence, which is in fact a thermodynamic process?

 

[Hurkyl]

You better quote the word choice in context so I can address it directly.

"The information must be classically observable"
"This dictates a classical description of the record of this measurement."

You just go on thinking that and see were it takes you.

It takes me pretty far, thank you. After all, it is the idea behind one of the most basic techniques in mathematics. (and it's pretty darned important in science too)

I'll be happy to sell you all the information about a Ferrari for one tenth the sticker price of a Ferrari and you just see how far you get down the highway.

Now you're just being silly. Would you reject the idea of using coordinate systems because you can get nonsensical results if you mix measurements done in one coordinate system with measurements done in another coordinate system? Then why would you do exactly the same thing here?

If we take your example and switch pictures, then my answer would be

No thank you -- after all, the object corresponding to "all information about all information about a Ferrari" doesn't drive nearly as well as the object corresponding to "all information about a Ferrari"



Edit, I missed this:

Again: measurement is a thermodynamic process.

Then you're not talking about any flavor of CI that I'm familiar with. What you describe looks more like a decoherence-based hidden variable interpretation rather than a collapse-based interpretation.

 

[alxm]

But you and Weinberg are both making a mistake in assuming ontological status to both the collapse of the wave function and to entanglement within the Copenhagen interpretation (CI).

Yes, I do. But I don't see why anyone would consider that a mistake. If you say 'it's just a model', then it raises the question of how you know that, then. In which case the 'model' can be improved. Also, it's been an extremely fruitful approach in general for Science. It turns out that Nature is logically consistent.

It is a subtle mistake but is there in the distinction being made between a classical and quantum mechanical description of the measuring device. [...]
Yes the measuring device and observer are fundamentally more accurately described quantum mechanically but there is no physical barrier between quantum and classical description across which information must traverse.

I don't know what you're getting at by 'physical barrier'. I didn't imply there was a physical barrier. There's no 'physical barrier' between classical and quantum mechanics either, as far as I'm concerned. But that doesn't mean the two theories are the the same or equivalent.

Where he says "this is surely wrong..." he makes the mistake of identifying the laws governing the behavior of the physical system with the choice of the description of the system. The classical description of the Moon is not "wrong" because it fundamentally obeys quantum mechanical rules. It is rather less than maximal.

That's not an appropriate analogy though. The CI is not 'surely wrong' in the sense that it's an known approximation, it's 'surely wrong' in the same way that the Bohr model of the atom was 'surely wrong', and for essentially the same reason: it's semi-classical. You are describing a system quantum-mechanically but describing the measurements classically. It works - nobody's disputing that the Copenhagen picture works - but we know for a fact that this cannot be the case, because this separation into 'measuring' and 'measured' hasn't been justified in physical theory. What is this 'collapse' of the wave function, or alternately, what is this 'decoherence'? We don't have an answer yet, but Weinberg alludes to progress being made on that.

But until this is explained, then we surely don't have the full picture.

However the critical issues is that we desire to speak in absolute terms about a specific outcome of a measurement. This dictates a classical description of the record of this measurement. There must be a classical/quantum cut between the piece of paper on which one writes down the result and the actual system for which this measurement is recorded.

This is not at issue. The question is how you physically justify doing so.

Where you and He state that the act of measurement is treated classically in CI "which is obviously false" the statement itself is false. It is the record of the measurement which is treated classically. (Or at worst the gross variables of the position and velocity of the measuring device where applicable). The act (those variables of the measuring device which interact with the system) is left without detailed description except that it must obey the rules predicted by QM, i.e. one must be able to re-measure the system immediately and obtain the same result for the act to be called a "measurement".

I know this, and Weinberg most certainly knows this. But that is also why he said it's 'wrong'. Again, not 'wrong' in the sense of 'giving the wrong results' but 'wrong' in the sense of not being a complete description of what's going on. 'Wrong' in the sense of not being physically justified even though it gives the right results. (Which is how the Bohr model was 'wrong', although it did in fact deviate from the correct results a bit)

It seems Count Ibis has more or less responded the way I did to your remaining bits.

In summary: it seems you hold that CI is not reality. (doesn't hold 'ontological status' in your words)
But we all do agree that it does work. If it's a picture of 'reality', then it's 'wrong' for physical reason. If it's not - then you don't get to say it's 'wrong' but the question of how it works remains open. Now we can sit here all day and shove the issue under different carpets, 'collapse', 'decoherence', 'dissipative processes'. But the bottom line is that the quantum-to-macroscopic transition isn't fully understood yet.

Which also kind of illustrates the fruitfulness of assuming that you actually are dealing with reality.

 

[Hurkyl]

If you say 'it's just a model', then it raises the question of how you know that, then.

Well, of course, it's always "just a model", whether it's Newtonian mechanics, special relativity, general relativity, quantum mechanics, or even a true GUT that gets everything exactly right.

The big question mark appears when we treat one of these "models" differently than the others; we use the elements of Newtonian mechanics to build up a reasonable, but not completely accurate, picture of "reality". We use the elements of special relativity to build up a reasonable, but not completely accurate, picture of "reality". We use the elements of quantum mechanics to compute numbers but avoid using them to build up a picture of "reality". Wait a minute -- why is that last one different than all of the others?

 

[jambaugh]

"The information must be classically observable"
"This dictates a classical description of the record of this measurement."

OK, that clarifies. The classical domain is well defined in the topic of quantum theory. Referring to it is not "deriving from classical mechanics". Indeed making the classical vs. quantum distinction is just the opposite. Classical mechanics sees no distinction. We must treat e.g. the ink and paper we use to report experimental research classically. Nothing is gained by using "quantum ink and quantum paper". Just the opposite. Now if you want to coin a new concept q-measurement or pre-measurement wherein the observable in question is correlated via entanglement with an auxiliary system then fine go right ahead. But ultimately if you wish to test a prediction of a transition probability you have to record in the classical sense measurements made in the CI sense.

Can you agree that it is reasonable and meaningful to speak of encoding an outcome of a quantum experiment on a physical system where the record variable by virtue of the controlled stability and macroscopic scale the record variable may be treated as a classical variable?

If you then so agree can you not appreciate that this is what measurement means in the context of CI?

Yes it agrees with the classical notion at this point as must be the case for the correspondence principle to apply.

It takes me pretty far, thank you. After all, it is the idea behind one of the most basic techniques in mathematics. (and it's pretty darned important in science too)

And that too is part of the problem. This is physics not mathematics. Indeed this was a very tough point for me to get right coming from an MS in math into a physics program. But I had a very good teacher and good fellow grad students with which to debate and discuss.

Beware of thinking too much in the mathematical context. Mathematical objects are ultimately classical in nature. They have objective properties to which may be assigned objective values. You however do understand the concept of say projective geometry and how within that context you can have distinct models with additional facts. You can appreciate therefore that the sphere and plane both model projective geometry. Thus you can understand how a model is distinct from what it models and there may be multiple models, each distinct and non-isomorphic which model a single class.

Now imagine if you will the reverse. A class of systems, these being systems of phenomena for which any objective model is invalid. Instead of more than one possible model we have less than one possible model. We cannot model the systems themselves but rather we must abstract one level and model the information about the systems.

Now you're just being silly.

No more so than Schrodigner was being in his famous cat experiment. I use a grandiose example to make the point but the example is valid. Indeed it is other's reinvention of Schrodinger's cat in their attempts to invalidate CI. Schrodinger was using the cat to show the absurdity of thinking that superposition was a property of the physical system rather than of the system's description as CI asserts.

Would you reject the idea of using coordinate systems because you can get nonsensical results if you mix measurements done in one coordinate system with measurements done in another coordinate system? Then why would you do exactly the same thing here?

I don't see your analogy. The way I see it others are trying to claim that using one coordinate system is "self contradictory" because they get different answers using a different coordinate system.

But more to the point I am not (in this discussion) rejecting anything except the fallacious arguments that "CI is self contradictory". I am pointing out that the arguments are misrepresenting CI to begin with and in fact implicitly negating it within their a priori assumptions.

Here's a simpler example: Consider the probability distribution for drawing either a red, green, or blue ball from a number of balls in a bag. It is nonsensical to speak of the pdf itself as having a color. It is likewise nonsensical to ask what is the standard deviation of the third red ball in the bag.

One may likewise describe how the probability distribution evolves as the balls roll through some machine. In fact imagine such a machine where the colors are read by a computer and the balls are sorted but then the computer ejects the balls with the same color sequence by which they enter. One would then see that the probability distribution for which color is in which position "evolves deterministically" through the machine. However imagine further that upon closer inspection, when we actually number them the balls of a given color are randomly permuted by the machine.

Now this example is not meant to model any kind of quantum process, only to show the distinction between the deterministic evolution of a probability distribution vs. the non-deterministic evolution of the system it describes.

I am using this one single point to show that within CI-QM the wave function is not modeling the system state but rather modeling the probabilities of outcomes of system measurements... and thus its deterministic evolution (which equates to conservation of information) is not the same as deterministic evolution of the state of the system it describes. Indeed CI is explicitly agnostic as to the system itself except for those observables measured during an act of measurement.

 

[jambaugh]

Yes, I do. But I don't see why anyone would consider that a mistake.

It is a mistake to take this interpretation which is not the interpretation CI takes while you are trying to show that CI is not self consistent. If you want to argue for an alternative to CI, fine we can argue that separately. But the gist of the arguments I've been replying to these past few posts is that CI is self inconsistent because it is not consistent with the thought experiment which the arguer is interpreting with an alternative to CI.

It is like arguing that Euclidean geometry is inconsistent by showing it doesn't hold on the sphere. Of course it doesn't hold if you are a priori adopting a non-euclidean example. It doesn't show Euclidean geometry is inconsistent it shows Euclidean geometry is not Non-Euclidean geometry which we already know.

If you say 'it's just a model', then it raises the question of how you know that, then. In which case the 'model' can be improved. Also, it's been an extremely fruitful approach in general for Science. It turns out that Nature is logically consistent.

Granted. But the distinction between a model and the theory is easy to parse. The theory is what it empirically predicts. The model asserts facts about that which cannot be observed. To excise model components from a theory you excise all references to unobservable entities or acknowledge them as purely mathematical constructs. Example: Prior to Einstein's SR the results of the Michelson-Morley experiment had been explained via Lorentz contraction of measuring rods and slowing of clocks. The frame transformations were already there in the model of the aether's effect on clocks and measuring rods. Einstein removed these components developing the theory apart from this frame specific model.

I don't know what you're getting at by 'physical barrier'. I didn't imply there was a physical barrier. There's no 'physical barrier' between classical and quantum mechanics either, as far as I'm concerned. But that doesn't mean the two theories are the the same or equivalent.

There is such an implication in the criticism that insisting on a classical description of the record of the measured quantity is less accurate than a quantum description. It is the implication that information is physically altered as we make this transition from quantum system to classically described record. If you acknowledge that no such barrier exists then you must revisit your point as it has no basis.

Perhaps you are confusing the classical description of the record with a classical description of the measurement process. CI doesn't assert any description of the measurement process beyond the rules QM imposes. No interpretation should! This is done within the theory or extensions of the theory. We need only know what is and what is not a proper measurement of a system.

The easiest way to do this is to show that what we consider a measurement actually is able to read a sent signal using the system to be measured. The signal itself is a classical bit, or trit or n-valued variable. The behavior of system into which it is encoded may be classically or quantum mechanically described depending on whether one is doing classical or quantum theory. But the act of measurement yields a classical variable, 1 vs 2 vs 3 vs 42... That is all that CI is saying! This is the essence of the measuring devices being "essentially classical". When we compare distinct physical devices which effect the same or isomorphic measurements we need only pay attention to the classically described variables of the devices, e.g. their classical position, velocity, or angular orientation.

You cannot say you've prepared a polarized photon with polarization angle 30deg if you can't classically observe a 30deg orientation of the polarizer used to prepare this photon.
It is unnecessary, for the purposes of describing the photon to delve into the quantum mechanical processes by which the polarizer interacts with the photon. It is sufficient to show that two (classically) parallel polarizers do not attenuate photons more than one and that two (classically) perpendicular polarizers do block all photons.

Well actually you need one other calibration, showing that in the classical limit the "vertical" polarizer actually does pass vertically polarized beams said vertical polarization being directly measurable via their action on a charged particle. This so polarization convention (direction of the E-field) matches the classical theory.

But there must always be a classical-quantum boundary somewhere in order to physically write down results of experiments on classical pieces of paper were our classical eyes can classically read the classical numbers. No interpretation can remove this cut without removing the empirical foundation of physics! How can someone independently replicate your experiment if you can't send them a copy of your results?

So given the necessity of this boundary (which again is one of convention and not sudden change in physical laws but which represents a physical transition from microscopic to macroscopic signal) it is sufficient to describe the measurement process within CI-QM by looking at a quantum description of the larger and larger systems interacting with the elementary system and through which the signal which becomes the measured quantity is transmitted.

But I have asserted repeatedly you cannot do so without working in the larger context of (quantum) thermodynamic systems.

That's not an appropriate analogy though. The CI is not 'surely wrong' in the sense that it's an known approximation, it's 'surely wrong' in the same way that the Bohr model of the atom was 'surely wrong', and for essentially the same reason: it's semi-classical. You are describing a system quantum-mechanically but describing the measurements classically.

Here again you are confusing the classical description of the measured value and/or of the measuring device with a classical description of the measurement process. How can CI be "surely wrong" in the same way as the Bohr model if CI doesn't give wrong answers where the Bohr model does?

Consider your example though in terms of using a Bohr model of an atom which is registering the value of the measurement of a separate quantum system. The only answer which is important to the measurement is whether the atom is excited or in the ground state. The Bohr model is sufficient for this purpose because we don't care about the answers to questions about exact energy values of the atom, just as we don't care if a particle detector has red vs. blue paint, only whether it detects the particle in question with sufficient fidelity. For the purposes of interpreting the measurement of the separate system we in fact must be classical with the description of the atom.

If on the other hand you want to delve into the quantum mechanics of this particular measurement process you'll have to describe how the description of the quantum evolves into one with an equivalent classical description. (equivalence here being equivalence with regard to the variable used to register the measurement being made.) This is the topic of decoherence.

It works - nobody's disputing that the Copenhagen picture works - ...

How can it "work" if it is not self consistent? All I've tried to do in these posts is clarify the mistakes made in arguments that CI is not self consistent, said arguments which are based on misrepresentations or a priori rejections of CI.

...but we know for a fact that this cannot be the case, because this separation into 'measuring' and 'measured' hasn't been justified in physical theory. What is this 'collapse' of the wave function, or alternately, what is this 'decoherence'? We don't have an answer yet, but Weinberg alludes to progress being made on that.

But again this need for a physical explanation of 'collapse' is exactly the assumption that collapse is a physical process, is the assumption that the wave-function is a physical object instead of a mathematical description of the actual physical entity. It is again a gross misunderstanding of CI to assume CI needs fixing because it doesn't agree with a non-CI interpretation of the wave-function.

But until this is explained, then we surely don't have the full picture.

Surely if you are assuming a non-CI interpretation.

This is not at issue. The question is how you physically justify doing so.

This is precisely the issue.

We come out of the study of classical mechanics prior to studying QM with the habit of looking for the "full picture" a.k.a. the ontological interpretation of the predictions of the theory. We hit QM and we look for the same but this is exactly the wrong habit if you adopt CI. CI asserts we should be agnostic about ontological reality (pardon the redundancy). Science dictates that the source of all knowledge is empirical observation. The foundation of any theory is thus the observables. QM is built upon these and CI makes this explicit. Rejecting CI because you still want "the full picture" is your choice. But you can't assert that CI-QM predicts anything less than non-CI-QM. I don't believe you have so asserted. But critiques of CI base on it not being self consistent are necessarily wrong because CI is the minimal interpretation incorporating the physical predictions of QM. It is impossible for CI to be self-inconsistent without QM itself being wrong.

This leaves the possibility of both CI and QM being incomplete as a theory which is to say there is a better theory, possibly growing out of a non-CI which extends QM making more predictions. Fine show me the empirical predictions which can be tested in a laboratory. But criticizing CI = the ontological agnosticism, for failing to be ontologically complete is like criticizing religious agnosticism for failing to believe in some version of God. One can agree to disagree but one is wrong to criticize the agnosticism on that basis.

In short CI is actually the "interpretationless interpretation", i.e. the rejection of ontological interpretations of what already has an epistemological interpretation *** namely Born's probability interpretation along with the identification of observables with acts of observation and Hilbert space vectors (and more generally density operators) with modes of system preparation.

I know this, and Weinberg most certainly knows this. But that is also why he said it's 'wrong'. Again, not 'wrong' in the sense of 'giving the wrong results' but 'wrong' in the sense of not being a complete description of what's going on. 'Wrong' in the sense of not being physically justified even though it gives the right results. (Which is how the Bohr model was 'wrong', although it did in fact deviate from the correct results a bit)

I'll add that "giving the right results" is the only justification physics requires. You (and Weinberg) are looking for a different kind of "justification", philosophical? aesthetic? ?

Now we can sit here all day and shove the issue under different carpets, 'collapse', 'decoherence', 'dissipative processes'. But the bottom line is that the quantum-to-macroscopic transition isn't fully understood yet.

Now here we can agree. This is a fruitful area of study. But we can study this within QM. Interpretations beyond the one true interpretation *** is irrelevant. I however have read through too many papers which get bogged down in side issues of interpretation and do not begin to address the physics of the measurement process.

Which also kind of illustrates the fruitfulness of assuming that you actually are dealing with reality.

Ahhh! this sentence most aptly encapsulates the meaning of the CI. It is fruitless within QM to assume you are dealing with reality...except at the points of measurement. "Reality" is an inherently classical concept. Attempts to (re)interpret QM in terms of an underlying reality are attempts to embed QM within a larger classical model. This requires a vast extension of the classical realm either via non-local interactions of unobservable pilot waves or postulating many unobservable alternative worlds.

All of these ontological models invoke unobservable entities on par with the Lorentzian aether which are better excised from the theory since they are immaterial to the prediction of observable phenomena.

[Here I am now arguing for CI vs other interpretations whereas before I was simply critiquing misunderstandings as to what CI asserts.]

 

[Count Iblis]

I still don't understand how one can make this "classical description of a record" rigorous. The record itself is, in general, some macrostate of a system. If you have a magnetic tape then a recorded bit is the average magnetization at a certain spot. But at the microscopic level you still have spins that, of course, are entangled with the rest of the universe.

When we compare distinct physical devices which effect the same or isomorphic measurements we need only pay attention to the classically described variables of the devices, e.g. their classical position, velocity, or angular orientation.

But even these classical observables are subject to commutation relations. What happens is that so-called "classical" positions, momenta etc. are specified with large errors ( large when expressd in natural quantum units so they are coarse grained variables). It then looks like these variables are classical variables, while in fact they are not.

 

[Dmitry67]

Also, I ask my unanswered question: what is measurement device in CI?
How small can it be? I am not asking something impossible, the expected answer is integer (number of atoms).
Or a failure to formally define what is a measurement device is.

 

[Hurkyl]

Can you agree that it is reasonable and meaningful to speak of encoding an outcome of a quantum experiment on a physical system where the record variable by virtue of the controlled stability and macroscopic scale the record variable may be treated as a classical variable?

"Treated as" is a key word here. Classical mechanics did a pretty good job of describing reality. In the domain where classical mechanics works, quantum mechanics has to approximately replicate the predictions of quantum mechanics.

If you then so agree can you not appreciate that this is what measurement means in the context of CI?

No, I cannot agree. CI goes above and beyond simply acknowledging that quantum mechanics has to yield approximately classical results when classical mechanics works. CI insists that the wavefunction, whatever it is, undergoes a collapse, and the system described by the wavefunction is left in a definite state corresponding to the collapsed wavefunction.

This contrasts with decoherence-based interpretations of quantum mechanics, which posits that Schrödinger's equation remainds valid through a measurement -- the (relative) wavefunction merely evolves into a mixed state. For example:

. MWI takes the wavefunction as a complete description of the system, and thus asserts that the system remains in an indeterminate state. However, each component of the mixture is exhibits the desired "controlled stability".

. The Bohm interpretation hypothesizes additional variables. It accepts the wavefunction as being correct, and so retains its evolution into a mixture of "stable" components, but it includes particles which I believe (I don't understand BI well) tend to organize themselves in some way corresponding to that.


CI rejects both of these possibilities (and more) -- it fixes upon specific properties of classical measurement, such as definite outcomes¹, and rather than allowing for it to be an approximately correct emergent property of the underlying mechanics, CI insists that it is the literal truth of the matter, and even makes some insistence on how it's the literal truth.


1: The ironic thing is that definite outcomes isn't required classically. It's just that in the classical case, the math behind mixed states is exactly identicial to the math behind ignorance probabilities, and for whatever reason, people preferred to think in terms of the latter rather than the former.

 

[Hurkyl]

Mathematical objects are ultimately classical in nature. They have objective properties to which may be assigned objective values.

I can't figure out how that even makes sense, let alone decide whether I agree or disagree with it.

A class of systems, these being systems of phenomena for which any objective model is invalid.

Formal logic has a word for such a thing: contradictary.

A collection of formal statements is consistent if and only if there is a mathematical model of those statements. If there isn't a model, then there is a contradiction.

 

[ThomasT]

Does everyone agree that the following is a good discussion
of the Copenhagen Interpretation?

http://plato.stanford.edu/entries/qm-copenhagen/

 

[meopemuk]

Firstly the hermitian operator represents the action of the measuring device on the system not the description of the actual measuring device itself. Note the hermitian operator is unchanged by the measuring process while the measuring device necessarily changes as it registers the measured quantity.

Suppose you are an experimentalist performing the double-slit experiment. You have a scintillating screen and you record positions of electrons by observing flashes on the screen. You know that each flash is a complicated process in which properties of both observed electrons and molecules of the screen change dramatically. But do you really care about that? Will you devote a section of your paper to the description of the molecular content of the screen and which reactions take place there? I guess not. It makes perfect sense to assume that your screen is an idealized position-measuring device, and it makes perfect sense to describe this device theoretically simply as an Hermitian operator in the 1-electron Hilbert space. All the details of the electron-screen interaction are irrelevant for the theoretical description of this experiment. If you are extra careful, you can say that molecular sizes introduce some uncertainty in position measurements, and you can take this uncertainty into account by assigning some error bars to your data points. That's what experimentalists normally do.

My claim is that in each realistic experiment (just as in the simple example described above) there is always a well-defined boundary between the physical system (which we want to describe dynamically as accurately as possible; the electron in my example) and the measuring apparatus (which can be described as an idealized device by using an Hermitian operator; the screen in my example). Each experimental setup has this (imaginary) boundary. If you don't accept the existence of such a boundary then your theoretical description of the double-slit experiment must involve electron-screen reactions, the resulting emission of photons, image formation in your eye, signal processing in your brain, etc. which is kind of ridiculous.

 

[Dmitry67]

My claim is that in each realistic experiment (just as in the simple example described above) there is always a well-defined boundary between the physical system (which you want to describe dynamically as accurately as possible; the electron in my example) and the measuring apparatus (which can be describe as an idealized device by using an Hermitian operator; the screen in my example).

Quantum computing makes this boundry fuzzy: you can store a state (or superposition of states) in a molecule and 'read' it later. On the other hand, you can put BILLIONS of electrons in a mixture of different states.

Also, I was always wondering what is a status of Quantum Decoherence in CI? Is it accepted, rejected or simply ignored?

 

[meopemuk]

Quantum computing makes this boundry fuzzy: you can store a state (or superposition of states) in a molecule and 'read' it later. On the other hand, you can put BILLIONS of electrons in a mixture of different states.

Yes, instead of the scintillating screen in my example we can use a photographic plate, and develop the image later, thus "storing the information". It doesn't make any difference. Still, for the purposes of description of the double-slit experiment the plate should be represented by the Hermitian operator of position in the Hilbert space, not as a dynamical system.

 

[Dmitry67]

Yes, instead of the scintillating screen in my example we can use a photographic plate, and develop the image later, thus "storing the information". It doesn't make any difference.

yes, it does: it can not put a photographic plate in a superposition of states, while you CAN do it with a qbit

 

[jambaugh]

Also, I was always wondering what is a status of Quantum Decoherence in CI? Is it accepted, rejected or simply ignored?

Decoherence is a qualitative description of a quantum mechanical process, just as is say entanglement. CI as with the other interpretations is just that, an interpretation and neither "accepts" nor "rejects" the process but rather again interprets it.

Understanding CI as interpreting the wave-function and density operator as descriptions of our knowledge about the physical system one then understands that within CI decoherence describes a particular class of evolutions of our knowledge about the system.

 

[jambaugh]

I can't figure out how that even makes sense, let alone decide whether I agree or disagree with it.


Formal logic has a word for such a thing: contradictary.

A collection of formal statements is consistent if and only if there is a mathematical model of those statements. If there isn't a model, then there is a contradiction.

Exactly! But my analogy was to distinguish model from that which is being modeled. In this case we are now speaking of an ontological model for observed quantum phenomena. I assert that no such model exists which is equivalent to saying no "collection of formal statements" about the system is possible, i.e. no state of reality.

In classical physics what we think of as "reality" is actually a model existing in our minds. What is being modeled is the actuality of phenomena. At the classical model it is possible to find a unique (up to gauge) "reality model". At the quantum level it is impossible (even with the non-CI interpretations.)

Hence the "no deep reality" and "the wave function describes (models) our knowledge about the system" of CI.

Our insistence on an underlying reality = system state = complete set of formal statements about the system itself leads to Bell's inequality. Quantum nature continues to ignore our insistence and violates BI at every turn.

 

[jambaugh]

Does everyone agree that the following is a good discussion
of the Copenhagen Interpretation?

http://plato.stanford.edu/entries/qm-copenhagen/

Yes, Quite.

 

[jambaugh]

...
No, I cannot agree. CI goes above and beyond simply acknowledging that quantum mechanics has to yield approximately classical results when classical mechanics works. CI insists that the wavefunction, whatever it is, undergoes a collapse,

yes...

and the system described by the wavefunction is left in a definite state corresponding to the collapsed wavefunction.

Arrrrrg! Again that word "state" CI says nothing about the system's state beyond what outcomes are actually measured. But yes the collapsing wave function expresses the new knowledge due to the physical change the act of measurement necessarily effects on the system.

This contrasts with decoherence-based interpretations of quantum mechanics, which posits that Schrödinger's equation remainds valid through a measurement -- the (relative) wavefunction merely evolves into a mixed state.

Keeping the CI of the wave function as modeling our knowledge about the system and this fine, one is simply examining the measurement process in more detail. It is not a re-interpretation. But you still have a classical collapse of probabilities into actualities when you select which value of the observable was made. Again the collapse is no different in quality than the collapse of the expected winnings of a lottery ticket once you know what number actually was drawn.

For example:
. MWI takes the wavefunction as a complete description of the system, and thus asserts that the system remains in an indeterminate state. However, each component of the mixture is exhibits the desired "controlled stability".

. The Bohm interpretation hypothesizes additional variables. It accepts the wavefunction as being correct, and so retains its evolution into a mixture of "stable" components, but it includes particles which I believe (I don't understand BI well) tend to organize themselves in some way corresponding to that.

CI rejects both of these possibilities (and more) -- it fixes upon specific properties of classical measurement, such as definite outcomes¹, and rather than allowing for it to be an approximately correct emergent property of the underlying mechanics, CI insists that it is the literal truth of the matter, and even makes some insistence on how it's the literal truth.

You mis-characterize. You still update the wave-function/density operator/system description in MWI and Bohm's Pilot-Wave Interp, once you assert that a given outcome to the measurement has been made!. It is simply Bayesian conditional probabilities. The probability distribution for future outcomes given a particular measurement had a particular value is "suddenly" different from the probability distribution prior to incorporating this information. No mystery. You can examine the process by which "quantum probabilities" become "classical probabilities" but there is in fact no distinction in the probabilities, they are relative frequencies for hypothetical outcomes and obey Bayesian inference rules. The only distinction is that in CM we can model the probability distribution with pdf over a state manifold whereas in QM given the absence of a state manifold we must revert to an amplitude distribution over a complete set of commuting observables along with the Born probability formula.

[EDIT: Let me add that it is only in the MWI or Bohmian interpretations, where the wave function is given ontological status that there is an issue with wave-function collapse because they are asserting some physical collapse must be occurring. In MWI the whole friggin' universe has to split and Bohm's pilot waves must execute some fancy fast stepping (>C or back in time) to update. In CI we simply are updating our records given new information.

Like the IRS registering a change of address. Confusing the company records with the person's actual location leads one to think they moved in the blink of an eye because the computer record changed in the blink of an eye.

1: The ironic thing is that definite outcomes isn't required classically. It's just that in the classical case, the math behind mixed states is exactly identicial to the math behind ignorance probabilities, and for whatever reason, people preferred to think in terms of the latter rather than the former.

The math is identical because the meanings are identical. CI => "mixed states" = "mixed states of probability".

 

[jambaugh]

I can't figure out how that even makes sense, let alone decide whether I agree or disagree with it.

Mathematical objects are completely defined. E.g. a line through two points on the Euclidean plane. Some properties are associated with the line, e.g. dimension, some are not, e.g. color or mass. For every associated property there is a definitive value e.g. dimension=1.

If one is talking about a dynamically changing line one can speak of its objective state (complete set of properties and their values) as a function of a "time" parameter.

Physical systems when treated classically are likewise assumed to have objective properties with constantly defined values. This means we can map the physical system to a mathematical representation. This is an ontological model of the system. The canonical method for so doing is to represent any system as a point on a state manifold. (phase space). However this doesn't always work well and we introduce gauge degrees of freedom wherein the system is represented by gauge orbits (branes) in an extended phase space. One can always "fix the gauge" i.e. mod out the gauge orbits and again recover a point on state manifold description.

To give this operational meaning we must assume that there exists a complete set of observables, "complete" meaning that the values determine the state of the classical system.

So classically properties correspond to observables with value = value. In quantum mechanics we can have observables ("q-properties"?) which do not have well defined values at all times. The shift from ontological to epistemological description is complete. Note classical "completeness" can no longer be given meaning since we negate the classical assumption of an underlying state. We replace it with the epistemological equivalent of "maximal" i.e. no more information can be gleaned without invalidating on of the prior measurements.

To make the classical to quantum transition we translate the ontological aspects of classical systems to their epistemological equivalents state variables -> observables.
We pay attention to the dynamics of the epistemological variables instead of the ontological ones.
We then map to the epistemological quantum description preserving the dynamics of the observables. In fact we take the dynamics more seriously preserving the non-commutative structure of the observables guided by Noether's correspondence between observables and generators of system/frame transformations. By invalidating the classical completeness assertion we invalidate the use of ontological models and stick to the heart of the physics, the epistemological model = the dynamics of what we know about the system = the dynamics of the wave-function/density operator.

Remember science and thus physics is an epistemological discipline. There is no metaphysics in physics. Ontological models are useful --sometimes-- as scaffolds for constructing epistemologically meaningful theories. But although the scaffolding dictates the shape of the building it is not the building. The model is not the theory. Carrying the analogy further the use of a scaffolding limits the form our buildings can take. To go beyond we must rather abandon the scaffolding method and grow the building up from its epistemological foundation.

 

[Hurkyl]

Decoherence is a qualitative description of a quantum mechanical process, just as is say entanglement. CI as with the other interpretations is just that, an interpretation and neither "accepts" nor "rejects" the process but rather again interprets it.

This is by no means clear. The collapse postulate of CI solves a particular problem related to measurement. Decoherence appears to solve that exact same problem. This leads to a very fundamental dichotemy in interpretations of quantum mechanics: are the properties of measurement
(1) The result of decoherence that occurs in the process of unitary evolution?
(2) The result of some other process that isn't described by unitary evolution?
(With (2) commonly resulting in a wavefunction collapse)

If you retain the collapse postulate of CI, that means you are rejecting the hypothesis that measurement could be described (in principle) via unitary evoultion, and that the effects of measurement are the result of decoherence.

 

[Hurkyl]

At the classical model it is possible to find a unique (up to gauge) "reality model".

(Depending on what you actually mean) mathematics does not support that level of specificity -- for example, given any formal language and mathematical structure into which that language can be interpreted, one can find a different, nonisomorphic mathematical structure that is completely indistinguishable from the original using just the chosen language.

Our insistence on an underlying reality = system state = complete set of formal statements about the system itself leads to Bell's inequality. Quantum nature continues to ignore our insistence and violates BI at every turn.

You're making a crucial mistake -- you are saying "complete set of formal statements about the system itself" but you are thinking "a complete set of formal statements about the system itself that has the qualities of being local, realistic, and counterfactually definite" (and whatever other assumptions Bell used in his theorem).

In quantum mechanics we can have observables ("q-properties"?) which do not have well defined values at all times.

There is nothing wrong with "wavefunction == deep reality", as demonstrated, for example, by the many worlds interpretation.

 

[Hurkyl]

But you still have a classical collapse of probabilities into actualities when you select which value of the observable was made.

Which is an unwarranted assumption! It's sufficient for the "perceived actuality" to be conditional on "observed observable" without requiring that there is a definite value of the observable which was observed. (i.e. it's enough for the observed value to be conditioned upon which value was observed)

It is simply Bayesian conditional probabilities.

No it's not. Pre-measurement, CI will compute conditional probabilities. Post-measurement, CI insists that a definite outcome occured, and asserts that the probabilities are now absolute probabilities.

e.g. When using the CI, after measuring the electron, one might say something like "the electron is definitely spin up", rather than saying "given that we measured the electron to be spin up, it is definitely spin up". Doing so is definitely good for economy of speech, but CI means it literally, not as a shortcut.

 

[jambaugh]

I think a good paradigm example of a measurement is to consider the Stern-Gerlach measurement of an electron's spin.

1.) We prepare the electon in a crisply defined momentum mode roughly orthogonal to the direction we wish to measure spin. w.o.l.o.g. define that as the z-direction.

2.) We allow the electron to evolve in a non-uniform B field said non-uniformity in the direction of the component of spin to be measured. The S-G magnets couple the electron's spin component to its momentum resulting in entanglement between z-component of momentum and z-component of spin. The coupling must occur to sufficient degree that the z-component of spin differs for distinct spin values more than the Delta P_z in the initial preparation.

3.) We then measure the z-component of momentum to within a resolution sufficient to distinguish the effect of spin. This is where the actual measurement occurs.

( and typically this is done by also preparing the electrons in step 1 with a certain Delta z resolution of z- position and allowing the vacuum propagation of the electron after the S-G magnet to couple z-momentum to z-position and thence measuring position to within a resolution sufficient to resolve the momentum and thence the spin.)

Note that prior to some decoherence inducing registration of the electron's position/momentum we cannot really say the value of the spin has been measured and yes we can "undo" in principle the entanglement created and recombine the two electron paths (modulo some random momentum variables for those who worry about determinism).

I'm trying to think of the simplest (rough) non-destructive (to spin) position or momentum measurement device. Consider a loop of wire with straight segments running close and parallel to the two beam paths. I'll draw a quick diagram:

Not shown in the diagram but implicit is the heat sink cooling the amplifier and wire down so that thermal fluctuations are below the signal level. Note the amplifier must be producing heat because it must maintain a subsystem with effective "negative temperature" in order to amplify the signal to the point of classical observability.

We then will see either a positive or negative spike in the output voltage indicating whether the electron took one path or the other. I am pretty sure (but not absolutely certain) that the interaction between electron and wire will not further affect the electron's spin. There should only be a slight back reaction as the magnetic field of the induced current in the wire acts on the electron. We should actually place the wire behind the beam path in the diagram so that the B-field for current in the wire will be parallel to the z-component of spin and not precess it any.

To keep things as simple as possible we can let the wire itself be near zero temp and super-conducting so that we may further treat the electron field in the wire as a quantum system. Ultimately the classical-quantum cut occurs within the amplifier. But due to the very close interaction between wire and amp we can treat the wire as a quantum system coupled immediately to an entropy dump and let it be the source of measurement.

Can anyone think of a simpler (actualizible in principle) non-destructive (of the quantity to be measured) measurement process? I first considered a cloud/bubble chamber but wasn't sure we could reliably assume the spin didn't get scrambled in the process.

 

[jambaugh]

Which is an unwarranted assumption! It's sufficient for the "perceived actuality" to be conditional on "observed observable" without requiring that there is a definite value of the observable which was observed. (i.e. it's enough for the observed value to be conditioned upon which value was observed)



No it's not. Pre-measurement, CI will compute conditional probabilities. Post-measurement, CI insists that a definite outcome occured, and asserts that the probabilities are now absolute probabilities.

But CI doesn't assert which outcome will occur. It let's QM tell us the probabilities of the various outcomes. The distinct modified wave-functions and their subsequently calculated probabilities are still conditional probabilities, said probabilities conditions on the measured value. It is only when we stop considering the probabilistic array of possible outcomes an say something like "suppose it was outcome 3!" that we update the wave function, (or pick a universe, or assert that the pilot waves have done some communicating.)

In your head you are still thinking in terms of "definite wave-function = definite state of the system" rather than watching as the information gets updated in CI.

e.g. When using the CI, after measuring the electron, one might say something like "the electron is definitely spin up", rather than saying "given that we measured the electron to be spin up, it is definitely spin up". Doing so is definitely good for economy of speech, but CI means it literally, not as a shortcut.

Let's take that example. Before measurement,
1.) we agree that we are going to measure "spin up" vs "spin down" and set things up.
2.) we write down the wave function or density matrix for the electron coming from our source S.
[You imagine this expresses the state of the electron, and I that it is just our encoding of what we know about the electron.]

3.) we calculate the probabilities of each measurement and say determine them to be 50% vs 50%.

4.) We do the experiment but neither of us look at the result just yet, a computer prints it on a card which we set face down. While we are at it we decide to see who gets to turn over the card so we rattle a die in a cup which is also hidden. Even and I get to flip, odd and you get to flip.

Now at this point I say: "OK, now that we've made the measurement we can express the system in terms of a density operator projecting with weight 50% onto one 'collapsed wave-function', and projecting with weight 50% onto the other 'collapsed wave function'."

I add "Oh by the way we can represent the outcome of the die toss as a probability distribution 50% even vs 50% odd".

5.) We look at the die and I win so I say "I'll update our die pdf to register 100% even"
I then flip the card and we see that the electron's spin was measured as "up" and so I say: "OK now that we know what was measured we can update the density operator to a projection onto the up 'collapsed' wave-function."

Now we didn't have to first write down a density operator between measuring and looking at the card. The original wave function and the updated density operator both expressed the same information about what we could observe after the fact. The only distinction is that the two descriptions may differ in calculated predictions about other outcomes which are now impossible since we cannot "undo" the measurement once the result is printed on the card.

(I thought of including your part of the conversation but didn't want to put words in your mouth.)

I assert that applying CI the wave function collapse was no different from the die pdf collapse. Something we do when we actually incorporate new information into our description of what we know about the system.