Determinism, Ignorance, and Quantum Mechanics

Peter Mittelstaedt

Juan Pablo Paz

Albert Einstein made fundamental contributions to the development of quantum mechanics. However, he was never satisfied with the quantum worldview. In fact, during most of his life he attempted to find inconsistencies and paradoxes within quantum mechanics. His famous quote "God does not play dice" shows how disturbing was to Einstein one of the most important aspects of quantum mechanics: non-determinism. In this paper we will present the basic concepts of quantum mechanics, we will describe Einstein's attempts to destroy it and we will discuss why we can nowadays state that, in this regard, Albert Einstein was not right.

Grete Hermann

Mosh� Flato

Asim Gangopadhyaya, Constantin Rasinariu

This chapter is a refresher on the fundamental concepts of quantum mechanics. One essential difference between classical and quantum mechanics is that in classical mechanics, we are used to deterministic and precise laws stemming from the fact that the act of measurement can be ignored. Indeed, for all practical purposes, the interaction with the macroscopic system to be measured can be rendered negligibly small. However, at very small scales, the situation changes radically. The assumption that the measurement is ignorable is not true for micro-objects. In order to perform a measurement, we must interact with the system we are measuring. We discovered experimentally that nature has an objective scale, encoded by Planck's constant, that limits our ability to perform perturbation-free measurements. All we can do is perform many measurements on identically prepared systems, which would allow us to determine the probability of a given outcome. Micro-objects behave non-intuitively, described by new laws, those of quantum mechanics. In this chapter, we will briefly cover the postulates of quantum mechanics and introduce the Schrodinger and Heisenberg pictures of quantum mechanics.

Niall Shanks