Notes on qm interpretation

[Lapidus]

Does anyone know good notes or a book on quantum mechanics that covers well the interpretational issues? Especially, which deals also with the last fifty or sixty years, i.e. that has Bell, decoherence, GHZ, Aspect experiment, Mach-Zehnder interferometer, delayed-choice, mesocopic Schrödinger cats, Bohm wave mechanics, many-world interpretation, etc. in it.

And a text/ notes that perhaps covers these topics in a more or less down-to-earth pedagogical manner.

I already looked hard, but for strange reasons I could not come up with any findings.

thanks

 

[vanhees71]

I think Ballentines book is a good no-nonsense source for studying such questions:

L. Ballentine, Quantum Mechanics - A modern approach

Another one is

A. Peres, Quantum Theory: Concepts and Methods

 

[audioloop]

Does anyone know good notes or a book on quantum mechanics that covers well the interpretational issues? Especially, which deals also with the last fifty or sixty years, i.e. that has Bell, decoherence, GHZ, Aspect experiment, Mach-Zehnder interferometer, delayed-choice, mesocopic Schrödinger cats, Bohm wave mechanics, many-world interpretation, etc. in it.

And a text/ notes that perhaps covers these topics in a more or less down-to-earth pedagogical manner.

I already looked hard, but for strange reasons I could not come up with any findings.

thanks

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

references herein.

------

http://plato.stanford.edu/

 

[bhobba]

I think Ballentines book is a good no-nonsense source for studying such questions:

L. Ballentine, Quantum Mechanics - A modern approach

Another one is

A. Peres, Quantum Theory: Concepts and Methods

What was it Meatloaf said - you took the words right out of my mouth.

Ballentine also develops QM axiomatically from just two axioms. Interestingly the second is more or less implied by the first by Gleason's Theorem:
http://kof.physto.se/theses/helena-master.pdf

Strange, but true - it really involves just one axiom - the rest follows from rather innocuous observations such as Schrodingers equation etc comes from probabilities should be coordinate independent ie symmetry.

Intrigued - get the book - it had a BIG effect on me - its basically the finest book on QM I have ever read.

After that check out Decoherence and the Quantum-to-Classical Transition by Schlosshauer:
https://www.amazon.com/dp/3540357734/?tag=pfamazon01-20

It examines interpretations in light of the recent advances in decoherence which Ballentine doesn't explore.

Thanks
Bill

 

[Demystifier]

Does anyone know good notes or a book on quantum mechanics that covers well the interpretational issues? Especially, which deals also with the last fifty or sixty years, i.e. that has Bell, decoherence, GHZ, Aspect experiment, Mach-Zehnder interferometer, delayed-choice, mesocopic Schrödinger cats, Bohm wave mechanics, many-world interpretation, etc. in it.

And a text/ notes that perhaps covers these topics in a more or less down-to-earth pedagogical manner.

I already looked hard, but for strange reasons I could not come up with any findings.

thanks

My recommendations:
https://www.amazon.com/dp/0199589135/?tag=pfamazon01-20
https://www.amazon.com/dp/110702501X/?tag=pfamazon01-20

If you want something free, then:
http://lanl.arxiv.org/abs/quant-ph/0209123

 

[stevendaryl]

Just a warning: If people simply post links to articles about the interpretation of quantum mechanics, that's fine. But if you actually discuss the interpretation of quantum mechanics, the thread will be closed by the moderators. At least, that's my observation.

 

[Demystifier]

Just a warning: If people simply post links to articles about the interpretation of quantum mechanics, that's fine. But if you actually discuss the interpretation of quantum mechanics, the thread will be closed by the moderators. At least, that's my observation.

If you discuss some specific interpretation at a thread which is from the beginning opened to be a thread on that specific interpretation, it is usually not closed by the moderators.

 

[Lapidus]

Thanks everybody!

My recommendations:
https://www.amazon.com/dp/0199589135/?tag=pfamazon01-20
https://www.amazon.com/dp/110702501X/?tag=pfamazon01-20

If you want something free, then:
http://lanl.arxiv.org/abs/quant-ph/0209123

Funny (or not so), after two hours searching the internet, I also felt these two books look best. Unfortunately, the "New quantum age" book has no working kindle format, only "Kindle for PC". I thought about downloading the second book, but now I will look first at the pdf of the same author from the link you gave. Thanks!

 

[vanhees71]

Are "interpretation of QM" threads really closed that quickly here in the forum? I've not that impression. However, the problem is that often such discussions leave the realm of hard sciences (physics) and enter the more philosophical kind ("cargo cult science", as Feynman called it). Then, of course, it's good when the moderators close the thread ;-)).

 

[stevendaryl]

Are "interpretation of QM" threads really closed that quickly here in the forum? I've not that impression. However, the problem is that often such discussions leave the realm of hard sciences (physics) and enter the more philosophical kind ("cargo cult science", as Feynman called it). Then, of course, it's good when the moderators close the thread ;-)).

I don't know about soon, but they are all closed eventually--long before they die from lack of new posts.

 

[DrChinese]

If they are going around in circles (which happens almost immediately in many): expect them to be closed more quickly than previously. Ditto for the extended debates about Bell, closed loopholes, etc. that seem to recur all too often and degrade into statements of personal opinion.

 

[Maui]

At any rate, i am convinced that the Mentor does not play dice with these threads.

 

[DevilsAvocado]

Determinism usually is a good closure...

 

[Nugatory]

I don't know about soon, but they are all closed eventually--long before they die from lack of new posts.

Usually they're brain-dead from oxygen and new-insight starvation before they run out of new posts.

 

[DevilsAvocado]

 

[Dale]

If they are going around in circles (which happens almost immediately in many): expect them to be closed more quickly than previously. Ditto for the extended debates about Bell, closed loopholes, etc. that seem to recur all too often and degrade into statements of personal opinion.

This is the main reason that interpretation threads are closed. Once everyone has had a chance to advertise for their favorite interpretation the rest of the discussion rapidly devolves into a shouting match about why their favorite is wonderful and why the other person's favorite is stupid.

 

[bhobba]

Are "interpretation of QM" threads really closed that quickly here in the forum? I've not that impression. However, the problem is that often such discussions leave the realm of hard sciences (physics) and enter the more philosophical kind ("cargo cult science", as Feynman called it). Then, of course, it's good when the moderators close the thread ;-)).

That's my feeling as well.

They aren't closed until everyone has had a chance to put their view, and in the past some have degenerated into philosophy. Personally I think the mods do a really good job monitoring that.

The only other observation I will make is a personal one about decoherence - I seem to go over the same thing again and again. The positive is the issues are really clear in my mind from that practice and I know the references off pat.

Thanks
Bill

 

[DevilsAvocado]

Once everyone has had a chance to advertise for their favorite interpretation the rest of the discussion rapidly devolves into a shouting match about why their favorite is wonderful and why the other person's favorite is stupid.

Yup, I have a very close friend (won't drop names due to discretion ) who basically thinks it's all pretty silly, and that the whole business have more in common with "religious war" (experiments is a waste of time since we all get the same results), than fundamental science.

Maybe he's right, I dunno?

 

[bhobba]

Maybe he's right, I dunno?

He is right

But its interesting understanding and comparing them.

Thanks
Bill

 

[audioloop]

This is the main reason that interpretation threads are closed. Once everyone has had a chance to advertise for their favorite interpretation the rest of the discussion rapidly devolves into a shouting match about why their favorite is wonderful and why the other person's favorite is stupid.

100 % concur.
pompous proselytism, apodictical dogmatism.

i think, various interpretations have possible and real experimental testing, so we have to discourse in that possibilities.
or we have to diferentiate among stand alone models and interpretations.

clear and cut, scientific standing..

 

[vanhees71]

I'd make a clear distinction between "interpretation of quantum theory" and "alternative new theories". Quantum theory in its minimal interpretation (a theory without an interpretation, i.e., without making contact to real-world observations and experiments is not a physical theory at all) defines a clear mathematical scheme and how it is applied to describe the phenomenology they are applicable (sometimes in exact ab-initio solutions of the quantum-theoretical equations, often in terms of approximations like perturbation theory in QFT) to make predictions that can be experimentally tested. Personally, I'm sticking to the minimal interpretation, because it's minimal. In my opinion, a physical theory is complete as soon as I can describe all known reproducible observations with it (that's the status of QT today) or as soon as I have found an experimental fact contradicting it, which doesn't make it obsolete completely but it leads to certain constraints on the applicability range of the theory. That's the case for all of classical physics (Newtonian mechanics was found to be invalid at high velocities and then has to be substituted by (special and general) relativity, electromagnetism needs the extension to relativistic field-theoretical descriptions (first the classical kind a la Maxwell); all of classical physics needs to be substituted by quantum theory after all, etc.). It's pretty likely that also quantum theory one day may be found to be an approximate description of Nature by finding some empirical contradiction to it and it must be substituted by a more comprehensive theory. That's progress of science and thus should not be taken as a "failure" in any way.

Some people are, however, not satisfied by the minimal interpretation because of its probabilistic nature, and they try to find other interpretations of quantum theory. These other interpretations lead to the same predictions about the outcome of measurements and thus from a physics point of view it's still the same theory. There are, however, different categories of "interpretations".

The first category are different mathematical techniques applied to quantum theory. This already started in the very beginning of quantum theory in 1925, when nearly at the same time, Heisenberg, Born, and Jordan came up with what is called "matrix mechanics" and Schrödinger with "wave mechanics". Independently Dirac came up with another formulation which is the most general one and was called "transformation theory" at the time. From the modern point of view, I'd call it representation-independent formulation. The non-relativistic QT was then completely formalized and understood by von Neumann in terms of Hilbert-space theory, which more recently has been reformulated in terms of the socalle "rigged Hilbert-space" formalism, which makes the hand-waving maths we physicists use in our calculations a mathematically strict formulation. Another equivalent (but as far as I know less strict) formulation is then Feynman's path-integral formulation, using functional methods to express the same theory. All this is not "interpretation" in the more narrow sense, but just different mathematical language to formulate the same theory. Which mathematical formalism you use doesn't so much imply which interpretation you follow, although often the path-integral formalism is interpreted somehow in the sense as if it were a new interpretation, a view also Feynman seems to have hold for some time. I think, that's not the case. It's just another way to express one and the same theory, and I (as a follower of the minimal interpretation) can use any mathematical tool without changing my view on interpretation. Which one I use, depends on the problem I like to solve and which one I'm able to use for that problem, but it's totally unimportant concerning my view on the interpretation.

The second category is to add some elements, concerning the philosophical implications of the theory. E.g., in Bohmian mechanics, one adds a kind of "trajectory picture" back into the physics of single particles which has been abandoned before due to the uncertainty relation that states that a particle cannot be prepared in a state such that both position and momentum are both determined to arbitrary precision, which implies that it does not make sense to talk about trajectories of a particle in phase space as is the case in classical mechanics. The Bohmian trajectories are determined by non-local equations with the "wave function" of the particles as "pilot waves". On the other hand it's still an open debate, whether the Bohmian trajectories are observable or not and if so, whether Bohmian mechanics is experimentally disproven already. I think we can say that's pretty undecided today. The same holds for other interpretations as the various flavor of the Copenhagen interpretation, which is a rather vague conglomerate of different ideas like "complementarity" (Bohr), "collapse of the state" (Bohr, Heisenberg, von Neumann), the "cut between quantum and classical behavior" (von Neumann). In my opinion the "collapse idea" is pretty useless if not misleading. At least it brings more problems with it than it solves with regard to Einstein causality in relativistic physics. This was already critizized by Einstein, Poldolsky, and Rosen in their famous paper. Then there is "many-worlds theory", which introduces the quite funny idea of parallel (unobservable!) universes, splitting up at every time one observes some clear fact about a quantum system. I never understood what this bizarre idea might solve in terms of the philosophical quibbles some people have with the (minimally interpreted) quantum theory and its probabilistic nature.

All this are, however, legitimate questions to be asked, and answers to them might lead to a deeper understanding of quantum theory. Of course, anything which doesn't lead to observable consequences that contradict quantum theory in its minimal interpretation, doesn't lead to a new theory in the sense of natural sciences and thus one can well say that such discussions are off topic in a scientific forum like this, and it's as legitimate to close threads on "philsophy" (humanities) without "scientific content", which of course includes also this posting itself ;-)).

 

[stevendaryl]

Some people are, however, not satisfied by the minimal interpretation because of its probabilistic nature

That is not a very good characterization of why people (today) are not satisfied by the minimal interpretation. There are no interpretational difficulties with a stochastic process, where the evolution equations are probabilistic, rather than deterministic. Einstein may not have liked nondeterminism, but that's not anywhere close to the main difficulty in interpreteting quantum mechanics.

The problems that I have with the minimal interpretation is that it seems incoherent. You use the wave function to compute a probability. Fine. But a probabilities of what? Is it a probability of some physical quantity having a certain value? No, that can't be the case. It is not consistent to assume that physical quantities have values before they are measured (because of incompatible observables). So what is it a probability of? You can say that it's the probability, not of something being a certain value, but of an experiment measuring a certain value. But that seems incoherent, as well. Measuring devices are physical objects, themselves. They obey the laws of physics, which presumably includes quantum mechanics. So if it is not consistent to assume that electrons have definite values of properties such as "z component of spin", then how is it consistent to assume that a measurement device has a definite value for something like "the measured value of spin"?

So the minimal interpretation seems completely incoherent to me, as a physical theory. You can make it into a recipe for doing physics by doing as the Copenhagen people suggested, which is to separate reality into macroscopic and microscopic realms, and to assume that in the macroscopic realm, objects have definite macroscopic properties at all times, while in the microscopic realm, there are only wave functions, which are used to compute probabilities for events in the macroscopic realm. I think that works in practice, but it is certainly unsatisfying, because the macroscopic/microscopic distinction seems ad hoc and subjective.

 

[atyy]

I'd make a clear distinction between "interpretation of quantum theory" and "alternative new theories". Quantum theory in its minimal interpretation (a theory without an interpretation, i.e., without making contact to real-world observations and experiments is not a physical theory at all) defines a clear mathematical scheme and how it is applied to describe the phenomenology they are applicable (sometimes in exact ab-initio solutions of the quantum-theoretical equations, often in terms of approximations like perturbation theory in QFT) to make predictions that can be experimentally tested. Personally, I'm sticking to the minimal interpretation, because it's minimal. In my opinion, a physical theory is complete as soon as I can describe all known reproducible observations with it (that's the status of QT today) or as soon as I have found an experimental fact contradicting it, which doesn't make it obsolete completely but it leads to certain constraints on the applicability range of the theory. That's the case for all of classical physics (Newtonian mechanics was found to be invalid at high velocities and then has to be substituted by (special and general) relativity, electromagnetism needs the extension to relativistic field-theoretical descriptions (first the classical kind a la Maxwell); all of classical physics needs to be substituted by quantum theory after all, etc.). It's pretty likely that also quantum theory one day may be found to be an approximate description of Nature by finding some empirical contradiction to it and it must be substituted by a more comprehensive theory. That's progress of science and thus should not be taken as a "failure" in any way.

Some people are, however, not satisfied by the minimal interpretation because of its probabilistic nature, and they try to find other interpretations of quantum theory. These other interpretations lead to the same predictions about the outcome of measurements and thus from a physics point of view it's still the same theory. There are, however, different categories of "interpretations".

The first category are different mathematical techniques applied to quantum theory. This already started in the very beginning of quantum theory in 1925, when nearly at the same time, Heisenberg, Born, and Jordan came up with what is called "matrix mechanics" and Schrödinger with "wave mechanics". Independently Dirac came up with another formulation which is the most general one and was called "transformation theory" at the time. From the modern point of view, I'd call it representation-independent formulation. The non-relativistic QT was then completely formalized and understood by von Neumann in terms of Hilbert-space theory, which more recently has been reformulated in terms of the socalle "rigged Hilbert-space" formalism, which makes the hand-waving maths we physicists use in our calculations a mathematically strict formulation. Another equivalent (but as far as I know less strict) formulation is then Feynman's path-integral formulation, using functional methods to express the same theory. All this is not "interpretation" in the more narrow sense, but just different mathematical language to formulate the same theory. Which mathematical formalism you use doesn't so much imply which interpretation you follow, although often the path-integral formalism is interpreted somehow in the sense as if it were a new interpretation, a view also Feynman seems to have hold for some time. I think, that's not the case. It's just another way to express one and the same theory, and I (as a follower of the minimal interpretation) can use any mathematical tool without changing my view on interpretation. Which one I use, depends on the problem I like to solve and which one I'm able to use for that problem, but it's totally unimportant concerning my view on the interpretation.

The second category is to add some elements, concerning the philosophical implications of the theory. E.g., in Bohmian mechanics, one adds a kind of "trajectory picture" back into the physics of single particles which has been abandoned before due to the uncertainty relation that states that a particle cannot be prepared in a state such that both position and momentum are both determined to arbitrary precision, which implies that it does not make sense to talk about trajectories of a particle in phase space as is the case in classical mechanics. The Bohmian trajectories are determined by non-local equations with the "wave function" of the particles as "pilot waves". On the other hand it's still an open debate, whether the Bohmian trajectories are observable or not and if so, whether Bohmian mechanics is experimentally disproven already. I think we can say that's pretty undecided today. The same holds for other interpretations as the various flavor of the Copenhagen interpretation, which is a rather vague conglomerate of different ideas like "complementarity" (Bohr), "collapse of the state" (Bohr, Heisenberg, von Neumann), the "cut between quantum and classical behavior" (von Neumann). In my opinion the "collapse idea" is pretty useless if not misleading. At least it brings more problems with it than it solves with regard to Einstein causality in relativistic physics. This was already critizized by Einstein, Poldolsky, and Rosen in their famous paper. Then there is "many-worlds theory", which introduces the quite funny idea of parallel (unobservable!) universes, splitting up at every time one observes some clear fact about a quantum system. I never understood what this bizarre idea might solve in terms of the philosophical quibbles some people have with the (minimally interpreted) quantum theory and its probabilistic nature.

All this are, however, legitimate questions to be asked, and answers to them might lead to a deeper understanding of quantum theory. Of course, anything which doesn't lead to observable consequences that contradict quantum theory in its minimal interpretation, doesn't lead to a new theory in the sense of natural sciences and thus one can well say that such discussions are off topic in a scientific forum like this, and it's as legitimate to close threads on "philsophy" (humanities) without "scientific content", which of course includes also this posting itself ;-)).

It's unclear to me if the minimal statistical interpretation without the projection postulate is correct. The ability to use a projection operator is a standard part of quantum mechanics, acknowledged eg. by Landau and Lifshitz and Cohen-Tannoudji, and even in modern formulations such as that by Hardy http://arxiv.org/abs/quant-ph/0101012 . So the use of the projection operator must be either derived or postulated. Without projection, the state of a sub-ensemble is undefined, and so filtering measurements used for state preparation cannot be described. If the reduced density matrix is interpreted as a proper mixture, that seems to me an unacknowledged use of the projection postulate, eg:

http://arxiv.org/abs/quant-ph/0312059 (p9) "The reduced density matrix looks like a mixed state density matrix because, if one actually measured an observable of the system, one would expect to get a definite outcome with a certain probability; in terms of measurement statistics, this is equivalent to the situation in which the system is in one of the states from the set of possible outcomes from the beginning, that is, before the measurement. As Pessoa (1998, p. 432) puts it, “taking a partial trace amounts to the statistical version of the projection postulate.”"

http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf (p37) "Ignorance interpretation: The mixed states we find by taking the partial trace over the environment can be interpreted as a proper mixture. Note that this is essentially a collapse postulate."

 

[vanhees71]

That is not a very good characterization of why people (today) are not satisfied by the minimal interpretation. There are no interpretational difficulties with a stochastic process, where the evolution equations are probabilistic, rather than deterministic. Einstein may not have liked nondeterminism, but that's not anywhere close to the main difficulty in interpreteting quantum mechanics.

The problems that I have with the minimal interpretation is that it seems incoherent. You use the wave function to compute a probability. Fine. But a probabilities of what? Is it a probability of some physical quantity having a certain value? No, that can't be the case. It is not consistent to assume that physical quantities have values before they are measured (because of incompatible observables). So what is it a probability of? You can say that it's the probability, not of something being a certain value, but of an experiment measuring a certain value. But that seems incoherent, as well. Measuring devices are physical objects, themselves. They obey the laws of physics, which presumably includes quantum mechanics. So if it is not consistent to assume that electrons have definite values of properties such as "z component of spin", then how is it consistent to assume that a measurement device has a definite value for something like "the measured value of spin"?

So the minimal interpretation seems completely incoherent to me, as a physical theory. You can make it into a recipe for doing physics by doing as the Copenhagen people suggested, which is to separate reality into macroscopic and microscopic realms, and to assume that in the macroscopic realm, objects have definite macroscopic properties at all times, while in the microscopic realm, there are only wave functions, which are used to compute probabilities for events in the macroscopic realm. I think that works in practice, but it is certainly unsatisfying, because the macroscopic/microscopic distinction seems ad hoc and subjective.

The problem here seems to be a misunderstanding of the idea of a "quantum state" within the minimal interpretation. I think it is very important to distinguish between "measurement" and "preoparation". This is very often mixed up and leads to the difficulties you seem to have with the minimal interpretation.

The probabilistic interpretation of the (pure) states in quantum theory, i.e., Born's postulate, implies that you can interpret the states as descriptions of (an equivalence class) of preparations, i.e., clear manipulations on a single quantum system, which prepare them in a certain state in a reproducible way. Then and only then you can prepare ensembles of independent systems in that given state.

This state preparation implies which observables take determined values and which don't. All you can say about the measurement of an observable is "encoded" in the (normalized) state vector (or the corresponding ray), and this is the probability to find a certain value of an observable when you measure it. This prediction can only be tested by preparing a sufficiently large ensemble of equally prepared systems such that you get the probabilities within a statistical limit of accuracy.

There is no necessity to assume a cut between a quantum realm and a classical realm. The classical behavior of macroscopic systems, as are necessarily measurement devices (as indeed already pointed out by Bohr), is understandable from quantum mechanics in terms of standard many-body theory (some coarse graining to average over many "micro states" making up a "macro state", leading to decoherence).

 

[vanhees71]

It's unclear to me if the minimal statistical interpretation without the projection postulate is correct. The ability to use a projection operator is a standard part of quantum mechanics, acknowledged eg. by Landau and Lifshitz and Cohen-Tannoudji, and even in modern formulations such as that by Hardy http://arxiv.org/abs/quant-ph/0101012 . So the use of the projection operator must be either derived or postulated. Without projection, the state of a sub-ensemble is undefined, and so filtering measurements used for state preparation cannot be described. If the reduced density matrix is interpreted as a proper mixture, that seems to me an unacknowledged use of the projection postulate, eg:

http://arxiv.org/abs/quant-ph/0312059 (p9) "The reduced density matrix looks like a mixed state density matrix because, if one actually measured an observable of the system, one would expect to get a definite outcome with a certain probability; in terms of measurement statistics, this is equivalent to the situation in which the system is in one of the states from the set of possible outcomes from the beginning, that is, before the measurement. As Pessoa (1998, p. 432) puts it, “taking a partial trace amounts to the statistical version of the projection postulate.”"

http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf (p37) "Ignorance interpretation: The mixed states we find by taking the partial trace over the environment can be interpreted as a proper mixture. Note that this is essentially a collapse postulate."

What's the problem with the "projection" postulate? I think, it's indeed one of the basic postulates which is part of the foundations of quantum theory. It's closely related to the Born postulate, i.e., how to calculate the probability for the outcome of measurements for a given prepration. There's a very nice discussion on the question, whether the Born postulate can be derived from the other postulates of quantum theory in Weinberg's newest textbook "Quantum Mechanics" with the conclusion that it is an independent postulate.

 

[bhobba]

There's a very nice discussion on the question, whether the Born postulate can be derived from the other postulates of quantum theory in Weinberg's newest textbook "Quantum Mechanics" with the conclusion that it is an independent postulate.

Weinberg is correct - and it has been known for a long time.

But I find the basis independence assumption of Gleason's Theorem very natural mathematically and personally is what I use use to justify it, which otherwise would seem rather ad-hoc.

Thanks
Bill

 

[atyy]

What's the problem with the "projection" postulate? I think, it's indeed one of the basic postulates which is part of the foundations of quantum theory. It's closely related to the Born postulate, i.e., how to calculate the probability for the outcome of measurements for a given prepration. There's a very nice discussion on the question, whether the Born postulate can be derived from the other postulates of quantum theory in Weinberg's newest textbook "Quantum Mechanics" with the conclusion that it is an independent postulate.

Yes, the way Weinberg states the Born rule includes the projection postulate (p26 of http://bks3.books.google.com/books?id=WfTq2W_LBlEC&source=gbs_navlinks_s ). But in your post you indicated that "collapse" was misleading. Isn't "collapse" just another name for the projection postulate?

 

[vanhees71]

Born's rule just says what are the probabilities for finding a certain value for an observable when this observable is measured on a system in a given (pure or mixed) state. It does not say that immediately after the measurement the system's state must instantaneously collapse into an eigenstate of this observable. This is most often not the case, because often the system gets destroyed being measured. Of course, there are cases of (almost) von Neumann ideal filter measurements. E.g., one can prepare (almost) pure spin states for an atom using a Stern Gerlach apparatus and just absorbing all partial beams except one, but here I don't need a collapse, but can understand from the quantum dynamics, how the positition of the partial beams gets to (nearly) 100% entangled with the spin state of the particle. Then, I just dump all "unwanted" partial beams into a wall and let all the "wanted" ones through. That's all, leading to the preparation of atoms in a definite spin state. No esoterics like collapses or the like needed.

 

[atyy]

Born's rule just says what are the probabilities for finding a certain value for an observable when this observable is measured on a system in a given (pure or mixed) state. It does not say that immediately after the measurement the system's state must instantaneously collapse into an eigenstate of this observable. This is most often not the case, because often the system gets destroyed being measured. Of course, there are cases of (almost) von Neumann ideal filter measurements. E.g., one can prepare (almost) pure spin states for an atom using a Stern Gerlach apparatus and just absorbing all partial beams except one, but here I don't need a collapse, but can understand from the quantum dynamics, how the positition of the partial beams gets to (nearly) 100% entangled with the spin state of the particle. Then, I just dump all "unwanted" partial beams into a wall and let all the "wanted" ones through. That's all, leading to the preparation of atoms in a definite spin state. No esoterics like collapses or the like needed.

Let me see if I understand what you are saying about the Stern Gerlach case. There position and spin are entangled, then the mathematical description of dumping the other beams is the partial trace over all unwanted beams, leaving the reduced density matrix for the wanted beam?

 

[vanhees71]

In a somwhat abstract sense yes. You just choose a subensemble from a larger ensemble. Of course, you ignore the pretty complicated dynamics leading to the absorption of particles in the beam dump ;-).

 

[atyy]

In a somwhat abstract sense yes. You just choose a subensemble from a larger ensemble. Of course, you ignore the pretty complicated dynamics leading to the absorption of particles in the beam dump ;-).

The reason I think the partial trace either involves the projection postulate, or must be introduced as a new postulate is that in the naive textbook formalism, the meaning of the partial trace is derived from the projection postulate. I think it is possible to do without the projection postulate in the ensemble interpretation, provided one replaces it with another postulate, such as postulating the interpretation of the partial trace directly. However, I am skeptical that the ensemble interpretation works without the projection postulate or a replacement.

There are similar thoughts that the partial trace has a hidden use of the projection postulate in eg.

http://arxiv.org/abs/quant-ph/0312059 (p9) "The reduced density matrix looks like a mixed state density matrix because, if one actually measured an observable of the system, one would expect to get a definite outcome with a certain probability; in terms of measurement statistics, this is equivalent to the situation in which the system is in one of the states from the set of possible outcomes from the beginning, that is, before the measurement. As Pessoa (1998, p. 432) puts it, “taking a partial trace amounts to the statistical version of the projection postulate.”"

http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf (p37) "Ignorance interpretation: The mixed states we find by taking the partial trace over the environment can be interpreted as a proper mixture. Note that this is essentially a collapse postulate."

 

[kith]

There position and spin are entangled, then the mathematical description of dumping the other beams is the partial trace over all unwanted beams, leaving the reduced density matrix for the wanted beam?

The final state is a superposition. How would you single out a certain term by taking a partial trace?

 

[atyy]

The final state is a superposition. How would you single out a certain term by taking a partial trace?

It doesn't work the way I initially thought it might. I looked up Ballentine, chapter 9, page 244, and it looks like he includes the environment, has decoherence, traces over the environment and gets a reduced density matrix that has the same form as a proper mixture.

 

[eloheim]

It doesn't work the way I initially thought it might.

I got a little lost in the last few posts of this discussion. How do you respond to vanhees71's claim about the projection postulate being inequivalent to collapse (which is what he calls extraneous)?

I was with it here:

Born's rule just says what are the probabilities for finding a certain value for an observable when this observable is measured on a system in a given (pure or mixed) state. It does not say that immediately after the measurement the system's state must instantaneously collapse into an eigenstate of this observable. This is most often not the case, because often the system gets destroyed being measured...<snip>... No esoterics like collapses or the like needed.

But then you go back to talking about whether the projection postulate needs to be postulated separately, or can be derived. I thought we're already past that, with vanhees71's granting that it is a separate postulate, but stating that we're debating the merits of collapse, not the postulate of projection (which brings us to the quote above)?

The reason I think the partial trace either involves the projection postulate, or must be introduced as a new postulate is that in the naive textbook formalism, the meaning of the partial trace is derived from the projection postulate.

I only pry because parts of this thread actually appear lucid, which is saying something considering the topic!

 

[bhobba]

It doesn't work the way I initially thought it might. I looked up Ballentine, chapter 9, page 244, and it looks like he includes the environment, has decoherence, traces over the environment and gets a reduced density matrix that has the same form as a proper mixture.

He actually does it two ways - the partial trace (which he thinks of as the environment changing the system) and a second method where the environment and system are combined and how the apparatus affects that combination.

Of course each view must give the same answer, and he gives a reference where the issue is examined.

I suspect this also has something to say about the factorization problem some worry about concerning decoherence.

Its interesting Ballentine does this because he doesn't really believe decoherence has anything to do with interpretation. I of course respectfully disagree.

Thanks
Bill