Einstein and "spooky actions"

[Mr Spinkles]

That's more or less my point.

Yes.

Okay thanks for humoring me and clarifying that for me. This part I understand. However I'm honestly confused by this:

"What is called a ‘‘state of a system’’, whether it is represented by a wavefunction, a ket or a density operator, refers to a statistical ensemble of systems, all prepared before the initial time under the same conditions as the system in hand."

At the risk of embarrassing myself in the face of what I presume to be a quotation of some eminent physicist, I am at a loss here. It was my understanding that, in principle, there is a ket which represents the complete microscopic state of a system. Period. (Or, to be more precise: my understanding is that QM allows for this interpretation, and it is the most common one.) Every identically-prepared system would have this same ket, and hence there is no need to refer to any 'statistical distribution' if we are simply talking about the complete quantum state. It is only the outcomes of measurements, and not the state itself, that must refer to a 'statistical ensemble', since outcomes would vary even in hypothetical identically-prepared systems.

Is it possible the author of your quotation would not object to what I said, because he is adopting an operational definition of "the state" for the convenience of experimentation? To wit, in practice experimentalists only prepare systems partially identically (e.g. the spin component of the state in a Bell-type experiment) whereas other components of the state vary according to some 'statistical ensemble' (e.g. the position component of the state). We might only worry about the spin-component part and therefore we call that component "the state" as a matter of convenience, even though the complete quantum state really involves other components drawn from a 'statistical ensemble'. Or we might not be able to isolate our system from random environmental perturbations (e.g. we have a hunk of metal at room temperature) and therefore we use a density operator to describe "the state" drawn from a statistical ensemble. But in such cases "the state" refers to a 'statistical ensemble' only because we have chosen to describe common features of systems which were not completely identically-prepared. I realize that even in principle, you can't prepare systems completely identically. But no matter. It's still acceptable to say (or at least I thought it was) that if you prepare a system even once, and never prepare any other system identically, there still exists a ket which does indeed describe the complete quantum state of that system, and that mathematical representation has what you call a "one-to-one correspondence" with the system.

It seems to me that even though there are differences between QM and classical physics, this is not one of them. Both say in principle that any given physical system has a one-to-one correspondence with its mathematical representation. In classical mechanics the mathematical representation is a list of all the positions and momenta of all the particles, i.e. a point in a 6N-dimensional phase space; in QM it's a vector in Hilbert space. I think PolyHedral is right that one key difference (of many) is that the former is more intuitive to our brains whereas the latter lacks an intuitive "everyday" picture to help us visualize the mathematical representation.

(Caveat: yes, of course, there isn't truly just one ket; we are free to pick from a limited range of kets which equally describe the system, e.g. the phase of the wavefunction might be arbitrary. So it's not a perfect one-to-one correspondence. But to me this is not significantly different from the case in classical mechanics. In the classical case, too, you are free to pick a limited range of states, e.g. a constant added to the positions or momenta is arbitrary.)

 

[PolyHedral]

(Caveat: yes, of course, there isn't truly just one ket; we are free to pick from a limited range of kets which equally describe the system, e.g. the phase of the wavefunction might be arbitrary. So it's not a perfect one-to-one correspondence.

It is if you define your equality operator correctly.

 

[idav]

It is completely different. It's so different that an entirely new set of fields in physics had to be created and centuries of work became approximations. Pretending otherwise is just denial.

Its not completely different since it retains some classical attributes. Do photons go through walls, no but it can bend and go around corners and be in multiple places. But it still obeys the laws, gravity affects it for example in a black hole.

 

[Mr Spinkles]

It is if you define your equality operator correctly.

I'm sorry I don't know what this means.

 

[PolyHedral]

I'm sorry I don't know what this means.

Oops, that's not the term usually used. I meant you can have one-to-one mappings between equivalence classes.

 

[LegionOnomaMoi]

At the risk of embarrassing myself in the face of what I presume to be a quotation of some eminent physicist

"'The attempt to conceive the quantum-theoretical description as the complete description of the individual systems leads to unnatural theoretical interpretations, which immediately become unnecessary if one accepts the interpretation that the description refers to ensembles of systems and not to individual systems.'
– Albert Einstein
This quotation is perhaps the most famous statement of the ensemble interpretation of quantum mechanics. The role of the ensemble in quantum mechanics ranges from innocuous to profound, and even controversial.
The innocuous role of the ensemble stems from the fact that quantum mechanics does not predict the actual events, but only the probabilities of the various possible outcomes of the various possible events. In order to compare the predictions of quantum mechanics with experiment, one must prepare a state and measure some dynamical variable, and repeat this preparation–measurement sequence many times. The relative frequencies of the various outcomes in this ensemble of results can then be compared with the theoretical probabilities predicted by quantum mechanics. Thus it is natural to say that quantum mechanics describes the statistics of an ensemble of similarly prepared systems."

Greenberger, D., Hentschel, K., & Weinert, F. (2009). Compendium of Quantum Physics: Concepts, Experiments, History and Philosophy (Springer)

It's the result of calling something "preparation of a system" when one isn't actually doing that: (italics in original):

"The purpose of measurements is the determination of properties of the physical system under investigation. In this sense the general conception of measurement is that of an unambiguous comparison: the object system S, prepared in a state T, is brought into a suitable contact - a measurement coupling- with another, independently prepared system, the measuring apparatus from which the result related to the measured observable E is determined by reading the value of the pointer observable. It is the goal of the quantum theory of measurement to investigate whether measuring processes, being physical processes, are the subject of quantum mechanics. This question, ultimately, is the question of the universality of quantum mechanics.
In classical physics all observables are objective in any state, that is, they always assume well-defined though possibly unknown values. Moreover, it is possible in principle to measure them without in any way changing the observed system. Hence the measurement outcome is nothing but the value of the observable before as well as after the measurement. On the other hand, in the case of quantum mechanical systems for any observable there exist states in which the observable is not objective. In that case the reading shown by the apparatus cannot refer to an objective value of the observable before the measurement. Furthermore, it is not evident that a measurement may be such that its outcome refers to an objective value of the observable after the measurement" p.25

Busch, P. Lahti, P.J. Mittelstaedt, P. (1996). The Quantum Theory of Measurement 2nd Ed. (Lecture Notes in Physics)

It was my understanding that, in principle, there is a ket which represents the complete microscopic state of a system. Period.

The ket represents the complete state, yes. But under that assumption, it doesn't represent a physical system: "The standard interpretation of QM, tells us nothing about the underlying physics of the system. The state vector represents our knowledge of the system, not its physics".

Caponigro, M. (2010) Interpretations of Quantum Mechanics: A Critical Survey. Prespacetime Journal, 1(5): 745-760

Every identically-prepared system would have this same ket

Yes, which is the problem: "The same classical state leads necessarily to the same observable events, but a new preparation of the same quantum state may lead to quite different observable outcomes." from Compendium of Quantum Physics: Concepts, Experiments, History and Philosophy

and hence there is no need to refer to any 'statistical distribution' if we are simply talking about the complete quantum state.

The complete quantum state is obtained by premeasurement, which not only means different identically prepared states can yield different results, but also that what we call "preparing" is really something quite different, and depending upon one's lab procedures, the methods (and in particular the mathematical methods) by which the "state" of this singular "system" is transcribed (e.g., via an interaction Hamiltonian) differs, especially when compared to the ways classical systems are transcribed based upon particular features and (obviously) the experimental design. But however this quantum systems are prepared, the "initial state" is always a compound system of repeated preparations of "one" system which isn't one system at all. To call it an initial system is necessarily a statistical interpretation. The ensemble interpretation is basically a class of interpretations held by those who refuse to call what is clearly multiple systems prepared over and over "the system". It's an objection to the singular idealized abstraction that is obtained through preparing an ensemble of systems. Considering the range of interpretations, with the holographic anthropic multiverse-type interpretations on the one hand, and Einstein's "screw you people- if you want to pretend the moon isn't there when you don't look, go ahead and have fun playing dice with god" take on the other hand, this is definitely closer to Einstein. And while I don't think the versions I've seen really warrant the distinctions made, I do think it's better than making the whole think disappear through largely unfalsifiable appeals to infinite universes and some ad hoc version of the projection postulate so that one can bypass the measurement problem by stealing everything that went into making QM successful and giving no justification for using these methods.

Is it possible the author of your quotation would not object to what I said, because he is adopting an operational definition of "the state" for the convenience of experimentation?

It's an interpretation (or rather, a class of interpretations) of quantum mechanics, so not really. That is, the way you describe it that I've cut out is pretty accurate, except that it is not convenience at all (anymore than the multiverse interpretation is, at least). For a somewhat outdated but rather thorough treatment (for a paper) see here. The paper (published in physics reports) refers to a "modern perspective" (why would anybody title a paper that was guaranteed to become a dated perspective in such a way?), but Smolin's is actually modern. However, it's also more exotic. I sometimes think cosmologists are competing with each other to see who can get away with the most bizarre interpretation. Tegmark's solution is a multiverse in which "the 'many-worlds' are all the same".

that mathematical representation has what you call a "one-to-one correspondence" with the system

The statistical nature is a result of the transcription process itself, which relies on theory not just to prepare but to characterize the system. At no time are the specifications of the system ever related to any single physical system nor is it known how the abstract system's description relates to the quantum system. Hence the plethora of interpretations.

Both say in principle that any given physical system has a one-to-one correspondence with its mathematical representation.

Of the classes of interpretations out there, I don't know of one in which this is true. Realists tend to interpret the formalism as the probability of finding a particle, Bohr/Copenhagen/various interpretations of the Copenhagen interpretation all tend to treat the system as nothing more than a mapping from the preparation devices (or, another variant, object-system apparatus state) to the measurement, and say nothing about the physical system other than that it is irreducibly statistical and the formalism is solely a method of obtaining measurements.

 

[Mr Spinkles]

Oops, that's not the term usually used. I meant you can have one-to-one mappings between equivalence classes.

Okay, so if I understand you, you are saying instead of a one-to-one correspondence between a ket and a physical system, there's a one-to-one correspondence between a set of kets and a physical system. Semantics aside, isn't that what I said?

 

[Mr Spinkles]

"'The attempt to conceive the quantum-theoretical description as the complete description of the individual systems leads to unnatural theoretical interpretations, which immediately become unnecessary if one accepts the interpretation that the description refers to ensembles of systems and not to individual systems.'
– Albert Einstein

Okay, that was Einstein's view, that QM is like classical statistical mechanics, it describes ensembles and is therefore an incomplete description. Nevertheless, it seems Einstein was wrong about QM and, as you say, "The ket represents the complete state, yes."

The ket represents the complete state, yes. But under that assumption, it doesn't represent a physical system: "The standard interpretation of QM, tells us nothing about the underlying physics of the system. The state vector represents our knowledge of the system, not its physics".

Caponigro, M. (2010) Interpretations of Quantum Mechanics: A Critical Survey. Prespacetime Journal, 1(5): 745-760

I'm not sure that's a reputable journal ... but in any case, I don't see how it logically follows that if "the ket represents the complete state" of a system, then the ket does not represent "a physical system". Or it only represents "our knowledge" of a system. I just can't make sense of that. E.g. if the ket only represented our knowledge of the system, then it seems to me almost by definition it would not represent the complete state of the system.

The alternative, however, seems to me quite straightforward: the ket represents the complete state of a physical system, not just our knowledge of it. While it's true that we don't "know" what the result of a spin measurement will be, that's because the system is in a state without a definite spin, and it does not adopt a definite spin in a deterministic way upon measurement. In other words, the system really is quantum mechanical, it's not just a statistical description of our knowledge. This was the common understanding I was taught by 3 different professors in 3 different QM courses, using 2 different textbooks. If I made this statement at one of the physics seminars I don't think anyone would find it controversial ... but maybe I'm wrong ...

Are you simply saying that we need more than just the state of the system, we need other ingredients, namely Schrodinger evolution of state + Born rule for state collapse? Whereas, in classical mechanics we only needed two ingredients (state of the system + Newtonian evolution)? That's certainly true ...

Yes, which is the problem: "The same classical state leads necessarily to the same observable events, but a new preparation of the same quantum state may lead to quite different observable outcomes." from Compendium of Quantum Physics: Concepts, Experiments, History and Philosophy

Right. The same quantum state leads to different observable outcomes. This corresponds in principle to the underlying reality, which is that the state of the system now does not determine one unique future state. I.e., the system does not obey deterministic laws as in classical mechanics. So I guess I should say, at any given moment, there is "a mathematical representation [which] has what you call a "one-to-one correspondence" with the system". Of course, you are right that the state does not evolve deterministically into only one possible future state. The same would be true if we lived in a classical world which obeyed any kind of stochastic dynamics. To me however if a physical system really hops around in a non-deterministic way, then it only adds confusion to say the state must refer to an ensemble, or only our knowledge, or "not the physical system". I can only make sense of those statements if one believes that physical systems really obey deterministic laws, and QM is an incomplete statistical description, like classical statistical mechanics ... but that's not what you believe, right?

The complete quantum state is obtained by premeasurement, which not only means different identically prepared states can yield different results, but also that what we call "preparing" is really something quite different, and depending upon one's lab procedures, the mathematical way in which the singular "system" is transcribed into a state (e.g., via an interaction Hamiltonian) differs, not just based upon the varying ways the ensemble and particular features (and obviously the experimental design). But however this is done, the "initial state" is always a compound system of repeated preparations of "one" system which isn't one system at all. To call it an initial system is necessarily a statistical interpretation. The ensemble interpretation is basically a class of interpretations which refuse to call what is clearly multiple systems prepared over and over "the system". It's an objection to the singular idealized abstraction that is obtained through preparing an ensemble of systems.

I'm just failing to see the need to raise such an objection. I acknowledged in my previous post the issue of 'premeasurement' (although I didn't use that term) and I explained why "there still exists a ket which does indeed describe the complete quantum state of that system, and that mathematical representation has what you call a "one-to-one correspondence" with the system".

It's an interpretation (or rather, a class of interpretations) of quantum mechanics, so not really. That is, the way you describe it that I've cut out is pretty accurate, except that it is not convenience at all (anymore than the multiverse interpretation is, at least). For a somewhat outdated but rather thorough treatment (for a paper) see here. The paper (published in physics reports) refers to a "modern perspective" (why would anybody title a paper that was guaranteed to become a dated perspective in such a way?), but Smolin's is actually modern. However, it's also more exotic. I sometimes think cosmologists are competing with each other to see who can get away with the most bizarre interpretation. Tegmark's solution is a multiverse in which "the 'many-worlds' are all the same".

Oh, okay. So you are talking about hidden-variables then (that's what Smolin's paper is proposing). Okay, that's one proposal .... obviously if QM turns out to be an incomplete description, then what we call "the state" must really just refer to a statistical ensemble, or to our limited knowledge of the system, etc.

But that's a statement about QM being a potentially incomplete or even wrong theory, like classical statistical mechanics. If QM is actually a correct and complete, then I just don't see how it can be anything other than confusion to say things like "we "talk" about a quantum state that isn't, strictly speaking, related to any state of a physical system" .... and "we cannot say how the state of the system in the model corresponds in a one-to-one way with the system itself (or even what that really means)". If QM is wrong, then of course that's all true. But if QM is right, then evidently we can say precisely how the state of the system in the model corresponds in a one-to-one way with the system itself, and precisely what that means. So I just don't think these particular claims capture the fundamental conceptual differences between QM and classical mechanics.

Of the classes of interpretations out there, I don't know of one in which this is true. Realists tend to interpret the formalism as the probability of finding a particle, Bohr/Copenhagen/various interpretations of the Copenhagen interpretation all tend to treat the system as nothing more than a mapping from the preparation devices (or, another variant, object-system apparatus state) to the measurement, and say nothing about the physical system other than that it is irreducibly statistical and the formalism is solely a method of obtaining measurements.

I'm just reiterating what Shankar and Griffiths say in their QM books. Griffiths acknowledges alternative interpretations and describes what I've said as the "orthodox" one. They say the ket or wavefunction represents the state of the system, period. They do not adorn this statement with the objections you've raised, namely that it doesn't represent "a physical system", or it's just "our knowledge", or it's really "an ensemble". The exception is that those objections come into play (as explained by Griffiths) if one objects to the orthodox interpretation and argues that QM is incomplete and/or wrong. But I'm pretty sure you aren't saying that so that's why I'm confused about what you are trying to say ...

 

[PolyHedral]

Okay, so if I understand you, you are saying instead of a one-to-one correspondence between a ket and a physical system, there's a one-to-one correspondence between a set of kets and a physical system. Semantics aside, isn't that what I said?

I mean that there's a one-to-one correspondance between a physical system and a blob, where there is a one-to-many correspondance between blobs and wavefunctions. It is a "semantics" issue, but that's important in maths.

Also, perhaps it'd be easier to work out when we're getting hung up on language issues if we focused on a specific experiment, like the double-slit apparatus?

 

[LegionOnomaMoi]

Okay, that was Einstein's view

Yes, but it was also a blurb. This part:
"This quotation is perhaps the most famous statement of the ensemble interpretation of quantum mechanics. The role of the ensemble in quantum mechanics ranges from innocuous to profound, and even controversial.
The innocuous role of the ensemble stems from the fact that quantum mechanics does not predict the actual events, but only the probabilities of the various possible outcomes of the various possible events. In order to compare the predictions of quantum mechanics with experiment, one must prepare a state and measure some dynamical variable, and repeat this preparation–measurement sequence many times. The relative frequencies of the various outcomes in this ensemble of results can then be compared with the theoretical probabilities predicted by quantum mechanics. Thus it is natural to say that quantum mechanics describes the statistics of an ensemble of similarly prepared systems."

was not Einstein.

Nevertheless, it seems Einstein was wrong about QM and, as you say, "The ket represents the complete state, yes."

Bohr's opinion was that it contained all the information. Not that it represented "the complete state". In fact, the idea of a "complete state" was nonsensical under his interpretation.

I'm not sure that's a reputable journal

It isn't. But I can only scan or type out lines for so long, and I wanted to provide at least some links.

Or it only represents "our knowledge" of a system. I just can't make sense of that.

It is all we know about a measurement we will get. That's it. That's the completeness.

E.g. if the ket only represented our knowledge of the system, then it seems to me almost by definition it would not represent the complete state of the system.

Sure. Unless you regard the relationship between the system and a physical system as meaningless, which has been continually repeated since Bohr and is advocated to day by e.g., The Frontiers Collection editor Mark P. Silverman.

The alternative, however, seems to me quite straightforward: the ket represents the complete state of a physical system, not just our knowledge of it.

Ok. Then the naturally question is how did we obtain this knowledge? By running repeat experiments on an ensemble of systems, each time altering them in non-trivial ways, yet somehow we wind up with a complete knowledge of a physical system? How?

This was the common understanding I was taught by 3 different professors in 3 different QM courses, using 2 different textbooks.

That's kind of like my experience in one of my undergrad majors with action potentials, so I do sympathize. In fact, one of the textbooks I have is designed to fill in the gap between courses in QM and the transition to quantum field theory. But then, I've never taken I QM course (not officially; I've sat in). But I do have a few hundred books on the subject that are either undergrad textbooks, grad textbooks, or reference material for physicist. I don't know if you've had the experience, but when you are reading about experimental procedures without having ever even seen the type of lab described, you need more than a few textbooks to get a feel for it (and that's assuming I do have one).

If I made this statement at one of the physics seminars I don't think anyone would find it controversial ... but maybe I'm wrong ...

It depends upon how you phrased it. I got into this stuff to show that the quantum consciousness theory was baloney. That was years ago and I've spent more time on quantum physics than I have neuroscience or cognitive science. Maybe it's because I'm not that intelligent, but I think some of the blame is due to the fact that physics textbooks talk about systems and states as if they were more or less classical and then once one starts reading monographs and journals it turns out that this is not only far from true, it takes reading lab procedures, techniques and methods manuals, not to mention the actual literature, just to get a grasp on what's actually being done.

Are you simply saying that we need more than just the state of the system, we need other ingredients, namely Schrodinger evolution of state + Born rule for state collapse?

No. I'm saying that it is a postulate that all the information is contained in the ket. The problem is that that could mean that system can be in infinitely many states, or that this is just a probability function.

So I guess I should say, at any given moment, there is "a mathematical representation [which] has what you call a "one-to-one correspondence" with the system".

And I would say this is generally regarded as clearly not true.

I'm just failing to see the need to raise such an objection. I acknowledged in my previous post the issue of 'premeasurement' (although I didn't use that term) and I explained why "there still exists a ket which does indeed describe the complete quantum state of that system, and that mathematical representation has what you call a "one-to-one correspondence" with the system".{/quote]
This is key. There is a ket which contains all the information of the system's state. But how? There isn't even a system for this to be true. The reason it is true is because the ket is treated as the system and the information part is again a postulate. There's no way to check for such a correspondence but we know that there cannot be one.

Oh, okay. So you are talking about hidden-variables then (that's what Smolin's paper is proposing).

Definitely not. I included that because it was linkable and was more modern, but I'm not a fan of Smolin.

Okay, that's one proposal .... obviously if QM turns out to be an incomplete description, then what we call "the state" must really just refer to a statistical ensemble, or to our limited knowledge of the system, etc.

It is simply a fact that "the state" contains all the information simply because we say so and because from a statistical point of view it works. But if we assume it works because of the statistical success then we're acknowledging we didn't have the information we claim, and if we don't acknowledge this than we have no reason to claim that the ket represents the state in the manner claimed.

But I'm pretty sure you aren't saying that so that's why I'm confused about what you are trying to say ...

I was hoping the quotes would do that, as my explanations tend to confuse more than clarify.

 

[LegionOnomaMoi]

Perhaps there's a solution to what is probably bad communication on my part, making it hard to see what I'm saying (especially as I've said the same thing in so many different ways in so many threads I've forgotten to whom I've said what for which reason and when.

Then there's my inability to use references and quotes effectively. I blame my undergrad years, because one major and my minor used APA citation methods (in which you only give sources and don't quote from them) while classical languages used some system that was similar to MLA but I still don't know what it was other than that
1) Different professors had different standards
2) It is essential to provide quotes, not just cite.

So I either don't cite at all and just explain (which is an improvement from my early days here, when I'd actually just cite APA style to support my statements; needless to say, when nobody can access your sources this is useless), or I provide a lot of quotes interspersed with bad commentary and poor explanations. So I'm going to try something new. I'm going to try to explain my position without using any of my words (all quote with references), but combined in a way that approximates how I'd explain if I weren't quoting anything. That, perhaps, will take care of my bad explanations, yet ensure nobody has to take my word for anything. And if that doesn't work, then we're no worse off then we are now. I hope.

 

[LegionOnomaMoi]

To start (I don't intend to just use one source per post, but I wanted to offer something fairly complete and early on rather than making anybody wait)

2.2 Statistics of an Experiment

In the quantum case experiments are by necessity of statistical nature. The most simple setup can typically be described as a suitably devised macroscopic apparatus, possibly made up of lots of smaller components, preparing the microscopical system we would like to study, which in turn triggers another macroscopic device designed to measure the value of a definite quantity. The reproducible quantity to be compared with the theory is the relative frequency according to which the preparation apparatus triggers the registration apparatus in a high enough number of repetitions of the experiment under identical circumstances.

More complicated setups can be traced back to this one by suitably putting together different apparatuses in order to build a new preparation apparatus, and similarly for the registration part. In order to describe such experiments one has to introduce a suitable probability theory, which can actually account for the various experimental evidences to be gained at microscopic level. This is accomplished by introducing mathematical objects describing the preparation and the registration, as well as a statistical formula to extract from these two objects the probability densities to be compared with the experimental outcomes.

States as preparation procedures

In the quantum case a preparation procedure is generally described by a statistical operator…We stress the fact that statistical operators are actually to be associated to the considered statistical preparation procedure, rather than to the system itself. More precisely they describe a whole equivalence class of preparation procedures which all prepare the system in the same state, even though by means of quite different macroscopic apparatuses. This correspondence between statistical operators and equivalence classes of preparation procedures is reflected in the fact that a statistical operator generally admits infinitely many different decompositions, as mixtures of pure states or other statistical operators.

Brüning, E., & Petruccione, F. (2010). Theoretical Foundations of Quantum Information Processing and Communication. In Lecture Notes in Physics, Berlin Springer Verlag (Vol. 787)

 

[LegionOnomaMoi]

The following are all from this volume:
Nieuwenhuizen, T. M., Mehmani, B., Spicka, V., Aghdami, M. J., & Khrennikov, A. Y. (2007). Beyond the Quantum. (World Scientific Publishing Co.)

W. M. de MUYNCK POVMs: A SMALL BUT IMPORTANT STEP BEYOND STANDARD QUANTUM MECHANICS

“In quantum mechanics textbooks measurement is generally treated in an axiomatic way, and a detailed description of it is virtually absent. Bohr was one of the few to take the problem seriously, but he was mainly interested in the macroscopic phase of the measurement, which, according to him, was to be described by classical mechanics. However, not the macroscopic but rather the microscopic phase of the measurement, in which the microscopic information is transferred from the microscopic object to the measuring instrument, is crucial for obtaining quantum information. This phase should be described by quantum mechanics.
The influence of measurement has been of the utmost importance in the early days of quantum mechanics. In particular has it been a crucial feature at the inception of the notion of complementarity…By hindsight it can be concluded that much confusion could have been prevented if at that time it would have been realized that the standard formalism of quantum mechanics (as laid down, for instance, in von Neumann's authoritative book) is just a preliminary step towards a more general formalism. As it is evident now, the standard formalism is not even able to yield a proper description of the so-called thought experiments, at that time being at the heart of our understanding of quantum mechanics.”

G. NIENHUIS: STATE REDUCTION BY MEASUREMENTS WITH A NULL RESULT


“The probabilistic nature of quantum mechanics implies that identical systems that are described by identical state vectors can produce different measurement outcomes. This raises the natural question: what is the cause of these differences? Interpretations of quantum mechanics mainly differ in their answer to this question. Here we distinguish only two possible answers, which gives a rough but broadly accepted first classification in the possible points of view.
The modest and wise answer to the question for the unknown causes of differences in measurement results is simply: These differences are caused by something unknown. This reflects the view of some of the greatest among the founders of quantum mechanics, such as Schrödinger, Einstein, De Broglie and Bohm. It regards the probabilistic nature of quantum mechanics as arising from uncertainty about the actual state of the system that is described by a state vector. The differences in measurement results are viewed as reflecting hidden differences in two systems with the same state vector. The existence of unknown causes for the quantum indeterminacy that is postulated here would imply that quantum mechanics is incomplete, which leaves room for the exploration of various kinds of hidden variables. This view allows one to maintain that the outcome of a measurement reflects a property that the system already had before the measurement. In this sense, this view may be termed realistic.

The main alternative answer to the question as to the causes of different measurement outcomes is best summarized by the reply: There is nothing that causes these differences. This reflects the view of Bohr and Heisenberg, and forms the basis of what is now termed the Copenhagen interpretation of quantum mechanics. It re- stores the completeness of quantum mechanics, but the price is non-negligible. When one holds this view, one can no longer insist that the outcome of a measurement reflects a property that the system had before and independent of the measurement. After all, the same system having the same properties could have produced a different outcome. Therefore the measurement result is fundamentally undetermined prior to the measurement. According to this interpretation, the probabilistic nature of quantum mechanics does not arise from a lack of knowledge. Uncertainty is replaced by indeterminacy. Presently, this view of quantum mechanics is the most widely accepted among physicists, even though differences remain in the precise wording.
The central problem in these considerations is the role of the measurement. In textbook quantum mechanics, it is normally stated that an observable quantity corresponds to a Hermitian operator Qˆ on state space, with eigenvectors |φn) and eigenvalues qn, so that Qˆ|φn ) = qn|φn ). When the state of the system is described by the normalized state vector |&#968, a measurement produces the eigenvalue qn with probability pn = |(ψ|φn )| , provided that the eigenstates |φn ) are normalized. After a measurement with this outcome, the state of the system is described by the eigenvector |φn), which replaces the original state |&#968. Here it is tacitly assumed that a measurement is instantaneous, and has no time duration.”

D. DIEKS: PROBABILITY IN NON-COLLAPSE INTERPRETATIONS OFQUANTUM MECHANICS

“Our task in non-collapse interpretations is therefore to endow Hilbert space, equipped with an exclusively unitary time evolution, with physical meaning. We need interpretational rules that tell us how this mathematical formalism relates to physical reality. To this end, we can safely use a number of the usual interpretative principles of quantum mechanics that have proved their mettle; in particular the one saying that physical quantities are represented by hermitian operators (observables). But we cannot accept everything from standard textbook interpretations. In particular, since superpositions are always maintained according to the non-collapse scheme, even in measurement interactions, we cannot assume that observables can only have a definite value if the state is an eigenstate of the observable in question. We want to be able to say, for example, that Schrödinger’s cat is either dead or alive in spite of the fact that the total state is a superposition of eigenstates corresponding to `dead' and `alive', respectively.
An important question thus becomes: which physical quantities—represented by hermitian operators, observables—can be assigned a definite value, when it is given that the physical system is represented by a particular state in Hilbert space. An answer to this question is needed in order to make it possible to define events, physical occurrences, to which probabilities can be assigned.”

 

[LegionOnomaMoi]

The final set for now. A few notes:
1) all italics from above and in this post are in originals. I have not added any emphases.
2) The first post was, as I said, a single description that was a decent description of some key issues. The second was similar in that all quotes were from the same source, but represented different views on the theme of the conference.
3) This post contains three sources, each quote addressing a separate issue.
- the 1st source addresses the way in which the quantum state contains all information about the system in it.
- The 2n is a brief and (deliberately) less radical comparison between classical states, systems, and measurements, and those in QM.
-The 3rd offers what I believe to be a bit overstated if one restricts one's view to those who regularly or solely work use QM formalisms for experimental quantum physics. However, I would argue that it explains more general views within the community of scientists (from nanotechnology and microsystems to materials science and atomic manipulation). First, because having talked to or read or contacted such scientists, I have found that most of this admittedly small sample argue that there most quantum physicists agree on X interpretation. However, what X is can be radically different. Second, because it seems to match the literature. That is, even for those who state unequivocally that QM is X, there are at least as many who disagree and plenty who don't seem to sure or are even explicit about being unsure.

"2.1.2 The Probabilistic Nature of Quantum States
In view of the properties of quantum states discussed in the preceding section, it has often been argued that these states represent only “potentialities” for the various observed “classical” states. At the same time, however, it is important to emphasize that (according to our current knowledge) quantum states represent a complete description of a quantum system, i.e., the quantum state encapsulates all there is to say about the physical state of the system. Yet, in general quantum states do not tell us which particular outcome will be obtained in a measurement but only the probabilities of the various possible outcomes. This seemingly intrinsic probabilistic character of quantum mechanics is one of the central features distinguishing this theory from classical physics. In an experimental situation, the probabilistic aspect is represented by the fact that, if we measure the same physical quantity on a collection of systems all prepared in exactly the same quantum state, we will in general obtain a set of different outcomes.
As is well known, throughout his life Einstein remained reluctant to accept this apparent intrinsic randomness of nature, as captured in his famous slogan that “God does not play dice with the universe.” This discomfort has been shared by others, who have sought a way out by suggesting that quantum mechanics does not constitute a complete theory, in the sense that the quantum state does not suffice to completely specify the physical state of a system. Thus, an ensemble of “identically prepared systems” would not actually represent a collection of physically identical systems. While each system in the collection would be described by the same quantum state, the “complete state” of each system, which determines the outcomes of all possible measurements on each individual system, would not be the same for every member in the ensemble."
Schlosshauer, M. A. (2007). Decoherence and the quantum-to-classical transition. Springer Verlag

“Recall that a quantum measurement is an irreversible process that transforms quantum information to classical information and that there is a strong coupling between the system being measured and the measuring system. The measurements postulate tells us that the outcome of a measurement of an observable, A, of a quantum system is an eigenvalue of the self-adjoint operator, A, associated with the measurement of the observable...
In classical physics there is an unambiguous distinction between a system and the measuring instrument. Also, a description of the system developed as a result of measurements does not depend on a measurement of the system in the same state at a later point in time; thus, we have reasons to believe that the description of a classical system is objective.
From the inception of quantum mechanics, the concept of “measurement” and the relationship between the outcome of the measurement and our knowledge of the state of the quantum system prior, during, and after the measurement proved to be intensely controversial.” P. 134

Marinescu, D. C. & Marinescu, G. M. (2012) Classical and Quantum Information. Amsterdam: Academic Press.

“The advent of Quantum Mechanics has created a puzzling and, in fact, unique situation in physics. On the one hand this theory turned out to be enormously successful as a framework for the explanation of the behavior of matter at all scales—from the level of elementary particles, atoms and molecules to the world of macroscopic and even cosmic phenomena; on the other hand, researchers have not been able, in more than eight decades, to reach a consensus on its interpretation. There is not even an agreement over the status and significance of such strange, uniquely quantum features as incommensurability, indeterminacy, indeterminism, and non-locality. Nor is it considered established whether the so-called quantum measurement problem or the classical limit problem are actually conceptual problems or are instead artifacts of some particular choices of interpretation…

Many physicists now adopt a pragmatic double approach: they practice a realist outlook for the purposes of heuristic explorations of new models and the discussion of experiments, using intuitive pictures of individual (sub)atomic objects; but when challenged, they only admit to the minimal probabilistic or statistical interpretation of Quantum Mechanics."

Busch, P. & Jaeger, G. (2010). Unsharp Quantum Reality. Found Phys 40: 1341–1367

 

[PolyHedral]

It is simply a fact that "the state" contains all the information simply because we say so and because from a statistical point of view it works. But if we assume it works because of the statistical success then we're acknowledging we didn't have the information we claim, and if we don't acknowledge this than we have no reason to claim that the ket represents the state in the manner claimed.

I'm not following. The sentence "if we assume it works because of the statistical success then we're acknowledging we didn't have the information we claim" would only appear to be true if we assume that reality is deterministic.

 

[LegionOnomaMoi]

I'm not following. The sentence "if we assume it works because of the statistical success then we're acknowledging we didn't have the information we claim" would only appear to be true if we assume that reality is deterministic.

You can't have statistical determinism (I realize that statistical mechanics deals with deterministic systems, but it does by treating them as not deterministic in order to simplify).

A statistically determined system entails a deterministic probability function. It's like saying this is a determinism: "if I draw a card from this deck, there is a 1 in 52 chance I'll get the ace of spades". Well, great, but the fact that you have those chances only determine your chances and determinism is about outcomes.

Let's assume we have a normal and randomly arranged deck of cards ("random" in the colloquial sense; let's avoid introducing whether Martin-Löf randomness is really random compared to other definitions). All of our knowledge about the system can be expressed in terms of probabilities: I'm more likely to get a number card than a "face" card, more likely to get a face card than an ace, equally likely to get any one of the 4 suits, etc.

This complete knowledge, however, is only a way to relate what I have to start (pretty limited knowledge) with a complete knowledge about the probability of drawing individual or sets of cards. Determinism would be the chances that, given all the cards are face up and I see an ace of spades, when I pick it up it will be the ace of spades.

For quantum systems, complete knowledge is the same: it is a complete knowledge that, given I've prepared X system, when I measure I'll get Y result with Z probability.

 

[PolyHedral]

If you have a quantum-shuffled deck of cards, then we're saying that the

superposition you get is all the information you can possibly have about the deck. When you compute probabilities, this is correct and we can say it's0 correct because of its statistical sucess in predicting the outcomes of drawing one card off the top.

Why does that require admitting that we don't know something about the deck? What don't we know?


Also, if we then draw a card from the deck, what's so impossible about the player superpoisitioning into 52 orthogonal states? Answer in your own words, please.

 

[idav]

Also, if we then draw a card from the deck, what's so impossible about the player superpoisitioning into 52 orthogonal states? Answer in your own words, please.

Quantum poker anyone?

 

[LegionOnomaMoi]

If you have a quantum-shuffled deck of cards, then we're saying that the

superposition you get is all the information you can possibly have about the deck.

Whatever a quantum-shuffled deck might be (and I agree with idav here on playing some poker), the formula you have doesn't represent anything:

You've summed 52 probability coefficients and pulled out a constant that looks like you've assumed each card has a 1/2 spin, but instead of using 1/ 2(^-2) or one over the square root of 2, you've pulled out the 1/2 and inserted what might be the mass m in the Klein-Gordon equation or h-bar in some Hamiltonian formulation but inserted the number of card in each suit and taken its square root multiplied by 1/2.

When you compute probabilities, this is correct and we can say it's0 correct because of its statistical sucess in predicting the outcomes of drawing one card off the top.

How on earth can it be correct when you have a coefficient you're summing 52 times and you don't have a number their? So you start at I= 1 and add i2 getting...(are we ensuring orthogonal states of Hilbert's card deck?) ? And when you've finally gotten to n (52) the total sum is 0 because for some reason you've decided that a linear combination of identical states results in the same 0 value you'd get by summing two orthogonal pure states.

Why does that require admitting that we don't know something about the deck? What don't we know?

Well, for starters, anything about what value we should multiply the expression to the right of the summation symbol. For this set of 52 (just like any finite set of pure states) we should have a summation of 52 projectors (corresponding to each pure state) and a value multiplied for each summation such that the summation of these values is equal to one (a normalized mixed state). However, now that we have a mixed state, in general we have infinitely many decompositions.

Also, if we then draw a card from the deck, what's so impossible about the player superpoisitioning into 52 orthogonal states? Answer in your own words, please.

If we have just 2 orthogonal (and normalized) pure state vectors, we have nothing. That is, as I've been saying the entire time, we're describing a situation that has no outcomes whatsoever, because we haven't had any measurement. Once we do, though, even just the projection of these two state vectors does not have a uniquely determined outcome. We now have a mixed state (a convex combination of 2 pure states). And you want to have add another orthogonal state. That's terrific. Only we don't even know if we need this (why do we assume we don't have the necessary eigenstate such that we don't need orthogonality to ensure particular eigenvalues?), let alone how it could be done. Because drawing cards from a deck is a measurement, and while we could describe (all at once) something like the probability of what states we'd get for mixing 52 superposition states at once, but you aren't doing that. I don't know what it is you are doing, but my answer would be "because you've confused several things, but in particular have conflated "measurement" (drawing a card) with the state vector.

 

[idav]

How is the probability of the deck of cards different in a quantum state? It is a 1 in 52 chance of picking any card. All 52 cards are possible but there will only be one choice. The randomness of QM is interesting but what is driving this randomness, for a regular deck of cards it is classical physics.