I briefly recall intersections of my research interests with those of John Bell. I then argue that the noise needed in theories of objective state vector reduction most likely comes from a fluctuating complex part in the classical spacetime metric; that is, state vector reduction is driven by complex-number-valued “ space–time foam.” Introduction My research interests have intersected those of John Bell three times. The first was when I found the forward lepton theorem for high-energy neutrino reactions, showing that for forward lepton kinematics, a conserved vector current (CVC) and a partially conserved axial vector current (PCAC) imply that the neutrino cross section can be related to a pion scattering cross section [1]. This led to an exchange of letters and discussions with Bell during 1964–5, which are described in the Commentaries for my selected papers [2]. The second was in the course of my work on the axial-vector anomaly [3], when I had further correspondence with John Bell, as described both in the Commentaries [4] and in the volume of essays on Yang–Mills theories assembled by 't Hooft [5]. The third time was a few years after Bell's death in 1990, when I became interested in the foundations of quantum theory and the quantum measurement problem, in the course of writing my book on quaternionic quantum mechanics [6]. Foundational issues in standard, complex quantum theory had preoccupied Bell for much of his career and led to his best known work. However, my correspondence with Bell in the 1960s never touched on quantum foundations, and I only read his seminal writings on the subject much later on. In this article I focus on this third area of shared interests. Objective Reduction Models There is now a well-defined phenomenology of state vector reduction, pioneered by the work of Ghirardi, Rimini, andWeber (GRW) and of Philip Pearle, and worked on by many others. John Bell was interested in this program from the outset.
I briefly recall intersections of my research interests with those of John Bell. I then argue that the noise needed in theories of objective state vector reduction most likely comes from a fluctuating complex part in the classical spacetime metric; that is, state vector reduction is driven by complex-number-valued “ space–time foam.” Introduction My research interests have intersected those of John Bell three times. The first was when I found the forward lepton theorem for high-energy neutrino reactions, showing that for forward lepton kinematics, a conserved vector current (CVC) and a partially conserved axial vector current (PCAC) imply that the neutrino cross section can be related to a pion scattering cross section [1]. This led to an exchange of letters and discussions with Bell during 1964–5, which are described in the Commentaries for my selected papers [2]. The second was in the course of my work on the axial-vector anomaly [3], when I had further correspondence with John Bell, as described both in the Commentaries [4] and in the volume of essays on Yang–Mills theories assembled by 't Hooft [5]. The third time was a few years after Bell's death in 1990, when I became interested in the foundations of quantum theory and the quantum measurement problem, in the course of writing my book on quaternionic quantum mechanics [6]. Foundational issues in standard, complex quantum theory had preoccupied Bell for much of his career and led to his best known work. However, my correspondence with Bell in the 1960s never touched on quantum foundations, and I only read his seminal writings on the subject much later on. In this article I focus on this third area of shared interests. Objective Reduction Models There is now a well-defined phenomenology of state vector reduction, pioneered by the work of Ghirardi, Rimini, andWeber (GRW) and of Philip Pearle, and worked on by many others. John Bell was interested in this program from the outset.
This paper argues that the case for “gravitizing” quantum theory is at least as strong as that for quantizing gravity. Accordingly, the principles of general relativity must influence, and actually change , the very formalism of quantum mechanics. Most particularly, an “Einsteinian”, rather than a “Newtonian” treatment of the gravitational field should be adopted, in a quantum system, in order that the principle of equivalence be fully respected. This leads to an expectation that quantum superpositions of states involving a significant mass displacement should have a finite lifetime, in accordance with a proposal previously put forward by Diósi and the author.
The problem of quantum state reduction The fundamental problem of quantum mechanics, as that theory is presently understood, is to make sense of the reduction of the state vector (i.e. collapse of the wave function ), denoted here by R . This issue is usually addressed in terms of the ‘quantum measurement problem’, which is to comprehend how, upon measurement of a quantum system, this (seemingly) discontinuous R -process can come about. A measurement, after all, merely consists of the quantum state under consideration becoming entangled with a more extended part of the physical universe, e.g. with a measuring apparatus. This measuring apparatus – together with the observing physicist and their common environment – should, according to conventional understanding, all also have some quantum description. Accordingly, there should be a quantum description of this entire quantum state, involving not only the original system under consideration but also the apparatus, physicist, and remaining environment – and this entire state would be expected to evolve continuously, solely according to the Schrödinger equation (unitary evolution), here denoted by the symbol U . Numerous different attitudes to R have been expressed over many years, ever since quantum mechanics was first clearly formulated. The most influential viewpoint has been the ‘Copenhagen interpretation’ of Niels Bohr, according to which the state vector │ψ〉 is not to be taken seriously as describing a quantum-level physical reality, but is to be regarded as merely referring to our (maximal) ‘knowledge’ of a physical system, and whose ultimate role is simply to provide us with a means to calculate probabilities when a measurement is performed on the system.
In 1964, John Stewart Bell famously demonstrated that the laws of standard quantum mechanics demand a physical world that cannot be described entirely according to local laws. The present article argues that this nonlocality must be gravitationally related, as it comes about only with quantum state reduction, this being claimed to be a gravitational effect. A new formalism for curved space–times, palatial twistor theory, is outlined, which appears now to be able to accommodate gravitation fully, providing a nonlocal description of the physical world. Nonlocality and Quantum State Reduction Although quantum entanglement is a normal consequence of the unitary (Schrödinger) evolution U of a multiparticle quantum system, this evolution is nevertheless local in the sense that it is described as the continuous (local) evolution in the relevant configuration space. What the EPR situations considered by John Stewart Bell [1] demonstrated was that when widely separated quantum measurements , of appropriate kinds, are performed on such entangled states (a current record for distance separation being 143 km, for entangled photon pairs [2]), the results of such measurements (which may be probabilistic or of a yes/no character) cannot be mimicked by any local realistic model. Thus, in trying to propose a mathematical model of what is going on realistically in the physical world, one would need to face up to the actual physical process involved in quantum state reduction R, which is an essential feature of quantum measurement. For many years, my own position on the state-reduction issue has been that R would have to involve a fundamental mathematical extension of current quantum theory, giving a description of something objectively taking place ‘ out there’ in the physical world (OR: objective reduction), rather than R being the effect of some kind of ‘interpretation’ of the standard unitary quantum formalism. Moreover, the extended theory should be able to describe the one physical world that we all experience, rather than some sort of coexisting superposition of vast numbers of alternatives. To be more specific about my own viewpoint, it has long been my position that such necessary deviation from unitarity U in this OR would result from a correct melding of the quantum formalism with that of general relativity .
Inspired by possible connections between gravity and foundational question in quantum theory, we consider an approach for the adaptation of objective collapse models to a general relativistic context. We apply these ideas to a list of open problems in cosmology and quantum gravity, such as the emergence of seeds of cosmic structure, the black hole information issue, the problem of time in quantum gravity and, in a more speculative manner, to the nature of dark energy and the origin of the very special initial state of the universe. We conclude that objective collapse models offer a rather promising path to deal with all of these issues.
John Bell was a staunch supporter of the dynamical wave function collapse approach to making a well-defined quantum theory. Through letters from him, I reminisce on my handful of interactions with him, all of which were memorable tome. Then I discuss nonlocality, violation of Bell's inequality and some further implications within the framework of the CSL (continuous spontaneous localization) model of dynamical collapse. Interactions I was an instructor at Harvard with a newly minted Ph.D. from MIT, earned with an indifferent thesis on particle theory. It took me two years to come to terms with, dare I say it, the fact that I did not care about the S-matrix. I was going to be out of a job anyway in 1966 so, in the fall of 1965, I put my full energy into writing my very first paper, about what I did care: that, to my eyes there was something deeply wrong with the quantum theory I had been taught; that the rules of how to use it were inadequate. The title of the paper [1] was “Elimination of the reduction postulate from quantum theory and a framework for hidden variable theories.” It was a long title, because it was really two rather separate papers. The first was based upon the perceived inadequacy that the collapse (reduction) postulate of the theory is ill-defined. The second stated some postulates I thought a good hidden variable theory ought to obey, and gave a model for their satisfaction in a two-dimensional (i.e., spin-1/2) Hilbert space. Try as I might, I was not able to generalize my model to a higher-dimensional (i.e., spin-1) Hilbert space, but I put it out there for someone more clever than I to achieve. I sent the paper to a very few people who I thought might be interested. One was John Bell, and he replied (see Figure 23.1)! So someone more clever than I pointed out that generalizing my model could not be achieved. I therefore excised the model and, after rewriting and retitling, published my very first paper [2]! After a three-year stint at Case Institute of Technology, which graduated to become Case Western Reserve University while I was there, in 1969 I became ensconced at Hamilton College.