What did Heisenberg know?

CONSTANCE A. WARNER

Zhaozhong Cao

The two most important areas in modern physics are quantum mechanics and the theory of relativity. Unlike classical physics, where Newton's mechanics dominates, these two areas change human beings' fundamental view of the universe. One of the theories that build up the base of quantum mechanics is Heisenberg's Uncertainty Principle. Starting from a thought experiment, Heisenberg's microscope in the setting of classical physics, Werner Heisenberg built a bridge between classical and quantum physics by presenting a counterintuitive outcome in the thought experiment. Since then, the observer of a physics phenomenon is no longer a bystander. The behavior of observation became a part of the physical experiment. To come up with a mathematical expression that can describe such a new discovery, Heisenberg came up with matrix mechanics and the concept of complementary variables. There is a trade-off between a pair of complementary variables. When one of them is measured precisely, meaning the information of that variable is known on a large scale, the other variable can not be measured precisely, meaning there is no way to know enough information about the other variable. The principle indicates a fundamental limit on what human beings can know about the unknown variables. The discoveries of other complementary variables help physicists know the new image of the physics world under new rules.

Robert Scott Root-Bernstein

M.J. Dance

Heisenberg's uncertainty relation means that one observer cannot know an exact position and velocity for another (finite mass) observer. By contrast, the Poincare transformation of classical special relativity assumes that one observer knows the other's position and velocity exactly. The present paper describes a simple-minded way to consider the issue using a semiclassical discussion of spacetime diagrams, and draws out some possible implications. Uncertainties arise in transformations. A consideration is raised regarding the use of light-cone coordinates.

Ramiro Délio Borges de Meneses

Heisenberg's uncertainty principle, which he announced in 1927, grow out of his attempts to explain some of the quantum mechanics peculiarities. This principle holds that it is impossible to determine simultaneously, with any certainty, the position, and the particle's momentum, the more accurately the investigator determines one, the less accurate by he can know the other, according to the metric expression: Δx·Δp x ≥ h. On this article I aim the philosophical certainty of Quantum Mechanics, because one effect of Heisenberg's research was to transform some physical laws into probability's statements.