II  INTERPRETATIONS

A.  Copenhagen interpretation

[Bohr 28, 34, 35 a, b, 39, 48, 49, 58 a, b, 63, 86, 96, 98] ([Bohr 58 b] was regarded by Bohr as his clearest presentation of the observational situation in QM. In it he asserts that QM cannot exist without classical mechanics: The classical realm is an essential part of any proper measurement, that is, a measurement whose results can be communicated in plain language. The wave function represents, in Bohr's words, "a purely symbolic procedure, the unambiguous physical interpretation of which in the last resort requires a reference to a complete experimental arrangement"), [Heisenberg 27, 30, 55 a, b, 58, 95] ([Heisenberg 55 a] is perhaps Heisenberg's most important and complete statement of his views: The wave function is "objective" but it is not "real", the cut between quantum and classical realms cannot be pushed so far that the entire compound system, including the observing apparatus, is cut off from the rest of the universe. A connection with the external world is essential. Stapp points out in [Stapp 72] that "Heisenberg's writings are more direct [than Bohr's]. But his way of speaking suggests a subjective interpretation that appears quite contrary to the apparent intention of Bohr". See also more precise differences between Bohr and Heisenberg's writings pointed out in [DeWitt-Graham 71]), [Fock 31] (textbook), [Landau-Lifshitz 48] (textbook), [Bohm 51] (textbook), [Hanson 59], [Stapp 72] (this reference is described in [Ballentine 87 a], p. 788 as follows: `In attempting to save "the Copenhagen interpretation" the author radically revises what is often, rightly or wrongly, understood by that term. That interpretation in which Von Neumann's "reduction" of the state vector in measurement forms the core is rejected, as are Heisenberg's subjectivistic statements. The very "pragmatic" (one could also say "instrumentalist") aspect of the interpretation is emphasized.'), [Faye 91] (on Bohr's interpretation of QM), [Zeilinger 96 b] ("It is suggested that the objective randomness of the individual quantum event is a necessity of a description of the world (...). It is also suggested that the austerity of the Copenhagen interpretation should serve as a guiding principle in a search for deeper understanding."), [Zeilinger 99 a] (the quotations are not in their original order, and some italics are mine: "We have knowledge, i.e., information, of an object only through observation (...). Any physical object can be described by a set of true propositions (...). [B]y proposition we mean something which can be verified directly by experiment (...). In order to analyze the information content of elementary systems, we (...) decompose a system (...) into constituent systems (...). [E]ach such constituent systems will be represented by fewer propositions. How far, then, can this process of subdividing a system go? (...). [T]he limit is reached when an individual system finally represents the truth value to one single proposition only. Such a system we call an elementary system. We thus suggest a principle of quantization of information as follows: An elementary system represents the truth value of one proposition. [This is what Zeilinger proposes as the foundational principle for quantum mechanics. He says that he personally prefers the Copenhagen interpretation because of its extreme austerity and clarity. However, the purpose of this paper is to attempt to go significantly beyond previous interpretations] (...). The spin of [a spin-1/2] (...) particle carries the answer to one question only, namely, the question What is its spin along the z-axis? (...). Since this is the only information the spin carries, measurement along any other direction must necessarily contain an element of randomness (...). We have thus found a reason for the irreducible randomness in quantum measurement. It is the simple fact that an elementary system cannot carry enough information to provide definite answers to all questions that could be asked experimentally (...). [After the measurement, t]he new information the system now represents has been spontaneously created in the measurement itself (...). [The information carried by composite systems can be distributed in different ways: E]ntanglement results if all possible information is exhausted in specifying joint (...) [true propositions] of the constituents". See ii G), [Fuchs-Peres 00 a, b] (quantum theory needs no "interpretation").

B.  De Broglie's "pilot wave" and Bohm's "causal" interpretations

1.  General

[Bohm 52], [de Broglie 60], [Goldberg-Schey-Schwartz 67] (computer-generated motion pictures of one-dimensional quantum-mechanical transmission and reflection phenomena), [Philippidis-Dewdney-Hiley 79] (the quantum potential and the ensemble of particle trajectories are computed and illustrated for the two-slit interference pattern), [Bell 82], [Bohm-Hiley 82, 89], [Dewdney-Hiley 82], [Dewdney-Holland-Kyprianidis 86, 87], [Bohm-Hiley 85], [Bohm-Hiley-Kaloyerou 87], [Dewdney 87, 92, 93], [Dewdney-Holland-Kyprianidis-Vigier 88], [Holland 88, 92], [Englert-Scully-Süssmann-Walther 93 a, b] ([Dürr-Fusseder-Goldstein-Zanghì 93]) [Albert 92] (Chap. 7), [Dewdney-Malik 93], [Bohm-Hiley 93] (book), [Holland 93] (book), [Albert 94], [Pagonis-Clifton 95], [Cohen-Hiley 95 b] (comparison between Bohmian mechanics, standard QM and consistent histories interpretation), [Mackman-Squires 95] (retarded Bohm model), [Berndl-Dürr-Goldstein-Zanghì 96], [Goldstein 96, 99], [Cushing-Fine-Goldstein 96] (collective book), [García de Polavieja 96 a, b, 97 a, b] (causal interpretation in phase space derived from the coherent space representation of the Schrödinger equation), [Kent 96 b] (consistent histories and Bohmian mechanics), [Rice 97 a], [Hiley 97], [Deotto-Ghirardi 98] (there are infinite theories similar to Bohm's -with trajectories- which reproduce the predictions of QM), [Dickson 98], [Terra Cunha 98], [Wiseman 98 a] (Bohmian analysis of momentum transfer in welcher Weg measurements), [Blaut-Kowalski Glikman 98], [Brown-Sjöqvist-Bacciagaluppi 99] (on identical particles in de Broglie-Bohm's theory), [Leavens-Sala Mayato 99], [Griffiths 99 b] (Bohmian mechanics and consistent histories), [Maroney-Hiley 99] (teleportation understood through the Bohm interpretation), [Belousek 00 b], [Neumaier 00] (Bohmian mechanics contradict quantum mechanics), [Ghose 00 a, c, d, 01 b] (incompatibility of the de Broglie-Bohm theory with quantum mechanics), [Marchildon 00] (no contradictions between Bohmian and quantum mechanics), [Barrett 00] (surreal trajectories), [Nogami-Toyama-Dijk 00], [Shifren-Akis-Ferry 00], [Ghose 00 c] (experiment to distinguish between de Broglie-Bohm and standard quantum mechanics), [Golshani-Akhavan 00, 01 a, b, c] (experiment which distinguishes between the standard and Bohmian quantum mechanics), [Hiley-Maroney 00] (consistent histories and the Bohm approach), [Hiley-Callaghan-Maroney 00], [Gr"ossing 00] (book; extension of the de Broglie-Bohm interpretation into the relativistic regime for the Klein-Gordon case), [Dürr 01] (book), [Marchildon 01] (on Bohmian trajectories in two-particle interference devices), [John 01 a, b] (modified de Broglie-Bohm theory closer to classical Hamilton-Jacobi theory), [Bandyopadhyay-Majumdar-Home 01], [Struyve-De Baere 01], [Ghose-Majumdar-Guha-Sau 01] (Bohmian trajectories for photons), [Shojai-Shojai 01] (problems raised by the relativistic form of de Broglie-Bohm theory), [Allori-Zanghì 01 a], (de Broglie's pilot wave theory for the Klein-Gordon equation:) [Horton-Dewdney 01 b], [Horton-Dewdney-Ne'eman 02]; [Ghose-Samal-Datta 02] (Bohmian picture of Rydberg atoms), [Feligioni-Panella-Srivastava-Widom 02], [Grübl-Rheinberger 02], [Dewdney-Horton 02] (relativistically invariant extension), [Allori-Dürr-Goldstein-Zanghì 02], [Bacciagaluppi 03] (derivation of the symmetry postulates for identical particles from pilot-wave theories).

2.  Tunneling times in Bohmian mechanics

[Hauge-Stovneng 89] (TT: A critical review), [Spiller-Clarck-Prance-Prance 90], [Olkhovsky-Recami 92] (recent developments in TT), [Leavens 93, 95, 96, 98], [Leavens-Aers 93], [Landauer-Martin 94] (review on TT), [Leavens-Iannaccone-McKinnon 95], [McKinnon-Leavens 95], [Cushing 95 a] (are quantum TT a crucial test for the causal program?; reply: [Bedard 97]), [Oriols-Martín-Suñe 96] (implications of the noncrossing property of Bohm trajectories in one-dimensional tunneling configurations), [Abolhasani-Golshani 00] (TT in the Copenhagen interpretation; due to experimental limitations, Bohmian mechanics leads to same TT), [Majumdar-Home 00] (the time of decay measurement in the Bohm model), [Ruseckas 01] (tunneling time determination in standard QM), [Stomphorst 01, 02], [Chuprikov 01].

C.  "Relative state", "many worlds", and "many minds" interpretations

[Everett 57 a, b, 63], [Wheeler 57], [DeWitt 68, 70, 71 b], [Cooper-Van Vechten 69] (proof of the unobservability of the splits), [DeWitt-Graham 73], [Graham 71], [Ballentine 73] (the definition of the "branches" is dependent upon the choice of representation; the assumptions of the many-worlds interpretation are neither necessary nor sufficient to derive the Born statistical formula), [Clarke 74] (some additional structures must be added in order to determine which states will determine the "branching"), [Healey 84] (critical discussion), [Geroch 84], [Whitaker 85], [Deutsch 85 a, 86] (testable split observer experiment), [Home-Whitaker 87] (quantum Zeno effect in the many-worlds interpretation), [Tipler 86], [Squires 87 a, b] (the "many-views" interpretation), [Whitaker 89] (on Squires' many-views interpretation), [Albert-Loewer 88], [Ben Dov 90 b], [Kent 90], [Albert-Loewer 91 b] (many minds interpretation), [Vaidman 96 c, 01 d], [Lockwood 96] (many minds), [Cassinello-Sánchez Gómez 96] (and [Cassinello 96], impossibility of deriving the probabilistic postulate using a frequency analysis of infinite copies of an individual system), [Deutsch 97] (popular review), [Schafir 98] (Hardy's argument in the many-worlds and in the consistent histories interpretations), [Dickson 98], [Tegmark 98] (many worlds or many words?), [Barrett 99 a], [Wallace 01 b], [Deutsch 01] (structure of the multiverse), [Butterfield 01], [Bacciagaluppi 01 b], [Hewitt-Horsman 03] (status of the uncertainty relations in the many worlds interpretation).

D.  Interpretations with explicit collapse or dynamical reduction theories (spontaneous localization, nonlinear terms in Schrödinger equation, stochastic theories)

[de Broglie 56], [Bohm-Bub 66 a], [Nelson 66, 67, 85], [Pearle 76, 79, 82, 85, 86 a, b, c, 89, 90, 91, 92, 93, 99 b, 00], [Bialynicki Birula-Mycielski 76] (add a nonlinear term to the Schrödinger equation in order to keep wave packets from spreading beyond any limit. Experiments with neutrons, [Shull-Atwood-Arthur-Horne 80] and [Gähler-Klein-Zeilinger 81], have resulted in such small upper limits for a possible nonlinear term of a kind that some quantum features would survive in a macroscopic world), [Dohrn-Guerra 78], [Dohrn-Guerra-Ruggiero 79] (relativistic Nelson stochastic model), [Davidson 79] (a generalization of the Fenyes-Nelson stochastic model), [Shimony 79] (proposed neutron interferometer test of some nonlinear variants), [Bell 84], [Gisin 84 a, b, 89], [Ghirardi-Rimini-Weber 86, 87, 88], [Werner 86], [Primas 90 b], [Ghirardi-Pearle-Rimini 90], [Ghirardi-Grassi-Pearle 90 a, b], [Weinberg 89 a, b, c, d] (nonlinear variant), [Peres 89 d] (nonlinear variants violate the second law of thermodynamics), (in Weinberg's attempt faster than light communication is possible:) [Gisin 90], [Polchinski 91], [Mielnik 00]; [Bollinger-Heinzen-Itano-(+2) 89] (tests Weinberg's variant), [Wódkiewicz-Scully 90]), [Ghirardi 91, 95, 96], [Jordan 93 b] (fixes the Weinberg variant), [Ghirardi-Weber 97], [Squires 92 b] (if the collapse is a physical phenomenon it would be possible to measure its velocity), [Gisin-Percival 92, 93 a, b, c], [Pearle-Squires 94] (nucleon decay experimental results could be considered to rule out the collapse models, and support a version in which the rate of collapse is proportional to the mass), [Pearle 97 a] explicit model of collapse, "true collapse", versus interpretations with decoherence, "false collapse"), [Pearle 97 b] (review of Pearle's own contributions), [Bacciagaluppi 98 b] (Nelsonian mechanics), [Santos-Escobar 98], [Ghirardi-Bassi 99], [Pearle-Ring-Collar-Avignone 99], [Pavon 99] (derivation of the wave function collapse in the context of Nelson's stochastic mechanics), [Adler-Brun 01] (generalized stochastic Schrödinger equations for state vector collapse), [Brody-Hughston 01] (experimental tests for stochastic reduction models).

E.  Statistical (or ensemble) interpretation

[Ballentine 70, 72, 86, 88 a, 90 a, b, 95 a, 96, 98], [Peres 84 a, 93], [Home-Whitaker 92].

F.  "Modal" interpretations

[van Fraassen 72, 79, 81, 91 a, b], [Cartwright 74], [Kochen 85], [Healey 89, 93, 98 a], [Dieks 89, 94, 95], [Lahti 90] (polar decomposition and measurement), [Albert-Loewer 91 a] (the Kochen-Healey-Dieks interpretations do not solve the measurement problem), [Arntzenius 90], [Albert 92] (appendix), [Elby 93 a], [Bub 93], [Albert-Loewer 93], [Elby-Bub 94], [Dickson 94 a, 95 a, 96 b, 98], [Vermaas-Dieks 95] (generalization of the MI to arbitrary density operators), [Bub 95], [Cassinelli-Lahti 95], [Clifton 95 b, c, d, e, 96, 00 b], [Bacciagaluppi 95, 96, 98 a, 00], [Bacciagaluppi-Hemmo 96, 98 a, 98 b], [Vermaas 96], [Vermaas 97, 99 a] (no-go theorems for MI), [Zimba-Clifton 98], [Busch 98 a], [Dieks-Vermaas 98], [Dickson-Clifton 98] (collective book), [Bacciagaluppi-Dickson 99] (dynamics for MI), [Dieks 00] (consistent histories and relativistic invariance in the MI), [Spekkens-Sipe 01 a, b], [Bacciagaluppi 01 a] (book), [Gambetta-Wiseman 03 b] (modal dynamics extended to include POVMs).

G.  "It from bit"

[Wheeler 78, 91, 95] (the measuring process creates a "reality" that did not exist objectively before the intervention), [Davies-Brown 86] ("the game of the 20 questions", pp. 23-24 [pp. 38-39 in the Spanish version], Chap. 4), [Wheeler-Ford 98] ([p. 338:] "A measurement, in this context, is an irreversible act in which uncertainty collapses to certainty. It is the link between the quantum and the classical worlds, the point where what might happen (...) is replaced by what does happen (...)". [p. 338:] "No elementary phenomenon, he [Bohr] said, is a phenomenon until it is a registered phenomenon". [pp. 339-340:] "Measurement, the act of turning potentiality into actuality, is an act of choice, choice among possible outcomes". [pp. 340-341:] "Trying to wrap my brain around this idea of information theory as the basis of existence, I came up with the phrase "it from bit." The universe an all that it contains ("it") may arise from the myriad yes-no choices of measurement (the "bits"). Niels Bohr wrestled for most of his life with the question of how acts of measurement (or "registration") may affect reality. It is registration (...) that changes potentiality into actuality. I build only a little on the structure of Bohr's thinking when I suggest that we may never understand this strange thing, the quantum, until we understand how information may underlie reality. Information may not be just what we learn about the world. It may be what makes the world.
An example of the idea of it from bit: When a photon is absorbed, and thereby "measured"-until its absortion, it had no true reality-an unsplittable bit of information is added to what we know about the word, and, at the same time that bit of information determines the structure of one small part of the world. It creates the reality of the time and place of that photon's interaction").

H.  "Consistent histories" (or "decoherent histories")

[Griffiths 84, 86 a, b, c, 87, 93 a, b, 95, 96, 97, 98 a, b, c, 99, 01], [Omnès 88 a, 88 b, 88 c, 89, 90 a, b, 91, 92, 94 a, b, 95, 97, 99 a, b, 01, 02], [Gell-Mann-Hartle 90 a, 90 b, 91, 93, 94], [Gell-Mann 94] (Chap. 11), [Halliwell 95] (review), [Diósi-Gisin-Halliwell-Percival 95], [Goldstein-Page 95], [Cohen-Hiley 95 b] (in comparation with standard QM and causal de Broglie-Bohm's interpretation), [Cohen 95] (CH in pre- and post-selected systems), [Dowker-Kent 95, 96], [Rudolph 96] (source of critical references), [Kent 96 a, b, 97 a, 98 b, c, 00 b] (CH approach allows contrary inferences to be made from the same data), [Isham-Linden-Savvidou-Schreckenberg 97], [Griffiths-Hartle 98], [Brun 98], [Schafir 98 a] (Hardy's argument in the many-world and CH interpretations), [Schafir 98 b], [Halliwell 98, 99 a, b, 00, 01, 03 a, b], [Dass-Joglekar 98], [Peruzzi-Rimini 98] (incompatible and contradictory retrodictions in the CH approach), [Nisticò 99] (consistency conditions for probabilities of quantum histories), [Rudolph 99] (CH and POV measurements), [Stapp 99 c] (nonlocality, counterfactuals, and CH), [Bassi-Ghirardi 99 a, 00 a, b] (decoherent histories description of reality cannot be considered satisfactory), [Griffiths-Omnès 99], [Griffiths 00 a, b] (there is no conflict between CH and Bell, and Kochen-Specker theorems), [Dieks 00] (CH and relativistic invariance in the modal interpretation), [Egusquiza-Muga 00] (CH and quantum Zeno effect), [Clarke 01 a, b], [Hiley-Maroney 00] (CH and the Bohm approach), [Sokolovski-Liu 01], [Raptis 01], [Nisticò-Beneduci 02], [Bar-Horwitz 02], [Brun 03], [Nisticò 03].

I.  Decoherence and environment induced superselection

[Simonius 78] (first explicit treatment of decoherence due to the environment and the ensuing symmetry breaking and "blocking" of otherwise not stable states), [Zurek 81 a, 82, 91 c, 93, 97, 98 a, 00 b, 01, 02, 03 b, c], [Joos-Zeh 85], [Zurek-Paz 93 a, b, c], [Wightman 95] (superselection rules), [Elby 94 a, b], [Giulini-Kiefer-Zeh 95] (symmetries, superselection rules, and decoherence), [Giulini-Joos-Kiefer-(+3) 96] (review, almost exhaustive source of references, [Davidovich-Brune-Raimond-Haroche 96], [Brune-Hagley-Dreyer-(+5) 96] (experiment, see also [Haroche-Raimond-Brune 97]), [Zeh 97, 98, 99], [Yam 97] (non-technical review), [Dugić 98] (necessary conditions for the occurrence of the "environment-induced" superselection rules), [Habib-Shizume-Zurek 98] (decoherence, chaos and the correspondence principle), [Kiefer-Joos 98] (decoherence: Concepts and examples), [Paz-Zurek 99] (environment induced superselection of energy eigenstates), [Giulini 99, 00], [Joos 99], [Bene-Borsanyi 00] (decoherence within a single atom), [Paz-Zurek 00], [Anastopoulos 00] (frequently asked questions about decoherence), [Kleckner-Ron 01], [Braun-Haake-Strunz 01], [Eisert-Plenio 02 b] (quantum Brownian motion does not necessarily create entanglement between the system and its environment; the joint state of the system and its environment may be separable at all times).

J.  Time symetric formalism, pre- and post-selected systems, "weak" measurements

[Aharonov-Bergman-Lebowitz 64], [Albert-Aharonov-D'Amato 85], [Bub-Brown 86] (comment: [Albert-Aharonov-D'Amato 86]), [Vaidman 87, 96 d, 98 a, b, e, 99 a, c, d, 03 b], [Vaidman-Aharonov-Albert 87], [Aharonov-Albert-Casher-Vaidman 87], [Busch 88], [Aharonov-Albert-Vaidman 88] (comments: [Leggett 89], [Peres 89 a]; reply: [Aharonov-Vaidman 89]), [Golub-Gähler 89], [Ben Menahem 89], [Duck-Stevenson-Sudarshan 89], [Sharp-Shanks 89], [Aharonov-Vaidman 90, 91], [Knight-Vaidman 90], [Hu 90], [Zachar-Alter 91], [Sharp-Shanks 93] (the rise and fall of time-symmetrized quantum mechanics; counterfactual interpretation of the ABL rule leads to results that disagree with standard QM; see also [Cohen 95]), [Peres 94 a, 95 d] (comment: [Aharonov-Vaidman 95]), [Mermin 95 b] (BKS theorem puts limits to the "magic" of retrodiction), [Cohen 95] (counterfactual use of the ABL rule), [Cohen 98 a], [Reznik-Aharonov 95], [Herbut 96], [Miller 96], [Kastner 98 a, b, 99 a, b, c, 02, 03], [Lloyd-Slotine 99], [Metzger 00], [Mohrhoff 00 d], [Aharonov-Englert 01], [Englert-Aharonov 01], [Aharonov-Botero-Popescu-(+2) 01] (Hardy's paradox and weak values), [Atmanspacher-Römer-Walach 02].

K.  The transactional interpretation

[Cramer 80, 86, 88].

L.  The Ithaca interpretation: Correlations without correlata

[Mermin 98 a, b, 99 a], [Cabello 99 a, c], [Jordan 99], [McCall 01], [Fuchs 03 a] (Chaps. 18, 33), [Plotnitsky 03].