In quantum theory, it is widely accepted that all experimental results must agree with theoretical predictions based on the Copenhagen interpretation. However the classical system in the Copenhagen interpretation has not been defined yet. On the other hand, although ongoing research of decoherence is trying to elucidate the emergence of the classical world, it cannot answer why we observe one of eigenstates in observed system. These situations show that the relation between what we observe and physical law has not been elucidated. Here I elucidate the relation by developing Everett's suggestion. Further, from this point of view, I point out that today's brain science falls into circular argument because it is trying to assign what we observe in the brain to process of the subjective perception, and I suggest the future research line in brain science.
In quantum theory, it is widely accepted that all experimental results must agree with theoretical predictions based on the Copenhagen interpretation. However the classical system in the Copenhagen interpretation has not been defined yet. On the other hand, although ongoing research of decoherence is trying to elucidate the emergence of the classical world, it cannot answer why we observe one of eigenstates in observed system. These situations show that the relation between what we observe and physical law has not been elucidated. Here I elucidate the relation by developing Everett's suggestion. Further, from this point of view, I point out that today's brain science falls into circular argument because it is trying to assign what we observe in the brain to process of the subjective perception, and I suggest the future research line in brain science.
The central part of Everett's formulation of quantum mechanics is a quantum mechanical model of memory and of observation as the recording of information in a memory. To use this model as an answer to the measurement problem, Everett has to assume that a conscious observer can be in a superposition of such memory states and be unaware of it. This assumption has puzzled generations of readers. The fundamental aim of this dissertation is to find a set of simpler assumptions which are sufficient to show that Everett's model is empirically adequate. I argue that Everett's model needs three assumptions to account for the process of observation: an assumption of decoherence of observers as quantum mechanical systems; an assumption of supervenience of mental states (qualities) over quantum mechanical properties; and an assumption about the interpretation of quantum mechanical states in general: quantum mechanical states describe ensembles of states of affairs coexisting in the same system. I argue that the only plausible understanding of such ensembles is as ensembles of possibilities, and that all standard no-collapse interpretations agree in this reading of quantum mechanical states. Their differences can be understood as different theories about what marks the real state within this ensemble, and Everett's theory as the claim that no additional 'mark of reality' is necessary. Using the three assumptions, I argue that introspection cannot determine the objective quantum mechanical state of an observer. Rather, the introspective qualities of a quantum mechanical state can be represented by a (classical) statistical ensemble of subjective states. An analysis of these subjective states and their dynamics leads to the conclusion that they suffice to give empirically correct predictions. The argument for the empirical adequacy of the subjective state entails that knowledge of the objective quantum mechanical state is impossible in principle. Empirical reality for a conscious observer is not described by the objective state, but by a Everettian relative state conditional on the subjective state, and no theoretical 'mark of reality' is necessary for this concept of reality. I compare the resulting concept of reality to Kant's distinction between empirical and transcendental reality.
Quantum mechanics is usually defined in terms of some loosely connected axioms and rules. Such a foundation is far from the beauty of, e.g., the `principles' underlying classical mechanics. Motivated, in addition, by notorious interpretation problems, there have been numerous attempts to modify or `complete' quantum mechanics. A first attempt was based on so-called hidden variables; its proponents essentially tried to expel the non-classical nature of quantum mechanics. More recent proposals intend to complete quantum mechanics not within mechanics proper but on a `higher (synthetic) level'; by means of a combination with gravitation theory (R Penrose), with quantum information theory (C M Caves, C A Fuchs) or with psychology and brain science (H P Stapp). I think it is fair to say that in each case the combination is with a subject that, per se , suffers from a very limited understanding that is even more severe than that of quantum mechanics. This was acceptable, though, if it could convincingly be argued that scientific progress desperately needs to join forces. Quantum mechanics of a closed system was a beautiful and well understood theory with its respective state being presented as a point on a deterministic trajectory in Liouville space---not unlike the motion of a classical N -particle system in its 6N -dimensional phase-space. Unfortunately, we need an inside and an outside view, we need an external reference frame, we need an observer. This unavoidable partition is the origin of most of the troubles we have with quantum mechanics. A pragmatic solution is introduced in the form of so-called measurement postulates: one of the various incompatible properties of the system under consideration is supposed to be realized (i.e. to become a fact, to be defined without fundamental dispersion) based on `instantaneous' projections within some externally selected measurement basis. As a result, the theory becomes essentially statistical rather than deterministic; furthermore there is an asymmetry between the observed and the observing. This is the point where consciousness may come in. Complemented by an introduction and several appendices, Henry Stapp's book consists essentially of three parts: theory, implications, and new developments. The theory part gives a very readable account of the Copenhagen interpretation, some aspects of a psychophysical theory, and, eventually, hints towards a quantum foundation of the brain--mind connection. The next part, `implications', summarizes some previous attempts to bridge the gap between the working rules of quantum mechanics and their possible consequences for our understanding of this world (Pauli, Everett, Bohm, Heisenberg). The last section, `new developments', dwells on some ideas about the conscious brain and its possible foundation on quantum mechanics. The book is an interesting and, in part, fascinating contribution to a field that continues to be a companion to `practical' quantum mechanics since its very beginning. It is doubtful whether such types of `quantum ontologies' will ever become (empirically) testable; right now one can hardly expect more than to be offered some consistent `grand picture', which the reader may find more or less acceptable or even rewarding. Many practicing quantum physicists, though, will remain unimpressed. The shift from synthetic ontology to analytic ontology is the foundation of the present work. This means that fundamental wholes are being partitioned into their ontologically subordinate components by means of `events'. The actual event, in turn, is an abrupt change in the Heisenberg state describing the quantum universe. The new state then defines the tendencies associated with the next actual event. To avoid infinite regression in terms of going from one state of tendencies to the next, consciousness is there to give these events a special `feel', to provide a status of `intrinsic actuality'. The brain of an alert human observer is similar in an important way to a quantum detection device: it can amplify small signals to large macroscopic effects. On the other hand, actual events are not postulated to occur exclusively in brains. They are more generally associated with the formation of records. Records are necessarily part of the total state of the universe: it is obvious that the state of the universe cannot undergo a Schrödinger dynamics and at the same time record its own history. `The full universe consists therefore of an exceedingly thin veneer of relatively sluggish, directly observable properties resting on a vast ocean or rapidly fluctuating unobservable ones.' The present ideas also bear on how the world should be seen to develop. While conventional cosmology encounters problems as to how to define the intial conditions, which would enter the governing equations of motion, here `the boundary conditions are set not at some initial time, but gradually by a sequence of acts that imposes a sequence of constraints. After any sequence of acts there remains a collection of possible worlds, some of which will be eliminated by the next act.' Connected with those acts is `meaning': there has always been some speculation about the special significance of local properties in our understanding of the world. One could argue that correlations (even the quantum correlations found, e.g., in the EPR-experiments) were as real as anything else. But also Stapp stresses the special role of locality: the `local observable properties, or properties similar to them are the natural, and perhaps exclusive, carriers of meaning in the quantum universe. From this point of view the quantum universe tends to create meaning.' This sounds like an absolute concept: meaning not with respect to something else, but defined intrinsically---not easy to digest. The role of consciousness in the developing quantum universe requires more attention. `The causal irrelevance of our thoughts within classical physics constitutes a serious deficiency of that theory, construed as a description of reality.' This is taken to be entirely different within quantum mechanics. `The core idea of quantum mechanics is to describe our activities as knowledge-seeking and knowledge-using agents.' `21st century science does not reduce human beings to mechanical automata. Rather it elevates human beings to agents whose free choices can, according to the known laws, actually influence their behaviour.' An example with respect to perception is discussed: `Why, when we look at a triangle, do we experience three lines joined at three points and not some pattern of neuron firings?' The brain `does not convert an actual whole triangle into some jumbled set of particle motions; rather it converts a concatenation of separate external events into the actualization of some single integrated pattern of neural activity that is congruent to the perceived whole triangle.' How convincing is this proposal? It is hard to tell. I think Henry Stapp did a good job, but there are tight limitations to any such endeavour. Quantum mechanics is often strange indeed, but it also gives rise to our classical world around us. For the emergence of classicality jumps and measurement projections (the basic phenomena connected with those fundamental events of choice) are not needed. Therefore, I doubt whether the explanation of the evolution of our world really allows (or requires) that much free choice. On the other hand, most scientist will agree that empirical science was not possible without free will: we could not ask independent questions if this asking was part of a deterministic trajectory. The fact that the result of a quantum measurement is indeterminate (within given probabilities) does certainly not explain free will. How about the type of measurment? The experimentalist will have to assume that he can select the pertinent observable within some limits. But given a certain design the so-called pointer basis (producing stable measurement results) is no longer a matter of free choice. `The main theme of classical physics is that we live in a clocklike universe.' Today it is often assumed that the universe was a big (quantum-) computer or a cellular automaton. Many would be all too happy to leave that rather restrictive picture behind. But where to go? Stapp suggests giving consciousness a prominent role: `The most profound alteration of the fundamental principles was to bring consciousness of human beings into the basic structure of the physical theory.' How far we are able to go in this direction will depend on the amount of concrete research results becoming available to support this view.
The problem of measurement taken at face value shows clearly that there is an inconsistency inside the quantum formalism.The phenomenon of decoherence is often presented as a solution to it.A widely debated question is to decide between two different interpretations.The first one is to consider that the decoherence process has the effect to actually project a superposed state into one of its classically interpretable component, hence doing the same job as the reduction postulate.For the second one, decoherence is only a way to show why no macroscopic superposed state can be observed and so, to explain the classical appearance of the macroscopic world, while the quantum entanglement between the system, the apparatus and the environment never disappears.In this case, explaining why only one single definite outcome is observed remains to do.In this paper, we examine arguments for and against both interpretations and defend a position according to which the outcome that is observed is relative to the observer in close parallel to the Everett interpretation.
Few, if any, issues in physics have engendered as much discussion as the measurement problem in quantum mechanics. It is generally agreed that the `normal' dynamical evolution of the state vector in quantum mechanics is given by a unitary map. The linearity of this map implies that the state vector will, in general, be found in a superposition of eigenstates of a given observable (or, similarly, that the density matrix describing a subsystem will not correspond to a definite value of this observable). However, when we make a measurement of an observable, we always obtain a define value—although it is impossible to predict with certainty which value will be obtained. The traditional response to this issue is to postulate that when a measurement is made, the wavefunction `collapses' to an eigenstate of the observable being measured, perhaps due to the inherent classicality of the measuring apparatus (Bohr), or to the consciousness of the observer (Wigner), or possibly to some modification of quantum dynamics that occurs even when observations are not being made. The main motivation for the Everett (`many worlds') interpretation is to avoid introducing any such collapse postulate. This volume commemorates the 50th anniversary of the publication of Everett's paper in 1957 and contains 20 original articles as well as the transcripts of several discussions that took place at meetings devoted to the Everett interpretation at Oxford University and the Perimeter Institute. The attractiveness of the Everett interpretation is very succinctly summarized by a sentence from Vaidman's contribution (p 582): `The collapse, with its randomness, non-locality and the lack of a well-defined moment of occurrence, is such an ugly scar on quantum theory, that I, along with many others, am ready to follow Everett and deny its existence.' But the main drawback of the interpretation is then equally succinctly stated in the next sentence: `The price is the many worlds interpretation, i.e., the existence of numerous parallel worlds.' In other words, if the state vector evolves to have a non-zero amplitude for two different values of an observable that I `measure' (i.e., interact with in an appropriate way), each of these alternatives remains equally `real', i.e., there is a `branch' of the wavefunction in which the observable takes the first value and I believe that it has this first value and a branch of the wavefunction where it takes the second value and I believe that it has this second value. Each of these `me's' sees a definite value for the observable, thus nicely accounting for what I believe I experience without invoking collapse. But then, it seems that I have to believe that there are many other `me's' around—even if they are very difficult for this particular me to access—and no way I can predict which `me' I will be in the future. Indeed, Saunders writes on p 192, `If Alice is a person (of course she is) then we must say, even prior to branching at tj that there are many Alices present, atom for atom duplicates...Alice should be uncertain after all— each Alice should be uncertain—for each as of tj does not (and as a matter of principle, cannot) know which of these branching persons she is.' Thus, if taken seriously, the Everett viewpoint leads directly to questions like `What determines which ``me'' I am now and/or will feel that I am in the future?' The response `You are all of them' somehow doesn't seem satisfying, and further pursuit of these issues would seem to lead to questions as fruitless as questions like `Why am I ``me'' and not ``you''?' I believe that this accounts for why the Everett interpretation does not have universal appeal. But enough of `me' for now (more later); let's discuss the book. Unlike many edited volumes and conference proceedings in physics—which often consist of hastily slapped-together re-hashes of previous papers—this volume meets very high standards in the choice of topics and authors and in the quality of the writing. Although each of the articles is closely tied in with the Everett interpretation, there are many articles of considerable value and interest in their own right, such as the discussion of quasiclassical realms by Hartle and and the discussion of the de Broglie–Bohm interpretation by Valentini. There is also an excellent introduction by Saunders to the quantum measurement problem and the main issues that arise in the Everett interpretation. A central issue in the Everett interpretation is the status of the `Born rule', which asserts that, for state ψ, the probability of obtaining a particular outcome of a measurement is ||Pψ||2, where P is the projection operator onto the eigensubspace associated with the measurement outcome. In traditional interpretations, the Born rule is simply postulated as part of the collapse hypothesis. In the Everett interpretation, it is far from obvious that the Born rule even has any meaning—if all outcomes occur, how can one talk about the probability of a particular outcome? Given the importance of this issue, it is highly appropriate that four chapters of the book (by Saunders, Papineau, Wallace, and Greaves and Myrvold) are devoted to addressing probability and the Born rule from the Everett viewpoint, and three chapters (by Kent, Albert, and Price) are devoted to criticising these views. As indicated by the above quote from Saunders' article, uncertainty and probability can enter the Everett interpretation via each Alice being uncertain as to which Alice she is or will be. However, in view of the difficulties to which this kind of argumentation will lead, it is perhaps not surprising that in the 123 pages of combined discussion by Saunders, Papineau, Wallace, and Greaves and Myrvold, there are only fleeting references to the use of probability along these lines. Rather, the approach taken is reminiscent of that of adept politicians: if you can't answer a question, then answer a different question, and answer it with conviction and detail. Instead of considering probabilities of outcomes—a highly problematical notion when all of the possible outcomes actually occur—consider only decision theory issues. In particular, Wallace gives a precise and detailed mathematical proof that, under certain hypotheses, the only rational strategy that a quantum observer can follow in making decisions is to weight the possible outcomes by Born rule probabilities. To illustrate this more graphically, suppose tomorrow's weather were determined by some quantum mechanical, Stern–Gerlach-like process. I would like to know whether it is likely to rain tomorrow. However, when I ask an Everett follower (who knows the state vector and has done the Born rule calculation), all she will tell me in direct response to my question is that `it will rain and it won't rain.' Nevertheless, she is willing tell me whether or not it is rational for me to take an umbrella. I suppose that if she tells me that it would be highly irrational for me to take an umbrella, I can take the hint and deduce that it is very unlikely to rain. However, there does seem something wrong with the fact that she is not allowed to say this directly. In any case, if the conclusion of a mathematically correct argument is that rational decision strategies require the Born rule, then there must be quite a bit lying in the assumptions. The articles by Kent, Albert, and Price do a good job of fleshing out these assumptions and pointing out the weaknesses and flaws in the probability and decision theory discussions within the Everett framework. I hope it is clear from what I have written above that this is an outstanding volume, which should be of great interest to anyone interested in the foundations of quantum theory. Indeed, I feel quite fortunate to be the particular `me' that happens to exist in the same branch of the wavefunction of the universe in which this book was published.
Everett wanted a formulation of quantum mechanics that (i) took the linear dynamics to be a complete and accurate description of the time-evolution of all physical systems and (ii) logically entailed the same subjective appearances predicted by the standard formulation of quantum mechanics. While most everyone would agree with this description of Everett's project, there is little agreement on exactly how his relative-state formulation was supposed to work. In this paper, I consider two very different readings of Everett: the bare reading and the splitting-worlds reading. What distinguishes these is their interpretation of the wave function and how one accounts for the experiences of observers. The difficulty in interpreting Everett, however, is illustrated by the fact that neither reading is entirely compatible with his own description of his project.
The starting point of this dissertation is that a quantum state represents the observer's knowledge about the system of interest. As it has been pointed out several times by the opponents of this epistemic interpretation, it is difficult to reconcile this point of view with our common notion of “physical reality”, which exists independently of our monitoring, and can be discovered without disturbance. Indeed, if quantum theory is correct, it should apply to classical systems—including measurement devices—as well as to any other system. In this dissertation, we will study the quantum mechanisms responsible for our perception of the world and demonstrate how they lead to the emergence of an operational objective reality from within quantum theory: several observers gathering information through these mechanisms will arrive at a common consensus about the properties of the world. The two mechanisms we study in great detail are the redundant proliferation of information in the environment and the direct measurement of a macroscopic observable. An example of the first mechanism is the photon environment which provides us with our visual data about the world. Several independent observers learning about their surroundings in this indirect fashion will agree on their findings. An example of the second mechanism is our tactile information: when the tip of our finger touches an object, it interacts collectively with a very large number of molecules. Again, under realistic assumptions, this type of information acquisition will lead to a classical perception of the world.