본문을 보고 물음에 답하시오. Quantum mechanics, according to its Schr¨odinger picture, is a non-relativistic theory about the wave function and its evolution. There are two main problems in the conceptual foundations of quantum mechanics. The first one concerns the physical meaning of the wave function in the theory. It has been widely argued that the probability interpretation is not wholly satisfactory because of resorting to the vague concept of measurement - though it is still the standard interpretation in textbooks nowadays. On the other hand, the meaning of the wave function is also in dispute in the alternatives to quantum mechanics such as the de Broglie-Bohm theory and the many-worlds interpretation (de Broglie 1928; Bohm 1952; Everett 1957; De Witt and Graham 1973). Exactly what does the wave function describe then? The second problem concerns the evolution of the wave function. It includes two parts. One part concerns the linear Schr¨odinger evolution. Why does the linear non-relativistic evolution of the wave function satisfy the Schr¨odinger equation? It seems that a satisfactory derivation of the equation is still missing (cf. Nelson 1966). The other part concerns the collapse of the wave function during a measurement, which is usually called the measurement problem. The collapse postulate in quantum mechanics is ad hoc, and the theory does not tell us how a definite measurement result emerges (Bell 1990). Although the alternatives to quantum mechanics already give their respective solutions to this problem, it has been a hot topic of debate which solution is right or in the right direction. In the final analysis, it is still unknown whether the wavefunction collapse is real or not. Even if the wave function does collapse under some circumstances, it remains unclear exactly why and how the wave function collapses. The measurement problem has been widely acknowledged as one of the hardest and most important problems in the foundations of quantum mechanics (see, e.g. Wheeler and Zurek 1983). In this thesis, we will try to solve these problems from a new angle. The key is to realize that the problem of interpreting the wave function may be solved independent of how to solve the measurement problem, and the solution to the first problem can then have important implications for the solution to the second one. Although the meaning of the wave function should be ranked as the first interpretative problem of quantum mechanics, it has been treated as a marginal problem, especially compared with the measurement problem. As noted above, there are already several alternatives to quantum mechanics which give respective solutions to the measurement problem. However, these theories at their present stages are unsatisfactory at least in one aspect; they have not succeeded in making sense of the wave function. Different from them, our strategy is to first find what physical state the wave function describes and then investigate the implications of the answer for the solutions to other fundamental problems of quantum mechanics. It seems quite reasonable that we had better know what the wave function is before we want to figure out how it evolves, e.g. whether it collapses or not during a measurement. However, these problems are generally connected to each other. In particular, in order to 10 know what physical state the wave function of a quantum system describes, we need to measure the system in the first place, while the measuring process and the measurement result are necessarily determined by the evolution law for the wave function. Fortunately, it has been realized that the conventional measurement that leads to the apparent collapse of the wave function is only one kind of quantum measurement, and there also exists another kind of measurement that avoids the collapse of the wave function, namely the protective measurement (Aharonov and Vaidman 1993; Aharonov, Anandan and Vaidman 1993; Aharonov, Anandan and Vaidman 1996). Protective measurement is a method to measure the expectation values of observables on a single quantum system without disturbing its state appreciably, and its mechanism is independent of the controversial process of wavefunction collapse and only depends on the linear Schr¨odinger evolution and the Born rule, which are two established parts of quantum mechanics. As a result, protective measurement can not only measure the physical state of a quantum system and help to unveil the meaning of the wave function, but also be used to examine the solutions to the measurement problem before experiments give the last verdict. A full exposition of these ideas will be given in the subsequent chapters. The plan of this thesis is as follows. In Chapter 2, we first investigate the physical meaning of the wave function. According to protective measurement, the mass and charge distributions of a quantum system as one part of its physical state can be measured as expectation values of certain observables. It turns out that the mass and charge of a quantum system are distributed throughout space, and the mass and charge density in each position is proportional to the modulus square of the wave function of the system there. The key to unveil the meaning of the wave function is to find the origin of the mass and charge distributions. It is shown that the density is not real but effective; it is formed by the time average of 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. Based on this result, we suggest that the wave function represents the state of random discontinuous motion of particles, and in particular, the modulus square of the wave function (in position space) gives the probability density of the particles appearing in certain positions in space. [Shan Gao, Dr. Dean Rickles, Prof. Huw Price, "Interporeting Quantum Mechanics in Terms of Random Discontinuious Motion of Particles", March 2012, Thesis submitted for the degree of Doctor of Philosophy, The university of SYDNEY] 1. 위 본문은 한 양자역학에 관한 논문의 일부이다. 이를 보고 느낀 감상과 함깨 양자역학이 무엇인지 정리하시오.