Gao presents a critical reconsideration of a paper I wrote on the subject of protective measurement. Here, I take the occasion to reply to his objections. In particular, I retract my previous claim to have proven that in a protective measurement, the observable being measured on a system must commute with the system's Hamiltonian. However, I do maintain the viability of the interpretation I offered for protective measurements, as well as my analysis of a thought experiment proposed by Aharonov, Anandan (...) and Vaidman against Gao's objections. (shrink)

We propose partial measurements as a conceptual tool to understand how to operate with counterfactual claims in quantum physics. Indeed, unlike standard von Neumann measurements, partial measurements can be reversed probabilistically. We first analyze the consequences of this rather unusual feature for the principle of superposition, for the complementarity principle, and for the issue of hidden variables. Then we move on to exploring non-local contexts, by reformulating the EPR paradox, the quantum teleportation experiment, and the entanglement-swapping protocol for the situation (...) in which one uses partial measurements followed by their stochastic reversal. This leads to a number of counter-intuitive results, which are shown to be resolved if we give up the idea of attributing reality to the wavefunction of a single quantum system. (shrink)

The ordinary quantum theory points out that general relativity (GR) is negligible for spatial distances up to the Planck scale lP=(hG/c3)1/2∼10−33cm. Consistency in the foundations of the quantum theory requires a “soft” spacetime structure of the GR at essentially longer length. However, for some reasons this appears to be not enough. A new framework (“superrelativity”) for the desirable generalization of the foundation of quantum theory is proposed. A generalized nonlinear Klein-Gordon equation has been derived in order to shape a stable (...) wave packet. (shrink)

It has been debated whether protective measurement implies the reality of the wave function. In this article, I present a new analysis of the relationship between protective measurements and the reality of the wave function. First, I briefly introduce protective measurements and the ontological models framework for them. Second, I give a simple proof of Hardy’s theorem in terms of protective measurements. Third, I analyse two suggested ψ -epistemic models of a protective measurement. It is shown that although these models (...) can explain the appearance of expectation values of observables in a single measurement, their predictions about the variance of the result of a non-ideal protective measurement are different from those of quantum mechanics. Finally, I argue that under an auxiliary finiteness assumption about the dynamics of the ontic state, protective measurement implies the reality of the wave function in the ontological models framework. (shrink)

Protective measurement is a new measuring method introduced by Aharonov, Vaidman, and Anandan, with the aim of measuring the expectation value of an observable on a single quantum system, even if the system is initially not in an eigenstate of the measured observable. According to these authors, this feature of protective measurements favors a realistic interpretation of the wave function. These claims were challenged by Uffink. He argued that only observables that commute with the system's Hamiltonian can be protectively measured, (...) and that an allegedly protective measurement of an observable that does not commute with the system's Hamiltonian does not actually measure this observable, but rather another related one that commutes with the system's Hamiltonian. In this paper we identify a number of unresolved issues in Uffink's proofs and argue that his alternative interpretation of what happens in a protective measurement has not been justified. (shrink)

This article re-examines Schrödinger’s charge density hypothesis, according to which the charge of an electron is distributed in the whole space, and the charge density in each position is proportional to the modulus squared of the wave function of the electron there. It is shown that the charge distribution of a quantum system can be measured by protective measurements as expectation values of certain observables, and the results as predicted by quantum mechanics confirm Schrödinger’s original hypothesis. Moreover, the physical origin (...) of the charge distribution is also investigated. It is argued that the charge distribution of a quantum system is effective, that is, it is formed by the ergodic motion of a localized particle with the charge of the system. (shrink)

There are three possible interpretations of the wave function in the de Broglie-Bohm theory: taking the wave function as corresponding to a physical entity or a property of the Bohmian particles or a law. In this paper, we argue that the first interpretation is favored by an analysis of protective measurements.

Recently the first protective measurement has been realized in experiment [Nature Phys. 13, 1191 ], which can measure the expectation value of an observable from a single quantum system. This raises an important and pressing issue of whether protective measurement implies the reality of the wave function. If the answer is yes, this will improve the influential PBR theorem [Nature Phys. 8, 475 ] by removing auxiliary assumptions, and help settle the issue about the nature of the wave function. In (...) this paper, we demonstrate that this is indeed the case. It is shown that a psi-epistemic model and quantum mechanics have different predictions about the variance of the result of a Zeno-type protective measurement with finite N. (shrink)

In this article, we give a clearer argument for the reality of the wave function in terms of protective measurements, which does not depend on nontrivial assumptions and also overcomes existing objections. Moreover, based on an analysis of the mass and charge properties of a quantum system, we propose a new ontological interpretation of the wave function. According to this interpretation, the wave function of an N-body system represents the state of motion of N particles. Moreover, the motion of particles (...) is discontinuous and random in nature, and the modulus squared of the wave function gives the probability density that the particles appear in certain positions in space. (shrink)

It has been debated whether protective measurement implies the reality of the wave function. In this paper, I present a new analysis of the relationship between protective measurement and the reality of the wave function. First, I briefly introduce protective measurements and the ontological models framework for them. Second, I give a simple proof of Hardy's theorem in terms of protective measurements. It shows that when assuming the ontic state of the protected system keeps unchanged during a protective measurement, the (...) wave function must be real. Third, I analyze two suggested psi-epistemic models of a protective measurement, in which the ontic state of the system is affected by the measurement. It is shown that although these models can explain the appearance of expectation values of observables in a single measurement, their predictions about the variance of the result of a non-ideal protective measurement are different from those of quantum mechanics. Finally, I argue that no psi-epistemic models exist for an ideal protective measurement in the ontological models framework, and in order to account for the definite result of an ideal protective measurement, the wave function must be a property of the protected system, defined either at a precise instant or during an infinitesimal time interval around an instant. Moreover, this result can also be extended to the wave function of an unprotected system. This new proof of the reality of the wave function does not rely on auxiliary assumptions, and it may help settle the issue about the nature of the wave function. (shrink)

We investigate the validity of the field explanation of the wave function by analyzing the mass and charge density distributions of a quantum system. It is argued that a charged quantum system has effective mass and charge density distributing in space, proportional to the square of the absolute value of its wave function. This is also a consequence of protective measurement. If the wave function is a physical field, then the mass and charge density will be distributed in space simultaneously (...) for a charged quantum system, and thus there will exist a remarkable electrostatic self-interaction of its wave function, though the gravitational self-interaction is too weak to be detected presently. This not only violates the superposition principle of quantum mechanics but also contradicts experimental observations. Thus we conclude that the wave function cannot be a description of a physical field. In the second part of this paper, we further analyze the implications of these results for the main realistic interpretations of quantum mechanics, especially for de Broglie-Bohm theory. It has been argued that de Broglie-Bohm theory gives the same predictions as quantum mechanics by means of quantum equilibrium hypothesis. However, this equivalence is based on the premise that the wave function, regarded as a Ψ-field, has no mass and charge density distributions, which turns out to be wrong according to the above results. For a charged quantum system, both Ψ-field and Bohmian particle have charge density distribution. This then results in the existence of an electrostatic self-interaction of the field and an electromagnetic interaction between the field and Bohmian particle, which contradicts both the predictions of quantum mechanics and experimental observations. Therefore, de Broglie-Bohm theory as a realistic interpretation of quantum mechanics is probably wrong. Lastly, we suggest that the wave function is a description of some sort of ergodic motion (e.g. random discontinuous motion) of particles, and we also briefly analyze the implications of this suggestion for other realistic interpretations of quantum mechanics including many-worlds interpretation and dynamical collapse theories. (shrink)

This article introduces the method of protective measurement and discusses its deep implications for the foundations of quantum mechanics.

This thesis is an attempt to reconstruct the conceptual foundations of quantum mechanics. First, we argue that the wave function in quantum mechanics is a description of random discontinuous motion of particles, and the modulus square of the wave function gives the probability density of the particles being in certain locations in space. Next, we show that the linear non-relativistic evolution of the wave function of an isolated system obeys the free Schrödinger equation due to the requirements of spacetime translation (...) invariance and relativistic invariance. Thirdly, we argue that the random discontinuous motion of particles may lead to a stochastic, nonlinear collapse evolution of the wave function. A discrete model of energy-conserved wavefunction collapse is proposed and shown to be consistent with existing experiments and our macroscopic experience. In addition, we also give a critical analysis of the de Broglie-Bohm theory, the many-worlds interpretation and other dynamical collapse theories, and briefly discuss the issue of unifying quantum mechanics and special relativity. (shrink)

We show that the physical meaning of the wave function can be derived based on the established parts of quantum mechanics. It turns out that the wave function represents the state of random discontinuous motion of particles, and its modulus square determines the probability density of the particles appearing in certain positions in space.

The meaning of the wave function and its evolution are investigated. First, we argue that the wave function in quantum mechanics is a description of random discontinuous motion of particles, and the modulus square of the wave function gives the probability density of the particles being in certain locations in space. Next, we show that the linear non-relativistic evolution of the wave function of an isolated system obeys the free Schrödinger equation due to the requirements of spacetime translation invariance and (...) relativistic invariance. Thirdly, we argue that the random discontinuous motion of particles may lead to a stochastic, nonlinear collapse evolution of the wave function. A discrete model of energy-conserved wavefunction collapse is proposed and shown consistent with existing experiments and our macroscopic experience. Besides, we also give a critical analysis of the de Broglie-Bohm theory, the many-worlds interpretation and other dynamical collapse theories, and briefly discuss the issues of unifying quantum mechanics and relativity. (shrink)

This article analyzes the implications of protective measurement for the meaning of the wave function. According to protective measurement, a charged quantum system has mass and charge density proportional to the modulus square of its wave function. It is shown that the mass and charge density is not real but effective, formed by the ergodic motion of a localized particle with the total mass and charge of the system. Moreover, it is argued that the ergodic motion is not continuous but (...) discontinuous and random. This result suggests a new interpretation of the wave function, according to which the wave function is a description of random discontinuous motion of particles, and the modulus square of the wave function gives the probability density of the particles being in certain locations. It is shown that the suggested interpretation of the wave function disfavors the de Broglie-Bohm theory and the many-worlds interpretation but favors the dynamical collapse theories, and the random discontinuous motion of particles may provide an appropriate random source to collapse the wave function. (shrink)

It is a fundamental and widely accepted assumption that a measurement result exists universally, and in particular, it exists for every observer, independently of whether the observer makes the measurement or knows the result. In this paper, we will argue that, based on an analysis of protective measurements, this assumption is rejected by the many-worlds interpretation of quantum mechanics, and worlds, if they indeed exist according to the interpretation, can only exist relative to systems which are decoherent with respect to (...) the measurement result. (shrink)

It is argued that the components of the superposed wave function of a measuring device, each of which represents a definite measurement result, do not correspond to many worlds, one of which is our world, because all components of the wave function can be measured in our world by a serious of protective measurements, and they all exist in this world.

Protective measurement is a new measuring method introduced by Aharonov, Anandan and Vaidman. By a protective measurement, one can measure the expectation value of an observable on a single quantum system, even if the system is initially not in an eigenstate of the measured observable. This remarkable feature of protective measurements was challenged by Uffink. He argued that only observables that commute with the system's Hamiltonian can be protectively measured, and a protective measurement of an observable that does not commute (...) with the system's Hamiltonian does not actually measure the observable, but measure another related observable that commutes with the system's Hamiltonian. In this paper, we show that there are several errors in Uffink's arguments, and his alternative interpretation of protective measurements is untenable. (shrink)

Recently Lewis et al. [Phys. Rev. Lett. 109, 150404 ] demonstrated that additional assumptions such as preparation independence are always necessary to rule out a psi-epistemic model, in which the quantum state is not uniquely determined by the underlying physical state. Their conclusion is based on an analysis of conventional projective measurements. Here we demonstrate that protective measurements, which are distinct from projective measurements, already shows that distinct quantum states cannot be compatible with a single state of reality. This improves (...) the interesting result obtained by Pusey, Barrett and Rudolph [Nature Phys. 8, 475 ]. (shrink)

Based on an analysis of protective measurements, we show that the quantum state represents the physical state of a single quantum system. This result is more definite than the PBR theorem [Pusey, Barrett, and Rudolph, Nature Phys. 8, 475 (2012)].

It is shown that the de Broglie-Bohm theory has a potential problem concerning the charge distribution of a quantum system such as an electron. According to the guidance equation of the theory, the electron's charge is localized in a position where its Bohmian particle is. But according to the Schrödinger equation of the theory, the electron's charge is not localized in one position but distributed throughout space, and the charge density in each position is proportional to the modulus square of (...) the wave function of the electron there. Although this tension may be resolved by assuming that the electron's charge is not e but 2e, one for its Bohmian particle and the other for its wave function, the resolution will introduce more serious problems. (shrink)

We show that the de Broglie-Bohm theory is inconsistent with the established parts of quantum mechanics concerning its physical content. According to the de Broglie-Bohm theory, the mass and charge of an electron are localized in a position where its Bohmian particle is. However, protective measurement implies that they are not localized in one position but distributed throughout space, and the mass and charge density of the electron in each position is proportional to the modulus square of its wave function (...) there. (shrink)

It is shown that the de Broglie-Bohm theory has a potential problem concerning the mass and charge distributions of a quantum system such as an electron. According to the de Broglie-Bohm theory, the mass and charge of an electron are localized in a position where its Bohmian particle is. However, protective measurement indicates that they are not localized in one position but distributed throughout space, and the mass and charge density of the electron in each position is proportional to the (...) modulus square of its wave function there. (shrink)

It is shown that Uffink's attempt to protect the interpretation of the wave function against protective measurements fails due to several errors in his arguments.

It is shown that the superposed wave function of a measuring device, in each branch of which there is a definite measurement result, does not correspond to many mutually unobservable but equally real worlds, as the superposed wave function can be observed in our world by protective measurement.