Ioannis G. Ntagkas

The conspicuous similarities between interpretive strategies in classical statistical mechanics and in quantum mechanics may be grounded on their employment of common implementations of probability. The objective probabilities which represent the underlying stochasticity of these theories can be naturally associated with three of their common formal features: initial conditions, dynamics, and observables. Various well-known interpretations of the two theories line up with particular choices among these three ways of implementing probability. This perspective has significant application to debates on primitive ontology and to the quantum measurement problem.

The Wigner’s friend type of thought experiments manifest the conceptual challenge on how different observers can have consistent descriptions of a quantum measurement event. In this paper, we analyze the extended version of Wigner’s friend thought experiment in detail and show that the reasoning process from each agent that leads to the no-go theorem is inconsistent. The inconsistency is with respect to the requirement that an agent should make use of updated information instead of outdated information. We then apply the relational formulation of quantum measurement to resolve the inconsistent descriptions from different agents. In relational formulation of quantum mechanics, a measurement is described relative to an observer. Synchronization of measurement result is a necessary requirement to achieve consistent descriptions of a quantum system from different observers. Thought experiments, including EPR, Wigner’s Friend and it extended version, confirm the necessity of relational formulation of quantum measurement when applying quantum mechanics to composite system with entangled but space-like separated subsystems.

We suggest a new answer to this intriguing question and argue that the answer may have implications for the solutions to the measurement problem. The main basis of our analysis is the doctrine of psychophysical supervenience. First of all, based on this doctrine, we argue that an observer in a quantum superposition or a quantum observer has a definite conscious experience, which is neither disjunctive nor illusive. The inconsistency of this result with the bare theory is further analyzed, and it is shown that an appropriate use of the strategy of analyzing the disposition of an observer to answer a particular question also leads to the same result. Next, we argue that this new result seems to disfavor Everett's and Bohm's approaches to quantum mechanics when considering the doctrine of psychophysical supervenience. This suggests that dynamical collapse theories are in the right direction to solve the measurement problem. Thirdly, we analyze the concrete content of the conscious experience of a quantum observer. It is argued that the mental content of a quantum observer is related to both the amplitude and relative phase of each branch of the superposition she is physically in, and it is composed of the mental content corresponding to every branch of the superposition. In addition, we argue that when assuming the modulus squared of the amplitude of each branch determines the vividness of the mental content corresponding to the branch, the structured tails problem of dynamical collapse theories can be solved.

The book explores several open questions in the philosophy of statistical mechanics. Each chapter is written by a leading expert in the field. Here is a list of some questions that are addressed in the book: 1) Boltzmann showed how the phenomenological gas laws of thermodynamics can be derived from statistical mechanics. Since classical mechanics is a deterministic theory there are no probabilities in it. Since statistical mechanics is based on classical mechanics, all the probabilities statistical mechanics talks about cannot be fundamental. However, if probabilities are epistemic, how can they play a role, as they seem to do, in laws, explanation, and prediction? 2) Many physicists use the notion of typicality instead of the one of probability when discussing statistical mechanics. What is the connection between the two notions? 3) How can one extend Boltzmann’s analysis to the quantum domain, where some theories are indeterministic? 4) Boltzmann’s explanation fundamentally involves cosmology: for the explanation to go through the Big Bang needs to have had extremely low entropy. Does the fact that the Big Bang was a low entropy state imply that it was, in some sense, “highly improbable” and requires an explanation? 5) What exactly is the connection between statistical and classical mechanics? Is the one of theory reduction or there is no such thing? 6) Statistical mechanics has two main formulation: one due to Botzmann and the other due to Gibbs. What is the connection between the two formulations

This is a preliminary version of an article to appear in the forthcoming Ashgate Companion to the New Philosophy of Physics.In it, I aim to review, in a way accessible to foundationally interested physicists as well as physics-informed philosophers, just where we have got to in the quest for a solution to the measurement problem. I don't advocate any particular approach to the measurement problem (not here, at any rate!) but I do focus on the importance of decoherence theory to modern attempts to solve the measurement problem, and I am fairly sharply critical of some aspects of the "traditional" formulation of the problem.

Beginning with Anderson, spontaneous symmetry breaking in infinite quantum systems is often put forward as an example of emergence in physics, since in theory no finite system should display it. Even the correspondence between theory and reality is at stake here, since numerous real materials show ssb in their ground states, although they are finite. Thus against what is sometimes called ‘Earman's Principle’, a genuine physical effect seems theoretically recovered only in some idealisation, disappearing as soon as the idealisation is removed.We review the well-known arguments that no finite system can exhibit ssb, using the formalism of algebraic quantum theory in order to control the thermodynamic limit and unify the description of finite- and infinite-volume systems. Using the striking mathematical analogy between the thermodynamic limit and the classical limit, we show that a similar situation obtains in quantum mechanics versus classical mechanics.This discrepancy between formalism and reality is quite similar to the measurement problem, and hence we address it in the same way, adapting an argument of the Landsman and Reuvers that was originally intended to explain the collapse of the wave-function within conventional quantum mechanics. Namely, exponential sensitivity to perturbations of the dynamics as the system size increases causes symmetry breaking already in finite but very large quantum systems. This provides continuity between finite- and infinite-volume descriptions of quantum systems featuring ssb and hence restores Earman's Principle.

This paper makes a collective biographical profile of a sample of physicists who were protagonists in the research on the foundations of quantum physics circa 1970. We study the cases of Zeh, Bell, Clauser, Shimony, Wigner, Rosenfeld, d’Espagnat, Selleri, and DeWitt, analyzing their training and early career, achievements, qualms with quantum mechanics, motivations for such research, professional obstacles, attitude towards the Copenhagen interpretation, and success and failures. Except for Rosenfeld, they were all dissidents, fighting against the dominant attitude among physicists at the time according to which foundational issues had already been solved by the founding fathers of the discipline. Theirs is a story of success as the foundations of quantum mechanics finally entered the physics mainstream despite the fact that their expectations of breaking down quantum mechanics were not fulfilled.

In 1966 the Brazilian physicist Klaus Tausk (b. 1927) circulated a preprint from the International Centre for Theoretical Physics in Trieste, Italy, criticizing Adriana Daneri, Angelo Loinger, and Giovanni Maria Prosperi`s theory of 1962 on the measurement problem in quantum mechanics. A heated controversy ensued between two opposing camps within the orthodox interpretation of quantum theory, represented by Leon Rosenfeld and Eugene P. Wigner. The controversy went well beyond the strictly scientific issues, however, reflecting philosophical and political commitments within the context of the Cold War, the relationship between science in developed and Third World countries, the importance of social skills, and personal idiosyncrasies

With many Hamiltonians one can naturally associate a |Ψ|2-distributed Markov process. For nonrelativistic quantum mechanics, this process is in fact deterministic, and is known as Bohmian mechanics. For the Hamiltonian of a quantum field theory, it is typically a jump process on the configuration space of a variable number of particles. We define these processes for regularized quantum field theories, thereby generalizing previous work of John S. Bell [3] and of ourselves [11]. We introduce a formula expressing the jump rates in terms of the interaction Hamiltonian, and establish a condition for finiteness of the rates.

Scientific realism is the view that our best scientific theories can be regarded as (approximately) true. This is connected with the view that science, physics in particular, and metaphysics could (and should) inform one another: on the one hand, science tells us what the world is like, and on the other hand, metaphysical principles allow us to select between the various possible theories which are underdetermined by the data. Nonetheless, quantum mechanics has always been regarded as, at best, puzzling, if not contradictory. As such, it has been considered for a long time at odds with scientific realism, and thus a naturalized quantum metaphysics was deemed impossible. Luckily, now we have many quantum theories compatible with a realist interpretation. However, scientific realists assumed that the wave-function, regarded as the principal ingredient of quantum theories, had to represent a physical entity, and because of this they struggled with quantum superpositions. In this paper I discuss a particular approach which makes quantum mechanics compatible with scientific realism without doing that. In this approach, the wave-function does not represent matter which is instead represented by some spatio-temporal entity dubbed the primitive ontology: point-particles, continuous matter fields, space-time events. I argue how within this framework one develops a distinctive theory-construction schema, which allows to perform a more informed theory evaluation by analyzing the various ingredients of the approach and their inter-relations.

Contrary to the widespread belief, the problem of the emergence of classical mechanics from quantum mechanics is still open. In spite of many results on the ¯h → 0 asymptotics, it is not yet clear how to explain within standard quantum mechanics the classical motion of macroscopic bodies. In this paper we shall analyze special cases of classical behavior in the framework of a precise formulation of quantum mechanics, Bohmian mechanics, which contains in its own structure the possibility of describing real objects in an observer-independent way.

In an old paper of our group in Milano a formalism was introduced for the continuous monitoring of a system during a certain interval of time in the framework of a somewhat generalized approach to quantum mechanics. The outcome was a distribution of probability on the space of all the possible continuous histories of a set of quantities to be considered as a kind of coarse grained approximation to some ordinary quantum observables commuting or not. In fact the main aim was the introduction of a classical level in the context of QM, treating formally a set of basic quantities, to be considered as beables in the sense of Bell, as continuously taken under observation. However the effect of such assumption was a permanent modification of the Liouville-von Neumann equation for the statistical operator by the introduction of a dissipative term which is in conflict with basic conservation rules in all reasonable models we had considered. Difficulties were even encountered for a relativistic extension of the formalism. In this paper I propose a modified version of the original formalism which seems to overcome both difficulties. First I study the simple models of an harmonic oscillator and a free scalar field in which a coarse grain position and a coarse grained field respectively are treated as beables. Then I consider the more realistic case of spinor electrodynamics in which only certain coarse grained electric and magnetic fields are introduced as classical variables and no matter related quantities.

We investigate the problem of “wave packet reduction” in quantum mechanics by solving the Schrödinger equation for a system composed of a model measuring apparatusM interacting with a microscopic objects. The “instrument” is intended to be somewhat more realistic than others previously proposed, but at the same time still simple enough to lead to an explicit solution for the time-dependent density matrix. It turns out that,practically, everything happens as if the wave packet reduction had occurred. This is a consequence of the fact that the apparatus is made up of a very large number of microsystems interacting withs. More precisely, our model shows that the “macroscopic size” of a measuring apparatus can lead by itself to a density matrix for the systemM + s which is physically equivalent to the density matrix of a statistical mixture corresponding to the reduced wave packet.

Bohmian mechanics and the Ghirardi-Rimini-Weber theory provide opposite resolutions of the quantum measurement problem: the former postulates additional variables (the particle positions) besides the wave function, whereas the latter implements spontaneous collapses of the wave function by a nonlinear and stochastic modification of Schrödinger's equation. Still, both theories, when understood appropriately, share the following structure: They are ultimately not about wave functions but about 'matter' moving in space, represented by either particle trajectories, fields on space-time, or a discrete set of space-time points. The role of the wave function then is to govern the motion of the matter.

The concept of fitness, central to population genetics and to the synthetic theory of evolution, is discussed. After a historical introduction on the origin of this concept, the current meaning of it in population genetics is examined: a cause of the selective process and its quantification. Several difficulties arise for its exact definition. Three adequacy criteria for such a definition are formulated. It is shown that it is impossible to formulate an adequate definition of fitness respecting these criteria. The propensity definition of fitness is presented and rejected. Finally it is argued that fitness is a conceptual device, a useful tool, only for descriptive purposes of selective processes, changing from case to case, and thus devoid of any substantial physical counterpart. Any attempt to its reification is an apport to the metaphysical load evolutionary theory has inherited from Natural Theology.

The meta-problem of consciousness prompts the metaquestion: is it the only problem consciousness poses? If we could explain all our phenomenal intuitions in topic-neutral terms, would anything remain to be explained? Realists say yes, illusionists no. In this paper I defend the illusionist answer. While it may seem obvious that there is something further to be explained -- consciousness itself -- this seemingly innocuous claim immediately raises a further problem -- the hard meta-problem. What could justify our continued confidence in the existence of consciousness once all our intuitions about it have been explained away? The answer would involve heavy-duty metaphysical theorizing, probably including a commitment either to substance dualism or to the existence of a mysterious intrinsic subjectivity. A far less extravagant option is to endorse the illusionist response and conclude that the meta-problem is not a meta-problem at all but the problem of consciousness.

The PBR theorem gives insight into how quantum mechanics describes a physical system. This paper explores PBRs’ general result and shows that it does not disallow the ensemble interpretation of quantum mechanics and maintains, as it must, the fundamentally statistical character of quantum mechanics. This is illustrated by drawing an analogy with an ideal gas. An ensemble interpretation of the Schrödinger cat experiment that does not violate the PBR conclusion is also given. The ramifications, limits, and weaknesses of the PBR assumptions, especially in light of lessons learned from Bell’s theorem, are elucidated. It is shown that, if valid, PBRs’ conclusion specifies what type of ensemble interpretations are possible. The PBR conclusion would require a more direct correspondence between the quantum state ) and the reality it describes than might otherwise be expected. A simple terminology is introduced to clarify this greater correspondence.

A recent no-go theorem gives an extension of the Wigner’s Friend argument that purports to prove the “Quantum theory cannot consistently describe the use of itself.” The argument is complex and thought provoking, but fails in a straightforward way if one treats QM as a statistical theory in the most fundamental sense, i.e. if one applies the so-called ensemble interpretation. This explanation is given here at an undergraduate level, which can be edifying for experts and students alike. A recent paper has already shown that the no-go theorem is incorrect with regard to the de Broglie Bohm theory and misguided in some of its general claims. This paper’s contribution is three fold. It shows how the extended Wigner’s Friend argument fails in the ensemble interpretation. It also makes more evident how natural a consistent statistical treatment of the wave function is. In this way, the refutation of the argument is useful for bringing out the core statistical nature of QM. It, in addition, manifests the unnecessary complications and problems introduced by the collapse mechanism that is part of the Copenhagen interpretation. The paper uses the straightforwardness of the ensemble interpretation to make the no-go argument and its refutation more accessible.

Quantum entanglement is widely believed to be a feature of physical reality with undoubted metaphysical implications. But Schrödinger introduced entanglement as a theoretical relation between representatives of the quantum states of two systems. Entanglement represents a physical relation only if quantum states are elements of physical reality. So arguments for metaphysical holism or nonseparability from entanglement rest on a questionable view of quantum theory. Assignment of entangled quantum states predicts experimentally confirmed violation of Bell inequalities. Can one use these experimental results to argue directly for metaphysical conclusions? No. Quantum theory itself gives us our best explanation of violations of Bell inequalities, with no superluminal causal influences and no metaphysical holism or nonseparability—but only if quantum states are understood as objective and relational, though prescriptive rather than ontic. Correct quantum state assignments are backed by true physical magnitude claims: but backing is not grounding. Quantum theory supports no general metaphysical holism or nonseparability; though a claim about a compound physical system may be significant and true while similar claims about its components are neither. Entanglement may well have have few, if any, first-order metaphysical implications. But the quantum theory of entanglement has much to teach the metaphysician about the roles of chance, causation, modality and explanation in the epistemic and practical concerns of a physically situated agent.

An intrinsic property, as David Lewis puts it, is a property "which things have in virtue of the way they themselves are", as opposed to an extrinsic property, which things have "in virtue of their relations or lack of relations to other things".1 Having long hair is an intrinsic property; having a long-haired brother is not. Intuitive as this notion is (and valuable in doing philosophy, I might add), it seems to resist analysis. Analysis, that is, to “quasi-logical” notions such as necessity, spatiotemporal location: using stronger tools, Lewis has given an analysis of intrinsicality that I take to be roughly correct. Lewis initially described intrinsic properties in his 1983 paper "Extrinsic Properties" as follows

Quantum entanglement is widely believed to be a feature of physical reality with undoubted (though debated) metaphysical implications. But Schrödinger introduced entanglement as a theoretical relation between representatives of the quantum states of two systems. Entanglement represents a physical relation only if quantum states are elements of physical reality. So arguments for metaphysical holism or nonseparability from entanglement rest on a questionable view of quantum theory. Assignment of entangled quantum states predicts experimentally confirmed violation of Bell inequalities. Can one use these experimental results to argue directly for metaphysical conclusions? No. Quantum theory itself gives us our best explanation of violations of Bell inequalities, with no superluminal causal influences and no metaphysical holism or nonseparability—but only if quantum states are understood as objective and relational, though prescriptive rather than ontic. Correct quantum state assignments are backed by true physical magnitude claims: but backing is not grounding. Quantum theory supports no general metaphysical holism or nonseparability; though a claim about a compound physical system may be significant and true while similar claims about its components are neither. Entanglement may well have have few, if any, first-order metaphysical implications. But the quantum theory of entanglement has much to teach the metaphysician about the roles of chance, causation, modality and explanation in the epistemic and practical concerns of a physically situated agent.

As far as classical physics is concerned, it is possible to trace causal relations between physical objects back to intrinsic properties of these objects. On this view, causal relations turn out to be internal instead of external relations, supervening on intrinsic properties of the relata. However, one can raise doubts about this view already in Newtonian mechanics. The decisive blow to this view comes from quantum physics, with Bell’s theorem proving that no dynamics based on local, intrinsic properties of quantum objects can yield the empirical predictions of quantum mechanics. Nonetheless, quantum entanglement by no means implies that we have to abandon an ontology of objects in favour of an ontology of structures. Any of the known proposals for a quantum ontology of matter in space-time is committed to objects. However, on any of these proposals, what determines the dynamics of these objects are not local, intrinsic properties, but a global or holistic property instantiated by all the objects together – that is, a structure that takes all the objects in the universe as its relata. The view set out in this paper thus amounts to combining ontic structural realism with an ontology of objects that can be conceived as substances. This suggestion is illustrated by drawing on the ontology of quantum physics worked out by Bohm and Bell.

Assuming that we find the concept of naturalness coherent, we shall no doubt wish to allow that certain relations count as highly natural. Many of us will think that various spatio-temporal and causal relations—is the cause of, is spatially separated from, is later than—are highly natural. Some of us will think that various basic semantic and mentalistic relations—refers to, attends to, believes.…--- are highly natural. Some will think that various logico-mathematical relations—being the successor of, being identical to…—are highly natural.