## Physics Beyond the Limits of Uncertainty Relations## by Micho Durdevich
Introduction
## 1. IntroductionQuantum mechanics is a physics ofmicroworld. Its principal aim is to provide a
mathematically coherent picture of physical reality at the deepest possible
experimentally accessible level--the quantum level. This means understanding
phenomenas involving elementary particles and quantas of interactions, and the study of
the internal structure of matter and fields.
Quantum world is very different from the picture given by One of the principal purely quantum phenomenas is
This is All the properties of a classical system form a Boolean algebra. All possible attributes of a quantum system form an essentially different structure---a non-distributive lattice. We can also say that quantum systems are never completely understandable with the help of one single system of classical-type attributes. On the other hand, in every concrete experimental context, the subset consisting precisely of the system attributes actualized in this context necessarily forms a classical Boolean algebra. The situation is somehow similar to the relation between Euclidean geometry--where the space is covered by a single coordinate system, and general Riemannian geometry--where it is only possible to cover the whole space by the atlas of local coordinate systems, each describing a portion of the space. Another fundamental difference between classical and
quantum mechanics is that quantum mechanics is an Accordingly, physical quantities (observables) do not possess definitive values
in quantum states. More precisely,
if a quantum system is described by a Hilbert space This situation is in a sharp contrast with classical mechanics, which is a completely causal theory. The states of a system are in one-one correspondence with points of the phase space
and physical observables are interpreted as the appropriate functions defined
on this space. The values of observables
in the states
are simply the corresponding values
of functions in points.
In classical mechanics, the probabilities appear as something secondary,
whenever we do not know exactly the state of the system. A standard
example is given by classical statistical mechanics, which studies very
complicated physical systems and so it is practically impossible to
determine the state of the system. Accordingly in classical statistical
mechanics the system is
effectively described by a probability distribution over the phase space
(for example--the canonical ensemble distribution).
It is natural to ask the following question: is it possible to explain the stochasticity of quantum mechanics as a simple consequence of an incompleteness of quantum theory. In other words, as a simple consequence of the fact that quantum theory does not include certain deeper parameters (=hidden variables), which if included in the game would re-establish causality as in the classical physics. In such a way we arive to the idea of subquantum mechanics. [Next Segment]: Subquantum Mechanics--Basic Ideas |