Once measured, a simple quantum system collapses into one state. Before that, it can be in a superposition of several states. Though these exist in a probabilistic interpretation, we often say that "the particle was in several states and collapsed to one". Although the theory and experiments agree to this, it is counter-intuitive. We give a model that delivers a possible viewpoint to overcome that strangeness. We introduce two computation ideas to interpret this apparent variation of the number of states and model its counting: computation without zero, and computing state probabilities as projections in probability dimensions of the particle positions. We bypass the physics and mathematical formalism involved, focusing not on the states and their physics, but solely on the counting of the “number of states”, given its strangeness. This model is a simplification for discussion purposes. From an arithmetical point of view, our findings suggest a conservation law for the number of states, before and after a measurement, in favor of a convergent quantum and classical physics interpretation.
Once measured, a simple quantum system collapses into one state. Before that, it can be in a superposition of several states. Though these exist in a probabilistic interpretation, we often say that "the particle was in several states and collapsed to one". Although the theory and experiments agree to this, it is counter-intuitive. We give a model that delivers a possible viewpoint to overcome that strangeness. We introduce two computation ideas to interpret this apparent variation of the number of states and model its counting: computation without zero, and computing state probabilities as projections in probability dimensions of the particle positions. We bypass the physics and mathematical formalism involved, focusing not on the states and their physics, but solely on the counting of the “number of states”, given its strangeness. This model is a simplification for discussion purposes. From an arithmetical point of view, our findings suggest a conservation law for the number of states, before and after a measurement, in favor of a convergent quantum and classical physics 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.
The basic mathematical structure, QM-A, of the many worlds interpretation consists solely of the linear mathematics plus the Hilbert space properties of the state vectors. There is no collapse and there are no particles or hidden variables. It is remarkable that QM-A alone can account for all our observations except probability. There is no need for particles, hidden variables or collapse to explain perception of only one classical version of reality, the photoelectric effect, localized effects from a spread-out wave function in scattering and interference experiments, wave-particle duality, and so on. But probability cannot be defined within QM-A. Nevertheless, because of its astonishing success, it seems reasonable to require (1) that the mathematics of an interpretation be limited to the highly successful QM-A and (2) that "matter" be composed of state vectors alone. But the probability law requires, in essence, that one version of the observer be singled out. The most straightforward way to accomplish this under (1) and (2) is to assume there is an aspect of the observer-the Mind-which is outside the laws of quantum mechanics and perceives just one version of reality. Under that assumption, the probability law can then be derived. Thus we have an interpretation, QM-A plus "outside" observer, which explains all our perceptions.
We present the quantum measurement problem as a serious physics problem. Serious because without a resolution, quantum theory is not complete, as it does not tell how one should - in principle - perform measurements. It is physical in the sense that the solution will bring new physics, i.e. new testable predictions, hence it is not merely a matter of interpretation of a frozen formalism. I argue that the two popular ways around the measurement problem, many-worlds and Bohmian-like mechanics, do, de facto, introduce effective collapses when "I" interact with the quantum system. Hence, surprisingly, in many-worlds and Bohmian mechanics, the "I" plays a more active role than in alternative models, like e.g. collapse models. Finally, I argue that either there are several kinds of stuffs out there, i.e. physical dualism, some stuff that respects the superposition principle and some that doesn't, or there are special configurations of atoms and photons for which the superposition principle breaks down. Or, and this I argue is the most promising, the dynamics has to be modified, i.e. in the form of a stochastic Schrödinger equation.
Irreversibility, strengthened by the idea of strong mixing, has been discussed in the last two chapters. We reached the conclusion that, once such processes have been involved in a quantum measurement, it is in principle impossible to perform an interference experiment that would demonstrate the continued existence of a superposition. It is then ‘safe’ to assume that the system has ‘really’ collapsed into a state corresponding to one of the possible measurement outcomes. Does this mean that the measurement problem has been solved? Clearly it has for all practical purposes, as has been pointed out several times in earlier chapters. But it may still not be sufficient to provide a completely satisfactory solution in principle: in particular, we note that we have still not properly addressed the question of actualisation outlined at the end of the first section of Chapter 8. In the present chapter we discuss an interpretation of quantum physics that was developed during the last 15 or so years of the twentieth century and is based on the idea of describing quantum processes in terms of ‘consistent histories’. As we shall see, the resulting theory has much in common with the Copenhagen interpretation discussed in Chapter 4 and when applied to measurement it connects with the viewpoint, discussed in the last chapter, in which irreversible processes are to be taken as the primary reality.
Quantum state collapse is a cornerstone of quantum mechanics, representing the irreversible transition from a superposition of states to a definite state. This phenomenon fundamentally challenges classical intuition and presents a significant hurdle in quantum information theory. This research proposes a novel method for analyzing this collapse process, leveraging Bayesian inference to model the probability of distinct collapse outcomes and ultimately providing a more precise predictive framework. The core mechanism centers around the creation of adaptive probabilistic models, enabling a deeper understanding of collapse events and their associated consequences. The method's potential impact lies in enhancing our comprehension of quantum phenomena and offering a pathway towards more robust quantum algorithms and systems.