UNIVERSITY OF REGENSBURG
Faculty of Philosophy, Art, History and Social Sciences
Bachelor Thesis in the degree program Philosophy
A Comparison of Two Presentations of Quantum Mechanics: Everett’s Relative-State and Rovelli’s Relational Quantum
Mechanics
First and Last Name: Matthias AckermannMatriculation Number: 1745485
First Referee: Prof. Dr. Hans RottSecond Referee: Dr. Tim Kraft
List of Contents
Abstract.................................................................................................................................................................
1. Introduction................................................................................................................................................ 1
2. Origins and the Unease of Quantum Mechanics – Why Everett and Rovelli...................2
2.1 Introduction to Quantum Mechanics – the Measurement Problem...........................................4
3. Everett’s Relative-States Presentation – Prior Remarks.........................................................5
3.1 Everett’s Relative-State Presentation......................................................................................................6
3.2 Idea Behind Relative States..........................................................................................................................7
3.3 Problem of Observation.................................................................................................................................9
3.4 Summarizing Crucial Elements in Relative-States...........................................................................13
3.5 Digression and Clarification - Everett and Experience..................................................................15
4. Rovelli’s Relational Quantum Mechanics – Prior Remarks..................................................17
4.1 Rovelli’s Relational Quantum Mechanics.............................................................................................18
4.2 RQM and the Problem of Observation...................................................................................................20
4.3 Quantum Theory’s Relational Feature in Depth...............................................................................22
4.4 The Notion of Information.........................................................................................................................24
4.4.1 Two Information Postulates.............................................................................................................26
4.5 Summary of Rovelli’s Ideas........................................................................................................................27
5. Philosophical Implications - Introducing Remarks.................................................................29
5.1 Everett and Rovelli in Respect to Realism...........................................................................................30
5.2 Moment of Consensus and Divergence.................................................................................................32
5.3 Relative-States and RQM and Structural Realism............................................................................34
5.3.1 Discussion of Epistemic and Ontic Elements in Relative-States and RQM...................35
Relativism Excursus....................................................................................................................................................40
5.3.1 Discussion of Epistemic and Ontic Elements in Relative-States and RQM...................42
6. Conclusion................................................................................................................................................. 44
List of Literature.......................................................................................................................................... 46
Abstract
Everett’s Relative State Formulation of Quantum Mechanics and Rovelli’s Relational Quantum Mechanics are two eminently interesting and impactful presentations of what the world of quantum mechanics is like. Beginning with a depiction of the theories and their physical implications I conclude with a comparison of their respective picture of reality. I propose here that by letting philosophical deliberations be guided by the very statements from within the theories, one arrives at a structural realist picture of what our world is like.
1. Introduction
“Concepts that have proven useful in ordering things easily achieve such an authority over us that we forget their earthly origins and accept them as unalterable givens. Thus they come to be stamped as “necessities of thought,” “a priori givens,” etc. The path of scientific advance is often made impassable for a long time through such errors” (Einstein 1916: 102).
Two prominent achievements of the twentieth century beard a radical rectification of
the physical view of the world – the Theory of Relativity and Quantum Mechanics 1.
Even though the former has permeated the public awareness much more, the latter
can be said to have presented a more radical change of perceptions of the world (cf.
Evans 2007: 2). Also because of their emergence the branch ‘philosophy of physics’
has become a lively and extensive part of philosophy itself and has thus been part of
various collected volumes of the philosophy of science during the last fifty years (cf.
Butterfield/ Earman 2007: xii). Beginning in the 1960’s, debates about the
interpretation of Quantum Mechanics that had taken place among its founders
witnessed a reignition. To show that and why the discussion is still worthwhile is
both kind of a secondary objective and the impetus of this paper. The present
scientific debates in the natural sciences are “characterized by an astonishing amount
of perplexity, and disagreement, about what time, space, matter, and causality are”
(Rovelli 1997: 180).
Putting my head above the parapet, I could, inspired by Rovelli’s 1997 article
“Halfway Through the Woods: Contemporary Research on Space and Time”, claim
that the last period where
“previously accepted assumptions were questioned as deeply as they are now, one must go back four centuries. Between the publication of Copernicus’s De Revolutionibus, which opened the scientific revolution by antonomasia, and the publication of Newton’s Principia, which brought it to a spectacularly successful conclusion, 150 years elapsed” (ibid.).
In the course of this time, the ideas about rationality, matter, cause, space and time
have underwent a radical change that in the end yielded a comprehensive synthesis.
Even though the protagonists of this “intellectual adventure” (ibid.) – Leibniz,
Descartes, Galileo or Kepler, just to name a few – didn’t know where it would take
them, they were quite aware of the changes their eras were going through. Taking
this at face value allows us to view our present age as also experiencing a change of
preliminary fundamental beliefs, similar to four hundred years ago.
1 Quantum Mechanics will often be abbreviated as QM below.
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Concerning this matter, the work at hand tries to portray two formulations of QM
that I think are both eminently interesting in respect to a physical as well as
philosophical understanding of our world. However, I do neither claim a full
representation of either of the theories or a take on advancing their respective ideas.
What I am trying to work out is presenting a description of the respective picture of
the world they sketch and, based on this, suggesting a possible philosophical ‘home’
for them. That implies not trying to frame them into philosophical theorems, but
rather letting philosophical ideas be shaped by the physical implications they give.
2. Origins and the Unease of Quantum Mechanics – Why Everett and Rovelli
The origin of the theory of Quantum Mechanics (QM) can be determined with
Werner Heisenberg’s 1925 work “Über quantentheoretische Umdeutung
kinematischer und mechanischer Beziehungen”. In a following series of fascinating
papers of Heisenberg, Born and Jordan the theory had, in the same year, “already
evolved into its current full set of equations” (Rovelli 2017: 1). Independently of those
works, P. A. M. Dirac, taking Heisenberg’s original paper as a basis, also arrived at the
same formalism with his 1925 paper “The fundamental equations of quantum
mechanics”. It was not until one year later that Erwin Schrödinger presented his
highly renowned work “Quantisierung als Eigenwertproblem (Erste Mitteilung)”
where he introduced the wave function 2.3
Following Rovelli’s description and considering that the formalism of QM already
existed in a complete manner, what was it that Schrödinger did in his 1926 paper? In
retrospect he took two actions: (1) a technical action that can be considered quite
unproblematic, as Schrödinger ‘merely’ changed the algebraic language of QM into
differential equations – a familiar language then – so that more theoretical physicists
were able to understand the mathematical formalism. (2) A conceptual action, that
introduced “the notion of “wave function” , soon to be evolved into the notion of
“quantum state4” , endowing it with heavy ontological weight” (Rovelli 2017: 1). The
second action, according to Rovelli, can be said not only to be misleading but, more
2 To avoid any discomfort, note that I will keep mathematical formalism, in respect to the issue and extent of my paper, at a minimum. Physically speaking, the wave function basically describes the quantum mechanical state of elementary particles and particle systems. The Quantum State, into which Schrödinger evolved the wave function, is a mathematical object that predicts the probability distribution of measured quantities. While both played only a ‘secondary’ role in Heisenberg’s depiction, Schrödinger, at least in his early works, took both fully into account/as a fundamental entity (cf. Heisenberg 1925; cf. Schrödinger 1926).3 For a historical account, see Fedak and Prentis (2009).
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importantly, deviating from the original formalism of Heisenberg. A more vivid
description of its defectiveness can be found in the following analogy with optics,
which, and that is important, is entirely interpretational and thus does not contribute
anything to the predictive power of the mathematical formalism of QM (as it was
already complete):
“[T]he trajectory of a particle is like the trajectory of a light ray: an approximation for the behavior of an underlying physical wave in physical space. That is: is the “actual stuff”, like the electromagnetic field is the “actual stuff” underlying the nature of light rays” (Rovelli 2017: 1).5
Even though one could state that Schrödinger’s second step differed considerably
from the original formulation, it strongly pervaded the later thinking about QM and is
present until this day.6 In the following discussion about this notion, even
Schrödinger himself became one of the most prominent figures to take part in the
debate and, in this regard, tried to kind of annul his prior statement about being the
‘real stuff’. Nevertheless, while the discussion was present, Heisenberg lost the debate
for a number of reasons, the most important one, concerning the issue of my paper, is
the following: Because it was more of an interpretational problem and many
physicists weren’t too much interested in ‘interpretational matters’, they didn’t pay
quite a lot attention to the debate (cf. Rovelli 2017: 1). The result was that “the
misleading idea of taking the “quantum state” as a faithful description of reality stuck”
(ibid.).
Concerning the above depiction, this paper compares Everett’s presentation of QM –
one that takes Schrödinger’s wave function , but without the collapse, as its basis –
and Rovelli’s formulation of QM – one that refers to Heisenberg’s picture and has
interactions between physical systems as its basis. It should be clear by now, why I
take on these two presentations of QM. In case it’s not yet, let me give you one
simplified, but crucial reason: Both can be attributed an original and novel
4 I will sometimes speak of the quantum state as the hypothetical universal wave function, thus not differentiating between both. In this sense, the quantum state is a “state [that] can be characterized by an assignment of expectation values to physical quantities (“observables”) (Myrvold 2018). As we will see, the meaning of the term quantum state is quite different in both theories. It’s important – as will be examined in the later – to keep this fundamental difference in mind: For Everett, the quantum state is basically everything ‘there is’, i.e. the quantum state acts as his universal fundamental postulate and has a unitary evolution (cf. Wallace 2002). For Rovelli the quantum state “is a theoretical devise we use for bookkeeping information about the variables of [a system] actualized in interactions with [another system]” (2007: 4).5 As it will gain importance later on: This is the most fundamental difference between Everett’s and Rovelli’s understanding of QM: The former takes on Schrodinger’s picture and the latter Heisenberg’s. In this light, Rovelli is closer to the very formalism of QM, while Everett begins at a kind of interpretational assertion/ontological proposition. 6 For a summary of the discussion about this notion among the founders of QM, see Rovelli 2017: 1-2.
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understanding of the original formalism. Everett regarding his theory to be a “totally
new view of the foundational character of physics” (Wheeler 1957: 465) and Rovelli
since his presentation is a radical continuation of the thought of relativity, introduced
with Einstein’s general and special relativity, itself.7
2.1 Introduction to Quantum Mechanics – the Measurement Problem
Before getting into both of the formulations, as a first step it is necessary, at least for
the sake of completeness of representation, to have a look at the core of the
philosophical issues within quantum mechanics, the so-called ‘measurement
problem’. Following Friebe et al.’s depiction of Maudlin (1995) one can call it a
trilemma that consists of the following three assumptions, which conjunct are
inconsistent, so that a possible solution requires to dismiss at least one of them. (1)
Assuming that the formalism of quantum mechanics is complete. (2) Adopting the
Schrödinger equation, in which vectors in Hilbert space8 are “always subject to a
linear temporal dynamics” (2018: 56). (3) Supposing that any measurement always
provides well-defined, definite results.
Now, how do Everett and Rovelli position themselves within this trilemma? Let me
summarize their respective position in an abridged manner: both can be attributed a
dismissing of the third assumption, however, they differ in the way of addressing the
premise; while Everett states that measurement results only “appear” (Everett
1957a: 457) to us to yield definite results, but, at the same time holds the wave
function to be describing the absolute state, Rovelli’s focus is a fundamental relational
character of states, completely dismissing absolute states as such.9 He furthermore
states that, if treating Schrödinger’s equation “as the real stuff, we fall immediately
into the horrendous “measurement” problem” (Rovelli 2017: 1). As my paper is less
concerned with a justification of their respective approach to a solution of this
problem – as will be shown that Rovelli even completely circumvents, though
7 There are many more important reasons to take on these two presentations of QM, e.g. Everett’s formulation being the foundation for the today highly advocated family of the ‚Many Worlds Interpretations’ or Rovelli since his presentation not only supplies a novel picture of what the world, in general, not only of quantum, but also of classical mechanics is like but also covers a fundamental divide within the philosophical debate itself (cf. van Fraassen 2010: 390).8 The Hilbert space can, in respect to the issues I’m dealing with, simply be understood as a generalization of the Euclidian space to an infinite number of dimensions.9 One could also say that Rovelli kind of dismisses the second assumption – concerning his understanding of the wave function as we will see later on – or, at least, his dismissing consists of a hybrid of (2) and (3).
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explicitly addressing it – and more with the picture of reality they promote as a
consequence of their understanding of it, a discussion of how justified their accounts
in respect to the measurement problem is shouldn’t be expected to be the concern of
this paper.10
3. Everett’s Relative-States Presentation – Prior Remarks
Everett’s relative-state formulation of quantum mechanics11 has frequently been
used to include metaphysical dedication in regard to the subsistence of many
‘branching worlds’, with each of them comprising physical duplicates of observers
and observed objects. This can mostly be attributable to DeWitt’s12 famous
presentation of Everett’s formulation, which helped greatly in popularizing the
theory. It’s of importance however to note that while the idea of splitting or parallel
existing worlds left an immense imprint on the perception of his theory, Everett
himself never mentioned the branching or parallel existence of worlds (cf. Barrett
2011: 277). Even though those kinds of interpretations (‘Many Worlds’) can be
considered as worthwhile in their own respect, they don’t inevitably fit well with
Everett’s own ideas.
What can be noted on a safe basis however is, for example, Everett’s dedication to
pure wave mechanics, investigated using the diction of ‘relative-states’ as well as his
devotedness towards the aim of demonstrating that his formulation of quantum
mechanics allows one to conclude the same empirical prognoses as the conventional
formulation (cf. ibid: 278). For Everett, pure wave mechanics meant “the standard
von Neumann-Dirac formulation of quantum mechanics without the collapse
dynamics” (ibid.). In that respect, he suggested accepting pure wave mechanics as a
thorough physical theory, while letting go of the collapse dynamics present in the
standard model. As will be outlined below, he aimed for a deduction of “the
probabilistic assertions of Process 113 as subjective appearances […] thus placing the
10 For an extensive review of Everett’s approach, see for example Barrett/Byrne (2012). For Rovelli, see e.g. “Relational Quantum Mechanics” (2008) or Laudisa/Rovelli (2013). 11 The ‘Relative State Formulation’ I am referring to is both the shortened version of Everett’s formulation of QM and his PhD thesis. I will from now on often abbreviate “Relative States Formulation of Quantum Mechanics” as Relative-States or simply R-S.12 DeWitt, B. S. (1970). Quantum mechanics and reality. Physics Today, 23, 30–35.13 The formalities of Process 1 and 2 are not of crucial importance here, rather their meaning: „a physical system always evolves according to the deterministic Process 2 unless a measurement is made; in which case, it evolves in according to the random collapse Process 1” (Barrett 2010: 225-226). In short: Process 1 represents the collapse of and Process 2 the deterministic evolution of the wave function.
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theory in correspondence with experience” (Everett 1973: 9). This brings up the
unprecedented setting in which the mathematical theory is causal and continuous,
whereas the subjective experience is probabilistic and discontinuous (cf. ibid.).
What Everett did was basically using the strategy of deduction to investigate a
“representation of our quantum mechanical experience in the correlation model
described by pure wave mechanics” (Barrett 2011: 279). What can be anticipated
however is that Everett finds this quantum mechanical experience in relative states,
which will be further outlined below.
3.1 Everett’s Relative-State Presentation
Everett’s primary aim in his 1957 thesis “Relative State Formulation of Quantum
Mechanics” was an attempt to clear up the very foundations of quantum mechanics
(p. 454). In its most basic form, one could say that his formulation tried to
reformulate quantum theory in a manner, which Everett believed to be reasonable to
be applicable to general relativity. It is of vital importance however, that he did not
strive for contradicting or denying the ‘traditional’ formulation; instead he was
seeking to establish a “more general and complete formulation, from which the
conventional interpretation [could be] deduced” (ibid.). In light of this, Everett’s new
formulation can be seen as a meta-theory to the conventional formulation, in the way
of being “an underlying theory in which the nature and consistency, as well as the
realm of applicability, of the older theory can be investigated and clarified” (ibid.).
What his meta-standpoint basically does is excluding the special postulates of the
classical formulation concerning observation (Process 1). Everett himself states that
his formulation “has to be analyzed in and for itself before any identification becomes
possible between the quantities of the theory and the properties of the world of
experience” (ibid.). After identifying those relations, one is lead back to the classical,
with observation dealing theory.
Based on Everett’s presentation of the conventional formulation of quantum
mechanics, the latter – in the terminology of von Neumann – can substantially be
understood as follows:
“A physical system is completely described by a state function , which is an element of a Hilbert space, and which furthermore gives information only to the extent of specifying the probabilities of the results of various observations which can be made on the system by external observers” (1957a: 454).
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Summarizing the conventional reading of quantum mechanics, Everett states that
there is no way of utilizing the standard model to a system that is not subject matter
to ‘external observation’, because the whole interpretative approach of it is based on
exactly this concept, represented by Process 1 (the collapse dynamics) (cf. 455).
Everett’s formulation therefore wants to omit Process 1 and solely view Process 2,
pure wave mechanics, as a complete physical theory. Within his approach, the wave
function is seen as the fundamental physical entity “with no a priori interpretation”
(Everett 1957a: 455). Note that this part belongs to the theory, so that there is no
interpretation included yet. Before interpretation comes into the picture,
“it is necessary to formulate abstract models for observers that can be treated within the theory itself as physical systems, to consider isolated systems containing such model observers in interaction with other subsystems14, to deduce the changes that occur in an observer as a consequence of interpretation with the surrounding subsystems, and to intercept the changes in the familiar language of experience” (ibid.)
Only after investigating the logical structure of the theory, one is able to put the
theoretical mathematical model into coherence with experience.
To provide a foundation for the philosophical implications, I will begin with the
conceptual basics of Everett’s formulation. Therefore, Everett’s idea behind Relative-
States and the concern of observation are given an attempted explanation,
summarizing with a recapitulation of Everett’s relative state formulation of quantum
mechanics.
3.2 Idea Behind Relative States
Everett analyzes corollaries of taking the wave mechanical formalism as a basis for
looking at composite systems. Therefore, he uses a system S composed of two
subsystems, namely S1 and S2, with their respective Hilbert spaces H1 and H2. In terms
of the classical formalism of composed systems, S’s Hilbert Space is seen as the tensor
product of H1 and H2 (written H = H1 H⊗ 2)” (Everett 1957a: 456). Even though the
general state of S can be illustrated as a superposition15, represented by the particular
state S, Everett claims that S1 and S2 cannot be viewed as having particular,
independent of one another existing states on their own. Nonetheless, he stresses the 14 To prevent misunderstandings: I will often not differentiate system from subsystem in the further course of the paper, i.e. a system is a subsystem and vice versa. The reason for this is simply the following: While for Everett a (composite) system consists of subsystems, for Rovelli a composite system consists of systems. Thus there would not be a change in the meaning if I say that e.g. two systems form a composite system or two subsystems form a composite system.15 Concerning the issues of my paper, I will simply understand a ‘superposition’ as an entanglement of states.
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fact, that “[w]e can, however, for any choice of a state in one subsystem, uniquely
assign a corresponding relative state in the other subsystem” (ibid.).
Taking the prior notions into account, Everett examines the depiction of the state of
a “composite system in terms of states of constituent subsystems” (ibid. 455). His
main insight (see Rovelli 2017) can be constituted of the recognition, that the
mathematics of the wave function directly ‘causes’ one to accept the ‘relativity of
states’; in the sense that a subsystem can’t be ascribed a single accurately defined
state, separately of the residue of the subsystem. In short: whenever (sub)systems
enter an interaction, the states adopted by the subsystems need to be seen as
correlated, not independent.
“There does not, in general, exist anything like a single state for one subsystem of a composite system. Subsystems do not possess states that are independent of the states of the remainder of the system, so that the subsystem states are generally correlated with one another. […]. Thus we are faced with a fundamental relativity of states, which is implied by the formalism of composite systems. It is meaningless to ask the absolute state of a subsystem – one can only ask the state relative to a given state of the remainder of the subsystem” (Everett 1957a: 465, own emphasis).16
Furthermore, something that’s going to be important later on, Everett views the
complete wave function in his von Neumann’s example “as a superposition of pairs of
subsystem states, each element of which has a definite […] value and a
correspondingly displaced apparatus state” (ibid.).
To break von Neumann’s example down, we could think up, in respect to Everett, a
general measurement situation. Contemplate an observing system O interacting with
any observed system S. Correspondingly, after the interaction, O is no longer
describable in an independent manner, thus only being able to be characterized
“relative to the state of the object system [S]” (ibid. 457). This means, that there no
longer exist O and S independently, but “only a correlation between the states of two
systems” (ibid.).
This result of a measurement seems to be fairly divergent with what we observe in
everyday life, since physical objects typically seem – at least to us – to have quite
distinct states. To clarify this unease, Everett asks himself here whether one can
“reconcile this feature wave mechanical theory built purely on Process 2 […]” (ibid.).
This directly leads to the ‘problem of observation’, which, Everett holds, helps
answering this question by including it into the framework of the relative-state
formulation.
16 See p. 456 for an example model of a measurement process, in respect to von Neumann.
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3.3 Problem of Observation
Having to deal with the effort of drawing inferences about the display of phenomena
occurring to observers – which are considered as entirely physical systems inside the
theory – one has, according to Everett, to recognize the observers present
characteristic properties as well as past ones. With regards to this, for the purpose of
saying that O has witnessed an event A17, it is essential for the state of O having
changed, through the interaction, from its previous to a recent state, which is
essentially dependent on A (cf. Everett 1957: 457).
Everett’s formal account of an observer differs in a quite particular kind from the
one that is used in the later sections of the paper, as well as from Rovelli’s.
Nevertheless, for a basic understanding of Everett’s formulation and its
consequences, it is necessary to keep his narrative in one’s mind.
Everett’s elementary condition for being accepted as an observer is the possession
of memories (having a memory configuration), “i.e., parts of a relatively permanent
nature whose states are in correspondence with past experience of the observers”
(Everett 1957a: 457). To deduce former actions of an observer, it is satisfactory to
infer present constituents of the memory, as it emerges from inside the mathematical
foundation.
“As models for observers we can, if we wish, consider automatically functioning
machines possessing sensory apparatus and coupled to recording devices capable of
registering past sensory data and machine configurations” (ibid.). One could further
presume that the machine’s current actions are determined by the elements of the
memory data, taken together with its recent perceptual data. Assuming that both its
present perceptual data and its configuration is directly registered in the memory,
any action of the machine can be considered solely as the operation of its memory
capacity. Because of the conclusions drawn from the mathematics, namely that the
prospective actions of the machine will be established upon the experience of A,
17 To prevent any possible problems of understanding, considering the hereafter depiction of Rovelli: ‘witnessing an event A’ equals ‘measuring a quantity q’. This has to be understood in the sense that witnessing event A means measuring a quantity q, or, equivalently, event A signifies that observing system (O) and observed system (S) interacted; i.e. O has measured a quantity q on S and this represents having witnessed event A.
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Everett uses, based on the depiction of A in its memory, expressions like “the machine
has perceived A or the machine is aware of A” (ibid: 457).18
Finally, to be able to view observers as characterizing (quantum) physical systems,
ascribing them the state function O is, for Everett, a necessary step in the procedure.
The purpose of this attribution is, simplified, to make use of the temporal ordered
memory elements of the occurrences denoted as “A, B, …, C” (ibid: 458).19 Those can
be regarded as for example “punches in a paper tape, […], configurations of a relay
switching circuit, or even configurations of brain cells” (ibid.). The only crucial point
here is that the observers are qualified “of the interpretation ‘[t]he observer has
experienced the succession of events A, B, …, C’” (ibid.).
In the further course, Everett outlines what qualifies an observation for being called
‘adequate’ and postulates two rules which are relevant for the conversion of the
complete state functions describing systems within observation processes (cf. 458).
Even though this stance is already going to be softened in chapter ‘RQM and the
Problem of Observation’, it helps in understanding his account. Since the two rules
follow the principle of superposition, they represent an appropriate mode for
determining the ultimate complete states for any quantity of observation processes in
any conjunctions. Only now, one can target the case of the interpretation of suchlike
final complete states (cf. Everett 1957a: 458).
Everett begins with the case of a simple observation of a quantity q in a system S by
an observer O. The consequence of the interaction, as outlined above, is the
superposition of the composite observer-system state S-O. That means, that there is
no longer an existing independent observer, nor system state. S and O “have become
correlated in a one-one manner” (ibid. 459). Nevertheless, it’s important to stress the
fact that
“in each element of the superposition […] the object-system state is a particular eigenstate20 of the observation, and furthermore the observer-system state describes the observer as definitely perceiving that particular system state” (ibid.).
Note that exactly this notion grants one to sustain the interpretation/conclusion that
a measurement has been conducted.
18 For further explanation and mathematical connotations, see Everett 1957a, p. 457ff.19 The dots ‘...’ represent the indication of „the possible presence of previous memories which are irrelevant to the case being considered“ (Everett 1957a: 457-458).20 The eigenstate is, simplified, the state of a physical system in which its quantity has a well-defined value.
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Secondly, and important to the conclusions being derived from it, let’s look at a
different situation explained by Everett. Note that this is done in an abridged manner,
therefore not claiming a full representation but only focusing on the most important
references, regarding the issues of this paper. Think about an observer O with the
same initial state as before, O, that measures exactly the same quantity q, but this
time, in a count of distinct, equivalent systems S1, S2, …, Sn, having the same initial
state (1= 2=…=n). Furthermore, assume that the measurements are done in a
time-wise manner, so that S1, S2, …, Sn.
Everett here invokes two rules whose formalities are of no further interest; putting
it simple: Rule 1 determines the complete state after the first measurement and Rule
2 the total state after the second measurement, as well as after performing r
measurements (r ≤ n). The resulting state of this sequence of measurements can be
written as r and, since it is constituted of a superposition of states, can be given the
consecutive interpretation: Each superposition of states “describes the observer with
a definite memory sequence […]. Relative to him the (observed) system states are the
corresponding eigenfunctions21 […], the remaining systems […] being unaltered”
(Everett 1957a: 459).
Everett concludes that an exemplary component of the conclusive superposition
characterizes a condition in which the observer has detected “an apparently random
sequence of definite results for the observations” (ibid.). Now, from considering a
redetermination of the measuring (observing) of S1, he deduces that every constituent
of the concluding complete superposition will delineate the observer with a
configuration of his memory so that any prior memory concurs with the later, in the
sense that the memory conditions are correlated (cf. Everett 1957a: 459).
“It will thus appear to the observer, as described by a typical element of the superposition, that each initial observation on a system caused the system to ‘jump’ into an eigenstate in a random fashion and thereafter remain there for subsequent measurements on the same system” (ibid.).
In this respect, the assertions made in Process 1 only “appear” (ibid.) to be justified to
O as pictured by an exemplary constituent of the conclusive superposition. Everett
concludes his remarks with this summary:
“We thus arrive at the following picture: Throughout all of a sequence of observation processes there is only one physical system representing the observer, yet there is no single unique state of the observer (which follows from the representations of interacting
21 Even though not a matter of further interest, an eigenfunction is, to put it simple, the solution of an eigenvalue-differential equation under given boundary conditions and to a given eigenvalue (differential equations), i.e. the realization of a distinct value (in Everett: relative to the remainder).
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systems). Nevertheless, there is a representation in terms of a superposition, each element of which contains a definite observer state and a corresponding system state. Thus with each succeeding observation (or interaction), the observer state ‘branches’22 into a number of different states. Each branch represents a different outcome of the measurement and the corresponding eigenstate for the object-system state. All branches exist simultaneously in the superposition after any given sequence of observations” (Everett 1957a: 459). 23
This means that the course which the configuration of the memory of the observer
takes while performing a sequence of observation is hence not a linear progression of
memory arrangements but can rather be seen as a ‘branching tree’; in the sense that
all conceivable results are happening in a conclusive superposition relative to some
systems.
This sums up Everett’s take on the ‘Problem of Observation’ since the most crucial
point is, for him, to be able to make assertions about “trajectories” (ibid: 460) of
observers, which equals, at least in my case, experience. Following this reasoning, a
course is perpetually altering from a state to a superposition, which equals
‘branching’, with each consecutive measurement interaction.24
Everett’s last stride is to consider both the aftermaths of granting interactions
(observations) of various observer systems with the same object system and
observations of one another. Whereas the latter can be seen as an interaction
between the respective memory configurations of the O’s that results in a correlation,
the former investigation (following from Rule 1 and 2) presents some more elaborate
conclusions, considering the conclusive superposition. For the scope of this paper,
we’ll be only considering one of the inferences and leave the rest aside.25
Considering the interaction between various O’s, after having individually observed
the same quantity q in a specific object system S, they notice that they are in
accordance in respect to their measurement result26. This accordance even endures in
the case that an observer executes his measurement following the ‘communication’ of
the outcome by another O, which, of course, already interacted with q of S (cf. Everett
1957a: 461f.).
22 What Everett may mean, in a philosophical manner, when talking about ‘branches’ or ‘branching’ will be cleared up later. In this regard, Everett’s letter to DeWitt will be used for clarification (1957b). 23 Note that this, which will become important in the further course of the paper, marks exactly the point of Rovelli’s departure from Everett’s presentation. The former holds that one can retain the notion of relative states in Everett’s theory without any need of taking as the ‘real stuff’ – i.e. also representing the absolute state.24 Since 'branching with each consecutive measurement interaction' is not going to be of further interest in my paper, see Everett 1957a 460ff. for an extensive account of his understanding.25 For conclusion two and three see Everett 1957a, p. 462.26 As will be shown below, this is not quite the way things work in Rovelli’s view.
12
Recapitulating, one can assess that Everett’s formulation of relative states coincides
entirely with the traditional ‘external observation’ presentation “in all those cases
where that familiar machinery is applicable” (ibid: 462); that means to every
formulation of quantum mechanics that sustains the principle of superposition.
Everett states that “the continuous evolution of the state function of a composite
system with time gives a complete mathematical model for processes that involve an
idealized observer”27 (ibid.). Every interaction implicates a superposition of states,
while every constituent (element of the superposition) of it ascribes a different state
to the memory configuration of the observer. To sum it up in Everett’s terms “pure
[…] wave mechanics, without any initial probability assertions, leads to all the
probability concepts of the familiar formalism” (ibid.).
3.4 Summarizing Crucial Elements in Relative-States
Certain experience is elucidated by the evidence of the fragmentation of the total
state in which one is able to encounter the specific experience of an observer. In other
words:
“a particular determinate experience is explained by there being a relative observer state that describes the observer as having the particular experience and by his relative state of the observer being associated with a corresponding relative state of the observed system” (Barrett 2011: 280).
In respect to the after DeWitt’s presentation emerging metaphysical commitments it’s
important to conclude once more, that Everett himself didn’t suppose his theoretical
framework to demand or promote any metaphysical obligation. This becomes clear
once one reviews a letter from Everett to DeWitt in which he explicates his
comprehension of the purpose and nature of physical theories:
To me, any physical theory is a logical construct (model), consisting of symbols and rules for their manipulation, some of whose elements are associated with elements of the perceived world. If this association is an isomorphism (or at least a homomorphism) we can speak of the theory as correct, or as faithful. […]. However, there is no reason why there cannot be any number of different theories satisfying these requirements, and further (somewhat arbitrary) criteria such as usefulness, simplicity, comprehensiveness, pictorability, etc., must be resorted to in such cases” (Everett 1957b).
This culminates in Everett’s additional explanation, that, for him, assuming a theory
to make metaphysical commitments about the world is regarded as a methodological
error (cf. Barrett 2011: 285). Concluding from this remark it becomes clear that
27 Problems that might arise by using idealized observer systems are, for the most part, uncared in my work.
13
Everett neither assumed nor thought of his theory promoting any definite
metaphysical implications.28
Considering Everett as a “methodological empiricist” (Barrett 2011: 299), what was
of importance to him was the empirical accuracy of his formulation of pure wave
mechanics. This also includes pointing out how an observer may ascertain his actual
experience depicted in the correlation structure delineated by the relative states
formulation.
The reason(s) for Everett’s take on pure wave mechanics as a fundament for his
formulation can be outlined as follows: both because (1) pure wave mechanics is
empirically accurate and consistent and (2) it is advantageous in respect to its
qualities as being more inclusive and simpler compared to other, equally consistent
presentations (interpretations) of the quantum mechanical formalism (cf. Barrett
2011: 300). This becomes plainest in terms of the equal treatment of all physical
systems, whether they are classical or quantum.
Everett also acknowledges the surplus29 represented by deducing ‘everything’ from
pure wave mechanics. Even though, following from the superposition, there are
measurement results that one can experience, as well as ones one cannot, he was not
too much concerned about this. Everett “simply required that one can be able to find
our actual experience in the model and that one to be able to understand this
experience as being appropriately typical” (ibid.). In this respect also, Everett was
able to both conclude the same measurement results as the conventional formalism
and avoid the burden of asserting a specific metaphysical interpretation of the
‘branching’ of states. One surely can view his explanation as not fully satisfactory, but
for now, in consideration of the extent of my paper, it should be regarded as enough.
Furthermore, I will accept the empirical faithfulness of Relative-States, in most cases
unquestioned; to see to how and to what extent the resulting picture of reality can be
explained philosophically reasonable.
28 So while Everett didn’t support nor even require any distinct metaphysical commitments, the paper will try both to stick as close as possible to his thoughts and conclude only what is reasonable to conclude; inspired by another of Everett’s notes to DeWitt: [o]nce we have granted that any physical theory is essentially only a model for the world of experience, we must renounce all hope of finding anything like “the correct theory.” There is nothing which prevents any number of quite distinct models from being in correspondence with experience (i.e., all “correct”) (1973: 134).29 Whether or not there ‘is’ a surplus is subject to interpretation on its own, see for example Barrett 2018.
14
3.5 Digression and Clarification - Everett and Experience
The following section will try to clarify what Everett’s understanding of the
correspondence of his formalism with our quantum mechanical experience is, or, at
least, in respect to the here interpreted understanding. In this sense, this subsection
serves for building up a prior understanding of what will be important in the last
chapter of the paper.
The elementary question is as follows: What can be extracted from the theory for
understanding its understanding of experience? What is an absolute state and what is
a relative state, moreover, what purpose do they take on?
What is somewhat crucial for Everett’s presentation of quantum mechanics is the
distinction between absolute and relative states, already depicted in a more or less
extensive manner in sections ‘Idea Behind Relative States’ and ‘Problem of
Observation’. Let us for now consider a simplified version to clarify the picture.
Assume an absolute state E, which is a superposition state (operating by the
eigenvalue-eigenstate link of von Neumann, or, equivalently, wave function) that
represents all possible outcomes for an interaction between two systems. 30 For
example, let there be a system S, a two spin particle (‘up’ and ‘down’), as well as an
observer O (another system). In this case, assuming no interaction between O and S
has been performed, E represents all possible outcomes of the measurement, i.e. E
recording O perceiving spin ‘up’ and S being spin ‘up’, as well as O receiving spin
‘down’, respectively S being spin ‘down’ (cf. Barrett 2018). In short: Both O and S do
not possess an “absolute determinate record state in E” (ibid.). Now, assuming an
observation has been performed, O and S became correlated, thus there has been an
actualization of the states of O and S, thus, e.g. O registers spin ‘up’, respectively S
being spin ‘up’. Exactly this marks the point where, through the interaction, both O
and S now have a “determinate relative record [state]” (Barrett 2018). In other
words: While E, the absolute state, can describe the complete composite system
(every possible outcome), the systems (sub-systems) are describable by the relative
states they have in respect to one another.
“Experience, then, is explained by the fact that there is a decomposition of the universal [absolute] state where one can find the particular experience of an observer; more precisely, a particular determinate experience is explained by there being a relative observer state that describes the observer as having the particular experience and by this
30 That means: E is able to describe absolute properties of complete composite systems. A composite system is, in this case, compound by two subsystems (cf. Barrett 2018).
15
relative state of the observer being associated with a corresponding relative state for the observed system” Barrett 2011: 280).
To sum it up: An absolute state (E), operating by the eigenvalue-eigenstate link of von
Neumann, provides “absolute properties for complete composite systems” (Barrett
2018), whereas relative-states “provide relative properties for subsystems of a
composite system” (ibid). It’s in this way that the ‘memory states’ (configurations),
depicted in chapter ‘Problem of Observation’, become ‘active’: The measurement
records an observer (O) perceives are identified with (are the) the observer’s (O)
relative memory states, or, equivalently “[e]xperience is found in the relative memory
records of observers” (Barrett 2018; cf. Barrett 2011: 279).
Thus, in Everett’s depiction of quantum mechanics, every interaction between
systems ‘produces’ an outcome – which will be denoted as information in the later –
that is always relative to the systems, thus meaning that experience can be
understood, simplified, as the instantiated variable of the interaction, relative to the
systems. Note again that what is interpreted in this cases doesn’t mean to cover,
neither in a general, nor in a particular way, literally what Everett would respond.
Keep in mind that with interpreting an interpretation, some information may be lost
and replaced with other information, independent of its use.
16
4. Rovelli’s Relational Quantum Mechanics – Prior Remarks
The starting point for Rovelli’s presentation of Relational Quantum Mechanics31 is
the location of a defective concept, namely the incorrect “notion of observer-
independent state of a system, or observer-independent values of physical quantities”
(Rovelli 2008: 1) from which the discomfort with viewing quantum mechanics as an
elemental description of nature emerges. He therefore attempted to derive the
standard formalism of quantum mechanics (Heisenberg-Dirac) through postulating a
simple, but elementary set of physical posits.
As with Everett’s relative-state presentation, Rovelli’s account correspondences
with the empirical results of the traditional collapse dynamics (external observer)
formalism. The basis for his deliberations is, as implied above, a
“critique of a notion generally assumed uncritically […;] the notion of absolute, or observer-independent, state of a system; equivalently, the notion of observer-independent values of physical quantities” (ibid.).
His hypothesis therefore is that quantum mechanics would be seen as much more
coherent, if one just allows oneself to dismiss this ‘incorrect notion’ in support of a
weaker one, namely the “notion of state –and values of physical quantities- relative to
something” (ibid.). Put simply, Rovelli derives those conclusions from the results of
observations that are performed in laboratories. He states: “evidence at the basis of
quantum mechanics forces us to accept that distinct observers give different
descriptions of the same events” (Rovelli 2008: 1). With this empirical evidence in
mind, he thus suggests substituting the notion ‘observer-independent’ (absolute
state) with a notion that concerns the “relation between physical systems” (ibid.).
What especially makes RQM, beyond its eminently interesting approach, fruitful for
the aim of this paper, is Rovelli’s own motivation for renewing the understanding of
the standard formulation of quantum mechanics:
“The issue is […] not to replace or fix it, but rather to understand what precisely it says about the world; or, equivalently: what precisely we have learned from experimental micro-physics” (Rovelli 2008: 1).
31 Relational Quantum Mechanics is often abbreviated as RQM below.
17
4.1 Rovelli’s Relational Quantum Mechanics
“The idea that states in quantum mechanics are relative states, namely states of a physical system relative to a second physical system is Everett’s lasting contribution to the understanding of quantum theory” (Rovelli 2017: 4, own emphasis).
Let’s first and foremost build up a basic understanding of Rovelli’s fundamental ideas
for being able to understand and carry on those deliberations in the further course of
the paper.
Rovelli’s RQM is fundamentally established upon two main notions:
(1) The discomfort with viewing quantum mechanics as a complete physical
theory may result from the usage of the inappropriate notion of ‘observer-
independent’ state of a system, or, equally, the idea of observer-independent
values of physical quantities.
(2) This unease may discontinue, once, as will be outlined below, Rovelli shows
how to deduce the formalism of quantum mechanics from a simple, yet
sophisticated set of principles about nature/the world (cf. Rovelli 2008: 2).
In respect to this, Rovelli uses the analogy of the historical antecedent ‘special
relativity’ for elucidating purposes, albeit the limitations of this analogy. As is well
known, special relativity became famous and gained public attention through
Einstein’s 1905 paper “On the Electrodynamics of Moving Bodies”. Nevertheless, what
Einstein did was not to establish a mathematical formalism and its consequent
interpretation, rather he took what was ‘already there’ – the Lorentz transformations
– and derived the formalism based on two physical postulates. “We could say –
admittedly in a provocative manner – that Einstein’s contribution to special relativity
has been the interpretation of the theory, not its formalism: the [latter] already
existed” (Rovelli 2008: 2).32 Summed up, Einstein clarified that, provided under high
velocities, the implied usage of an ‘observer-independent time’ was inadequate to
picture reality, e.g. time passes more slowly for an object moving faster than another
object relative to the former and vice versa. Thus, ‘branching off’ the analogy, Rovelli
investigated whether the discomfort with quantum mechanics may emerge from a
comparable incorrect concept (namely the assumption of observer-independent
values or states).
32 There has been much debate and many interpretational issues with the Lorentz transformations, kind of similar to the ones that arose with quantum mechanics. What Einstein did then, was to point out how the discomfort with interpreting those transformations could be cleared up (cf. Rovelli 2008: 2/ cf. Einstein 1905).
18
Following from these remarks, we’ll now try to understand Rovelli’s approach,
which he outlines as a triad. Firstly, he establishes experimentally verified assertions
about the world. Secondly, he parses those postulates and shows what follows from a
connection of them. Finally, he deduces the complete formalism of quantum
mechanics from the physical assertions (cf. ibid: 2). The main issue of my paper
though is to follow Rovelli’s analysis/understanding of the measurement process and
its consequences – as one could say it carries the most philosophical weight – and
derive philosophical implications about our reality from it. What will become of
importance in the later, but should be indicated here already, is the concept of
information – i.e. its aid in understanding what RQM and R-S say about the world.
Before attending to Rovelli’s approach any further, we should consider some
terminological specifications. The term ‘observer’ is used in a general way, or,
equivalently, an observer can be “any physical object having a definite state of
motion” (Rovelli 2008: 3). It’s important to note that ‘observer’ doesn’t solely include
animate, conscious or computing systems, any physical system can serve as an
observer.
“For instance, I say that my hand moves at a velocity with respect to the lamp on my table. Velocity is a relational notion […] and thus it is always (explicitly or implicitly) referred to something” (ibid.).
Furthermore, Rovelli’s use of the term ‘information’ is in terms of its sense in
Shannon’s information theory:
“information is a measure of the number of states in which a system can be –or in which several systems whose states are physically constrained (correlated) can be” (ibid.).
At this point a first conclusion can be drawn: (1) Rovelli addresses the incorrect
notion of observer-independent states and values of a system (2) in a manner so to
derive the formalism of quantum mechanics from a simple set of empirically verified
postulates in order to show (3) that with the usage of information theory one can (4)
conclude that physical interactions always have to be understood trough the lens of
relations.
19
4.2 RQM and the Problem of Observation
Based on the following fundamental observation of a quantum mechanical
measurement process between an observer O, a system S and a second observer33 P,
Everett’s fundamental observation can be written consequently:
“In quantum mechanics different observers may give different accounts of the same sequence of events” (Rovelli 2008: 4, own emphasis).34
Contemplate a system S observed by an observer O at time T = t 1 and let O measure a
quantity q on S. For now, according to Rovelli, it suffices to regard O as a “classical
macroscopic measuring apparatus, including or not including a human being” (ibid:
3). Note furthermore that S can be delineated by vectors in a two dimensional Hilbert
space Hs and let q take on two distinct values, 1 and 2.
Let us now suppose that “in a given specific measurement” (Rovelli 2008: 3) the
result yields ‘1’. After the measurement process, at time T = t2, system S is in the state
1, essentially because of the affection of the interaction between O and S. Let this be
a sequence of events F.
Now, this sequence F shall be delineated by the second observer P. Therefore, let P
describe the interacting system that is formed by O and S, written S-O. Note that P
does not interact with S-O in the time interval t1–t2, but assume P knows the initial
states (before the interaction, at time t1) of both S and O and is thus capable of a
description of F. This means, simplified, from the perspective of P, S-O is in a
superposition that yields the possibility of both 1 and 2. Only if P then, at later time T
= t3, measures q on S as well as O’s result, P will find that S and O agree in their
respective outcome. So, while in the first description, the system-observer dividing
line was set between S and O, the second description had an altered distinction,
namely between S-O and P (cf. Rovelli 2008: 3).
Concluding this, we see two different but correct descriptions of the same F. At time
t2 O’s description yields q having the value 1 and S being in the state 1, but P’s
description doesn’t conclude that. This aforementioned depiction is Rovelli’s main
observation, put in strongly simplified terms.35
33 „Standard quantum mechanics requires us to distinguish system from observer, but it allows us freedom in drawing the line that distinguishes the two. [...] This freedom [is] exploited in order to describe the same sequence of physical events in terms of two different descriptions“ (Rovelli 2008: 3-4).34 For the full account of the conventional description, see: Rovelli 2008: 3. Note that the presentation may leave out some important/specific remarks, nevertheless, what is shown, is enough regarding the aim of the paper.35 For both an extensive description of the main observation and objections to it, see Rovelli 2008: 3ff.
20
The following first hypothesis follows directly from the main observation and builds
the grounding for the further examination:
H1: “All systems are equivalent: Nothing distinguishes a priori macroscopic systems from quantum systems. If the observer O can give a quantum description of the system S, then it is also legitimate for an observer P to give a quantum description of the system formed by the observer O” (Rovelli 2008: 4).
In other words: In this paper I will “reject any fundamental distinctions as:
system/observer, quantum/classical system, physical system/consciousness” (ibid:
10).
Everything that follows from now on is based on both the pivotal observation and
this basic hypothesis established by the fundamental observation. In short:
investigating the repercussions of occupying this observational result.
“If different observers give different accounts of the same sequence of events, then each quantum mechanical description has to be understood as relative to a particular observer” (Rovelli 2008: 6).
What follows from this consequence of an interaction (measurement) is that any
quantum mechanical depiction of any specific system – equally for the ‘state’ and
‘value’ of physical quantities – cannot be presumed as an observer-independent
(absolute) delineation of our reality, instead it should, according to Rovelli, be seen as
a codification of characterizations of a system “relative to a given observer. Quantum
mechanics can therefore be viewed as a theory about the states of systems and values
of physical quantities relative to other systems” (ibid.). In short: the existence of a
quantum description of, for example, the state of a system S is dependent on the
interaction with another system O (observer) or, equivalently, on the description of O.
This means that any quantum state of any given system can only be taken as a
quantum state with respect to another given system.
Subsequent to these considerations Rovelli “suggest[s] that in quantum mechanics
“state” as well as “value of a variable” –or “outcome of a measurement-“ are relational
notions in the same sense in which velocity is relational in classical mechanics”
(Rovelli 2008: 6). This means that every physical variable in quantum mechanics is
considered as relational and, as we will see, this also accounts for classical mechanics;
thus concluding a quite radical statement, namely that any physical variable must be
understood in relation to something.
Attributable to this relational stance, one could surely think about incoming
criticism about RQM’s approach being close to, e.g. the realm of the ‘incompleteness
theories’ à la Born (1926) or ‘hidden variable theories’ à la Bohm (1951). In addition,
21
alternative objections could be made, but any relevant ones regarding the issue of this
paper will be discussed in the later. Thus, reconsidering the reformulation of the
difficulties arising in interpreting quantum mechanics, we follow Rovelli in
concluding the second hypothesis:
H2: “(Completeness): Quantum mechanics provides a complete and self-consistent scheme of description of the physical world, appropriate to our present level of experimental observations” (Rovelli 2008: 7).
In combination with the examination so far and the main observation, see above, one
gets to the following picture:
“Quantum mechanics is a theory about the physical description of physical systems relative to other systems, and this is a complete description of the world” (ibid.).
Taking this at a face value, what follows? If we accept Rovelli’s explanation, then the
notion of an absolute (observer-independent) description of our world becomes
untenable, even unphysical, and a total description is thus wearied by the information
systems have about one another. This means that there neither are observer-
independent values (properties) at any specific moment nor is there an observer-
independent state of a system. What follows, in short, is that “[p]hysics is fully
relational, not just as far as the notions of rest and motion are considered, but with
respect to all physical quantities” (Rovelli 2008: 7, own emphasis).
What should get concluded in a reasonable manner after these sections is Rovelli’s
claim that the conception of an absolute, or equivalently, universal depiction of the
state of our world, occupied by each and every observer – which seems to be
indicated in the conventional reading of quantum mechanics – is something that is, in
respect to empirical results, physically indefensible and therefore philosophically
arid.
4.3 Quantum Theory’s Relational Feature in Depth
“The values that a variables [sic] of a physical system takes are such only relative to another physical system. Values taken relatively to distinct physical systems do not need to precisely fit together coherently, in general” (Rovelli 2017: 2).
This feature is exactly the one difference between quantum and classical mechanics
that bears “heavy philosophical implications” (ibid.).36
36 For a detailed account of Rovelli’s view of the core differences between classical and quantum mechanics, see 2017: 2ff. The two distinctions I’m not mentioning in a thorough manner are ‘Discreteness’ and ‘Probability’. In short: “There is fundamental discreteness in nature, because of which many physical variables can take only certain specific values and not others” (ibid: 2). “Predictions can be made only probabilistically in general” (ibid.).
22
The short answer to the question above can be expressed as follows: ‘Whenever a
system O interacts (physically) with another system S, a probabilistic prediction
about a variable ‘a’ of the system S resolves into a factual value’. In short: Any value
actualizes at the base of interactions. This means that physical variables mirror the
ways different systems influence one another (cf. ibid: 3). This is accepted
irrespectively of any specifications, e.g. decoherence37, size of the system,
consciousness or extent of S’s classicality, “because none of these pertain to
elementary physics” (ibid.) and I, in this thesis, mostly only care about essential,
fundamental assertions.
The key point of the relational aspect is thus as follows: “The actualisation of the
value of [q] is such only relative to the system [O]” (ibid.).38
For more diversity, let us have a look at the conventional workbook answer. The
classical response is “”when we measure it”” (ibid: 4), but, according to the presented
account, this doesn’t seem meaningful, as “the grammar of Nature certainly does not
care whether you or I are “measuring” anything” (ibid.). A measurement, in respect to
what is examined until now, can simply be denoted as an interaction, like any
interaction between physical systems is a measurement. Thus with any interaction,
variables take value.
“But, (this is the key point) if a system S interacts with a system [O], QM predicts that in a later interaction with a further system [P], a variable b of the S [O] system is not determined by [the quantum state ]. Rather, it is determined by the joint dynamical evolution of the S [O] quantum system” (ibid., partly own emphasis).
With the answer of RQM to the resulting interference between ‘q’ does take a value
and ‘q’ does not take a value, we arrive at the pivotal idea underlying the RQM
interpretation:
“[T]he variable [q] of the system S actualized in the interaction with [O] takes value with respect to [O], but not with respect to [another system P]” (ibid.).
As an interim conclusion of the relational feature of quantum mechanics, one could
say –exhausting the previous remarks to the fullest – the feature becomes, from the
standpoint of RQM, a fundamental characteristic:
“[T]he actual value of all physical quantities of any system is only meaningful in relation to another system” (ibid: 4).39
37 For a basic understanding of decoherence, see for example Friebe et. al 2018: 63ff.38 For a view of the detailed argument that leads to the conclusion, see Rovelli (1996).39 Considering the relation of a variable that is relative to one system and the relation of the same variable to another system, Rovelli states: “It is possible to compare different views, but the process of comparison is always a physical interaction, and all physical interactions are quantum mechanical in nature. I think that this simple fact is forgotten in most discussions on quantum mechanics, yielding
23
4.4 The Notion of Information
This section deals with the term information, as, on the one hand, Rovelli’s
formulation of QM is in terms of information theory and, on the other hand, his
24
formulation can be coded within the following deliberations.40 Before investigating
the physical meaning of this notion, we try to acquire a general understanding of
25
Rovelli’s use and conception of information, which is based on Shannon’s information
26
theory.41
The basic question is: “[w]hat is the precise nature of the relation between the
variable q and the system O expressed in the statement “q = 1 relative to O”?” (Rovelli
2008: 9). To clear this up I follow Rovelli and iterate the idea behind it, from an
information-theoretical view, i.e. I now target the physical nature of the statement.
The assertion, e.g. ‘q = 1 relative to O’ both has no absolute (observer-independent)
relevance and belongs to the conditional of the coupled S – O system. This means,
recapitulating, statements about S – O can only be made relative to a ‘third party’, e.g.
P. Thus, the assertions (descriptions) made by P can only be understood quantum
mechanically, not classical. Following this, the result of P’s description reveals a
correlation between q and O, which means that P, on this basis, is able to measure
subsequent sequences of events on q that will be correlated with O’s variables (cf.
Rovelli 2008: 9).
27
“Correlation is “information” in the sense of information theory [Shannon 1949]. […]. I will from now on express the fact that q has a certain value with respect to O by saying: O has
28
the “information” that q =1” (ibid., partly own emphasis).42
Respectively, considering that any physical system is understood as a quantum
mechanical system, the term information used here also doesn’t need a
differentiation, neither between systems that are able to make use of meaning or do
not, nor simple or complex systems or even non-human or human observers. In short:
“Observers are not “physically special systems” in any sense” (Rovelli 2008: 10).
“[I]n the technical sense of information-theory, the amount of information is the number of the elements of a set of alternatives out of which a configuration is chosen. Information expresses the fact that a system is in a certain configuration, which is correlated to the configuration of another system (information source)” (Rovelli 2008: 10).
29
This notion of information represents a minimal and weak condition, from which
30
more sophisticated ones can be deduced (e.g. Quantum Information43). For Rovelli, as
well as for my concerns, this notion shall be enough, due to its fit both for a physical
theory as well as for subsequent philosophical deliberations.
“(i.) information can be lost dynamically (correlated state may become uncorrelated); (ii.) we do not distinguish between correlation obtained on purpose and accidental correlation; Most important: (iii.) any physical system may contain information about another physical system” (ibid. 10).
Consider for example a Stern-Gerlach apparatus where there are two spin (‘up’ or
‘down’) particles – which allows them to act as a physical system in the sense of
Rovelli, because they are able to be in more than one state – having the same spin
value, in the same direction (e.g. ‘up’). Thus, one is allowed to say that one of them has
information about the other one. Recapitulating the present argumentation, we arrive
at a first, even though only partial, answer to the question posed in the beginning of
the section:
“the physical nature of the relation between S and O expressed in the fact that q has a value relative to O is captured by the fact that O has information (in the sense of information theory) about q. By “q has a value relative to O” we mean “relative to P, there is a certain correlation in the S and O states”, or, equivalently, “O has information about q” (Rovelli 2008: 10, partly own emphasis).
This answer can be considered ‘partial’ in two senses, notice that one of which is left
out here. The response kind of postpones the issue outlined above by explaining the
‘information occupied by O’ in form of the ‘information occupied by P’. Following this,
one finds that Rovelli’s use of the term information entails a double significance:
(1) Rovelli wants to mitigate physical statements of the form ‘the spin is down’
into ‘O has information that the spin is down’, which implies or enables
another O (e.g. P) having different information about the spin. Consequently,
information suggests the usual attribution of values to quantities that
substantiates physics, but accentuates their relational aspect.
(2) The just mentioned attribution can be explained as correlation – the notion of
information-theoretical information – from within information theory itself. As
we have seen above, such a depiction is viewed as an observer-dependent and
quantum mechanical one, as an observer-independent (absolute) state of our
world doesn’t exist in these terms.
“Finally, there is a key irreducible distinction between P’s knowledge that O has information about q and O’s knowledge of q. Physics is the theory of the relative information that systems have about each other. This information exhausts everything we can say about the world” (Rovelli 2008: 10, partly own emphasis).
31
This sums up both Rovelli’s understanding of the term information as well as its
implications for the picture of the world it entails, which will be further examined in
the last chapter of my paper, where the philosophical implications of both
formulations of QM will be discussed and compared. Subsequent to the above
description one arrives at Rovelli’s first main postulate. Note that from both the
formalism of quantum mechanics is derived, but that’s not the main focus of the
paper. Therefore, solely the postulates and their physical implications are presented,
regarding the concluding discussion of their philosophical implications, in respect to
the prior accounts. Additionally, for now at least, I will claim that this delineation also
applies to Relative-States, independent of contextual differences.
4.4.1 Two Information Postulates
P1 “(Limited information). There is a maximum amount of relevant information that can be extracted from a system” (Rovelli 2008: 11, own emphasis).
What this postulate means, physically, can be summarized as follows: “it is possible to
exhaust, or give a complete description of the system” (ibid.). Therefore, based on the
complete description any future prognosis about the system can be concluded.
Clarifying, one could say that S possesses a “maximal “information capacity” N, where
N, an amount of information, is expressed in bits. This means that N bits exhaust
everything we can say about S. Thus each system is characterized by a number N”
(ibid.). Pictorial: Consider a cup of coffee that is placed on the table in the library. One
could ask about e.g. the spatial location of the table within the library, the amount of
coffee left in the cup, whether its coffee from beans or powder, the kind of coffee in it
etc.
At this point, one may ask himself ‘what happens if system O asks an additional
question, denoted as QN+1, after N questions have been asked, insofar as the
mentioned maximal amount of information about a system has been reached?’ This
leads to the second main postulate:
P2: “(Unlimited information). It is always possible to acquire new information about a system” (ibid: 12, own emphasis).
According to Rovelli’s examination, the possible consequences can be summed up as
two extremes. The first simply states that, if the further question QN+1 is already
completely defined by previous Q’s, no novel information is acquired (because this is
not subject to further eventually arising problems, it will not be considered from now
32
on). What is striking is that P2 obviously dissents with P1. It is crucial though, for the
sake of argumentation, and more importantly because P2 is, as we will see, not just
added ad hoc to verify the concept, to accept that “the sequence of responses we
obtain from observing a system cannot be fully deterministic” (Rovelli 2008: 12). P2
is not added, as noted, to ‘make the argumentation work’, but rather entirely
derivated from experimental results (cf. ibid.). In Rovelli’s words:
“Since the amount of information that O can have about S is limited by [P1], when new information is acquired, part of the old relevant-information becomes irrelevant. In particular, if a new question Q (not determined by the previous information gathered), is asked, then O looses (at least) one bit of the previous information. So that, after asking the
33
question Q, new information is available, but the total amount of relevant information
34
about the system does not exceed N bits” (ibid.).44
4.5 Summary of Rovelli’s Ideas
Before moving on to the philosophical implications of Rovelli’s and Everett’s ideas,
let us recapitulate the most important steps in the formers conception.
Beginning with H1 (that all and every system is considered equivalent) one is able to
acknowledge that any system (observer) can be described using the same physics as
can be any other system. Particularly, this means that it is possible to describe any O
that interacts with (equally measures, observes) a system S quantum mechanically.
Therefore Rovelli set up a sequence of events F, which was analyzed from two distinct
perspectives of observation (one observer O and a third, initially external to the
observation, P). The conclusion of this thought was the main observation, namely that
‘different observers may give different accounts of the same sequence of events’.
Taking this as a basis for a understanding of the world, Rovelli concluded that “[ i]f
different observers give different descriptions of the state of the same system, this means
that the notion of state is observer dependent” (Rovelli 2008: 15).
The next step was crucial, insofar as it also laid the basis for Rovelli’s understanding
of quantum mechanics in information theoretical terms. What happened was a
replacement of the notion ‘absolute (observer-independent) state of a system’ with
the notion of ‘information that systems have about each other’. Therefore, Rovelli
introduced three postulates (of which we only considered two as valuable for the aim
of the paper) that his conception of information had to fulfill and, from there, derived
the complete formalism of quantum mechanics. Note once more, that all three
postulates express the current experimental argument about the world and thus,
haven’t been added ad hoc or the like.
In one sentence: Rovelli’s formulation doesn’t only seem to be buff or attractive, but
also let’s one appreciate that what is at the core of quantum mechanics could quite
well be relationalism.
35
5. Philosophical Implications - Introducing Remarks
“This problem of getting the interpretation proved to be rather more difficult than just working out the equation” (Dirac 1977: 2).
After having examined the physical implications of both presentations of quantum
mechanics, we now focus on their respective implicit philosophical stance. Before that
I have to clarify though that both the Relative-State and the Relational presentation
are only investigated from a certain perspective. The latter has already been
analysed, e.g. in a rigorously empiricist reading (van Fraassen 2010) or in a neo-
Kantian one (Bitbol 2007), to name the most prominent interpretations. A greatly
interesting approach to try and give RQM a philosophical ‘home’ has been performed
by Candiotto (2017) in “The Reality of Relations” where she tried to frame RQM into
the abstract context of Ontic Structural Realism. Everett’s formulation on the other
side served as the foundation for the family of the so-called ‘Many-Worlds
Interpretation’s’ (DeWitt 1970; see Saunders, Barrett, Kent, Wallace 2010 or
Butterfield, Earman 2007 for an extensive review), which is, in spite of the difficulties
Everett faced after his 1957 paper, nowadays the most prominent interpretation of
quantum mechanics among physicists. See furthermore Wallace (2012) for a defence
of the Everettian interpretation of QM or Conroy (2012) for a ‘Relative Facts’
interpretation closely linked to Everett’s ‘note added in proof’.
Even though Candiotto’s reading seems not only to be philosophically fruitful but
also exceedingly interesting to me, it would go beyond the spectre of this thesis to try
and express both ‘Relative States’ and ‘RQM’ from within Epistemic and/or Ontic
Structural Realism; this should, in respect to its scope, be left for another paper.
However, as will get clearer later on, the reading I offer strongly relates to both
versions of structural realism, albeit in a more general manner.
The aim of this final chapter is to deduce a fundamental, though approximate,
picture of how Rovelli’s and Everett’s formulations differ in their respective
philosophical image of reality. What, in the light of the theories, can be regarded as
‘reality’? or, more specific: If RQM and R-S make different statements about what is
reality, how may one meet their claims in a reasonable manner?
36
37
5.1 Everett and Rovelli in Respect to Realism
38
When talking about the term realism45, I follow Rovelli’s depiction of both weak and
strong realism.
39
In its weak meaning, realism refers to “the assumption that there is a world outside
40
our mind46, which exists independently from our perceptions, beliefs or thoughts”
(Rovelli 2017: 6). In other words: Outside our own experience, there exist a vast
amount of physical systems that are interacting with each other and we, as physical
systems on our own, can gain knowledge about them by means of interaction. In
respect to the language used by Rovelli and the language I make use of in Everett
(some variable taking a value in relation to a certain system, or, a system recording a
value relative to another system), any system capable of more than one state is
qualified as a system. Thus, speaking in an analogy, the velocity of the Moon is 1km/s
with respect to the Earth, or, the velocity of the Moon recorded by the Earth is
1km/s). Ignoring the small differences of this assertion, I will treat both in the same
manner from now on. Concluding, quantum theory doesn’t qualify in a different
manner to realism as classical mechanics does (recall that we treat both classical as
well as quantum mechanical systems in the same way). The difference between
Everett and Rovelli – note that it’s not ‘the’ difference, but my main focus – thus lies in
their diverging understanding of . While in Everett’s account takes on a crucial
role as being the absolute state from which, simplified, relative states are realized,
Rovelli’s RQM can be said to be “anti-realist about the wave-function, but […] realist
about quantum events, systems, interactions [and so forth]” (Rovelli 2017: 6). In
short: In respect to Rovelli is not more than a bookkeeping devise storing the
information of interactions, thus ‘breaking down’ at interactions, i.e. representing
kind of an ‘update’ of the stored information.
As opposed to this weak meaning, strong realism entails the assumption
“that it is in principle possible to list all the features of the world, all the values of all variables describing it at some fundamental level, at each moment of continuous time, as is the case in classical mechanics” (Rovelli 2017: 6).
As is almost obvious, while RQM doesn’t fulfill this requirement at all, Relative-States
seems to fit quite well to this condition – at least at first glance since it depends on the
reading of the latters interpretation. The reason for Rovelli’s RQM not to fit into this
picture is, in a technical sense, related to its stance towards the Kochen-Specker
theorem, which, to put it simply, states that only at interactions variables take on
41
values (cf. ibid.).47 According to Rovelli not taking this theorem at face value thus
results in being in, at least somewhat, tension with the very formalism of quantum
mechanics (Heisenberg). From a less technical stance, Rovelli offers three more
reasons for RQM not dwelling well with strong realism. I will only refer to two of
them, of which kind of a blending of them will be object of further investigation. The
first one is the concern of QM needing a sparser ontology than classical mechanics,
since within RQM there is no meaning in what happens between interactions, all one
can meaningful talk about are interactions (cf. Rovelli 2017: 5ff). The second reason is
RQM’s implicit anti-monistic point of view, i.e. since the theory understands the
quantum state solely as a bookkeeping device for the state of a system – that is the
result of interactions – there is thus nothing to gain from talking about “”the quantum
state of the full universe”” (ibid: 7).
Depending on the reading, of which I will mention two, we obtain different results
for Everett. In the first reading – referred to DeWitt – one will surely state that
Everett’s formulation makes sense even in the strong meaning of realism. This is
because, focusing on two crucial points, both circumventing the Kochen-Specker
theorem and thus allowing values to be realized even without interaction and
adhering to a branching of the world at each interaction, that results in every possible
outcome of the interaction being realized in different worlds, fulfills the requirement
of ‘listing all the features of the world, all the values of all variables describing it at
some fundamental level, at each moment of continuous time’. The second reading –
referred to be Everett’s own – splits up into at least two possible versions. When
looking at strong realism from the perspective of the mathematics, from ‘within the
theory’, Relative-States surely fulfils the requirements, since every element of the
superposition is denoted as ‘real’ as any other. On the other hand, taking on the side
of experience, Everett would state that nothing is ever ‘absolutely’ or ‘actually’
realized, unless relative to another system, i.e. states of systems are only ‘real’ relative
to the state of some other system (cf. Everett 1957b,c). Following this, Everett thus
kind of seems to be making hybrid statements. In other words: “Everett was an
operational realist concerning all branches in every basis insofar as they might be
detected” (Barrett 2018). An attempt of further elaboration and clarification of both
stances towards a more sophisticated stance of realism is therefore found in section
‘Relative-States and RQM and Structural Realism’.
42
As it would seem quite intuitive, I could also compare R-S and RQM in respect to
anti-realism, or, more accurate, investigate anti-realistic elements within the theories.
However, as I already accepted, or, to be more precise assumed the premise that both
justify empirically faithful assertions about the world, I will leave arguments denying
43
a fully realist account aside and focus on whether and to what extent both theories
44
can be said to imply structural realist assertions.48
5.2 Moment of Consensus and Divergence
At the cost of repeating myself, I will stress again the, in my understanding, most
important factors of divergence to give a comprehensive account of the philosophical
‘cost’ and consequences of both theories. The main reason for my focusing on the
differences, or rather a certain parting of their ways, as opposed to similarities or
consensus among R-S and RQM is that I want to understand whether, or to what
extent, there could be a reason for both pertaining to relative-states but at the same
time implying different pictures of reality, or, equally, there could be a meaningful
45
comparison or a discrepancy.49 More precisely, this section should serve as a
foundation for answering the general question; which picture of reality can be
deduced from the respective theories? In this respect, it is necessary to delineate the
crossroad that is essential for the following deduction.
According to the presented literature, many if not most of the points present in
Everett can be ascribed to Rovelli, especially the novel notion of relative-states the
former introduced into the debate of the interpretation of QM. That both accounts
share many conceptions is painfully obvious, as of the decisive role Relative-States
can be ascribed in the product of RQM, the latter kind of representing a radical
furthering of the notion of relative-states. What shall be illustrated therefore, or at
46
least be aimed at in this section, is to identify a core difference50 of the theories, which
shall subsequently take on a crucial role in extracting, or, equivalently, deducing their
respective philosophical conceptions of reality.
The origin of divergence between Everett and Rovelli can thus be detected as
follows: “Everett’s relative states are the only quantum states we can meaningfully
talk about. Every quantum state is an Everett’s quantum state” (Rovelli 2017: 7). In
my reading, this quote expresses both the point of outmost consensus and a possible
47
point of divergence.51 Whereas Rovelli agrees with Everett that an attribution of
definite values of dynamical values to a system is only meaningful relative to the
states of different systems; the ‘moment’ of divergence is that while Everett takes the
quantum state (wave function) as the basis of reality (in the sense of being the basic
physical entity) Rovelli does not (remember that the quantum state is solely a
‘bookkeeping devise’) (cf. Myrvold 2018).
In other words: Whereas in Everett’s picture, the wave function can be said to be
the totality of possible information an observer could theoretically attain on the
system, i.e. information is relative to the state of a system, and the state is relative to
the remainder of the system; in Rovelli’s picture the wave function can be said to
describe the information an observer has on the system, i.e. information is relative to
a system.
Again in other words: While the wave function in Everett’s formulation is the basic
entity of reality, the wave function in Rovelli’s formulation is relative to the observer.
This also means that while in the former depiction the wave function isn’t relative to
a observer and evolves with time, it works contrary in the latter depiction; not the
wave function evolves with time but the observer does.
Speaking in Everett’s terms, there is always one distinct physical system (observer)
for whom a multiplicity of possible resulting relative states of measurements obtain,
i.e. each of the relative states representing a different relative experience of reality
(cf. Barrett 2011: 290). Compared to that, in Rovelli’s presentation we also find one
physical system (observer) but only one distinct relative state, i.e. a state that is
relative only to the observing and observed system.
From this illustration it should be clear by now, that the focus of my argumentation
are the consequences both theories and thus I can draw from their respective
understanding of a relative-state; that also includes the wave function (quantum
state) and the respective picture of reality it ‘resonates’. How one can picture this in
more philosophical precise terms is the task of the next section. For this, we will also
take into account the information-theoretical stance we already reflected upon in
Rovelli’s terms – note again however, that Rovelli’s use of information is almost
completely transferable to Everett’s account, albeit a small but crucial difference, as
will be examined below.
48
5.3 Relative-States and RQM and Structural Realism
As I already somewhat cleared up both theories standing in respect to a weak and
strong version of realism, we now try to focus on a more elaborate one, namely
49
structural realism52. Doing this can be said to be justified mainly because structural
realism deduces its main argument from quantum mechanics itself (cf. Candiotto
2017: 3). However, referring to both ‘Relative States’ and the ‘Relational Presentation’
in this framework doesn’t mean that I’m striving for a complete representation of the
contemporary debate about the metaphysics of quantum mechanics. Rather I will
focus on the ‘core difference’ worked out in the last section and take this as a starting
point for an understanding in structural realist terms. This implies not taking the
ontic and epistemic variant of structural realism as a frame and see how well RQM
and R-S dwell within it, but rather investigating whether, and if so, to what extent
both theories’ statements fit into statements made in ontic or epistemic structuralist
50
terms53. In doing this I may add philosophical notions to both theories or fine-tune
some parameters in order to show both a possible embedded philosophical stance
and make the argumentation more coherent. Nevertheless, as I already mentioned, I
want to stick closely to both accounts of quantum mechanics (sparse ontology) in
order not to manipulate their respective image of the world too much and thus be
able to answer my guiding question as reasonable as possible.
5.3.1 Discussion of Epistemic and Ontic Elements in Relative-States and RQM
The question kind of leading through this final section is the following: Whether,
and to what extent imply RQM and R-S statements that are adequate to be
understood in structural realist terms? or, more rough: What is the ‘actual stuff’ both
in the Everett and Rovelli picture that is capable of taking us from the very formalism
to our experience?
I will seamlessly attach to the remarks concluded in section ‘Moment of Consensus
and Divergence’ and to a certain degree take Candiotto’s (2017) investigation as a
guiding idea and foundation for my argument.
When talking about realism in a broad sense, according to RQM relations can both
be identified as information and stated to be the very building blocks of reality (cf.
51
Candiotto 2017: 3). Compared with this, in Relative-States the wave function54 can be
52
considered as the building block of reality55 as well as, in respect to viewing the
structure as information, absolute, thus observer-independent. Insofar as information
is taken to be observer-independent in both accounts, I will state that information as
such exists in relations that are independent of observers both manifesting
themselves through interactions and being constituent for the interaction itself.
Accentuating the relationship between the observing and observed system, one
could easily state that both the theories, at least implied, question the foundational
relation between ontology and epistemology. While RQM can be said to aim for an
ontology that views properties or states of systems as being fundamentally relative to
other systems – remembering that different observers can give different accounts of
the same sequence of events – and thus resulting in a state that is essentially
observer-dependent; Almost the same can be ascribed to R-S, with a important
difference: Different observers can, without any problem, give the same account of
the same sequence of events, which not only weakens the point of observer-
dependence but kind of makes it obsolete. Clarifying: subsequently to those
deliberations we can differentiate between two types of questions: “(i) Does P “know”
that [O] “knows” the value of q? (ii) Does P know what is the value of q relative to O?”
(Rovelli 2008: 8). Vivid: I know that you know about the reasons for climate change,
but I don’t know what you know about the reasons for climate change. While this is
what one would respond in RQM’s terms, taking on the perspective of R-S both that
and what you know about climate change is possible to answer – states are always
relative-states, but they are not distinct to only one observer system.
Based on Candiotto, RQM implicitly “argues against the notion of “object” as an
“entity” that possesses intrinsic properties” (p. 3) and is thus relativizing states (or
properties) of systems to other systems. In comparison, R-S doesn’t necessarily argue
against a system as an entity that possesses intrinsic properties, but one can surely
claim so considering the addition that states (or properties) always have to be
understood as relative states once an interaction has been performed, i.e. the state of
a system is always relative to a given state of the remainder of the system –
remember the fundamental relativity of states.
Referring to the information theoretical stance, RQM began with an identification of
the ‘observer-independent’ state of a system as an incorrect notion and, in the further
course, replaced the notion of an observer-dependent ‘state of a system’ with the
‘information a system has about another one’, meaning that information is exchanged
53
via physical interactions. In R-S terms however, we identified the ‘absolute state’ as
the structure that can be said to be containing the ‘complete information a interaction
can yield’, but only ontologically (from the mathematics), as the structure is only
partly realized in ones distinct experience. Note that all outcomes are realized, though
not possible to experience once a certain result is obtained or, equally, an interaction
has begun. We can state here, as an interim conclusion, that R-S’s epistemic and
ontological reality is quite distinct. Nevertheless, to clear possible misunderstandings
about ‘a system having information about another system’ (which I accept for both
theories to work): even the table I am sitting at right now can be seen as having
information about the bottle of water that is placed on it, or, a notepad that is full of
notes about travel ideas, or, two-spin (‘up’ or ‘down’) particles having the same value
in the same direction. Anything is considered a physical system, as long as it is
capable of being in more than just one state.
54
Carrying on, in respect to RQM, relations can be stated to be “modalities of
55
processes56, structures through which the systems interact and communicate. The
structure of reality is not made of connections among objects, but of interrelated
relations” (Candiotto 2017: 4). Rephrasing this statement in R-S language: Relations
are a modality of processes as well, a structure through which the systems interact
and communicate. The ontological structure of reality is thus not made of connections
among objects, but an underlying entity; experiential reality is made of connections
among objects, based on the wave function (QS), i.e. that these connections have
always to be understood as relative among them, thus being relations among
interrelated objects. To make this point more clear or vivid, consider a certain
physical quantity q that has a value related to you as well as with respect to me
(imagine being the same room, looking at the same cup of coffee on a table). We can
compare the values we perceive (e.g. spatial location of the cup) by going into an
interaction, namely communicating. Regarding the remarks above, this
communication, in terms of RQM, is quantum mechanical in nature and thus
“intrinsically probabilistic” (Rovelli 2008: 8) which therefore means your inquiry
about my location-value of the cup is a quantum measurement. However, in terms of
R-S, comparing the perceived values poses no difficulties, as it both does not
56
represent a quantum measurement and one can ‘for any choice of a state in one
57
subsystem, uniquely assign a corresponding relative state in the other subsystem’.57
Concluding from these remarks: Both R-S and RQM, in my reading, understand
correlation as information, i.e. referring to the dynamic character of processes that is
closely-linked with Rovelli’s second postulate of quantum mechanics (P2). From a
philosophical stance, P1 clarifies that the character of the processes is discrete
(limited information); P2 (unlimited information) both emphasizes that knowledge
acquisition is procedural and includes the empiricist account in which discoveries
58
made a posteriori should always imply a deviance of prior knowledge 58. Explaining
this thought more precise: While, in RQM’s terms, P1 allows us to give a complete,
coherent and discrete description of a system, P2 gives us the opportunity to modify
the description, including an epistemic success (cf. Candiotto 2017: 4). Speaking in R-
S’s terms, P1 does kind of the same, albeit a significant difference: the formalism lets
it only ‘appear’ to us as if we have a discrete, complete and coherent description of a
system; P2 can be ascribed to R-S easily, assuming that no other observer observed
another quantity on the same system, not commuting with the one that was observed
by the former (cf. Everett 1957a: 462).
Taking a little departure from the present argumentation and looking at some work
that has already been done in a quite comparable manner we can spot for example
van Fraassen’s reading of RQM within the frame of informational structural realism.
This more epistemic variant, which can be said to be particularly argued for by
Rovelli, is based on the latters assertion that ‘the amount of information is the
number of elements of a set of alternatives out of which the configuration is chosen’.
In short: van Fraassen furthers the thought that RQM describes solely the information
systems have about another. More precisely, van Fraassen stated that RQM “offers a
program to derive the theory’s formalism from a set of simple postulates pertaining
to information processing” (p. 390). That means, in the connection between system O
and system S, let O gain information about S. This signifies explicitly that the states
are the information of the observer. In other words, in respect to RQM: what the wave
function does in Rovelli’s picture is thus describing the information system O has on
system S. Paraphrasing this in R-S terms: the wave function describes the complete
information an interaction could result in, in any possible correlation configuration;
but as the observer is only able to receive one element of the possible configuration,
the resulting correlation describes system O and system S as subsystems perceiving
59
one ‘branch’59 relative to the wave function. Summarizing: One could say that both
RQM and R-S claim the ‘same’ statement based on a different foundation. Taking on
van Fraassen’s reading, both the theories seem to be quite tenable within epistemic
structural realism. On the one hand RQM, because it promotes the relational
(observer-dependent) characterization of reality and on the other hand R-S, because
of its implied divergence of epistemic and ontic reality, of which we, seen as physical
systems, are only able to perceive the former. Nevertheless, as we shall see below,
they also seem reasonable in a more ontic reading of structural realism.
For now I will try to demonstrate how both the theories, one of them maybe better
than the other, may be framed within the latter reading of structural realism. First of
all we have to find a basis for interpreting them within this framework. As I depicted
above, the ontological value of R-S and RQM may be derived from the importance of
relations understood as information – may it be on basis of the wave function or
interactions between systems (physical variables) – and thus being able to be
apprehended as the bedrock building block of reality and our experience. Candiotto
for example claims that RQM can very well be interpreted as “a realistic theory that
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assumes the notion of relation as primitive60” (p. 5), or, equivalently, viewing the
physical interactions among systems as primitive; the same goes for R-S, though, in an
ontic reading ‘interactions between systems’ has to be replaced with the ‘structure’
(wave function). Taking on this perspective we acknowledge that structures,
generally speaking, represent the (axiomatic) foundation of reality from which
entities (objects) ‘hatch out’ as the relational crossroads of the respective relevant
relations. Comparing the ontic with the epistemic perspective it becomes clear that
while in the latter the existence of these junctions is preliminary for emerging
relations, the former basically states that the crossroads originate from the relational
web. While the ontic reading and RQM harmonize pretty well, we have to point out, as
has already been indicated, an important fact in respect to R-S: as I state the wave
function (QS) to be the absolute foundation, we have to take ‘absolute’ with a grain of
salt; objects do not emerge as relational crossroads within R-S, they rather experience
(record, perceive) a elementary part of the set of the relation that is the basis of
ontology. Thus, while RQM takes relations as axiomatic, R-S views the wave function
(structure) as an axiomatic concept, not being able to be proven precisely because we
can’t, in principle, experience it. This means, while from RQM’s stance nature is
relations, from R-S’s perspective relations are the way we experience nature, but
nature is not relations.
Relativism Excursus
Heretofore, I spoke of structural realism only in terms of relations, respectively to
both theories. Let us for a moment – in order to make evident not to mistake
relationalism for relativism – take on a relativist stance, following Baghramian
(2018):
““[R]elativism” covers views which maintain that—at a high level of abstraction—at least some class of things have the properties they have […] not simpliciter, but only relative to a given framework of assessment […]. Relativists characteristically insist, furthermore, that if something is only relatively so, then there can be no framework-independent vantage point from which the matter of whether the thing in question is so can be established.”
In that respect, paraphrasing this to fit for my interpretation of RQM and R-S, both
theories can be said to hypothesize or theorize the impracticality of absolute states or
inherent properties of systems, i.e. absolute image of reality; albeit R-S only
epistemically, not ontologically. That means there is only a web of relations that
surfaces trough the relations between systems (cf. Candiotto 2017: 5). In other
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words: There are neither inherent properties of systems nor absolute states – for now
we will disregard the essential ontic absolute state (wave function) of R-S. What an
observer O perceives can thus be different from what an observer P perceives – from
this perspective, RQM seems to fit quite well into the scheme of relativism. Even R-S
seems to fit, if we fine-tune some parameters: In general, what an observer O detects
can be the same another observer P detects, assuming that both are in the same
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‘branch’61, or, more specific, though simplified and contentious; once an observer O
has measured a quantity q, P can get the same result about q (see climate change
example). The wave function (structure) is deterministic and experience ‘appears’ to
be probabilistic. What accounts for RQM can account for R-S if we say that, simplified,
the observer O and P are the same physical system, but representing a different
outcome of the interaction, thus receiving different results. Somehow vivid: (1) ‘My
cup of coffee is actually on my desk, relative to my having it put there’ is relative to
me sitting on my desk, writing this paper. (2) ‘My cup of coffee is actually at the lost
and found, relative to my having it forgotten on the campus’ is relative to me having
taken a walk at the campus, drinking coffee out of my cup and having forgotten the
cup somewhere. Both (1) and (2) represent ‘actual’ events, depending on the relative
reference frame. In other words: “The suggestion seems to be that there is always
precisely one physical observer for whom multiple post-measurement relative states,
each characterizing different relative experiences, fully obtain” (Barrett 2011: 290)
Summing up this statement about perceiving an outcome, from the perspective of a
relativist, a quantity q is relative to O and thus there are no absolute states and
absolutes in general. While this fits tout court to RQM, in R-S terms it would be like
this: q can be relative to O and P, both detecting the same value and thus the
statement is epistemically (in reference to our experience) true; in other words, not
reality is relative, but the states observers perceive. In one sentence: Until now both
RQM and R-S fit into relativism, though dissimilarly well; RQM fits completely, while
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R-S only in respect to states of systems, meaning everything we, as systems, can
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quantum mechanical experience.62
It’s important however that particularly because of the conclusions RQM pulls of
such definitions the theory doesn’t really fit into a relativist approach. While in R-S’s
terms true assertions about the nature of things are always epistemically relative,
RQM’s aim is to provide a complete description of reality, based on the relations
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among systems. In that respect I follow Candiotto’s reading of Rovelli and state that
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RQM is a relational63 theory, not a relativistic one. While relativism kind of implies an
“inescapable relationship that determines the knowledge of reality, consisting in the duality between the observer and observed; relationalism is rather characterized by an objectivist emphasis, indicating the relational structure that constitutes two or more realities that do not exist independently” (p.6).
Regarding this understanding of relationalism and relativism, R-S places itself as
follows: Concerning relativism R-S indicates that what is the inescapable relationship
determining the knowledge of reality, is exactly the crucial dependence of a system
on a reference frame for experiencing a certain value; but, and this is important, in
Everett’s picture there is no duality between observer and observed, it is a rather
monistic image based on the wave function. In respect to relationalism, the wave
function is an objective, not perceivable entity (structure); at the same time the wave
function is the structure that constitutes two or more realities that do not exist
independently, but only from the perspective of the relative state of the observer,
because the wave function never ‘collapses’ in Everett’s formulation.
5.3.1 Discussion of Epistemic and Ontic Elements in Relative-States and RQM
Let me now return to my main argument between ontic and epistemic implications
of R-S and RQM. Disregarding the underlying structure of R-S, and assuming systems
do not possess intrinsic properties in Everett’s picture, the following depiction is
ascribable to both theories. Everett and Rovelli both can be interpreted to describe
the essential structure of matter itself. Any interaction among systems is an axiomatic
(primitive) notion, thus, speaking in information-theoretical terms, physical
interactions allow the exchange of information. The reason for this assumption is
basically that there is no possibility to ascribe systems any inherent properties
impartial of their interactions that result in information acquisition.
Taking these remarks fully into account, while I would not regard RQM within
patterns of epistemic structural realist approaches, one surely can place R-S within
them. This is exactly because, in epistemic accounts, “what the scientific theories
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explain are the structures through which we know the world, but its not nature. ESR64
does not undertake any ontological commitment” (Candiotto 2017: 7). In Everett’s
own words:
“Once we have granted that any physical theory is essentially only a model for the world of experience, we must renounce all hope of finding anything like “the correct theory.” There is nothing which prevents any number of quite distinct models from being in correspondence with experience (i.e., all “correct”) (1973: 134).
Speaking in an epistemic account, the world may be constituted of individual objects
– replaced by the wave function as ‘the structure’ in R-S terms – that are preliminary
to the relational structure between systems; thus relations are only representing the
various ways in which systems can be known by other systems (cf. Candiotto 2017:
7).
Following this, what can we conclude up until now?
Summing up my understanding of the ‘information a system possesses’ (RQM) or
‘the state a system is in, relative to another’ (R-S) and so forth: When using these
statements/notions I mean the location of a system within a certain web of relations,
and, insofar as relations are correlations and correlation is information, relations are
information. The phrases signify a certain configuration of the information a system
‘possesses’ or, equivalently, ‘has relative to another S’. Talking about those notions in
relational terms thus only simplifies the narrative and makes it livelier. Concluding
this understanding, the ‘information of a system’ is essentially dependent on the
relational structure of reality, and, thus there is the possibility that relation can
always be replaced with information or correlation and vice versa.
Now, why should one favor the ontic approach over the epistemic one? A possible
answer can be to say that any realist approach should be able to support a
metaphysical account that is reconcilable with the discoveries of quantum mechanics;
in other words letting philosophical beliefs being shaped through empirical
exploration. In this respect an ontic account is quite reasonable since it both
postulates relations, not substances (systems) as fundamental and argues for the
impossibleness of individuation, i.e. in a vivid reading, being able to gain information
without interaction. More specific; while R-S postulates ‘the structure’ (wave
function) as its fundamental, from which relative states are realized, RQM posits
relations as fundamental, from which relative states are realized. Therefore, both
pertain to ‘the information a system has about another one’; that means a first
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conclusion can be said to be a difference in concept but a correspondence in
conclusions.
An argument for an epistemic approach is found in Schaffer (2010). In regard to
this, R-S can be stated to fit well for an epistemic reading, since in structuralist terms
the whole is pivotal for the parts, in the sense that the structure, in a general meaning,
both is constituent for the existence and definition of the identity of the systems. In
other words: In the language of R-S the wave function (structure) is prior to the
experience of an observer as well as constituent of the possibility of the actual
experience.
An objection to framing RQM within an ontic reading and promoting to understand
it within the epistemic is the following, based on Dorato (2013). As information takes
on a crucial role in Rovelli’s depiction of quantum mechanics, and thus reality, it can
be said to promote a more epistemic, than ontic, reading of RQM. Splitting this into
two parts: (1) as delineated, the information systems possess need to be described
within the information that is acquired through interaction and the web of
interactions is cohesive. (2) the correlation (information) of two systems has no
meaning on its own (absolute meaning), as it is only information a third system that is
extern to the prior interaction can gain (cf. Candiotto 2017: 10)
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Candiotto dissolves this objection in a simple manner: As the argument is solely
70
based on the thought that the epistemic and ontic tier are disjoint65, considering that a
physical action, in general, marks the emergence of information, both postulates (P1
and P2) assort well with each other. Thus, understanding information as relation, one
can easily derive the ontology of RQM as delineated (cf. Candiotto 2017: 10). Reading
information as the foundational relation possessing ontological value for RQM means
consequently that relations as such are prior to the relations that emerge through
interactions.
Summarizing: What is the ‘actual stuff’ taking us from the very formalism to reality?
Speaking in Rovelli’s terms, I would state that ‘Relations are the actual stuff’
compared to Everett, in which case I’d assert that ‘Even when there is no sense in
talking about actual stuff, relations are the way we experience things, and this is our
reality’.
6. Conclusion
As I have tried to delineate, both Rovelli’s RQM and Everett’s R-S share common
traits. This is kind of obvious, as Rovelli was significantly influenced or inspired by
Everett’s idea of relative-states. In a sense he took “Everett’s lasting contribution to
the understanding of quantum theory” (Rovelli 2017: 4) and carried on that thought
into the extreme. Apart from their similarities, both accounts also diverge in their
respective picture of reality – at least when examined in structural realist terms. In a
general sense, different concepts lead to a consensus in consequences, uncared their
mathematical or physical specifications. A generalized version of the question posed
in the beginning of this chapter: How do Rovelli’s and Everett’s formulations differ in
their respective philosophical picture of reality? was refined in this section, based on
the prior examination and the self-imposed focus. Finally, I state that Relative-States
implies rather an epistemic structural realism, as the theory can be said to explicate a
structure through which we know the world, but that this structure is not nature.
RQM on the other hand implies the fundamental relationality of nature, thus stating
that nature itself is relations. Now, what would I answer when getting asked whether
and to what extent RQM and R-S may imply statements able to be localized within
structural realist terms? My most likeliest answer might be, in one sentence: While
RQM may better be understood in the framework of an ontological structuralist
reading, R-S may be better apprehended within a epistemic structuralist reading.
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“If we want to understand nature, our task is not to frame nature into our philosophical prejudices, but rather to learn how to adjust our philosophical prejudices to what we learn from nature” (Laudisa/Rovelli 2013).
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List of Literature
1. Adriaans, P. (2019). Information, The Stanford Encyclopedia of Philosophy,
https://plato.stanford.edu/archives/spr2019/entries/information/ Cited
1 March 2019.
2. Baghramian, M. & Carter, J. A. (2018). Relativism, The Stanford
Encyclopedia of Philosophy,
https://plato.stanford.edu/archives/win2018/entries/relativism/ Cited 6
March 2019.
3. Barrett, J. A. (2010). A structural interpretation of pure wave mechanics.
HUMANA. MENTE Journal of Philosophical Studies, 4(13), 225-235.
4. Barrett, J. A. (2011). Everett’s pure wave mechanics and the notion of
worlds. European Journal for Philosophy of Science, 1(2), 277-302.
5. Barrett, J. A., & Byrne, P. (Eds.). (2012). The Everett interpretation of
quantum mechanics: Collected works 1955-1980 with commentary.
Princeton University Press.
6. Barrett, J. (2018). Everett’s Relative-State Formulation of Quantum
Mechanics, The Stanford Encyclopedia of Philosophy,
https://plato.stanford.edu/archives/win2018/entries/qm-everett/ Cited
3 March 2019.
7. Bitbol, M. (2007). Physical relations or functional relations. A non-
metaphysical construal of Rovelli’s relational quantum mechanics. See
http://philsci-archive. pitt. edu/3506/.
8. Bohm, D. (1951). Quantum Theory. Englewood Cliffs, NJ.
9. Born, M. (1926). Zeitschrift für Physik 38, 803.
10. Butterfield, J. (1995). Worlds, minds and quanta. In Aristotelian Society
Supplementary Volume (Vol. 69, pp. 113-158).
11. Butterfield, J., & Earman, J. (Eds.). (2007). Philosophy of physics (Vol. 2).
Elsevier.
12. Candiotto, L. (2017). The reality of relations. See http://philsci-
archive.pitt.edu/14165/.
13. Conroy, C. (2012). The relative facts interpretation and Everett's note
added in proof. Studies in History and Philosophy of Science Part B: Studies
in History and Philosophy of Modern Physics, 43(2), 112-120.
73
14. DeWitt, B. S. (1970). Quantum mechanics and reality. Physics today, 23(9),
30-35.
15. Dirac, P. A. M. (1925). The fundamental equations of quantum mechanics.
Proceedings of the Royal Society of London. Series A, Containing Papers of a
Mathematical and Physical Character, 109(752), 642-653.
16. Dirac, P. A. M. (1977). The relativistic electron wave equation. Europhysics
News, 8(10), 1-4.
17. Dorato, M. (2013). Rovelli's relational quantum mechanics, monism and
quantum becoming. arXiv preprint arXiv:1309.0132.
18. Einstein, A. (1905). On the electrodynamics of moving bodies. Annalen der
Physik, 17(891), 50.
19. Einstein, A. (1916). Ernst Mach. Physikalische Zeitschrift, 17, p. 101-104.
20. Evans, J. (2007). Introduction: Contexts and Challenges for Quantum
Mechanics. In Quantum Mechanics at the Crossroads (pp. 1-20). Springer,
Berlin, Heidelberg.
21. Everett III, H. (1957a). “Relative state” formulation of quantum mechanics.
Reviews of modern physics, 29(3), 454-462.
22. Everett III, H. (1957b). Letter from Hugh Everett III to Bryce DeWitt dated
May 31, 1957. Forthcoming in the UCISpace Everett archive funded by NSF
Award No. SES-0924135.
23. Everett III, H. (1957c). Wiener, Norbert to John. A. Wheeler and Hugh
Everett III, April 9, 1957. Forthcoming in the UCISpace Hugh Everett III
Archive at UC Irvine, see http://ucispace.lib.uci.edu/
24. Everett III, H. (1957d). Letter to Norbert Wiener. May 31, 1957.
Forthcoming in the UCISpace Hugh Everett III Archive at UC Irvine.
http://ucispace.lib.uci.edu/
25. Everett III, H. (1973). The theory of the universal wave function. In B. S.
DeWitt, & N. Graham (Eds.), The many-worlds interpretation of quantum
mechanics (pp. 3–140). Princeton University Press.
26. Fedak, W. A., & Prentis, J. J. (2009). The 1925 Born and Jordan paper “On
quantum mechanics”. American Journal of Physics, 77(2), 128-139.
27. Friebe, C., Kuhlmann, M., Lyre, H., Näger, P. M., Passon, O., & Stöckler, M.
(2018). Philosophie der Quantenphysik: Zentrale Begriffe, Probleme,
Positionen. Springer. 2. Auflage.
74
28. Friebe, C., Kuhlmann, M., Lyre, H., Näger, P. M., Passon, O., & Stöckler, M.
(2018). The philosophy of quantum physics. Springer.
29. Heisenberg, W. (1925). Über quantentheoretische Umdeutung
kinematischer und mechanischer Beziehungen. Zeitschrift für Physik 33 no.
1, 879–893.
30. Ismael, J. (2015). Quantum Mechanics, The Stanford Encyclopedia of
Philosophy, https://plato.stanford.edu/archives/spr2015/entries/qm/
Cited 15 March 2019.
31. Ladyman, J. (2016). Structural Realism, The Stanford Encyclopedia of
Philosophy,
https://plato.stanford.edu/archives/win2016/entries/structural-realism/
Cited 4 March 2019.
32. Laudisa, F., & Rovelli, C. (2013). Relational Quantum Mechanics, The
Stanford Encyclopedia of Philosophy,
https://plato.stanford.edu/archives/sum2013/entries/qm-relational/
Cited 16 March 2019.
33. Maudlin, T. (1995). Three measurement problems. topoi, 14(1), 7-15.
34. Myrvold, W. (2018). Philosophical Issues in Quantum Theory, The Stanford
Encyclopedia of Philosophy,
https://plato.stanford.edu/archives/fall2018/entries/qt-issues/ Cited 1
March 2019.
35. Rovelli, C. (1996). Relational quantum mechanics. International Journal of
Theoretical Physics, 35(8), 1637-1678.
36. Rovelli, C. (1997). Half way through the woods. The cosmos of science, 180-
223.
37. Rovelli, C. (2007). Quantum gravity. Cambridge university press.
38. Rovelli, C. (2008). Relational Quantum Mechanics. International Journal of
Theoretical Physics 35 (1996). Substantially revised version, pp. 1-21.
39. Rovelli, C. (2015). The strange world of quantum spacetime. In: General
Relativity: The Most Beautiful of Theories. Applications and Trends after
100 years, Berlin/Munich/Boston, pp. 189-202.
40. Rovelli, C. (2017). Space is blue and birds fly through it. Presented to the
meeting “Foundations of quantum mechanics and their impact on
contemporary society”, The Royal Society, London, 11–12/12/2017; to
75
appear in Philosophical Transactions A.
41. Ruyant, Q. (2016). Primitive Ontology or Primitive Relations?, http://philsci-
archive.pitt.edu/12120/ Cited 12 March 2019.
42. Ruyant, Q. (2017). Can we make sense of Relational Quantum Mechanics?
Preprint November, pp. 1-18. Published in Foundations of Physics (2018),
48(4), 440-455.
43. Saunders, S., Barrett, J., Kent, A., & Wallace, D. (Eds.). (2010). Many worlds?:
Everett, quantum theory, & reality. Oxford University Press.
44. Schaffer, J. (2010). Monism: The priority of the whole. The Philosophical
Review, 119(1), 31-76.
45. Schrödinger, E. (1926). Quantisierung als Eigenwertproblem (Erste
Mitteilung). Annalen der Physik 79, 361–76.
46. Van Fraassen, B. C. (2010). Rovelli’s world. Foundations of Physics, 40(4),
390-417.
47. Wallace, D. (2002). Worlds in the Everett interpretation. Studies in History
and Philosophy of Science Part B: Studies in History and Philosophy of
Modern Physics, 33(4), 637-661.
48. Wallace, D. (2012). The emergent multiverse: Quantum theory according to
the Everett interpretation. Oxford University Press.
49. Wheeler, J. A. (1957). Assessment of Everett's “relative state” formulation
of quantum theory. Reviews of modern physics, 29(3), 463-465.
50. Wheeler, J. A. (1992). It from Bit and Quantum Gravity, Princeton
University Report.
76
serious conceptual errors” (Rovelli 2008: 8). For a detailed account, see p. 7ff. 40 The pertinence of information theory for a comprehension of quantum physics has also been endorsed by e.g. Wheeler (1992). Furthermore, allude that I accept the following depiction of Information as being applicable to Everett’s Relative-States, for the moment uncared about distinctions. These will become important later on. 41 Note that, regarding the further course of the paper, the factual procedure of how information is accumulated and stored is not of further interest here. It’s sufficient, also according to Rovelli, to accept the fact that the procedure of information gathering can be described physically, in any certain example (cf. Rovelli 2008:10).42 Following Rovelli’s remarks and describing them livelier, one can label the process of information acquisition as “a “question” that a system (observing system) asks another system (observed system)“ (p. 10).43 For an extensive account of the term information, see Adriaans (2019).44 For Rovelli’s derivation of the entire formalism of quantum mechanics, based on these to postulates, see 2008: 12ff.45 Realism is understood in a broad sense here, not referring particularly to a certain form of scientific realism, which is left for later.46 „There is nothing similar to ‘mind’ required to make sense of the theory“ (Rovelli 2017: 6). This applies to both theories. 47 More precisely: The Kochen-Specker theorem “states that in general there is no consistent assignment of a definite values to all variables, by restricting the set of elementary variables describing the world (to the quantum state itself, or to Bohmian trajectories, or else)“ (Rovelli 2017: 6). 48“Structural [R]ealism is considered by many realists and antirealists alike as the most defensible form of scientific realism” (Ladyman 2016). I will make full use of this statement and let this grant me an omission of anti-realist arguments.49 What is evident yet is that while Everett began with the mathematics and arrived at experience, Rovelli started with experimental results (experience) and from there deduced the formalism (mathematics).50 Surely one can detect more important differences within the two theories, but regarding the extent and elementary question/argumentation of this paper, I will focus on the consequences of their diverging understanding of the wave function (thus relative states) and their respective resulting pictures of reality.51 ‘The’ moment of divergence – already presented in chapter ‘Problem of Observation’ – can be recorded with the following statement of Everett: “Nevertheless, there is a representation in terms of a superposition, each element of which contains a definite observer state and a corresponding system state. Thus with each succeeding observation (or interaction) the observer state ‘branches’ into a number of different states.” (Everett 1957a: 459).52 For further arguments why a structural reading of quantum mechanics is reasonable, see for example Candiotto (2017) or Ladyman (2016); the latter also for an extensive account on structural realism. 53 This is also the reason for not providing a distinct definition for both Ontic Structural Realism (OSR) and Epistemic Structural Realism (ESR). 54 For the sake of argumentation often pictured as ‚structure’ subsequently, in respect to R-S (earlier: QS and wave function understood as ‘the same thing’ in my work, regardless of formal differences).
55 It is of crucial importance to once more emphasize Everett’s understanding of the term ‘reality’: “From the viewpoint of the theory, all elements of a superposition (all “branches”) are “actual,” none any more “real” than another. It is completely unnecessary to suppose that after an observation somehow one element of the final superposition is selected to be awarded with a mysterious quality called “reality” and the others condemned to oblivion. We can be more charitable and allow the others to coexist – they won't cause any trouble anyway because all the separate elements of the superposition (“branches”) individually obey the wave equation with complete indifference to the presence or absence (“actuality” or not) of any other elements.” (Everett 1957b, own emphasis). Thus, each element of the superposition is viewed as ‘real’ as any other.56 A process is understood as “those transitions from an interaction to another that constitute reality as a series of events, and not of objects“ (Candiotto 2017: 4). Or, in Rovelli’s terms: “Spacial and temporal specifications make sense only on the boundary of a process, in the context of an interaction. In other words, space and time themselves are reduced to quantum entities like the position of a quantum particle, which is determined only at interaction time, otherwise is fluctuating” (Rovelli 2015: 198). 57 Furthermore Everett’s and Rovelli’s take on ‘probability’ is distinct. For an overview of Everett’s understanding, see Barrett/Byrne (2012).58 “Quantum mechanics is the theoretical formalization of the experimental discovery that the descriptions that different observers give of the same events are not universal” (Rovelli 2008: 16). In R-S however, it is universal, though only for each ‘branch’. 59 Branch simply means, within this statement, that the state is relative to the branch; recall that a state always has to be understood as relative to something.60 Primitive understood as axiomatic (cf. Candiotto 2017: 5). Taking on the view of relations as axiomatic allows us to circumvent a possible criticism pointed out by Dorato (2013), which simplified states: RQM, in referring to a ‘primitive’ notion, is dealing with a void of explanatory power – ‘sweeping the dust under the rug’ – in implying relations “as a brute fact about the world” (p. 10). Thus, for the sake of argumentation, viewing relations as axiomatic is not even exposed to criticism as being improvable or explanatory poor (even though one may answer it kind of makes things ‘too easy’).61 ‘Branch’ here simply means the epistemic reality where one of the possible outcomes is realized. Recall however that “no such statements ever made in the theory like “case A actually realized”, except relative to some other state! All possibilities “actually realized”, with corresp[onding] observer states” (Everett 1957c, own emphasis). In other words, one may “raise the question of what it means to say that a fact or a group of facts is actually realized. Now I realize that this question poses a serious difficulty for the conventional formulation of quantum mechanics, and was in fact one of the main motives for my reformulation. The difficulty is removed in the new formulation, however, since it is quite unnecessary in this theory ever to say anything like “Case A is actually realized" (Everett 1957d). Concluding: the states of systems can be considered ‘actual’ only relative to the state of some other subsystem (cf. Conroy 2012: 15). When talking about ‘reality’ and R-S, this is what I mean by it.62 For an interpretation quite close to Relativism, see Conroy (2012).63 “In the history of Western philosophy, the name "relationism" has been referred to Leibniz’s conception of space and time – a conception opposed to Newton’s substantivism. The Principle of Identity of Indiscernibles, a cornerstone of Leibniz’s philosophy, ensures the individuality of objects, understood as "bundles" of properties“ (Candiotto 2017: 6). Furthermore, see Rovelli 2007: 52ff. 64 ESR, in my reading, as already delineated, is not ‘the’ Epistemic Structural Realism, but ‘a’ general perspective an epistemic structural realist would take on, or, equally, remarks fitting into the framework of ESR.
65 While this argument does not need to apply to RQM, it surely does fit for R-S since Everett himself only requires the theory to be accurate considering ‚trajectories of observers’. See for example Everett 1957a,b.
