Shan Gao

It is widely accepted that continuity is the most essential characteristic of motion; the motion of macroscopic objects is apparently continuous, and classical mechanics, which describes such motion, is also based on the assumption of continuous motion. But is motion really continuous in reality? In this paper, I will try to answer this question through a new analysis of the cause of motion. It has been argued that the standard velocity in classical mechanics cannot fulfill the causal role required for explaining continuous motion in a deterministic way. However, there is a hot debate over the solution to this causal explanation problem. The existing solutions, i.e. the "at-at" theory, the impetus view and the "no instants" view, have serious drawbacks. After reviewing their drawbacks and presenting my own objections, I propose a new solution to this causal explanation problem. It is argued that the relativity of motion or the equivalence between motion and rest demands that motion has no deterministic cause, and thus no causal explanation is needed for motion. Based on this result, I further argue that the uncaused motion is not deterministic and continuous but essentially random and discontinuous. Moreover, objects have a potential that determines the probabilities of their future positions. This suggests a possible connection with quantum mechanics. Lastly, I give a brief explanation for the apparent inconsistency between the suggested potential theory of motion and the appearance of continuous motion in the macroscopic world.

The remarkable connections between gravity and thermodynamics seem to imply that gravity is not fundamental but emergent, and in particular, as Verlinde suggested, gravity is probably an entropic force. In this paper, we will argue that the idea of gravity as an entropic force is debatable. It is shown that there is no convincing analogy between gravity and entropic force in Verlinde’s example. Neither holographic screen nor test particle satisfies all requirements for the existence of entropic force in a thermodynamics system. As a result, there is no entropic force in the gravity system. Furthermore, we show that the entropy increase of the screen is not caused by its statistical tendency to increase entropy as required by the existence of entropic force, but in fact caused by gravity. Therefore, Verlinde’s argument for the entropic origin of gravity is problematic. In addition, we argue that the existence of a minimum size of spacetime, together with the Heisenberg uncertainty principle in quantum theory, may imply the fundamental existence of gravity as a geometric property of spacetime. This provides a further support for the conclusion that gravity is not an entropic force.

The ontological model framework provides a rigorous approach to address the question of whether the quantum state is ontic or epistemic. When considering only conventional projective measurements, auxiliary assumptions are always needed to prove the reality of the quantum state in the framework. For example, the Pusey-Barrett-Rudolph theorem is based on an additional preparation independence assumption. In this paper, we give a new proof of psi-ontology in terms of protective measurements in the ontological model framework. It is argued that the proof needs not rely on auxiliary assumptions, and also applies to deterministic theories such as the de Broglie-Bohm theory. In addition, we give a simpler argument for psi-ontology beyond the framework, which is only based on protective measurements and a weaker criterion of reality. The argument may be also appealing for those people who favor an anti-realist view of quantum mechanics.

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.

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.

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.

The ontological status of the wave function in quantum mechanics has been analyzed in the context of conventional projective measurements. These analyses are usually based on some nontrivial assumptions, e.g. a preparation independence assumption is needed to prove the PBR theorem. In this paper, we give a PBR-like argument for psi-ontology in terms of protective measurements, by which one can directly measure the expectation values of observables on a single quantum system. The proof does not resort to nontrivial assumptions such as preparation independence assumption.

It has been realized that in order to solve the measurement problem, the physical state representing the measurement result is required to be also the physical state on which the mental state of an observer supervenes. This introduces an additional restriction on the solutions to the measurement problem. In this paper, I give a new formulation of the measurement problem which lays more stress on psychophysical connection, and analyze whether Everett's theory, Bohm's theory and dynamical collapse theories can satisfy the restriction of psychophysical supervenience and thus can indeed solve the measurement problem. My analysis of the potential problems of the forms of psychophysical supervenience required by Everett's and Bohm's theories suggests that dynamical collapse theories might provide a promising solution to the measurement problem. Finally, by further analyzing how the mental state of an observer supervenes on her wave function, I also propose a possible solution to the structured tails problem of dynamical collapse theories.

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.