An interpretation of quantum mechanics is
an attempt to explain how the mathematical
theory of quantum mechanics corresponds to
reality. Although quantum mechanics has held
up to rigorous and extremely precise tests
in an extraordinarily broad range of experiments,
there exist a number of contending schools
of thought over their interpretation. These
views differ on such fundamental questions
as whether quantum mechanics is deterministic
or random, which elements of quantum mechanics
can be considered "real", and what is the
nature of measurement, among other matters.
Despite nearly a century of debate and experiment,
some physicists and philosophers of physics
continue to disagree and actively contest
the interpretation.
== History ==
The definition of quantum theorists' terms,
such as wave functions and matrix mechanics,
progressed through many stages. For instance,
Erwin Schrödinger originally viewed the electron's
wave function as its charge density smeared
across the field, whereas Max Born reinterpreted
the absolute square value of the wave function
as the electron's probability density distributed
across the field.
Although the Copenhagen interpretation was
originally most popular, quantum decoherence
has gained popularity. Thus the many-worlds
interpretation has been gaining acceptance.
Moreover, the strictly formalist position,
shunning interpretation, has been challenged
by proposals for falsifiable experiments that
might one day distinguish among interpretations,
as by measuring an AI consciousness or via
quantum computing.As a rough guide development
of the mainstream view during the 1990s to
2000s, consider the "snapshot" of opinions
collected in a poll by Schlosshauer et al.
at the 2011 "Quantum Physics and the Nature
of Reality" conference of July 2011.
The authors reference a similarly informal
poll carried out by Max Tegmark at the "Fundamental
Problems in Quantum Theory" conference in
August 1997. The main conclusion of the authors
is that "the Copenhagen interpretation still
reigns supreme", receiving the most votes
in their poll (42%), besides the rise to mainstream
notability of the many-worlds interpretations:
"The Copenhagen interpretation still reigns
supreme here, especially if we lump it together
with intellectual offsprings such as information-based
interpretations and the Quantum Bayesian interpretation.
In Tegmark's poll, the Everett interpretation
received 17% of the vote, which is similar
to the number of votes (18%) in our poll."It
is noteworthy that only Cramer's transactional
interpretation, published in 1986, assigns
physical basis to Max Born's assertion that
the absolute square of the wave function is
a probability density.
== Nature ==
More or less, all interpretations of quantum
mechanics share two qualities:
They interpret a formalism—a set of equations
and principles to generate predictions via
input of initial conditions
They interpret a phenomenology—a set of
observations, including those obtained by
empirical research and those obtained informally,
such as humans' experience of an unequivocal
worldTwo qualities vary among interpretations:
Ontology—claims about what things, such
as categories and entities, exist in the world
Epistemology—claims about the possibility,
scope, and means toward relevant knowledge
of the worldIn philosophy of science, the
distinction of knowledge versus reality is
termed epistemic versus ontic. A general law
is a regularity of outcomes (epistemic), whereas
a causal mechanism may regulate the outcomes
(ontic). A phenomenon can receive interpretation
either ontic or epistemic. For instance, indeterminism
may be attributed to limitations of human
observation and perception (epistemic), or
may be explained as a real existing maybe
encoded in the universe (ontic). Confusing
the epistemic with the ontic, like if one
were to presume that a general law actually
"governs" outcomes—and that the statement
of a regularity has the role of a causal mechanism—is
a category mistake.
In a broad sense, scientific theory can be
viewed as offering scientific realism—approximately
true description or explanation of the natural
world—or might be perceived with antirealism.
A realist stance seeks the epistemic and the
ontic, whereas an antirealist stance seeks
epistemic but not the ontic. In the 20th century's
first half, antirealism was mainly logical
positivism, which sought to exclude unobservable
aspects of reality from scientific theory.
Since the 1950s, antirealism is more modest,
usually instrumentalism, permitting talk of
unobservable aspects, but ultimately discarding
the very question of realism and posing scientific
theory as a tool to help humans make predictions,
not to attain metaphysical understanding of
the world. The instrumentalist view is carried
by the famous quote of David Mermin, "Shut
up and calculate", often misattributed to
Richard Feynman.Other approaches to resolve
conceptual problems introduce new mathematical
formalism, and so propose alternative theories
with their interpretations. An example is
Bohmian mechanics, whose empirical equivalence
with the three standard formalisms—Schrödinger's
wave mechanics, Heisenberg's matrix mechanics,
and Feynman's path integral formalism—has
been demonstrated.
== Challenges ==
Abstract, mathematical nature of quantum field
theories: the mathematical structure of quantum
mechanics is mathematically abstract without
clear interpretation of its quantities.
Existence of apparently indeterministic and
irreversible processes: in classical field
theory, a physical property at a given location
in the field is readily derived. In most mathematical
formulations of quantum mechanics, measurement
is given a special role in the theory, as
it is the sole process that can cause a nonunitary,
irreversible evolution of the state.
Role of the observer in determining outcomes:
the Copenhagen Interpretation implies that
the wavefunction is a calculational tool,
and represents reality only immediately after
a measurement, perhaps performed by an observer;
Everettian interpretations grant that all
the possibilities can be real, and that the
process of measurement-type interactions cause
an effective branching process.
Classically unexpected correlations between
remote objects: entangled quantum systems,
as illustrated in the EPR paradox, obey statistics
that seem to violate principles of local causality.
Complementarity of proffered descriptions:
complementarity holds that no set of classical
physical concepts can simultaneously refer
to all properties of a quantum system. For
instance, wave description A and particulate
description B can each describe quantum system
S, but not simultaneously. This implies the
composition of physical properties of S does
not obey the rules of classical propositional
logic when using propositional connectives
(see "Quantum logic"). Like contextuality,
the "origin of complementarity lies in the
non-commutativity of operators" that describe
quantum objects (Omnès 1999).
Rapidly rising intricacy, far exceeding humans'
present calculational capacity, as a system's
size increases: since the state space of a
quantum system is exponential in the number
of subsystems, it is difficult to derive classical
approximations.
Contextual behaviour of systems locally: Quantum
contextuality demonstrates that classical
intuitions in which properties of a system
hold definite values, independent of the manner
of their measurement, fails even for local
systems. Also, physical principles such as
Leibnitz's Principle of the identity of indiscernibles
no longer apply in the quantum domain, signalling
that most classical intuitions may be incorrect
about the quantum world.
== Summaries ==
=== Classification adopted by Einstein ===
An interpretation (i.e. a semantic explanation
of the formal mathematics of quantum mechanics)
can be characterized by its treatment of certain
matters addressed by Einstein, such as:
Realism
Completeness
Local realism
DeterminismTo explain these properties, we
need to be more explicit about the kind of
picture an interpretation provides. To that
end we will regard an interpretation as a
correspondence between the elements of the
mathematical formalism M and the elements
of an interpreting structure I, where:
The mathematical formalism M consists of the
Hilbert space machinery of ket-vectors, self-adjoint
operators acting on the space of ket-vectors,
unitary time dependence of the ket-vectors,
and measurement operations. In this context
a measurement operation is a transformation
which turns a ket-vector into a probability
distribution (for a formalization of this
concept see quantum operations).
The interpreting structure I includes states,
transitions between states, measurement operations,
and possibly information about spatial extension
of these elements. A measurement operation
refers to an operation which returns a value
and might result in a system state change.
Spatial information would be exhibited by
states represented as functions on configuration
space. The transitions may be non-deterministic
or probabilistic or there may be infinitely
many states.The crucial aspect of an interpretation
is whether the elements of I are regarded
as physically real. Hence the bare instrumentalist
view of quantum mechanics outlined in the
previous section is not an interpretation
at all, for it makes no claims about elements
of physical reality.
The current usage of realism and completeness
originated in the 1935 paper in which Einstein
and others proposed the EPR paradox. In that
paper the authors proposed the concepts element
of reality and the completeness of a physical
theory. They characterised element of reality
as a quantity whose value can be predicted
with certainty before measuring or otherwise
disturbing it, and defined a complete physical
theory as one in which every element of physical
reality is accounted for by the theory. In
a semantic view of interpretation, an interpretation
is complete if every element of the interpreting
structure is present in the mathematics. Realism
is also a property of each of the elements
of the maths; an element is real if it corresponds
to something in the interpreting structure.
For example, in some interpretations of quantum
mechanics (such as the many-worlds interpretation)
the ket vector associated to the system state
is said to correspond to an element of physical
reality, while in other interpretations it
is not.
Determinism is a property characterizing state
changes due to the passage of time, namely
that the state at a future instant is a function
of the state in the present (see time evolution).
It may not always be clear whether a particular
interpretation is deterministic or not, as
there may not be a clear choice of a time
parameter. Moreover, a given theory may have
two interpretations, one of which is deterministic
and the other not.
Local realism has two aspects:
The value returned by a measurement corresponds
to the value of some function in the state
space. In other words, that value is an element
of reality;
The effects of measurement have a propagation
speed not exceeding some universal limit (e.g.
the speed of light). In order for this to
make sense, measurement operations in the
interpreting structure must be localized.A
precise formulation of local realism in terms
of a local hidden-variable theory was proposed
by John Bell.
Bell's theorem, combined with experimental
testing, restricts the kinds of properties
a quantum theory can have, the primary implication
being that quantum mechanics cannot satisfy
both the principle of locality and counterfactual
definiteness.
It should be noted that regardless of Einstein's
concerns about interpretation issues, Dirac
and other quantum notables embraced the technical
advances of the new theory while devoting
little or no attention to interpretational
aspects.
=== Copenhagen interpretation ===
The Copenhagen interpretation is the "standard"
interpretation of quantum mechanics formulated
by Niels Bohr and Werner Heisenberg while
collaborating in Copenhagen around 1927. Bohr
and Heisenberg extended the probabilistic
interpretation of the wavefunction proposed
originally by Max Born. The Copenhagen interpretation
rejects questions like "where was the particle
before I measured its position?" as meaningless.
The measurement process randomly picks out
exactly one of the many possibilities allowed
for by the state's wave function in a manner
consistent with the well-defined probabilities
that are assigned to each possible state.
According to the interpretation, the interaction
of an observer or apparatus that is external
to the quantum system is the cause of wave
function collapse, thus according to Paul
Davies, "reality is in the observations, not
in the electron". In general, after a measurement
(click of a Geiger counter or a trajectory
in a spark or bubble chamber) it ceases to
be relevant unless subsequent experimental
observations can be performed.
=== Many worlds ===
The many-worlds interpretation is an interpretation
of quantum mechanics in which a universal
wavefunction obeys the same deterministic,
reversible laws at all times; in particular
there is no (indeterministic and irreversible)
wavefunction collapse associated with measurement.
The phenomena associated with measurement
are claimed to be explained by decoherence,
which occurs when states interact with the
environment producing entanglement, repeatedly
"splitting" the universe into mutually unobservable
alternate histories—effectively distinct
universes within a greater multiverse.
=== Consistent histories ===
The consistent histories interpretation generalizes
the conventional Copenhagen interpretation
and attempts to provide a natural interpretation
of quantum cosmology. The theory is based
on a consistency criterion that allows the
history of a system to be described so that
the probabilities for each history obey the
additive rules of classical probability. It
is claimed to be consistent with the Schrödinger
equation.
According to this interpretation, the purpose
of a quantum-mechanical theory is to predict
the relative probabilities of various alternative
histories (for example, of a particle).
=== Ensemble interpretation ===
The ensemble interpretation, also called the
statistical interpretation, can be viewed
as a minimalist interpretation. That is, it
claims to make the fewest assumptions associated
with the standard mathematics. It takes the
statistical interpretation of Born to the
fullest extent. The interpretation states
that the wave function does not apply to an
individual system – for example, a single
particle – but is an abstract statistical
quantity that only applies to an ensemble
(a vast multitude) of similarly prepared systems
or particles. Probably the most notable supporter
of such an interpretation was Einstein:
The attempt to conceive the quantum-theoretical
description as the complete description of
the individual systems leads to unnatural
theoretical interpretations, which become
immediately unnecessary if one accepts the
interpretation that the description refers
to ensembles of systems and not to individual
systems.
The most prominent current advocate of the
ensemble interpretation is Leslie E. Ballentine,
professor at Simon Fraser University, author
of the graduate level text book Quantum Mechanics,
A Modern Development. An experiment illustrating
the ensemble interpretation is provided in
Akira Tonomura's Video clip 1. It is evident
from this double-slit experiment with an ensemble
of individual electrons that, since the quantum
mechanical wave function (absolutely squared)
describes the completed interference pattern,
it must describe an ensemble.
A new version of the ensemble interpretation
that relies on a reformulation of probability
theory was introduced by Raed Shaiia.
=== De Broglie–Bohm theory ===
The de Broglie–Bohm theory of quantum mechanics
(also known as the pilot wave theory) is a
theory by Louis de Broglie and extended later
by David Bohm to include measurements. Particles,
which always have positions, are guided by
the wavefunction. The wavefunction evolves
according to the Schrödinger wave equation,
and the wavefunction never collapses. The
theory takes place in a single space-time,
is non-local, and is deterministic. The simultaneous
determination of a particle's position and
velocity is subject to the usual uncertainty
principle constraint. The theory is considered
to be a hidden-variable theory, and by embracing
non-locality it satisfies Bell's inequality.
The measurement problem is resolved, since
the particles have definite positions at all
times. Collapse is explained as phenomenological.
=== Relational quantum mechanics ===
The essential idea behind relational quantum
mechanics, following the precedent of special
relativity, is that different observers may
give different accounts of the same series
of events: for example, to one observer at
a given point in time, a system may be in
a single, "collapsed" eigenstate, while to
another observer at the same time, it may
be in a superposition of two or more states.
Consequently, if quantum mechanics is to be
a complete theory, relational quantum mechanics
argues that the notion of "state" describes
not the observed system itself, but the relationship,
or correlation, between the system and its
observer(s). The state vector of conventional
quantum mechanics becomes a description of
the correlation of some degrees of freedom
in the observer, with respect to the observed
system. However, it is held by relational
quantum mechanics that this applies to all
physical objects, whether or not they are
conscious or macroscopic. Any "measurement
event" is seen simply as an ordinary physical
interaction, an establishment of the sort
of correlation discussed above. Thus the physical
content of the theory has to do not with objects
themselves, but the relations between them.An
independent relational approach to quantum
mechanics was developed in analogy with David
Bohm's elucidation of special relativity,
in which a detection event is regarded as
establishing a relationship between the quantized
field and the detector. The inherent ambiguity
associated with applying Heisenberg's uncertainty
principle is subsequently avoided.
=== Transactional interpretation ===
The transactional interpretation of quantum
mechanics (TIQM) by John G. Cramer is an interpretation
of quantum mechanics inspired by the Wheeler–Feynman
absorber theory. It describes the collapse
of the wave function as resulting from a time-symmetric
transaction between a possibility wave from
the source to the receiver (the wave function)
and a possibility wave from the receiver to
source (the complex conjugate of the wave
function). Since the possibility wave is collapsed
by interaction with the receiver, consciousness
plays no role in the theory, eliminating Schrödinger's
cat paradox. This interpretation of quantum
mechanics is unique in that it not only views
the wave function as a real entity, but the
complex conjugate of the wave function, which
appears in the Born rule for calculating the
expected value for an observable, as also
real.
=== Stochastic mechanics ===
An entirely classical derivation and interpretation
of Schrödinger's wave equation by analogy
with Brownian motion was suggested by Princeton
University professor Edward Nelson in 1966.
Similar considerations had previously been
published, for example by R. Fürth (1933),
I. Fényes (1952), and Walter Weizel (1953),
and are referenced in Nelson's paper. More
recent work on the stochastic interpretation
has been done by M. Pavon. An alternative
stochastic interpretation was developed by
Roumen Tsekov.
=== Objective collapse theories ===
Objective collapse theories differ from the
Copenhagen interpretation by regarding both
the wave function and the process of collapse
as ontologically objective (meaning these
exist and occur independent of the observer).
In objective theories, collapse occurs either
randomly ("spontaneous localization") or when
some physical threshold is reached, with observers
having no special role. Thus, objective-collapse
theories are realistic, indeterministic, no-hidden-variables
theories. Standard quantum mechanics does
not specify any mechanism of collapse; QM
would need to be extended if objective collapse
is correct. The requirement for an extension
to QM means that objective collapse is more
of a theory than an interpretation. Examples
include
the Ghirardi-Rimini-Weber theory
the Penrose interpretation.
the deterministic variant of an objective
collapse theory
=== Consciousness causes collapse (von Neumann–Wigner
interpretation) ===
In his treatise The Mathematical Foundations
of Quantum Mechanics, John von Neumann deeply
analyzed the so-called measurement problem.
He concluded that the entire physical universe
could be made subject to the Schrödinger
equation (the universal wave function). He
also described how measurement could cause
a collapse of the wave function. This point
of view was prominently expanded on by Eugene
Wigner, who argued that human experimenter
consciousness (or maybe even dog consciousness)
was critical for the collapse, but he later
abandoned this interpretation.Variations of
the consciousness causes collapse interpretation
include:
Subjective reduction research
This principle, that consciousness causes
the collapse, is the point of intersection
between quantum mechanics and the mind/body
problem; and researchers are working to detect
conscious events correlated with physical
events that, according to quantum theory,
should involve a wave function collapse; but,
thus far, results are inconclusive.Participatory
anthropic principle (PAP)
John Archibald Wheeler's participatory anthropic
principle says that consciousness plays some
role in bringing the universe into existence.Other
physicists have elaborated their own variations
of the consciousness causes collapse interpretation;
including:
Henry P. Stapp (Mindful Universe: Quantum
Mechanics and the Participating Observer)
Bruce Rosenblum and Fred Kuttner (Quantum
Enigma: Physics Encounters Consciousness)
Amit Goswami (The Self-Aware Universe)
=== Many minds ===
The many-minds interpretation of quantum mechanics
extends the many-worlds interpretation by
proposing that the distinction between worlds
should be made at the level of the mind of
an individual observer.
=== Quantum logic ===
Quantum logic can be regarded as a kind of
propositional logic suitable for understanding
the apparent anomalies regarding quantum measurement,
most notably those concerning composition
of measurement operations of complementary
variables. This research area and its name
originated in the 1936 paper by Garrett Birkhoff
and John von Neumann, who attempted to reconcile
some of the apparent inconsistencies of classical
boolean logic with the facts related to measurement
and observation in quantum mechanics.
=== Quantum information theories ===
Quantum informational approaches have attracted
growing support. They subdivide into two kinds
Information ontologies, such as J. A. Wheeler's
"it from bit". These approaches have been
described as a revival of immaterialism
Interpretations where quantum mechanics is
said to describe an observer's knowledge of
the world, rather than the world itself. This
approach has some similarity with Bohr's thinking.
Collapse (also known as reduction) is often
interpreted as an observer acquiring information
from a measurement, rather than as an objective
event. These approaches have been appraised
as similar to instrumentalism.
The state is not an objective property of
an individual system but is that information,
obtained from a knowledge of how a system
was prepared, which can be used for making
predictions about future measurements.
...A quantum mechanical state being a summary
of the observer's information about an individual
physical system changes both by dynamical
laws, and whenever the observer acquires new
information about the system through the process
of measurement. The existence of two laws
for the evolution of the state vector...becomes
problematical only if it is believed that
the state vector is an objective property
of the system...The "reduction of the wavepacket"
does take place in the consciousness of the
observer, not because of any unique physical
process which takes place there, but only
because the state is a construct of the observer
and not an objective property of the physical
system
=== Modal interpretations of quantum theory
===
Modal interpretations of quantum mechanics
were first conceived of in 1972 by B. van
Fraassen, in his paper "A formal approach
to the philosophy of science." However, this
term now is used to describe a larger set
of models that grew out of this approach.
The Stanford Encyclopedia of Philosophy describes
several versions:
The Copenhagen variant
Kochen-Dieks-Healey Interpretations
Motivating Early Modal Interpretations, based
on the work of R. Clifton, M. Dickson and
J. Bub.
=== Time-symmetric theories ===
Several theories have been proposed which
modify the equations of quantum mechanics
to be symmetric with respect to time reversal.
(E.g. see Wheeler-Feynman time-symmetric theory).
This creates retrocausality: events in the
future can affect ones in the past, exactly
as events in the past can affect ones in the
future. In these theories, a single measurement
cannot fully determine the state of a system
(making them a type of hidden-variables theory),
but given two measurements performed at different
times, it is possible to calculate the exact
state of the system at all intermediate times.
The collapse of the wavefunction is therefore
not a physical change to the system, just
a change in our knowledge of it due to the
second measurement. Similarly, they explain
entanglement as not being a true physical
state but just an illusion created by ignoring
retrocausality. The point where two particles
appear to "become entangled" is simply a point
where each particle is being influenced by
events that occur to the other particle in
the future.
Not all advocates of time-symmetric causality
favour modifying the unitary dynamics of standard
quantum mechanics. Thus a leading exponent
of the two-state vector formalism, Lev Vaidman,
highlights how well the two-state vector formalism
dovetails with Hugh Everett's many-worlds
interpretation.
=== Branching space-time theories ===
BST theories resemble the many worlds interpretation;
however, "the main difference is that the
BST interpretation takes the branching of
history to be a feature of the topology of
the set of events with their causal relationships...
rather than a consequence of the separate
evolution of different components of a state
vector." In MWI, it is the wave functions
that branches, whereas in BST, the space-time
topology itself branches.
BST has applications to Bell's theorem, quantum
computation and quantum gravity. It also has
some resemblance to hidden-variable theories
and the ensemble interpretation: particles
in BST have multiple well defined trajectories
at the microscopic level. These can only be
treated stochastically at a coarse grained
level, in line with the ensemble interpretation.
=== Other interpretations ===
As well as the mainstream interpretations
discussed above, a number of other interpretations
have been proposed which have not made a significant
scientific impact for whatever reason. These
range from proposals by mainstream physicists
to the more occult ideas of quantum mysticism.
== Comparison ==
The most common interpretations are summarized
in the table below. The values shown in the
cells of the table are not without controversy,
for the precise meanings of some of the concepts
involved are unclear and, in fact, are themselves
at the center of the controversy surrounding
the given interpretation. For another table
comparing interpretations of quantum theory,
see reference.No experimental evidence exists
that distinguishes among these interpretations.
To that extent, the physical theory stands,
and is consistent with itself and with reality;
difficulties arise only when one attempts
to "interpret" the theory. Nevertheless, designing
experiments which would test the various interpretations
is the subject of active research.
Most of these interpretations have variants.
For example, it is difficult to get a precise
definition of the Copenhagen interpretation
as it was developed and argued about by many
people.
1 According to Bohr, the concept of a physical
state independent of the conditions of its
experimental observation does not have a well-defined
meaning. According to Heisenberg the wavefunction
represents a probability, but not an objective
reality itself in space and time.
2 According to the Copenhagen interpretation,
the wavefunction collapses when a measurement
is performed.
3 Both particle AND guiding wavefunction are
real.
4 Unique particle history, but multiple wave
histories.
5 But quantum logic is more limited in applicability
than Coherent Histories.
6 Quantum mechanics is regarded as a way of
predicting observations, or a theory of measurement.
7 Observers separate the universal wavefunction
into orthogonal sets of experiences.
8 In the TI the collapse of the state vector
is interpreted as the completion of the transaction
between emitter and absorber.
9 Comparing histories between systems in this
interpretation has no well-defined meaning.
10 Any physical interaction is treated as
a collapse event relative to the systems involved,
not just macroscopic or conscious observers.
11 The state of the system is observer-dependent,
i.e., the state is specific to the reference
frame of the observer.
12 The transactional interpretation is explicitly
non-local.
13 The assumption of intrinsic periodicity
is an element of non-locality consistent with
relativity as the periodicity varies in a
causal way.
14 In the stochastic interpretation is not
possible to define velocities for particles,
i.e. the paths are not smooth. Moreover, to
know the motion of the particles at any moment,
you have to know what the Markov process is.
However, once we know the exactly initial
conditions and the Markov process, the theory
is in fact a realistic interpretation of quantum
mechanics.
15 The kind of non-locality required by the
theory, sufficient to violate the Bell inequalities,
is weaker than that assumed in EPR. In particular,
this kind non-locality is compatible with
no signaling theorem and Lorentz invariance.
16 A wavefunction merely encodes an agent’s
expectations for future experiences. It is
no more real than a probability distribution
is in subjective Bayesianism.
17 Quantum theory is a tool any agent may
use to help manage their expectations. The
past comes into play only insofar as an agent’s
individual experiences and temperament influence
their priors.
18 Although QBism would eschew this terminology.
A change in the wavefunction that an agent
ascribes to a system as a result of having
an experience represents a change in his or
her beliefs about further experiences they
may have. See Doxastic logic.
19 Observers, or more properly, participants,
are as essential to the formalism as the systems
they interact with.
== See also ==
== References ==
== Sources ==
Bub, J.; Clifton, R. (1996). "A uniqueness
theorem for interpretations of quantum mechanics".
Studies in History and Philosophy of Modern
Physics. 27B: 181–219.
Rudolf Carnap, 1939, "The interpretation of
physics", in Foundations of Logic and Mathematics
of the International Encyclopedia of Unified
Science. University of Chicago Press.
Dickson, M., 1994, "Wavefunction tails in
the modal interpretation" in Hull, D., Forbes,
M., and Burian, R., eds., Proceedings of the
PSA 1" 366–76. East Lansing, Michigan: Philosophy
of Science Association.
--------, and Clifton, R., 1998, "Lorentz-invariance
in modal interpretations" in Dieks, D. and
Vermaas, P., eds., The Modal Interpretation
of Quantum Mechanics. Dordrecht: Kluwer Academic
Publishers: 9–48.
Fuchs, Christopher, 2002, "Quantum Mechanics
as Quantum Information (and only a little
more)." arXiv:quant-ph/0205039
-------- and A. Peres, 2000, "Quantum theory
needs no ‘interpretation’", Physics Today.
Herbert, N., 1985. Quantum Reality: Beyond
the New Physics. New York: Doubleday. ISBN
0-385-23569-0.
Hey, Anthony, and Walters, P., 2003. The New
Quantum Universe, 2nd ed. Cambridge Univ.
Press. ISBN 0-521-56457-3.
Jackiw, Roman; Kleppner, D. (2000). "One Hundred
Years of Quantum Physics". Science. 289 (5481):
893. arXiv:quant-ph/0008092. doi:10.1126/science.289.5481.893.
Max Jammer, 1966. The Conceptual Development
of Quantum Mechanics. McGraw-Hill.
--------, 1974. The Philosophy of Quantum
Mechanics. Wiley & Sons.
Al-Khalili, 2003. Quantum: A Guide for the
Perplexed. London: Weidenfeld & Nicolson.
de Muynck, W. M., 2002. Foundations of quantum
mechanics, an empiricist approach. Dordrecht:
Kluwer Academic Publishers. ISBN 1-4020-0932-1.
Roland Omnès, 1999. Understanding Quantum
Mechanics. Princeton Univ. Press.
Karl Popper, 1963. Conjectures and Refutations.
London: Routledge and Kegan Paul. The chapter
"Three views Concerning Human Knowledge" addresses,
among other things, instrumentalism in the
physical sciences.
Hans Reichenbach, 1944. Philosophic Foundations
of 
Quantum Mechanics. Univ. of California Press.
Tegmark, Max; Wheeler, J. A. (2001). "100
Years of Quantum Mysteries". Scientific American.
284: 68–75. Bibcode:2001SciAm.284b..68T.
doi:10.1038/scientificamerican0201-68.
Bas van Fraassen, 1972, "A formal approach
to the philosophy of science", in R. Colodny,
ed., Paradigms and Paradoxes: The Philosophical
Challenge of the Quantum Domain. Univ. of
Pittsburgh Press: 303-66.
John A. Wheeler and Wojciech Hubert Zurek
(eds), Quantum Theory and Measurement, Princeton:
Princeton University Press, ISBN 0-691-08316-9,
LoC QC174.125.Q38 1983.
== Further reading ==
Almost all authors below are professional
physicists.
David Z Albert, 1992. Quantum Mechanics and
Experience. Harvard Univ. Press. ISBN 0-674-74112-9.
John S. Bell, 1987. Speakable and Unspeakable
in Quantum Mechanics. Cambridge Univ. Press,
ISBN 0-521-36869-3. The 2004 edition (ISBN
0-521-52338-9) includes two additional papers
and an introduction by Alain Aspect.
Dmitrii Ivanovich Blokhintsev, 1968. The Philosophy
of Quantum Mechanics. D. Reidel Publishing
Company. ISBN 90-277-0105-9.
David Bohm, 1980. Wholeness and the Implicate
Order. London: Routledge. ISBN 0-7100-0971-2.
Adan Cabello (15 November 2004). "Bibliographic
guide to the foundations of quantum mechanics
and quantum information". arXiv:quant-ph/0012089.
David Deutsch, 1997. The Fabric of Reality.
London: Allen Lane. ISBN 0-14-027541-X; ISBN
0-7139-9061-9. Argues forcefully against instrumentalism.
For general readers.
Bernard d'Espagnat, 1976. Conceptual Foundation
of Quantum Mechanics, 2nd ed. Addison Wesley.
ISBN 0-8133-4087-X.
Bernard d'Espagnat, 1983. In Search of Reality.
Springer. ISBN 0-387-11399-1.
Bernard d'Espagnat, 2003. Veiled Reality:
An Analysis of Quantum Mechanical Concepts.
Westview Press.
Bernard d'Espagnat, 2006. On Physics and Philosophy.
Princeton Univ. Press.
Arthur Fine, 1986. The Shaky Game: Einstein
Realism and the Quantum Theory. Science and
its Conceptual Foundations. Univ. of Chicago
Press. ISBN 0-226-24948-4.
Ghirardi, Giancarlo, 2004. Sneaking a Look
at God's Cards. Princeton Univ. Press.
Gregg Jaeger (2009) Entanglement, Information,
and the Interpretation of Quantum Mechanics.
Springer. ISBN 978-3-540-92127-1.
N. David Mermin (1990) Boojums all the way
through. Cambridge Univ. Press. ISBN 0-521-38880-5.
Roland Omnès, 1994. The Interpretation of
Quantum Mechanics. Princeton Univ. Press.
ISBN 0-691-03669-1.
Roland Omnès, 1999. Understanding Quantum
Mechanics. Princeton Univ. Press.
Roland Omnès, 1999. Quantum Philosophy: Understanding
and Interpreting Contemporary Science. Princeton
Univ. Press.
Roger Penrose, 1989. The Emperor's New Mind.
Oxford Univ. Press. ISBN 0-19-851973-7. Especially
chpt. 6.
Roger Penrose, 1994. Shadows of the Mind.
Oxford Univ. Press. ISBN 0-19-853978-9.
Roger Penrose, 2004. The Road to Reality.
New York: Alfred A. Knopf. Argues that quantum
theory is incomplete.
Styer, Daniel F.; Balkin, Miranda S.; Becker,
Kathryn M.; Burns, Matthew R.; Dudley, Christopher
E.; Forth, Scott T.; Gaumer, Jeremy S.; Kramer,
Mark A.; et al. (March 2002). "Nine formulations
of quantum mechanics". American Journal of
Physics. 70 (3): 288–297. Bibcode:2002AmJPh..70..288S.
doi:10.1119/1.1445404.
== External links ==
Stanford Encyclopedia of Philosophy:
"Bohmian mechanics" by Sheldon Goldstein.
"Collapse Theories." by Giancarlo Ghirardi.
"Copenhagen Interpretation of Quantum Mechanics"
by Jan Faye.
"Everett's Relative State Formulation of Quantum
Mechanics" by Jeffrey Barrett.
"Many-Worlds Interpretation of Quantum Mechanics"
by Lev Vaidman.
"Modal Interpretation of Quantum Mechanics"
by Michael Dickson and Dennis Dieks.
"Quantum Entanglement and Information" by
Jeffrey Bub.
"Quantum mechanics" by Jenann Ismael.
"Relational Quantum Mechanics" by Federico
Laudisa and Carlo Rovelli.
"The Role of Decoherence in Quantum Mechanics"
by Guido Bacciagaluppi.
Internet Encyclopedia of Philosophy:
Interpretations of Quantum Mechanics
Everettian Interpretations of Quantum Mechanics
Willem M. de Muynck, Broad overview of the
realist vs. empiricist interpretations, against
oversimplified view of the measurement process.
Schreiber, Z., "The Nine Lives of Schrodinger's
Cat." Overview of competing interpretations.
Interpretations of quantum mechanics on arxiv.org.
The many worlds of quantum mechanics.
Erich Joos' Decoherence Website.
Quantum Mechanics for Philosophers. Argues
for the superiority of the Bohm interpretation.
Hidden Variables in Quantum Theory: The Hidden
Cultural Variables of their Rejection.
Numerous Many Worlds-related Topics and Articles.
Relational Approach to Quantum Physics.
Theory of incomplete measurements. Deriving
quantum mechanics axioms from properties of
acceptable measurements.
Alfred Neumaier's FAQ.
Measurement in Quantum Mechanics FAQ.
