Content uploaded by Oliver Passon
Author content
All content in this area was uploaded by Oliver Passon on Jan 04, 2022
Content may be subject to copyright.
Online Encyclopedia Philosophy of Nature
Online Lexikon Naturphilosophie
©
Philosophy of Quantum Mechanics
Oliver Passon and Marij van Strien
Quantum physics is one of the cornerstones of modern physics and a scientifically informed philosophy of
nature needs to integrate it. In particular, quantum mechanics is thought to have implications for example
for the question whether nature is deterministic, the (im)possibility to observe without intervening, and the
possibility of non-local interactions. However, if we look more carefully at what exactly quantum mechanics
implies, we encounter a problem: there are different interpretations of quantum mechanics, which are all
compatible with observations but which paint very different pictures of physical reality. This entry tries to
orient the reader within this complex debate. We introduce briefly what quantum physics is about, what its
main interpretations look like and whether some general conclusions with regard to metaphysics and natural
philosophy can be drawn from it.
Citation and licensing notice
Passon, Oliver/van Strien, Marij (2022): Philosophy of Quantum Mechanics. In: Kirchhoff, Thomas (ed.):
Online Encyclopedia Philosophy of Nature / Online Lexikon Naturphilosophie. Heidelberg University
Publishing. ISSN 2629-8821. doi: 10.11588/oepn.2022.1.85573.
This work is published under the Creative Commons 4.0 (CC BY-ND 4.0) licence.
1. Introduction
Quantum mechanics or quantum physics – we use
these terms interchangeably – originated in 1900 from
investigations into the theory of heat radiation (Max
Planck), had early applications, e.g. in solid state phys-
ics in 1907 (Albert Einstein) and eventually, starting
with Niels Bohr’s famous model of the atom from
1913, became the “new atomic physics”. The current
formulation of quantum mechanics was developed by
Werner Heisenberg (1925) and Erwin Schrödinger
(1926). The name “quantum” refers to “discrete quan-
tity”, and one feature of quantum physics is indeed
the fact that (for bound states) certain measured
quantities do not take on a continuous range of values
but can only take on a restricted number of values
(like a dice that can show six values, but no values in
between). If, for example, a quantum system (e.g.
some atom bound in a crystal) oscillates with the fixed
frequency, its energy is given by the discrete
amount (or integral multiples of it) with,
the so-called Planck constant, having the (compared
to everyday standards) very small value
Js.
According to present knowledge, quantum mechanics
is needed to describe the behaviour of all matter at the
atomic and subatomic scale, and its predictions are sup-
ported by countless experiments. Today also the estab-
lished standard model of elementary particles is formu-
lated as a quantum (field) theory. But famously, until
now the general theory of relativity defies all attempts
to be reconciled with quantum theory. However, quan-
tum effects, e.g. the discreteness of energy levels, are
often negligible in macroscopic circumstances, as the
Planck constant is generally too small to let its discon-
tinuous character lead to observable effects. But there
are also macroscopic quantum phenomena, such as
superconductivity (i.e. the sudden disappearance of
electrical resistance at low temperatures due to quan-
tum effects which couple electrons to so-called Cooper
pairs) and the so-called giant magnetoresistance (i.e.
the influence of magnetization and electrical resistance
in specific materials which is exploited in many
computer hard drives). Furthermore, genuine effects
of atomic physics have real-world impact, for example
the fusion of hydrogen atoms which fuels our sun or
the working of lasers and semiconductor technology
(products of the so-called “first quantum revolution”).
Online Encyclopedia Philosophy of Nature | Online Lexikon Naturphilosophie
Passon, Oliver/van Strien, Marij | Philosophy of Quantum Mechanics | 2022 |
doi: 10.11588/oepn.2022.1.85573
Online Encyclopedia Philosophy of Nature | Online Lexikon Naturphilosophie 2
Right now we find ourselves in the midst of the “second
quantum revolution” which is driven by quantum com-
puters, quantum cryptography and other technologies
which exploit the novelties of quantum physics more
directly. Thus, the importance of quantum physics can
hardly be overstated. This extends also to issues in the
philosophy of nature (and beyond).
Quantum mechanics is routinely presented as puzzling
or mysterious, and many different (sometimes very
startling) conclusions about physical reality have been
drawn from it. Quantum mechanics is thought to have
implications for example for the question whether nature
is deterministic, the (im)possibility to observe without
intervening, and the possibility of non-local interactions.
However, if we look more carefully at what exactly
quantum mechanics implies, we encounter a problem:
there are different interpretations of quantum me-
chanics, which are all compatible with observation, but
which paint very different pictures of physical reality.
After the modern theory of quantum mechanics was
introduced in 1925 and 1926, physicists debated about
the foundations and proper interpretation of the theory
(on the distinction between ‘theory’ and ‘interpretation’,
see 4.). In the 1950s, the view became established that
the main foundational issues had been solved and that
a general consensus had been reached, although there
were always a few dissidents (Howard 2004; Camilleri
2009). Since then, however, several alternative inter-
pretations have been developed and new insights in the
foundations of quantum mechanics have been obtained
(Freire 2014). The present situation is that among physi-
cists there is still a widespread view that there is only
a single satisfactory interpretation (the ‘Copenhagen in-
terpretation’, discussed in 2.2 – although in fact, there
are significant differences in how it is understood by dif-
ferent physicists), but it is less universally accepted than
before, while among philosophers of physics there is a
wide variety of views and a great lack of consensus
(Schlosshauer et al. 2013).
Therefore, if we want to say anything about the philo-
sophical implications of quantum mechanics, we have to
be aware of this plurality of interpretations.
We will first give an extremely short introduction
to quantum mechanics and briefly introduce its
mathematical formalism (we restrict ourselves to a
non-relativistic formulation). We then present some of
the main interpretations of quantum mechanics, which
each try to give a specific meaning to the formalism.
Finally, we will outline what the main messages for the
philosophy of nature might be.
2. The formalism of quantum mechanics
For those readers with some background knowledge in
linear algebra and calculus, the quantum novelties can
be most easily explained with the help of the mathe-
matical formalism of the theory (2.1). For an in-depth
understanding of quantum mechanics, this is even a
prerequisite. However, we conclude this section with a
non- (or rather less-) technical summary for readers
who lack this background knowledge (2.2).
2.1 The technical version …
While in other areas of physics the state of a system can
generally be characterized by a full list of all its proper-
ties (say, positions, momenta etc.), quantum mechanics
represents the state of a system by a wave function
, or, equivalently, by a state-vector in
some abstract state space. This vector is the solution
of the corresponding Schrödinger equation
,
which describes how the wave function of a system
evolves in time. The resulting evolution is “unitary”, i.e.
among other things deterministic, reversible and linear.
Dynamical quantities like position or momentum
(“observables”) are represented by so-called Hermitian
operators, i.e. something that takes a vector
as input and spits out another vector:
.
If the result is we say that is an eigen-
vector of O with eigenvalue. These eigenvalues are real
numbers and correspond to the possible measurement
values. For instance, the symbol used in the Schrödinger
equation is such an operator: it denotes the Hamilton
operator which represents the energy of the system.
Generally, the concepts used in quantum physics to
describe the properties of systems are the same as those
used in pre-quantum physics: position, momentum, en-
ergy, etc. The only exception is a property called “spin”
which is introduced in quantum physics. For example,
electrons (but also, e.g. silver atoms) are spin-
objects.
A spin measurement along a specific direction can yield
only
or
(in units of
). These states are often
called “spin up” and “spin down”. This discreteness is
again a typical feature of quantum physics. Given the
Online Encyclopedia Philosophy of Nature | Online Lexikon Naturphilosophie
Passon, Oliver/van Strien, Marij | Philosophy of Quantum Mechanics | 2022 |
doi: 10.11588/oepn.2022.1.85573
Online Encyclopedia Philosophy of Nature | Online Lexikon Naturphilosophie 3
simplicity of spin-
systems (being only two-valued), they
serve as a popular example for quantum effects.
1
With an orthonormal basis of eigenvectors of a
Hermitian operator, any state can be expanded as
(with
). The so-called Born-rule states that for such a
state the probability to obtain the value upon meas-
uring the quantity represented by is given by.
Given this probability interpretation, expectation values
and standard deviations can be defined accordingly.
Under a given basis any (Hermitian) operator can
be represented by a matrix. Unlike numbers, matrices
generally do not commute under multiplication, i.e.
. It is a basic result from linear algebra that
operators which do not commute have no common
basis of eigenvectors. Within the quantum mechanical
formalism this implies that the corresponding observa-
bles cannot have sharp values simultaneously. The Heisen-
berg uncertainty relation for position and momentum,
, is a direct implication of this relationship
(another example would be spin measurements along
different directions). And this brings us back to our first
remark: Unlike classical physics, quantum mechanics
cannot describe a state by a full list of all of its properties,
since the uncertainty relations restrict the quantities
which can have sharp values at a certain moment in
time. Additionally, all quantum mechanical predictions
are merely probability statements for possible measure-
ment outcomes.
2.2 … and the less technical version
The less technical summary of the above is the following:
In quantum physics a system is described by a wave
function . This wave function is complex valued,
and it is an abstract entity which is not easily inter-
preted as a physical object. The wave function and its
time evolution are calculated from the fundamental
Schrödinger equation, i.e. the quantum analogon to
Newton’s law of motion (i.e. “force equals
mass times acceleration”) in classical mechanics.
A distinctive feature of quantum mechanics is that a
system can be in a superposition of different states,
1
In addition, the corresponding system is a possible
realization of a “qbit”, i.e. the quantum bit of quantum
information theory. While the classical bit can have only
which means that a system can be in a combination of
two states: if and are possible states of the system,
then also (with complex numbers) is
a possible state of the system. For example: if an electron
may be located in region A or region B, then it can also
be in a superposition of being in region A and being in
region B.
Importantly, the properties of the system (say
position, momentum or energy) may not always be
well-defined. In particular, the Heisenberg uncertainty
relation states that the position and momentum of a
particle cannot simultaneously have a sharp value.
A state which possesses a well-defined property is
called an eigenstate with respect to this property.
Generally, quantum theory only yields probabilities
for different measurement outcomes, and no exact
predictions. These probabilities can be calculated from
the wave function.
A curious fact about quantum physics is that it
introduces no new elementary properties, and the pre-
quantum concepts of position, momentum, energy, etc.
retain their significance. The only exception is the so-called
“spin”— a novel quantum property which is a kind of
angular momentum. Spin takes discrete values, for ex-
ample, the measurement of the spin of an electron in
a certain direction can only yield one of two possible
values (which are called spin up and spin down).
Already at this point a number of “quantum novel-
ties” are notable, namely states with apparently no
well-defined properties (or being in a superposition of
different properties) and fundamentally probabilistic
predictions. Furthermore, because the theory does not
give exact predictions for measurement outcomes but
only yields probabilities, there is the question of how
the measurement of a single value actually comes
about. The latter turns out to be a major problem for
interpreting the theory.
In closing we should emphasize that also in classical
(pre-quantum) physics quantities may superimpose
(e.g. forces or directions of movement). However, the
corresponding (classical) system is nevertheless in a well-
defined state with well-defined properties. Furthermore,
classical physics also includes probability statements
two values (say, “0” and “1”) the qbit can possess any
superposition of these two states, which gives rise to the
famous “quantum parallelism” in quantum computing.
Online Encyclopedia Philosophy of Nature | Online Lexikon Naturphilosophie
Passon, Oliver/van Strien, Marij | Philosophy of Quantum Mechanics | 2022 |
doi: 10.11588/oepn.2022.1.85573
Online Encyclopedia Philosophy of Nature | Online Lexikon Naturphilosophie 4
(e.g. in statistical mechanics). However, these probabili-
ties express only our ignorance about the specific state,
i.e., are just epistemic.
An entertaining way to learn more about quantum
superpositions and quantum probabilities is by playing
“Quantum Tic-Tac-Toe”. In this quantum version of the
familiar game one can place the game icons on several
fields simultaneously (i.e. in a “superposition” of several
fields). Only after all fields being filled a “measurement”
is performed and the “actual” positions appear randomly.
Check it out!
3. Measurement problem
The “measurement problem” in quantum mechanics is
the problem of how the measurement of a physical
quantity can yield a definite outcome, even though
according to the theory of quantum mechanics, the
quantity had no well-defined value before the measure-
ment was made. For example, a silver atom can have a
spin up or a spin down, but can also be in a superposition
of a spin-up and a spin-down state. When you measure
the spin, however, it is always found to be either spin-up
or spin-down, and never in a superposition. This has
brought about the idea that it is only through the process
of measurement that a quantum system obtains well-
defined properties. This issue has generated much debate
in the philosophy of quantum physics, and many differ-
ent views have been proposed on how to understand
the measurement process in quantum mechanics. (See
Schlaudt 2020 for a general discussion of measurement.)
This measurement problem becomes clearer if you
consider that measurement instruments are built out of
atoms and should therefore themselves obey quantum
mechanics. In the above example, the spin of silver atoms
can be measured by directing a beam of silver atoms
through a so-called Stern-Gerlach magnet: thereby a
splitting into the spin-up or spin-down state is observed
on the screen. However, in principle the measuring de-
vice could also be treated quantum mechanically; but
then it seems that it should evolve into a superposition
of “screen showing spin-up” and “screen showing spin-
down”. Thus, John Bell famously asked the question how
a measurement turns an “and” (i.e. the sum of different
terms in the superposition) into an “or” (i.e. the mutually
exclusive and definite result of each measurement). This
is one way to put the infamous “measurement problem”.
An extreme version of the problem is the one pro-
posed in Schrödinger’s famous cat-article from 1935.
Schrödinger proposed a thought experiment in which a
cat is trapped in a box together with a poison which is
released upon a radioactive decay. After some time, the
radioactive atom is in the superposition of already de-
cayed and not yet decayed. Hence, the cat is apparently
in the superposition of “dead” and “alive”, and only by
opening the box (‘measuring’) does the cat obtain a well-
defined state of being either dead or alive. This is clearly
an absurd result: the thought experiment was designed
by Schrödinger to show the absurdity of the implications
which quantum mechanics appeared to have.
An especially helpful formulation of the measurement
problem in the form of a trilemma was given by Tim
Maudlin (1995). Slightly simplified, the three horns of
the trilemma read:
● (comp) The wave function provides a complete
description of the individual state.
● (schrö) The time evolution is always given by the
Schrödinger equation.
● (def) Measurements have a definite outcome.
While all of these propositions seem reasonable at first,
any two of them imply the negation of the third: there-
fore, at least one of these three propositions must be
false. For example, suppose that (comp) and (schrö) are
valid: this means that the state of a system is com-
pletely described by the wave function, which evolves
according to the Schrödinger equation. In this case, if
the system is in superposition, then an interaction with
a measurement instrument results in the measurement
instrument being in a superposition as well, and the
measurement cannot not yield a definite outcome: thus,
(def) cannot hold. Next, suppose that (comp) and (def)
are valid: then the state of the system is completely
described by a wave function, and a measurement of
this state yields a definite outcome. This means that when
a measurement takes place, the wave function changes
in a way which is not described by the Schrödinger
equation: the measurement brings about a “collapse” of
the wave function, a sudden and unexplained reduction
to the observed eigenstate. This means that (schrö) is
false. Finally, suppose that (schrö) and (def) hold. Then
some piece of information seems to be missing in the state
description, in order to single out the definite outcome
of each individual measurement. This would imply that
the wave function provides only an incomplete state
Online Encyclopedia Philosophy of Nature | Online Lexikon Naturphilosophie
Passon, Oliver/van Strien, Marij | Philosophy of Quantum Mechanics | 2022 |
doi: 10.11588/oepn.2022.1.85573
Online Encyclopedia Philosophy of Nature | Online Lexikon Naturphilosophie 5
description, i.e. (comp) has to be false. Essentially all inter-
pretations of quantum mechanics can be classified by
their strategy to avoid this trilemma, i.e. by rejecting one
of its horns.
4. Interpretations
The interpretation of quantum mechanics is among the
most debated issues in the philosophy of physics. The very
need to “interpret” the mathematical formalism is intri-
guing and is arguably without precedent in science. It is
true that in a sense, a mathematical theory in physics al-
ways needs to be interpreted, given that the mathemat-
ical symbols need to be assigned to natural phenomena;
and it is true as well that also, e.g. Newtonian mechanics,
statistical physics or electrodynamics are subjects to
philosophical debates on how the theory should best be
understood. But in the case of quantum mechanics, the
way the mathematical formalism relates to the natural
world is not at all evident: the complex valued wave func-
tion does not refer to any physical object in an obvious
manner, and the theory of quantum mechanics does not
give a description of the process of measurement. This
has given rise to a plurality of interpretations of quantum
mechanics, which give different accounts of how the
formalism relates to the natural world.
However, the huge success of quantum physics
indicated in the introduction illustrates that the corre-
sponding theory is operationally well understood and
that, e.g., the measurement problem apparently provides
no immediate threat to scientific progress. This reflects
the fact that the different interpretations typically
agree in all predictions.
Presumably most practicing physicists (who try to avoid
philosophical debates) endorse a minimal interpretation
of the theory (4.1) or some variant of the “Copenhagen
interpretation” (4.2). Rivals are the “many-worlds inter-
pretation” (4.3) and the “de Broglie-Bohm theory” (4.4)
which introduce a trade-off between philosophically desir-
able and awkward features. Finally, there is a class of inter-
pretations which tackles the measurement problem head-
on by introducing an explicit collapse mechanism (4.5).
It has to be noted that some of these ‘interpretations’
should perhaps rather be viewed as alternative theories
of quantum mechanics, rather than as interpretations
of the same theory, given that they modify the Schrödin-
ger equation or posit extra theoretical structure (although
the precise definition of the term “theory” is a debated
issue as well). This holds in particular for the “de Broglie-
Bohm theory” and for collapse interpretations. However,
these theories have exactly the same predictions as
standard quantum mechanics and are traditionally
subsumed under the label “interpretation”.
Within philosophy of science, there is a debate about
the possibility that scientific theories are underdeter-
mined by the empirical data: This means that there can
be more than one theory compatible with the available
empirical evidence, so that the evidence does not suffice
to choose the right theory (Stanford 2017). There are
often thought to be few examples of underdetermination
in actual scientific research. However, insofar as some
of the ‘interpretations’ of quantum mechanics can be
regarded as alternative theories, which can account for
exactly the same observations as the standard theory,
quantum physics provides a strong example of the under-
determination of scientific theories by data (Cushing
1994; Acuña 2021; on underdetermination in philosophy
of science, see Stanford 2017).
Our list of interpretations is not even complete. As
noted by David Mermin (2012): “New interpretations
appear every day. None ever disappear.”
4.1 The minimal interpretation
A simple way to circumvent the measurement problem
is to deny that quantum physics is supposed to describe
individual systems at all (be it cats – recall Schrödinger’s
cat discussed in section 3 – or measurement devices).
On this reading, the Born rule provides only the statistics
of repeated measurements, and the wave function is
the description of an “ensemble” of identically prepared
systems – and not of individual systems (thus, this specific
version of (comp) is rejected). This view has been cham-
pioned by Ballentine (1970) but, e.g., some of Einstein’s
writing is pointing into a similar direction.
This interpretation fits the needs of practicing physi-
cists who often deal with huge samples of quantum
systems in their labs. But this “ensemble” interpretation
seems philosophically unsatisfying since it remains unclear,
e.g. whether these probabilities refer to “objective” facts
or express merely “subjective” knowledge. Friebe et al.
(2018: 44) conclude: “For the metaphysics of science,
this is not sufficient, and most physicists would also prefer
to have some idea of what is behind those measurements
Online Encyclopedia Philosophy of Nature | Online Lexikon Naturphilosophie
Passon, Oliver/van Strien, Marij | Philosophy of Quantum Mechanics | 2022 |
doi: 10.11588/oepn.2022.1.85573
Online Encyclopedia Philosophy of Nature | Online Lexikon Naturphilosophie 6
and observational data, i.e. just how the microscopic
world which produces such effects is really structured.”
For some of these reasons this “ensemble interpretation”
plays only a minor role in the current debate.
4.2 The Copenhagen interpretation
Many textbooks call the Copenhagen interpretation (CI)
the “standard interpretation” of quantum mechanics.
The common claim is that this view was developed by
Niels Bohr and his colleagues in the late 1920s. However,
as discussed more closely in the entry on the “history of
quantum mechanics”, the CI was never codified and the
members of the corresponding school (say, Heisenberg,
Pauli, Born, Jordan and von Neumann) held partly dis-
senting views on important issues.
At the basis of Bohr’s thought on quantum mechanics
is the idea that experiments necessarily have to be de-
scribed with classical concepts, while at the same time,
these concepts are subject to restrictions and cannot all
be applied simultaneously (Bohr 1928). Bohr coined the
term “complementarity” for the mutually exclusive but
jointly necessary descriptions which can be given with
different concepts. For example, one can either attribute
a position or a momentum to a particle, but not both at
the same time; and in Bohr’s view this has to do with
the fact that to measure the position or the momentum
of a particle requires different experimental setups,
which exclude each other.
This seems (in the view of some commentators) to
imply that measuring devices belong to a separate
“classical domain” beyond the scope of quantum
physics, which compromises the completeness of the
(state-)description (i.e. (comp) in the terminology of
Maudlin). Most important is the fact that according to
Bohr, there is always an interaction between measure-
ment and the observed system which compromises the
“independent reality” of both, the “phenomena” and
the “agencies of observation” (Bohr 1928: 580).
In Bohr’s version of the CI there is no “collapse” of the
wave function; however, it is often taken to be part of
the CI that a collapse of the wave function takes place
with measurement. This is the case, e.g. in the versions
of von Neumann and Heisenberg. If the collapse (or pro-
jection) postulate is included into the CI this is at odds
with the universal validity of the Schrödinger equation,
i.e. (schrö) – but without detailing this process further.
Whether the CI allows for a satisfactory solution of the
measurement problem is therefore debated. Famously,
Schrödinger and Einstein, two founding fathers of quan-
tum theory, remained hostile to this interpretation.
4.3 The many-worlds interpretation
According to Maudlin’s trilemma, the measurement
problem can only be solved if one of its premises is
dropped. The many-worlds interpretation challenges the
claim that measurements have definite outcomes. This
view was developed in 1957 by Hugh Everett III under the
name “relative state formulation” and is also sometimes
known as “Everett interpretation”; it was popularized
by de Witt and Graham (1973) who also coined the
catchy name “many-worlds interpretation”. According to
this view, only the appearance of definite outcomes needs
to be explained. If, according to quantum mechanics, a
wave function splits into different branches (say, upon
measuring the spin state of a silver atom in a Stern-
Gerlach experiment) the many-worlds interpretation
assumes that both components of the superposition
represent an actual state of the system. Metaphorically
speaking, the corresponding spin-up and spin-down
states are realized in different “worlds” which are sepa-
rated not in space-time but dynamically. Wallace (2012:
37) puts it pointedly: “Macroscopic superpositions do
not describe indefiniteness, they describe multiplicity.”
In order to explain the appearance of definite outcomes,
one extra step is needed, namely that the observer is
subject to this multiplicity as well. Thus, this interpreta-
tion assumes that “the universe is constantly splitting
into a stupendous number of branches, all resulting from
measurement-like interactions between its myriads of
components” (De Witt/Graham 1973: 161).
Obviously, this interpretation has the air of extra-
vagance. But there are also serious technical problems
with it. At the time it was popularized by De Witt in the
early 1970s Leslie Ballentine was among the first to point
out that this interpretation suffers from the so-called
“non-uniqueness of the state decomposition”. After all,
a quantum mechanical state can be mathematically
decomposed in many different ways and the question
which of these decompositions underlies the actual
splitting needs to be answered (Ballentine 1973). The
solution of this problem was eventually achieved by
decoherence theory, first introduced by Heinz-Dieter Zeh
Online Encyclopedia Philosophy of Nature | Online Lexikon Naturphilosophie
Passon, Oliver/van Strien, Marij | Philosophy of Quantum Mechanics | 2022 |
doi: 10.11588/oepn.2022.1.85573
Online Encyclopedia Philosophy of Nature | Online Lexikon Naturphilosophie 7
already in 1970 (and unnoticed by the community at that
time). The key insight was to include the unavoidable
interaction with the environment (i.e. degrees of freedom
which are not under control). In decoherence theory,
detailed models of the interaction process between the
environment and the quantum system give rise to a
privileged status of a specific decomposition (i.e. the
so-called pointer basis).
Zeh’s work did not receive the deserved recognition
and the decoherence theory only gained more momen-
tum with the work of Wojciech H. Zurek since the 1980s.
Importantly, its results hold independent of any specific
interpretation, or, to put it differently, are exploited in
many different interpretations (see, e.g., 4.4 below).
Hence, decoherence theory holds the promise to con-
tribute to any solution of the measurement problem
that may be achieved in the future.
In recent years the decoherence-based approaches to
the many-worlds interpretation have gained popularity
among philosophers of physics. Its modern version is
championed, e.g. by David Wallace. However, this inter-
pretation struggles hard in order to explain the role of
probability. According to widespread understanding, a
probability assignment needs several possible outcomes
and uncertainty about the actual occurrence. In the
many-worlds interpretation both premises are missing
because (so to say) “everything” is “always” happening
(see Wallace 2012 for a possible way out by applying
techniques from decision theory). Despite these difficul-
ties, the consistency of the many-worlds interpretation
is generally accepted.
4.4 The de Broglie-Bohm theory
The de Broglie-Bohm (dBB) theory (aka Bohmian me-
chanics, pilot wave theory, causal or ontological inter-
pretation) challenges the claim that the wave function
provides a complete description of individual systems,
i.e. (comp). The many names reflect that this theory
was anticipated by Louis de Broglie already at the 5th
Solvay conference in 1927, independently rediscovered
by David Bohm (1952) and further developed by various
people including John Bell, Peter Holland, Detlef Dürr,
Sheldon Goldstein, Nino Zanghì and others. The strategy
of the dBB theory is to add a specification of the positions
of all particles (i.e. the configuration) to the description of
a quantum system. In contrast to most other inter-
pretations, here particles always have a well-defined
position. The precise formulation of the theory needs
to answer two questions, namely (i) what law governs
the particle motion and (ii) how are the initial positions
distributed. The answer to the first question is given by
the so-called guidance equation (a first-order differential
equation for the particle positions). Metaphorically
speaking the particles are guided (or piloted) by the
wave function (which is still governed by the Schrödinger
equation). Here, measurements have definite results
because the particle position selects a (decoherent)
branch of the wave function which corresponds to the
observed outcome. A collapse of the universal wave
function does not occur. It is curious to note that here
solely the position determines the outcome of measure-
ments of, e.g. spin, momentum or energy. That is, no
additional variables are needed to fix these quantities
(see Passon 2018).
However, a unique solution of the guidance equation
requires initial conditions, which brings us to the second
question raised above. If the initial positions are chosen
according to Born’s rule (this is called the “quantum equi-
librium hypothesis”) the Schrödinger equation ensures
that all predictions of quantum mechanics will be repro-
duced. This includes the violation of Bell’s inequality (see
5.5) and the impossibility to violate Heisenberg’s uncer-
tainty principle (see Dürr et al. 1992; Norsen 2018 for
the justification of the quantum equilibrium hypothesis).
Thus, no experiment can distinguish between the dBB
theory and any other interpretation. While the con-
sistency of this (non-relativistic) formulation is generally
accepted, the extra structure it introduces has arguably
the air of being only fictitious.
4.5 Collapse interpretations
Another school of interpretation has challenged the
validity of the Schrödinger equation and has replaced it
by a modified equation which includes additional (in
general non-linear and stochastic) terms. These terms are
designed in order to account for an (objective) collapse
of the wave function upon, e.g. measurements. Already
on a formal level, these models are extremely diverse.
The original model by Giancarlo Ghirardi, Alberto Rimini
and Tullio Weber (1986) had the quantum state occasion-
ally collapse without any apparent reason, at a rate that
was treated as a free parameter in the model. This is
Online Encyclopedia Philosophy of Nature | Online Lexikon Naturphilosophie
Passon, Oliver/van Strien, Marij | Philosophy of Quantum Mechanics | 2022 |
doi: 10.11588/oepn.2022.1.85573
Online Encyclopedia Philosophy of Nature | Online Lexikon Naturphilosophie 8
different in the model first defined by Pearle (1989),
where the stochastic interaction with a new, otherwise
undetermined field makes the quantum state collapse.
There are several issues that could be discussed in
connection to objective collapse models, but we would
like to focus on their “ontological” implications. Since the
wave function is a highly abstract entity which is defined
on a high-dimensional so-called configuration space, it is
not immediately clear how the wave function relates to
our ordinary experience. There are two possible ontolo-
gies that have been discussed in the context of collapse
models, the matter density ontology (Ghirardi et al. 1995),
in which the dynamics of the wave function determines
the behavior of a (derivative) matter field on space-time,
and the flash ontology (Bell [1987a] 2004), according to
which tiny bits of matter flash in and out of existence in
accord with the collapse dynamics on the configuration
space. However, neither of these specify exactly how
the wave function ‘steps down’ from configuration space
to effect these changes, and ’s exact role in the ontology
hence remains rather unclear.
4.6 Quantum Bayesianism
In closing our section on interpretations, we would like
to mention a more recent suggestion, namely quantum
Bayesianism or QBism. Some ideas of quantum Bayes-
ianism were anticipated by Edwin Thompson Jaynes
already in 1990. Its main proponents are Christopher
Fuchs, Rüdiger Schack and David Mermin. The name
QBism was coined by Fuchs (2010) and denotes a further
development of this view.
Some of Bohr’s writing on the interpretation of quan-
tum theory stresses its subjective character (compare,
e.g. the above quote in 4.2 on the need to give up
the “independent reality” of the phenomena). A similar
attitude shines through in the so-called QBism. Here,
the starting point is the observation that the notion
of probability has no generally accepted meaning. Pre-
sumably a majority of physicists (and mathematicians
or statisticians) sides with the frequentist interpretation
of probability which links the probability of an event to
the relative frequency of its occurrence. This interpre-
tation of probability is debated for a number of reasons
which are beyond the present scope.
Another influential camp emphasizes the logical
simplicity of probability and adheres to the so-called
“subjective interpretation”. The slogan here reads
“probability is the degree of belief” and in order to work
with this interpretation one needs to apply a well-
known theorem of statistics, called the Bayes theorem.
Hence, this school of statistics is called Bayesianism. In
brief, QBism results from applying this interpretation to
the probabilities of quantum theory. On this view, any
user of quantum physics (an “agent”) is applying the
formalism in order to assign personal judgments on an
event – based on his or her experience. This results in a
rather fundamental reinterpretation of scientific theories.
The adherents of this view claim that QBsim provides a
more balanced view on the relation of subjective and
objective features of the quantum world (Fuchs et al
2014). According to Qbism, the act of measurement is
simply a process in which the corresponding agent
gains knowledge about a system and the apparent (or:
“subjective”) collapse simply reflects the fact that this
gain happens suddenly.
5. Conclusions for specific metaphysical issues
After we have gained an overview of some of the major
interpretations of quantum physics, we are in the
position to explore its metaphysical implications more
closely. Before entering the discussion on continuity
versus discreteness (5.2), determinism versus indeter-
minism (5.3), observation, objectivity and the mind
(5.4) as well as holism and non-locality (5.5), we should
say a word on the infamous “wave-particle dualism”
(5.1), an issue which is less dependent on the specific
interpretational stance.
5.1 Wave-particle dualism
Sometimes the novelty of quantum physics is framed as
the claim that quantum objects are neither particles nor
waves but exhibit a certain “wave-particle dualism” (or
“duality”). While this notion played an important heu-
ristic role in the early history of the theory (and may still
serve a doubtful educational purpose) it should be rather
viewed as outmoded. It is true that, say, an electron is
described by a wave function which suggests “wave
properties” for this object (most notably interference
effects). At the same time an electron exhibits particle
properties (like a discrete mass). These observations lie
at the basis of the duality-heuristics.
Online Encyclopedia Philosophy of Nature | Online Lexikon Naturphilosophie
Passon, Oliver/van Strien, Marij | Philosophy of Quantum Mechanics | 2022 |
doi: 10.11588/oepn.2022.1.85573
Online Encyclopedia Philosophy of Nature | Online Lexikon Naturphilosophie 9
However, for a system of N electrons the wave function
is defined on a 3N dimensional space. Thus, the wave
function does not describe a “wave” in the ordinary sense
(let alone that it is complex valued and specifies only
probabilities). Furthermore, quantum objects are “in-
distinguishable”, i.e. the permutation of “particles” in an
N-particle state has no observable effect. In other words,
quantum objects have no individuality, which is in stark
contrast to ordinary particles. In this sense the wave-
particle duality of electrons has to be understood meta-
phorically at best. Some authors relate this alleged
“duality” to Bohr’s notion of complementarity. However,
while the early Bohr used the wave-particle duality as an
example for complementarity, he avoided this application
after 1934 (see Held 1994).
The so-called “photons”, or light quanta, are even less
particle-like than electrons. We have dealt so far with the
non-relativistic theory of quantum mechanics, which is
relevant for systems which move much slower than the
speed of light in vacuum. Photons are obviously moving
at the speed of light, thus they cannot be described by
ordinary, non-relativistic quantum mechanics but rather
by the generalization called quantum electrodynamics.
This entails that there is no wave function for the photon
with a probability interpretation in 3D position-space
(Peierls 1979: 10 f.). In fact, the observable “position” is
not even defined for photons (Newton/Wigner 1948).
It is true that a photon state exhibits discrete energy
and momentum; however, these quantities cannot be
localized and belong to the whole space which is filled
by the electromagnetic field. Thus, also here the wave-
particle duality is highly misleading.
Summing up, it may be said that quantum objects share
some properties which bear a loose resemblance with
“particles” and “waves”, but that these classical notions
do not provide adequate tools for the description. The
reference to a vague “dualism” or “duality” between these
two types ignores the autonomy of quantum physics,
which postulates a completely different kind of “matter”.
This holds even for the de Broglie-Bohm theory, which
apparently introduces “particles” (in the literal sense) into
the description. First, also here any vague “dualism” is
rejected. Secondly – and more importantly – the “Bohmian
particles” are very different from ordinary matter as well.
These objects have no properties other than position
and velocity; other properties, such as charge and spin,
are assigned to the wave function (compare 4.4).
5.2 Continuity versus discreteness
A related issue is the question of continuity versus dis-
creteness. Since antiquity, there have been discussions
about whether nature has a continuous or discrete
character (Bell 2019). Here, one should distinguish be-
tween spatial discreteness, property discreteness and
the discreteness of processes. Prima facie quantum
theory is by its very definition claiming that the world
has discrete properties (i.e. comes in “quanta”). But
note that the wave function evolves continuously and
apparently only the act of measurement introduces
the discrete results. Hence, the question of continuity
versus discreteness (of the time-evolution) depends on
the interpretation one adopts. To Bohr (1928) the dis-
creteness was the essential feature of the theory
(called the “quantum postulate”). But on the minimal
(or ensemble-) interpretation one needs to be silent
about this issue on the level of individual entities. If,
however, one follows the many-worlds interpretation,
the (continuous) wave function is all there is, and on the
de Broglie-Bohm interpretation the dynamics is supple-
mented by the continuous movement of quantum
particles. These “Bohmian particles”, however, are
discrete entities. Thus, quantum mechanics gives us
no definite answer to the question whether nature is
continuous or discrete.
5.3 Determinism versus indeterminism
It is generally thought that before the introduction of
quantum mechanics, physics was strictly deterministic:
given the current state of a system, the laws of physics
would uniquely determine its future evolution (on the
degree to which this image is correct, see van Strien
2021). This was often seen as a problem for free will:
if the laws of physics determine exactly what will happen
in the future, it can be hard to see how we can be free
in our choices and acts. Quantum mechanics seems to
have introduced fundamental chance in our physical
world view, thereby making an end to determinism in
physics. It is therefore no surprise that quantum me-
chanics is often invoked in discussions about free will
(see Esfeld 2000; Hodgson 2002). However, there are
several challenges to accounting for free will on the
basis of quantum mechanics. First, it would have to be
shown that quantum effects can make a difference on
Online Encyclopedia Philosophy of Nature | Online Lexikon Naturphilosophie
Passon, Oliver/van Strien, Marij | Philosophy of Quantum Mechanics | 2022 |
doi: 10.11588/oepn.2022.1.85573
Online Encyclopedia Philosophy of Nature | Online Lexikon Naturphilosophie 10
the level of our thoughts and acts, even though they are
generally negligible on a macroscopic scale. Secondly,
it seems that to account for free will, the introduction
of an element of chance or randomness does not suffice:
the fact that our choices are partly random would not
make us any more responsible for our choices.
Finally, we have to ask whether quantum mechanics is
indeed indeterministic. The laws of quantum mechanics
only yield probabilities for measurement outcomes but
no exact predictions: it therefore seems that there is
an element of randomness in the evolution of systems
in quantum mechanics. However, since the different
interpretations of quantum mechanics give very differ-
ent accounts of the process of measurement, they also
give different answers to the question whether nature
is deterministic.
On the ensemble view one needs to be silent (again),
and Ballentine states: “Strictly speaking, quantum me-
chanics is silent on the question of determinism versus
indeterminism: the absence of a prediction of determinism
is not a prediction of indeterminism” (Ballentine 1998:
592, emphasis in original). However, in von Neumann’s
version of the Copenhagen interpretation, the measure-
ment introduces an indeterministic “collapse” of the wave
function. In contrast, the de Broglie-Bohm interpretation
is drawing the picture of quantum particles which move
deterministically, and the probabilities for measurement
outcomes which quantum mechanics yields reflect only
the ignorance about the precise initial conditions: This
account of quantum mechanics is therefore deterministic.
On the many-worlds interpretation, determinism is also
restored since the time evolution is governed entirely
by the Schrödinger equation and no collapse is needed.
Some (objective) collapse theories, on the other hand,
involve an explicit stochastic term to account for measure-
ment outcomes; but according to quantum Bayesianism
this collapse only reflects that some agent gains addi-
tional information, i.e. is a purely subjective matter.
5.4 Observation, objectivity and the mind
Quantum mechanics is often thought to tell us some-
thing significant about observation: the idea is that in
quantum mechanics, it is not possible to observe some-
thing without changing it. This is based on the wide-
spread idea that, in quantum mechanics, quantities
only gain an exact value through measurement (which
does not hold strictly, given that e.g. the ionization
energy of hydrogen can be predicted exactly inde-
pendently of any measurement; moreover, as we will
see, also this depends on interpretation). The idea that
what we observe partly depends on our presence as
observers has implications for philosophical debates
on whether it is possible for us to have knowledge of
the world as it really is, independently of us. Quantum
mechanics is sometimes taken to imply an extreme
view: It is sometimes claimed that consciousness plays
an essential role in the measurement process, and
that quantum systems only gain well-defined proper-
ties when they are observed by a conscious being.
Although there are indeed well-known physicists who
have made this claim, it is certainly not a generally
accepted view. First, it is widely acknowledged that
the term “measurement” in quantum mechanics is an
awkward expression: if observables indeed only gain
an exact value through the process of measurement,
this means that the measurement does not inform us
about a property that was already there: rather, the
measurement brings about the measured outcome,
and this process is rather more a process of “creating”
than of “measuring”. But this creation does not have
to be explained through the “mind” or “consciousness”
of the observer: it is far more plausible that the inter-
action between the measurement instrument and the
observed system plays an essential role here. A measure-
ment is then a process of intervention, rather than a
passive observation.
But secondly, also in this case, different interpretations
offer significantly different views on the matter. The
picture we have just discussed agrees with the Copen-
hagen interpretation, according to which the interac-
tion between the quantum system and the “classical”
measurement device brings about the observed out-
come. However, in the many-worlds interpretation, a
measurement does not have a single definite outcome,
but rather all outcomes are realized in some “world”, and
the observer shares in this multiplicity. According to the
de Broglie-Bohm view the outcome of any measurement
is uniquely determined; however, for measurements of
variables other than position, the values are determined
by the whole context of measuring apparatus, wave
function and configuration of particles (which implies
a specific meaning to the claim that measurements
“create” their outcome).
Online Encyclopedia Philosophy of Nature | Online Lexikon Naturphilosophie
Passon, Oliver/van Strien, Marij | Philosophy of Quantum Mechanics | 2022 |
doi: 10.11588/oepn.2022.1.85573
Online Encyclopedia Philosophy of Nature | Online Lexikon Naturphilosophie 11
5.5 Quantum non-locality and holism
A physical theory is called “local” if any action can only
affect nearby regions in space (more technically: ac-
tions propagate slower than the speed of light in the
vacuum). Given that the wave function for an N-parti-
cle state is defined on the 3N-dimensional configura-
tion space, it is rather apparent that “being nearby in
(3D) position-space” has no immediate significance
within quantum theory. This feature supports the idea
that there is some kind of “holism” or “non-locality” in
quantum physics. In 1964, John Bell published a result
which is often taken to mean there are exactly such
non-local effects in quantum physics, that is, what
happens at one location can have an instant effect on
a distant location. His argument was based on the
famous Einstein-Podolsky-Rosen (EPR) thought experi-
ment, suggested already in 1935. If a two-particle
system is in a specific superposition (called “en-
tangled”), you can construct situations in which the
particles are far apart, but measurement outcomes of
experiments on each particle separately show correla-
tions (this can be verified experimentally). Technically,
one speaks of Bell’s inequality being violated by quan-
tum physics. If such entangled states could be used to
communicate faster than light, this would violate a
basic postulate of special relativity. However, this is
not possible because the corresponding correlations
are between “random numbers” (i.e. you cannot de-
liberately generate one of the two possible states on
either side of the coupled system) and can be checked
only with the help of a “classical” (that is local) com-
munication line, after the experiment has been done.
Still, according to many, these correlations beg for an
explanation and compromise the relation between
quantum physics and special relativity. On a different
reading the EPR-correlations indicate no superluminal
exchange of an effect, but rather the non-locality of
the corresponding state (see e.g. Friebe et al. 2018:
chapter 4). However, either way, some locality as-
sumptions are compromised.
But also here the assessment depends on the in-
terpretational choice: Due to the vague definition of
the “Copenhagen interpretation”, it is debated
whether non-locality is present there. Ballentine, the
vocal proponent of the ensemble interpretation,
accepts the conclusion that the violation of Bell’s
inequality implies some sort of non-locality (see Bal-
lentine 1998: chapter 20 for an extremely readable
introduction to the whole subject). The de Broglie-
Bohm theory fully endorses non-locality since it
accounts for this violation of Bell’s inequality by an
explicitly non-local mechanism. Within the many-
world interpretation, however, it has been argu ed
that one may avoid any non-locality (see e.g. Baccia-
galuppi 2002). The same holds with quantum Baye-
sianism: given that this interpretation deals with
personal judgments of individual (i.e. local) agents, it
also can avoid the threat of non-locality (Fuchs et al.
2014).
6. Concluding remarks
We have seen that quantum mechanics indeed has
remarkable features, which seem to have implications
for our understanding of nature. However, we have
also seen that there are a variety of interpretations of
quantum mechanics, and that what quantum mechanics
shows us about various issues in the philosophy of nature
is highly dependent upon the interpretation. This raises
an awkward question: if quantum mechanics can give
us so few definite answers about what the world is like,
is it from a philosophical point of view worth learning
about quantum mechanics?
In answer to this question, we first have to say: Al-
though the different interpretations do yield very differ-
ent pictures of physical reality, this does not mean that
all options remain open. Quantum mechanics does not
force us to accept extreme conclusions such as the
claim that things only come into being when we look at
them. However, in each interpretation, some common-
sense assumption is given up, and it is therefore clear
that somehow or other, the world is different than it
was imagined before, at least on the quantum scale. In
any case, if ‘billiard ball’ or ‘clockwork’ conceptions of
physical reality, in which everything is reducible to simple
mechanisms, were ever plausible, they definitely have
to be given up in the light of quantum mechanics.
A further issue which is relevant to the philosophy of
nature relates to the question of part-whole relations
(i.e. mereology). We tend to think of matter as being
composed of some fundamental building blocks, be
it atoms or subatomic particles. Quantum mechanics
indicates – rather independent of any choice in the
Online Encyclopedia Philosophy of Nature | Online Lexikon Naturphilosophie
Passon, Oliver/van Strien, Marij | Philosophy of Quantum Mechanics | 2022 |
doi: 10.11588/oepn.2022.1.85573
Online Encyclopedia Philosophy of Nature | Online Lexikon Naturphilosophie 12
interpretational debate – that on the quantum scale
the part-whole relation is not aggregation (as in the
simple picture of “fundamental building blocks”) but
superposition (Healey 2013).
Furthermore, the very plurality of interpretations is
itself philosophically interesting. It is remarkable that
such a successful and well-established theory as quantum
mechanics can fail to give us a definite account of what
the world is like, and that it allows for such a variety of
interpretations which paint very different pictures of
physical reality. As we have seen in section 4., some of
these interpretations should perhaps rather be viewed
as alternative theories of quantum mechanics, and since
these theories yield the same predictions as the standard
theory, this would provide a strong example of under-
determination of scientific theories by empirical data.
At the same time, it highlights that the choice of a theory
(or interpretation) depends on non-empirical criteria
like simplicity, symmetry, or its ability of being general-
izable.
2
Basic literature
Bohr, Niels 1928: The quantum postulate and the recent
development of atomic theory. In: Nature 121
(3050): 580–590.
Bell, John S. (ed.) [1987b] 2004: Speakable and Unspeak-
able in Quantum Mechanics. Collected Papers on
Quantum Philosophy. Second Edition. With a New
Introduction by Alain Aspect. Cambridge/New York,
Cambridge University Press.
Cushing, James T. 1994: Quantum Mechanics. Historical
Contingency and the Copenhagen Hegemony.
Chicago, University of Chicago Press.
Freire Junior, Olival 2014: The Quantum Dissidents.
Rebuilding the Foundations of Quantum Mechanics
(1950–1990). Berlin/Heidelberg, Springer.
Friebe, Cord/Kuhlmann, Meinard/Lyre, Holger/Näger,
Paul M./Passon, Oliver/Stöckler, Manfred 2018:
The Philosophy of Quantum Physics. Berlin/New
York, Springer.
2
Acknowledgement: We like to thank Florian J. Boge
for fruitful and intense discussion.
Literature
Acuña, Pablo 2021: Charting the landscape of inter-
pretation, theory rivalry, and underdetermination
in quantum mechanics. In: Synthese 198 (2): 1711–
1740.
Bacciagaluppi, Guido 2002: Remarks on space-time and
locality in Everett’s interpretation. In: Placek, Tomasz/
Butterfield, Jeremy (eds): Non-Locality and Modality.
Dordrecht, Kluwer: 105–122.
Ballentine, L. E. 1970: The Statistical Interpretation of
Quantum Mechanics. In: Reviews of Modern Physics
42 (4): 358–381.
Ballentine, Leslie E. 1973: Can the statistical postulate
of quantum theory be derived? – A critique of the
many-universes interpretation. In: Foundations of
Physics 3 82): 229–240.
Ballentine, Leslie E. 1998: Quantum Mechanics – A
Modern Development. Singapore, World Scientific.
Bell, John Stewart 1987a: Are there quantum jumps? In:
Bell, John Stewart (ed.): Speakable and Unspeaka-
ble in Quantum Mechanics. Cambridge/New York,
Cambridge University Press: 201–212.
Bell, John Stewart [1987b] 2004: Speakable and Un-
speakable in Quantum Mechanics. Collected Papers
on Quantum Philosophy. Second Edition. With a
New Introduction by Alain Aspect. Cambridge/New
York, Cambridge University Press.
Bell, John L. 2019: The Continuous, the Discrete and the
Infinitesimal in Philosophy and Mathematics. Cham,
Springer Nature Switzerland.
Bohm, David 1952: A suggested interpretation of the
quantum theory in terms of “hidden” variables. In:
Physical Review 85 (2): 166–179 (part 1), 180–193
(part 2).
Bohr, Niels 1928: The quantum postulate and the re-
cent development of atomic theory. In: Nature
121 (3050): 580–590.
Camilleri, Kristian 2009: Constructing the myth of the
Copenhagen interpretation. In: Perspectives on
Science 17 (1): 26–57.
Online Encyclopedia Philosophy of Nature | Online Lexikon Naturphilosophie
Passon, Oliver/van Strien, Marij | Philosophy of Quantum Mechanics | 2022 |
doi: 10.11588/oepn.2022.1.85573
Online Encyclopedia Philosophy of Nature | Online Lexikon Naturphilosophie 13
Cushing, James T. 1994: Quantum Mechanics. Historical
Contingency and the Copenhagen Hegemony.
Chicago, University of Chicago Press.
De Witt, Bryce Seligman/Graham, Neill 1973: The Many-
Worlds Interpretation of Quantum Mechanics.
Princeton, Princeton University Press.
Dürr, Detlef/Goldstein, Sheldon/Zanghí, Nino 1992:
Quantum equilibrium and the origin of absolute
uncertainty. In: Journal of Statistical Physics 67:
843–907.
Everett III, Hugh 1957: “Relative state” formulation of
quantum mechanics. In: Reviews of Moderne Phys-
ics 29: 454–462.
Esfeld, Michael 2000: Is quantum indeterminism relevant
to free will? In: Philosophia Naturalis 37 (1): 177–187.
Freire Junior, Olival 2014: The Quantum Dissidents. Re-
building the Foundations of Quantum Mechanics
(1950–1990). Berlin/Heidelberg, Springer.
Friebe, Cord/Kuhlmann, Meinard/Lyre, Holger/Näger,
Paul M./Passon, Oliver/Stöckler, Manfred 2018:
The Philosophy of Quantum Physics. Berlin/New
York, Springer.
Fuchs, Christopher A. 2010: QBism, the perimeter of
quantum Bayesianism. In: arXiv:1003.5209.
Fuchs, Christopher A./Mermin, N. David/Schack, Rüdiger
2014: An introduction to QBism with an application
to the locality of quantum mechanics. In: American
Journal of Physics 82 (8): 749–754.
Ghirardi, Giancarlo/Rimini, Alberto/Weber, Tullio
1986: Unified dynamics for microscopic and macro-
scopic systems. In: Physical Review D 34 (2): 470–
491.
Ghirardi, Giancarlo/Grassi, Renata/Benatti, Fabio 1995:
Describing the macroscopic world: closing the circle
within the dynamical reduction program. In: Foun-
dations of Physics 25 (1): 5–38.
Healey, Richard 2013: Physical composition. In: Studies
in History and Philosophy of Modern Physics 44 (1):
48–62.
Held, Carsten 1994: The meaning of complementarity.
In: Studies in History and Philosophy of Science Part
A 25 (6): 871–893.
Hodgson, David 2002: Quantum physics, consciousness,
and free will. In: Kane, Robert H. (ed.): The Oxford
Handbook of Free Will. New York, Oxford University
Press.
Howard, Don 2004: Who invented the “Copenhagen Inter-
pretation”? A study in mythology. In: Philosophy of
Science 71 (5): 669–682.
Maudlin, Tim 1995: Three measurement problems. In:
Topoi 14 (1): 7–15.
Mermin, N. David 2012: Quantum mechanics: fixing the
shifty split. In: Physics Today 65 (7): 8–10.
Newton, Theodore Duddell/Wigner, Eugene Paul 1949:
Localized states for elementary systems. In: Reviews
of Modern Physics 21 (3): 400–406.
Norsen, Travis 2018: On the explanation of Born-rule
statistics in the de Broglie-Bohm pilot-wave theory.
In: Entropy 20 (6): 422. https://doi:10.3390/e20060422.
Passon, Oliver 2018: On a common misconception regard-
ing the de Broglie-Bohm theory. In: Entropy 20 (6):
440. https://doi.org/10.3390/e20060440.
Pearle, Philip 1989: Combining stochastic dynamical
state-vector reduction with spontaneous localization.
In: Physical Review A 39 (5): 2277–2289.
Peierls, Rudolf 1979: Surprises in Theoretical Physics.
Princeton, Princeton University Press.
Schlaudt, Oliver 2020: Measurement. In: Kirchhoff,
Thomas (ed.): Online Encyclopedia Philosophy
of Nature/Online Lexikon Naturphilosophie.
Heidelberg, Heidelberg University Publishing:
https://doi.org/10.11588/oepn.2020.0.76654.
Schlosshauer, Maximilian/Kofler, Johannes/Zeilinger,
Anton 2013: A snapshot of foundational attitudes
toward quantum mechanics. In: Studies in History
and Philosophy of Science Part B: Studies in History
and Philosophy of Modern Physics 44 (3): 222–230.
Stanford, Kyle 2017: Underdetermination of scientific
theory. In: Zalta, Edward N. (ed.): The Stanford
Encyclopedia of Philosophy (Winter 2017 Edition),
https://plato.stanford.edu/archives/win2017/en-
tries/scientific-underdetermination/.
Van Strien, Marij 2021: Was physics ever deterministic?
The historical basis of determinism and the image of
classical physics. In: The European Physical Journal
H 46 (1): 1–20.
Wallace, David 2012: The Emergent Multiverse: Quan-
tum Theory According to the Everett Interpretation.
Oxford, Oxford University Press.
Zeh, Heinz-Dieter 1970: On the interpretation of meas-
urement in quantum theory. In: Foundations of
Physics 1 (1): 69–76.
