The speculation that gravity is the key to solving the quantum measurement problem has been alive for decades, without any convincing demonstration of a solution. One necessary factor in the relevant proposals is that the gravitational energy of mutual interaction, which scales quadratically with the mass, facilitates the spontaneous collapse of the wavefunctions in spatially separated superpositions. Relying on a simple physical input from electrodynamics, supported by robust first principle calculations, we show that the speculations connecting gravity and the hypothetical spontaneous collapse of the wavefunction are inconsistent and not tenable. The result suggests that the gravitational solution to the problem of the collapse of the wavefunction be put to rest.
The speculation that gravity is the key to solving the quantum measurement problem has been alive for decades, without any convincing demonstration of a solution. One necessary factor in the relevant proposals is that the gravitational energy of mutual interaction, which scales quadratically with the mass, facilitates the spontaneous collapse of the wavefunctions in spatially separated superpositions. Relying on a simple physical input from electrodynamics, supported by robust first principle calculations, we show that the speculations connecting gravity and the hypothetical spontaneous collapse of the wavefunction are inconsistent and not tenable. The result suggests that the gravitational solution to the problem of the collapse of the wavefunction be put to rest.
Inspired by an ontic view of the wavefunction in quantum mechanics and motivated by the universal interaction of gravity, we discuss a possible gravity implication in the state collapse mechanism. Concretely, we investigate the stability of the spatial superposition of a massive quantum state under the gravity effect. In this context, we argue that the stability of the spatially superposed state depends on its gravitational self-energy originating from the effective mass density distribution through the spatially localized eigenstates. We reveal that the gravitational self-interaction between the different spacetime curvatures created by the eigenstate effective masses leads to the reduction of the superposed state to one of the possible localized states. Among others, we discuss such a gravity-driven state reduction. Then, we approach the corresponding collapse time and the induced effective electric current in the case of a charged state, as well as the possible detection aspects.
According to Penrose, the fundamental conflict between the superposition principle of quantum mechanics and the general covariance principle of general relativity entails the existence of wavefunction collapse, e.g. a quantum superposition of two different space-time geometries will collapse to one of them due to the ill-definedness of the time-translation operator for the superposition. In this paper, we argue that Penrose's conjecture on gravity's role in wavefunction collapse is debatable. First of all, it is still a controversial issue what the exact nature of the conflict is and how to resolve it. Secondly, Penrose's argument by analogy is too weak to establish a necessary connection between wavefunction collapse and the conflict as understood by him. Thirdly, the conflict does not necessarily lead to wavefunction collapse. For the conflict or the problem of ill-definedness for a superposition of different space-time geometries also needs to be solved before the collapse of the superposition finishes, and once the conflict has been resolved, the wavefunction collapse will lose its physical basis relating to the conflict. In addition, we argue that Penrose's suggestions for the collapse time formula and collapse states are also problematic.
According to Penrose, the fundamental conflict between the superposition principle of quantum mechanics and the principle of general covariance of general relativity entails the existence of wavefunction collapse, e.g. a quantum superposition of two different space-time geometries will collapse to one of them due to the ill-definedness of the time-translation operator for the superposition. In this paper, we argue that Penrose's conjecture on gravity's role in wavefunction collapse is debatable. First of all, it is still a controversial issue what the exact nature of the conflict is and how to resolve it. Secondly, Penrose's argument by analogy is too weak to establish a necessary connection between wavefunction collapse and the conflict as understood by him. Thirdly, the conflict does not necessarily lead to wavefunction collapse. For the conflict or the problem of ill-definedness for a superposition of different space-time geometries also needs to be solved before the collapse of the superposition finishes, and once the conflict has been resolved, the wavefunction collapse will lose its physical basis relating to the conflict. In addition, we argue that Penrose's suggestions for the collapse time formula and the preferred basis are also problematic.
The stability of a quantum superposition f two different stationary mass distributions is examined, where the perturbing effect of each distribution on the space-time structure is taken into account, in accordance with the principles of general relativity. It is argued that the definition of the time-translation operator for the superposed space-times involves an inherent ill-definedness, leading to an essential uncertainty in the energy of the superposed state which, in the Newtonian limit, is proportional to the gravitational self-energy EA of the difference between the two mass distributions. This is consistent with a suggested finite lifetime of the order of?t/ELx for the superposed state, in agreement with a certain proposal made by the author for a gravitationally induced spontaneous quantum state reduction, and with closely related earlier suggestions by Di6si and by Ghirardi et al. 1. 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 wavefunction), 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 (seem-ingly) discontinuous R-process can come about. A measurement, after all, merely consists of the quantum state under consideration becoming en-tangled with a more extended part of the physical universe, e.g. with a
At present, there are two possible, and equally plausible, explanations for the physics of quantum measurement. The first explanation, known as the many-worlds interpretation, does not require any modification of quantum mechanics, and asserts that at the time of measurement the Universe splits into many branches, one branch for every possible alternative. The various branches do not interfere with each other because of decoherence, thus providing a picture broadly consistent with the observed Universe. The second explanation, which requires quantum mechanics to be modified from its presently known form, is that at the time of measurement the wavefunction collapses into one of the possible alternatives. The two explanations are mutually exclusive, and up until now, no theoretical reasoning has been put forward to choose one explanation over the other. In this article, we provide an argument which implies that the collapse interpretation is favored over the many-worlds interpretation. Our starting point is the assertion (which we justify) that there ought to exist a reformulation of quantum mechanics which does not refer to a classical spacetime manifold. The need for such a reformulation implies that quantum theory becomes nonlinear on the Planck mass/energy scale. Standard linear quantum mechanics is an approximation to this nonlinear theory, valid at energy scales much smaller than the Planck scale. Using ideas based on noncommutative differential geometry, we develop such a reformulation and derive a nonlinear Schrödinger equation, which can explain collapse of the wavefunction. We also obtain an expression for the lifetime of a quantum superposition. We suggest ideas for an experimental test of this model.
Abstract Inspired by an ontic view of the wave function in quantum mechanics and motivated by the universal interaction of gravity, we discuss a possible gravity implication in the state collapse mechanism. Concretely, we investigate the stability of the spatial superposition of a massive quantum state under the gravity effect. In this context, we argue that the stability of the spatially superposed state , depends on its gravitational self-energy originating from the effective mass density distribution through the spatially localized eigenstates . We reveal that the gravitational self-interaction between the different spacetime curvatures created by the eigenstate effective masses leads to the reduction of the superposed state to one of the possible localized states . Among others, we discuss such a gravity-driven state reduction. Then, we approach the corresponding collapse time and the induced effective electric current in the case of a charged state, as well as the possible detection aspects.