Relational Quantum Mechanics is an interpretation of quantum theory based on the idea of abolishing the notion of absolute states of systems, in favor of states of systems relative to other systems. Such a move is claimed to solve the conceptual problems of standard quantum mechanics. Moreover, RQM has been argued to account for all quantum correlations without invoking non-local effects and, in spite of embracing a fully relational stance, to successfully explain (...) how different observers exchange information. In this work, we carry out a thorough assessment of RQM and its purported achievements. We find that it fails to address the conceptual problems of standard quantum mechanics—related to the lack of clarity in its ontology and the rules that govern its behavior—and that it leads to serious conceptual problems of its own. We also uncover as unwarranted the claims that RQM can correctly explain information exchange among observers, and that it accommodates all quantum correlations without invoking non-local influences. We conclude that RQM is unsuccessful in its attempt to provide a satisfactory understanding of the quantum world. (shrink)

The idea that the dynamical properties of quantum systems are invariably relative to other systems has recently regained currency. Using Relational Quantum Mechanics (RQM) for a case study, this paper calls attention to a question that has been underappreciated in the debate about quantum relativism: the question of whether relativity iterates. Are there absolute facts about the properties one system possesses relative to a specified reference, or is this again a relative matter, and so on? (...) It is argued that RQM (in its best-known form) is committed to what I call the Unrestricted Iteration Principle (UIP), and thus to an infinite regress of relativisations. This principle plays a crucial role in ensuring the communicability and coherence of interaction outcomes across observers. It is, however, shown to be incompatible with the widespread, conservative reading of RQM in terms of relations, instead necessitating the adoption of the more unorthodox notion of perspectival facts. I conclude with some reflections on the current state of play in perspectivist versions of RQM and quantum relativism more generally, underscoring both the need for further conceptual development and the importance of the iteration principle for an accurate cost-benefit analysis of such interpretations. (shrink)

Carlo Rovelli's relational interpretation of quantum mechanics holds that a system's states or the values of its physical quantities as normally conceived only exist relative to a cut between a system and an observer or measuring instrument. Furthermore, on Rovelli's account, the appearance of determinate observations from pure quantum superpositions happens only relative to the interaction of the system and observer. Jeffrey Barrett ([1999]) has pointed out that certain relational interpretations suffer from what we might (...) call the ‘determinacy problem', but Barrett misclassifies Rovelli's interpretation by lumping it in with Mermin's view, as Rovelli's view is quite different and has resources to escape the particular criticisms that Barrett makes of Mermin's view. Rovelli's interpretation still leaves us with a paradox having to do with the determinacy of measurement outcomes, which can be accepted only if we are willing to give up on certain elements of the ‘absolute’ view of the world. (shrink)

According to Relational Quantum Mechanics the wave function \ is considered neither a concrete physical item evolving in spacetime, nor an object representing the absolute state of a certain quantum system. In this interpretative framework, \ is defined as a computational device encoding observers’ information; hence, RQM offers a somewhat epistemic view of the wave function. This perspective seems to be at odds with the PBR theorem, a formal result excluding that wave functions represent knowledge of (...) an underlying reality described by some ontic state. In this paper we argue that RQM is not affected by the conclusions of PBR’s argument; consequently, the alleged inconsistency can be dissolved. To do that, we will thoroughly discuss the very foundations of the PBR theorem, i.e. Harrigan and Spekkens’ categorization of ontological models, showing that their implicit assumptions about the nature of the ontic state are incompatible with the main tenets of RQM. Then, we will ask whether it is possible to derive a relational PBR-type result, answering in the negative. This conclusion shows some limitations of this theorem not yet discussed in the literature. (shrink)

In recent works, Časlav Brukner and Jacques Pienaar have raised interesting objections to the relational interpretation of quantum mechanics. We answer these objections in detail and show that, far from questioning the viability of the interpretation, they sharpen and clarify it.

Relational quantum mechanics is an interpretation of quantum theory which discards the notions of absolute state of a system, absolute value of its physical quantities, or absolute event. The theory describes only the way systems affect each other in the course of physical interactions. State and physical quantities refer always to the interaction, or the relation, between two systems. Nevertheless, the theory is assumed to be complete. The physical content of quantum theory is understood as (...) expressing the net of relations connecting all different physical systems. (shrink)

The Ozawa’s intersubjectivity theorem (OIT) proved within quantum measurement theory supports the new postulate of relational quantum mechanics (RQM), the postulate on internally consistent descriptions. But from OIT viewpoint postulate’s formulation should be completed by the assumption of probability reproducibility. We remark that this postulate was proposed only recently to resolve the problem of intersubjectivity of information in RQM. In contrast to RQM for which OIT is a supporting theoretical statement, QBism is challenged by OIT.

We present a derivation of the third postulate of relational quantum mechanics from the properties of conditional probabilities. The first two RQM postulates are based on the information that can be extracted from interaction of different systems, and the third postulate defines the properties of the probability function. Here we demonstrate that from a rigorous definition of the conditional probability for the possible outcomes of different measurements, the third postulate is unnecessary and the Born’s rule naturally emerges (...) from the first two postulates by applying the Gleason’s theorem. We demonstrate in addition that the probability function is uniquely defined for classical and quantum phenomena. The presence or not of interference terms is demonstrated to be related to the precise formulation of the conditional probability where distributive property on its arguments cannot be taken for granted. In the particular case of Young’s slits experiment, the two possible argument formulations correspond to the possibility or not to determine the particle passage through a particular path. (shrink)

We propose a model of physics that blends Rovelli’s relational quantum mechanics (RQM) interpretation with the language of finite information quantities (FIQs), defined by Gisin and Del Santo in the spirit of intuitionistic mathematics. We discuss deficiencies of using real numbers to model physical systems in general, and particularly under the RQM interpretation. With this motivation for an alternative mathematical language, we propose the use of FIQs to model the world under the RQM interpretation, wherein we view (...) the propensities that make up a FIQ as quantifications of potential interaction. Under this model, the stable facts, relative facts, and shifting perspectives that make up the relational interpretation correspond to shifting digits and propensities of the FIQs. The model’s predictions agree with those of both classical and quantum physics, and it is indeterministic. We also propose explanations, with examples, for how the propensities of a FIQ are distributed, and how its digits become actualized. This is equivalent to the notion of the measurement problem, and the question of what causes wave function collapse. In short, by stepping through the “new door” opened by the language of FIQs, we attempt to describe the world under the relational interpretation. (shrink)

Franklin and Seifert (2021) argue that solving the measurement problem of quantum mechanics (QM) also answers a question central to the philosophy of chemistry: that of how to reconcile QM with the existence of definite molecular structures. This conclusion may appear premature, however, because interactions play a crucial role in shaping molecules, but we generally lack detailed models of how this is accomplished. Given this explanatory gap, simply choosing an interpretation of QM is insufficient, unless the interpretation also (...) has relevant conceptual resources that address how spatially organized molecules are composed. This article seeks to close the gap, using the interpretation provided by relational quantum mechanics (RQM), along with a posited causal ontology. This framework, which entails the co-existence of multiple perspectives on systems within a single world, offers a path toward reconciling the quantum mechanical view of molecules with another conception more congenial to chemistry: that of molecules shaped by patterns of localizing interactions. (shrink)

Relational Quantum Mechanics is an interpretation of quantum mechanics proposed by Carlo Rovelli. Rovelli argues that, in the same spirit as Einstein’s theory of relativity, physical quantities can only have definite values relative to an observer. Relational Quantum Mechanics is hereby able to offer a principled explanation of the problem of nested measurement, also known as Wigner’s friend. Since quantum states are taken to be relative states that depend on both the (...) system and the observer, there is no inconsistency in the descriptions of the observers. Federico Laudisa has recently argued, however, that Rovelli’s description of Wigner’s friend is ambiguous, because it does not take into account the correlation between the observer and the quantum system. He argues that if this correlation is taken into account, the problem with Wigner’s friend disappears and, therefore, a relativization of quantum states is not necessary. I will show that Laudisa’s criticism is not justified. To the extent that the correlation can be accurately reflected, the problem of Wigner’s friend remains. An interpretation of quantum mechanics that provides a solution to it, like Relational Quantum Mechanics, is therefore a welcome one. (shrink)

This paper discusses the question of stable facts in relational quantum mechanics (RQM). I examine how the approach to quantum logic in the consistent histories formalism can be used to clarify what infomation about a system can be shared between different observers. I suggest that the mathematical framework for Consistent Histories can and should be incorporated into RQM, whilst being clear on the interpretational differences between the two approaches. Finally I briefly discuss two related issues: the (...) similarities and differences between special relativity and RQM and the recent Cross-Perspectival Links modification to RQM. (shrink)

Relational quantum mechanics (RQM) is an interpretation of quantum mechanics based on the idea that quantum states do not describe an absolute property of a system but rather a relationship between systems. There have recently been some criticisms of RQM pertaining to issues around intersubjectivity. In this article, we show how RQM can address these criticisms by adding a new postulate which requires that all of the information possessed by a certain observer is stored (...) in physical variables of that observer and thus is accessible by measurement to other observers. This makes it possible for observers to reach intersubjective agreement about quantum events that have occurred in the past. We suggest a possible ontology for a version of RQM employing this postulate; this ontology upholds the principle that quantum states are always relational, but it also postulates a set of quantum events that are not strictly relational. We show that the new postulate helps address the preferred basis problem in RQM. (shrink)

In this paper, we evaluate some proposals that have been put forward to clarify the ontological consequences of relational quantum mechanics. We first focus on priority monism and ontic structural realism and argue that these views are not suitable for providing an ontological interpretation of the theory. Then, we discuss an alternative interpretation that we regard as more promising, based on so-called ‘metaphysical coherentism’, which we also connect to the idea of an event-based, or ‘flash’, ontology.

The subjective Bayesian interpretation of quantum mechanics and Rovelli’s relational interpretation of quantum mechanics are both notable for embracing the radical idea that measurement outcomes correspond to events whose occurrence is relative to an observer. Here we provide a detailed study of their similarities and especially their differences.

El inspirador Relational Quantum Mechanicsde Carlo Rovelli cumple varios propósitosde manera simultánea: proporciona unanueva visión de cómo es el mundo de lamecánica cuántica y ofrece un programapara derivar el formalismo de la teoría deun conjunto de postulados simples quepertenecen al procesamiento de la información.Enesteartículopropongoquenosconcentremostotalmente en lo primero,para explorar el mundo de la mecánicacuántica tal como lo representa Rovelli.Es un mundo fascinante, en parte debidoa la dependencia de Rovelli sobre el enfoquedelateoríadelainformaciónparalosfundamentosdelamecánicacuántica,yen parte debido a que su presentaciónimplica asumir una (...) postura en un partefundamental en la filosofía misma.Ca r l o Ro v e l l i ’ s i n s p i r i n g Re l a t i o n a lQuantum Mechanics serves several aims atonce: it provides a new vision of what theworld of quantum mechanics is like, andit offers a program to derive the theory’sformalism from a set of simple postulatespertai ni ng to i nformati on processi ng.I propose here to concentrate entirelyon the former, to explore the world ofquantum mechanics as Rovelli depicts it.It is a fascinating world in part becauseof Rovelli’s reliance on the informationtheory approach to the foundations ofquantum mechanics, and in part becauseits presentation involves taking sides on afundamental divides within philosophyitself. (shrink)

In this paper I present and defend Rovelli's relation quantum mechanics from some foreseeable objections, so as to clarify its philosophical implications vis a vis rival interpretations. In particular I will ask whether RQM presupposes a hidden recourse to both a duality of evolutions and of ontology. I then concentrate on the pluralistic, antimonistic metaphysical consequences of the theory, due to the impossibility of assigning a state to the quantum universe. Finally, in the last section I note (...) interesting consequences of RQM with respect to the possibility of defining a local, quantum relativistic becoming.Given the difficulties of having the cosmic form of becoming that would be appropriate for priority monism, RQM seems to present an important advantage with respect to monistic views, at least insofar as far as the possibility of explaining our experience of time is concerned. (shrink)

The present essay provides a new metaphysical interpretation of Relational Quantum Mechanics (RQM) in terms of mereological bundle theory. The essential idea is to claim that a physical system in RQM can be defined as a mereological fusion of properties whose values may vary for different observers. Abandoning the Aristotelian tradition centered on the notion of substance, I claim that RQM embraces an ontology of properties that finds its roots in the heritage of David Hume. To this (...) regard, defining what kind of concrete physical objects populate the world according to RQM, I argue that this theoretical framework can be made compatible with (i) a property-oriented ontology, in which the notion of object can be easily defined, and (ii) moderate structural realism, a philosophical position where relations and relata are both fundamental. Finally, I conclude that under this reading relational quantum mechanics should be included among the full-fledged realist interpretations of quantum theory. (shrink)

The Rovelli relational interpretation of quantum mechanics is based on the assumption that the notion of observer-independent state of a physical system is to be rejected. In RQM the primary target of the theory is the analysis of the whole network of relations that may be established among quantum subsystems, and the shift to a relational perspective is supposed to address in a satisfactory way the general problem of the interpretation of quantum mechanics. (...) Here I discuss two basic issues, that I take to be serious open problems of the interpretation. First, I wish to show—mainly through an analysis of the so-called third person problem—that it is far from clear what a relativization of states to observers exactly achieves and in what sense such an approach really advances our understanding of the peculiar features of quantum phenomena. Second, I argue that the claim, according to which RQM is able to preserve locality, is at best dubious. I conclude that further work needs to be done before RQM may aspire to become a satisfactory interpretational framework for the main foundational issues in quantum mechanics. (shrink)

The term ‘locality’ is used in different contexts with different meanings. There have been claims that relational quantum mechanics is local, but it is not clear then how it accounts for the effects that go under the usual name of quantum non-locality. The present article shows that the failure of ‘locality’ in the sense of Bell, once interpreted in the relational framework, reduces to the existence of a common cause in an indeterministic context. In particular, (...) there is no need to appeal to a mysterious space-like influence to understand it. (shrink)

A recent paper has given a lucid treatment of Bell’s notion of local causality within the framework of the relational interpretation of quantum mechanics. However, the authors went on to conclude that the quantum violation of Bell’s notion of local causality is no more surprising than a common cause. Here, I argue that this conclusion is unwarranted by the authors’ own analysis. On the contrary, within the framework outlined by the authors, I argue that far from (...) saving the notion of ‘locality’ from the grip of Bell’s theorem, the authors have deprived it of a meaningful definition. (shrink)

Bob hides a ball in one of four drawers. Alice is to locate it. Classically she has to open up to three drawers, quantally just one. The fundamental reason for this quantum speedup is not known. The usual representation of the quantum algorithm is limited to the process of solving the problem. We extend it to the process of setting the problem. The number of the drawer with the ball becomes a unitary transformation of the random outcome of (...) the preparation measurement. This extended, time-symmetric, representation brings in relational quantum mechanics. It is with respect to Bob and any external observer and cannot be with respect to Alice. It would tell her the number of the drawer with the ball before she opens any drawer. To Alice, the projection of the quantum state due to the preparation measurement should be retarded at the end of her search; in the input state of the search, the drawer number is determined to Bob and undetermined to Alice. We show that, mathematically, one can ascribe any part of the selection of the random outcome of the preparation measurement to the final Alice’s measurement. Ascribing half of it explains the speedup of the present algorithm. This leaves the input state to Bob unaltered and projects that to Alice on a state of lower entropy where she knows half of the number of the drawer with the ball in advance. The quantum algorithm turns out to be a sum over histories in each of which Alice knows in advance that the ball is in a pair of drawers and locates it by opening one of the two. In the sample of quantum algorithms examined, the part of the random outcome of the initial measurement selected by the final measurement is one half or slightly above it. Conversely, given an oracle problem, the assumption it is one half always corresponds to an existing quantum algorithm and gives the order of magnitude of the number of oracle queries required by the optimal one. (shrink)

Aurélien Drezet has attempted in Found. Phys. 54(1), 5 (2023) to defend Relational Quantum Mechanics (RQM) against our recent critique, entitled Relational Quantum Mechanics is incompatible with quantum mechanics, published in Quantum 7, 1015 (2023). Drezet not only misrepresents our work, but he also misconstructs the very theory (RQM) that he claims to defend.

Rovelli’s RQM is first characterized by contrast with both Everett’s and Bohr’s interpretations of quantum mechanics. Then, it is shown that a basic difficulty arises from the choice of formulating RQM in a naturalistic framework. Even though, according to Rovelli’s interpretation, statements about the world only make sense relative to certain naturalized observers described by means of quantum mechanics, this very meta-statement seems to make sense relative to a sort of super-observer which does not partake of (...) the naturalized status of ordinary observers. The difficulty is solved by substituting functional reference frames for physical (or naturalized) observers throughout. Instead of being relative to physical observers, statements about the state vector of physical systems are here relative to well-defined projects of probabilistic prediction which may be embodied by several physical observers. (shrink)

This article sets forth and discusses the Ithaca Interpretation of Quantum Mechanics. Section 1 presents the standard formalism of quantum mechanics and the measurement problem. Section 2 sketches Everett's interpretation as a preamble to IIQM. Section 3 sets out IIQM's central claim: it is possible to make sense of quantum mechanics by taking as the proper subject of physics the correlations among subsystems. Section 4 introduces a theorem of quantum mechanics, the SSC (...) theorem, which supports this claim. Section 5 contends that at least two problems exist with IIQM, and one serious objection against it. Section 6 discusses a strategy based on relational probabilities to go around the objection. /// Este artículo presenta y discute la Interpretación de la Mecánica Cuántica de Ithaca. La sección 1 expone el formalismo estándar de la mecánica cuántica y el problema de la medición. La sección 2 bosqueja la interpretación de Everett como preámbulo a la IIQM. La sección 3 plantea la tesis central de la IIQM: es posible dar sentido a la mecánica cuántica tomando como sujeto propio de la física las correlaciones entre subsistemas. La sección 4 expone el teorema SSC de la mecánica cuántica que sustenta esta tesis. En la sección 5 se sostiene que existen al menos dos problemas con la IIQM, y una seria objeción en su contra. Para sortear esta objeción, la sección 6 discute una estrategia basada en probabilidades relacionales. (shrink)

We discuss a recent work by J. Lawrence et al. [arxiv.org/abs/2208.11793] criticizing relational quantum mechanics (RQM) and based on a famous nonlocality theorem Going back to Greenberger Horne and Zeilinger (GHZ). Here, we show that the claims presented in this recent work are unjustified and we debunk the analysis.

The relational interpretation of quantum mechanics (RQM) has received a growing interest since its first formulation in 1996. Usually presented as an interpretational layer over the usual quantum mechanics formalism, it appears as a philosophical perspective without proper mathematical counterparts. This state of affairs has direct consequences on the scientific debate on RQM which still suffers from misunderstandings and imprecise statements. In an attempt to clarify those debates, the present paper proposes a radical reformulation of (...) the mathematical framework of quantum mechanics which is relational from the start: fact-nets. The core idea is that all statements about the world, facts, are binary entities involving two systems that can be symmetrically thought of as observed and observer. We initiate a study of the fact-nets formalism and outline how it can shed new relational light on some familiar quantum features. (shrink)

The relational interpretation of quantum mechanics proposes to solve the measurement problem and reconcile completeness and locality of quantum mechanics by postulating relativity to the observer for events and facts, instead of an absolute “view from nowhere”. The aim of this paper is to clarify this interpretation, and in particular, one of its central claims concerning the possibility for an observer to have knowledge about other observer’s events. I consider three possible readings of this claim, (...) and develop the most promising one, relativism, to show how it fares when confronted with the traditional interpretative problems of quantum mechanics. Although it provides answers to some problems, I claim that there is currently no adapted locality criterion to evaluate whether the resulting interpretation is local or not. (shrink)

In the literature on the interpretation of quantum mechanics, not many works attempt to adopt a proactive perspective aimed at seeing how different interpretations can enrich each other through a productive dialogue. In particular, few proposals have been devised to show that different approaches can be clarified by comparing them, and can even complement each other, improving or leading to a more fertile overall approach. The purpose of this paper is framed within this perspective of complementation and mutual (...) enrichment. In particular, the Relational Quantum Mechanics and the Modal-Hamiltonian Interpretation are compared, highlighting their differences and points of contact. The final purpose is to show that, in spite of their disagreements, they are not contradictory but, on the contrary, they can be made compatible from an overarching perspective and can even complement each other in a fruitful way. (shrink)

Advocates of the New Mechanicism in philosophy of science argue that scientific explanation often consists in describing mechanisms responsible for natural phenomena. Despite its successes, one might think that this approach does not square with the ontological strictures of quantum mechanics. New Mechanists suppose that mechanisms are composed of objects with definite properties, which are interconnected via local causal interactions. Quantum mechanics calls these suppositions into question. Since mechanisms are hierarchical it appears that even macroscopic mechanisms (...) must supervene on a set of “objects” that behave non-classically. In this paper we argue, in part by appeal to the theory of quantum decoherence, that the universal validity of quantum mechanics does not undermine neo-mechanistic ontological and explanatory claims as they occur within in classical domains. Additionally, we argue that by relaxation of certain classical assumptions, mechanistic explanatory strategies can sometimes be carried over into the quantum domain. (shrink)

Standard canonical quantum mechanics makes much use of operators whose spectra cover the set of real numbers, such as the coordinates of space, or the values of the momenta. Discrete quantum mechanics uses only strictly discrete operators. We show how one can transform systems with pairs of integer-valued, commuting operators $P_i$ and $Q_i$ , to systems with real-valued canonical coordinates $q_i$ and their associated momentum operators $p_i$ . The discrete system could be entirely deterministic while the (...) corresponding (p, q) system could still be typically quantum mechanical. (shrink)

Quantum mechanics has recently indicated that temporal order is not always fixed, a finding that has far-reaching philosophical and theological implications. The phenomena, termed “indefinite causal order,” shows that events can be in a superposition with regard to their order. In the experimental setting with which this article is concerned, two events, A and B, were shown to be in the ordering relations “A before B” and “B before A” at the same time. This article introduces an ongoing (...) project that seeks to make sense of this result, with a particular focus on the methodology by which this research will be undertaken. Specific research questions, particularly regarding what indefinite causal order might mean for the metaphysics of time and the doctrine of salvation, are introduced. The collaborative approach detailed brings together the disciplinary skills of a working scientist and a working theologian. What is offered is a collaborative methodology for interaction between science and religion that is more than the sum of its parts. Alister McGrath’s idea of multiple rationalities is employed as an epistemological framework within which this research takes place. Within an epistemologically pluralistic model, collaborative efforts are not only encouraged but necessary. Complex reality requires an equally complex, usually interdisciplinary, explanation. I argue that such dialogue is both theologically justified and culturally valuable and indicates the direction in which this research will be taken. (shrink)

My propositions serve as elucidations in this way: he who understands me eventually recognises them as nonsensical, when he has used them – as steps – to climb up over them. (He must, so to speak,...

We articulate the problems posed by the quantum liar experiment (QLE) for backwards causation interpretations of quantum mechanics, time-symmetric accounts and other dynamically oriented local hidden variable theories. We show that such accounts cannot save locality in the case of QLE merely by giving up “lambda-independence.” In contrast, we show that QLE poses no problems for our acausal Relational Blockworld interpretation of quantum mechanics, which invokes instead adynamical global constraints to explain Einstein–Podolsky–Rosen (EPR) correlations (...) and QLE. We make the case that the acausal and adynamical perspective is more fundamental and that dynamical entities obeying dynamical laws are emergent features grounded therein. (shrink)

By the relational realist interpretation of wave function collapse, the quantum mechanical actualization of potentia is defined as a decoherence-driven process by which each actualization (in “orthodox” terms, each measurement outcome) is conditioned both by physical and logical relations with the actualities conventionally demarked as “environmental” or external to that particular outcome. But by the relational realist interpretation, the actualization-in-process is understood as internally related to these “enironmental” data per the formalism of quantum decoherence. The concept (...) of “actualization via wave function collapse” is accounted for solely by virtue of these presupposed logical relations—the same logical relations otherwise presupposed by the scientific method itself—and thus requires no “external” physical-dynamical trigger: e.g., the Gaussian hits of GRW, acts of conscious observation, etc. By the relational realist interpretation, it is the physical and logical relations among quantum actualities (quantum “final real things”) that drives the process of decoherence and, via the latter, the logically conditioned actualization of potentia. In this regard, the relational realist interpretation of quantum mechanics is a praxiological interpretation; that is, these physical and logical relations are ontologically active relations, contributing not just to the epistemic coordination of quantum actualizations, but to the process of actualization itself. (shrink)

We show that the formulations of non-relativistic quantum mechanics can be derived from an extended least action principle. The principle can be considered as an extension of the least action principle from classical mechanics by factoring in two assumptions. First, the Planck constant defines the minimal amount of action a physical system needs to exhibit during its dynamics in order to be observable. Second, there is constant vacuum fluctuation along a classical trajectory. A novel method is introduced (...) to define the information metrics to measure additional observability due to vacuum fluctuations, which is then converted to an additional action through the first assumption. Applying the variational principle to minimize the total actions allows us to recover the basic quantum formulations including the uncertainty relation and the Schrödinger equation in the position representation. In the momentum representation, the same method can be applied to obtain the Schrödinger equation for a free particle while further investigation is still needed for a particle with an external potential. Furthermore, the principle brings in new results on two fronts. At the conceptual level, we find that the information metrics for vacuum fluctuations are responsible for the origin of the Bohm quantum potential. Even though the Bohm potential for a bipartite system is inseparable, the underlying vacuum fluctuations are local. Thus, inseparability of the Bohm potential does not justify a non-local causal relation between the two subsystems. At the mathematical level, quantifying the information metrics for vacuum fluctuations using more general definitions of relative entropy results in a generalized Schrödinger equation that depends on the order of relative entropy. The extended least action principle is a new mathematical tool. It can be applied to derive other quantum formalisms such as quantum scalar field theory. (shrink)

A variety of ideas arising in decoherence theory, and in the ongoing debate over Everett's relative-state theory, can be linked to issues in relativity theory and the philosophy of time, specifically the relational theory of tense and of identity over time. These have been systematically presented in companion papers (Saunders 1995; 1996a); in what follows we shall consider the same circle of ideas, but specifically in relation to the interpretation of probability, and its identification with relations in the Hilbert (...) Space norm. The familiar objection that Everett's approach yields probabilities different from quantum mechanics is easily dealt with. The more fundamental question is how to interpret these probabilities consistent with the relational theory of change, and the relational theory of identity over time. I shall show that the relational theory needs nothing more than the physical, minimal criterion of identity as defined by Everett's theory, and that this can be transparently interpreted in terms of the ordinary notion of the chance occurrence of an event, as witnessed in the present. It is in this sense that the theory has empirical content. (shrink)

The probability ‘measure’ for measurements at two consecutive mo- ments of time is non-additive. These probabilities, on the other hand, may be determined by the limit of relative frequency of measured events, which are by nature additive. We demonstrate that there are only two ways to resolve this problem. The first solution places emphasis on the precise use of the concept of conditional probability for successive mea- surements. The physically correct conditional probabilities define additive probabilities for two-time measurements. These probabilities (...) depend ex- plicitly on the resolution of the physical device and do not, therefore, correspond to a function of the associated projection operators. It follows that quantum theory distinguishes between physical events and proposi- tions about events, the latter are not represented by projection operators and that the outcomes of two-time experiments cannot be described by quantum logic. The alternative explanation is rather radical: it is conceivable that the relative frequencies for two-time measurements do not converge, unless a particular consistency condition is satisfied. If this is true, a strong revision of the quantum mechanical formalism may prove necessary. We stress that it is possible to perform experiments that will distinguish the two alternatives. (shrink)

There have been a number of recent attempts to identify the best metaphysical framework for capturing Rovelli’s Relational Quantum Mechanics (RQM). All such accounts commit to some form of fundamentalia, whether they be traditional objects, physical relations, events or ‘flashes’, or the cosmos as a fundamental whole. However, Rovelli’s own recommendation is that ‘a natural philosophical home for RQM is an anti-foundationalist perspective' (Rovelli in Philos Trans R Soc 376:10, 2018). This gives us some prima facie reason (...) to explore options beyond these foundationalist frameworks, and take seriously a picture that lacks fundamentalia. I construct an argument from elimination in favour of an anti-foundationalist interpretation of RQM. The argument notes that _priority monism_ and _priority pluralism_ are exhaustive foundationalist options, and then shows that there are reasons to reject their union with RQM. I finish by recommending _metaphysical coherentism_ as a promising anti-foundationalist alternative, which captures the key characteristics of RQM through accepting symmetrical dependence, whilst avoiding challenges by jettisoning any commitment to fundamental entities. (shrink)

We develop and defend the thesis that the Hilbert space formalism of quantum mechanics is a new theory of probability. The theory, like its classical counterpart, consists of an algebra of events, and the probability measures defined on it. The construction proceeds in the following steps: (a) Axioms for the algebra of events are introduced following Birkhoff and von Neumann. All axioms, except the one that expresses the uncertainty principle, are shared with the classical event space. The only (...) models for the set of axioms are lattices of subspaces of inner product spaces over a field K. (b) Another axiom due to Soler forces K to be the field of real, or complex numbers, or the quaternions. We suggest a probabilistic reading of Soler's axiom. (c) Gleason's theorem fully characterizes the probability measures on the algebra of events, so that Born's rule is derived. (d) Gleason's theorem is equivalent to the existence of a certain finite set of rays, with a particular orthogonality graph (Wondergraph). Consequently, all aspects of quantum probability can be derived from rational probability assignments to finite "quantum gambles". (e) All experimental aspects of entanglement- the violation of Bell's inequality in particular- are explained as natural outcomes of the probabilistic structure. (f) We hypothesize that even in the absence of decoherence macroscopic entanglement can very rarely be observed, and provide a precise conjecture to that effect .We also discuss the relation of the present approach to quantum logic, realism and truth, and the measurement problem. (shrink)

Quantum Mechanics has faced deep controversies and debates since its origin when Werner Heisenberg proposed the first mathematical formalism capable to operationally account for what had been recently discovered as the new field of quantum phenomena. Today, even though we have reached a standardized version of QM which is taught in Universities all around the world, there is still no consensus regarding the conceptual reference of the theory and, if or if not, it can refer to something (...) beyond measurement outcomes. In this work we will argue that the reason behind the impossibility to reach a meaningful answer to this question is strictly related to the 20th Century Bohrian-positivist re-foundation of physics which is responsible for having introduced within the theory of quanta a harmful combination of metaphysical dogmatism and naive empiricism. We will also argue that the possibility of understanding QM is at plain sight, given we return to the original framework of physics in which the meaning of understanding has always been clear. (shrink)

The paper address the question of whether quantum mechanics (QM) favors Priority Monism, the view according to which the Universe is the only fundamental object. It develops formal frameworks to frame rigorously the question of fundamental mereology and its answers, namely (Priority) Pluralism and Monism. It then reconstructs the quantum mechanical argument in favor of the latter and provides a detailed and thorough criticism of it that sheds furthermore new light on the relation between parthood, composition and (...) fundamentality in QM. (shrink)

I summarise some aspects of the relation between quantum mechanics and the macroscopic world in the context of the multiverse or Everett theory. I do so with particular reference to the results of the theory of decoherence, the notions of reduction and emergence, and agents' decisions.

It is shown that quantum mechanics is a plausible statistical description of an ontology described by classical electrodynamics. The reason that no contradiction arises with various no-go theorems regarding the compatibility of QM with a classical ontology, can be traced to the fact that classical electrodynamics of interacting particles has never been given a consistent definition. Once this is done, our conjecture follows rather naturally, including a purely classical explanation of photon related phenomena. Our analysis entirely rests on (...) the block-universe view entailed by relativity theory. (shrink)

A formulation of relativistic quantum mechanics is presented independent of the theory of Hilbert space and also independent of the hypothesis of spacetime manifold. A hierarchy is established in the nondistributive lattice of physical ensembles, and it is shown that the projections relating different members of the hierarchy form a semigroup. It is shown how to develop a statistical theory based on the definition of a statistical operator. Involutions defined on the matrix representations of the semigroup are interpreted (...) in terms ofCPT conjugations. The theory of particles of spin one-half and systems with higher spin is developed from first principles. Methods are also developed for defining energy, momentum, orbital angular momentum, and weighted spacetime coordinates without reference to a manifold. (shrink)

The first issue of JCS published an interview with Roger Penrose on his recent book Shadows of the Mind: A Search for the Missing Science of Consciousness . In it Professor Penrose, among other subjects, presented his views on the role of quantum mechanics on our way towards a better understanding of brain functioning and its relation to consciousness. In this note we comment on some aspects of his reasoning.

Whereas one can conceive of a relational classical mechanics in which absolute space and time do not play a fundamental role, quantum mechanics does not readily admit any such relational formulation.