In 1930. D.Ivanenko and
V.Ambarzumian put forward the idea of discreteness of space-time inside an
atomic nuclear that, by means of introducing the fundamental length, to solve
some of the problems encountered at that time in nuclear physics.
The idea of discreteness then
was not constructively developed, but many scientists from time to time turned
to this concept from general considerations, but restricted themselves, as a
rule, to examination of lattices. A kind of its embodiment is theory of gauge
fields on a lattice, which enabled one to do some incentive calculations. In
1965, the historically-review book "Discrete space-time" (M.,
Science) by A.Vialtcev came out. D.Ivanenko himself repeatedly returned to this
idea. In the 1970s, his Ph.D. student G.Gorelik was engaged in this subject,
but nothing new has happened. Of course, all of this was discussed at the
seminars of Ivanenko, and these discussions have led me to think about the
problem.
From the beginning, I refused
the discrete space-time as a discrete topological space (which lattices belong
to). Then what? I suggested totally disconnected topological spaces that occur
in a number of theoretical models (such is, for example, the set of rational
numbers). D.Ivanenko again enjoyed it, and we published a few works.
Moreover, it was so well-defined mathematical model that my article "Discrete
space-time" was taken in very responsible "Mathematical
encyclopedia":
“One
conceivable hypothesis on the structure of space in the microcosmos, conceived
as a collection of disconnected elements in space (points) which cannot be
distinguished by observations. An acceptable formalization of discrete
space-time can be given in terms of topological spaces Y in which the connected component of its point y is its closure, and, in a Hausdorff
space Y, is this point itself
(totally disconnected spaces). Examples of Y
include a discrete topological space, a rational straight line, analytic
manifolds, and Lie groups over fields with ultra-metric absolute values.
The discrete
space-time hypothesis was originally developed as a variation of a finite
totally-disconnected space, in models of finite geometries on Galois fields
V.A. Ambartsumyan and D.D. Ivanenko (1930) were the first to treat it in the
framework of field theory (as a cubic lattice in space). In quantum theory the
hypothesis of discrete space-time appeared in models in which the coordinate
(momentum, etc.) space, like the spectrum of the C*-algebra of corresponding operators, is totally disconnected
(e.g. like the spectrum of the C*-algebra
of probability measures). It received a serious foundation in the concept of "fundamental
lengths" in non-linear generalizations of electrodynamics, mesondynamics
and Dirac's spinor theory, in which the constants of field action have the
dimension of length, and in quantum field theory, where it is necessary to
introduce all kinds of
"cut-off" factors.
These ideas, later in conjunction with non-local models, served as the base for
the formulation of the concept of minimal domains in space in which it appears
no longer possible to adopt the quantum-theoretical description of
micro-objects in terms of their interaction with a macro-instrument. As a
result, the space-time continuum is unacceptable for the parameterization of
spatial-evolutionary relations in these domains (e.g. the Hamilton
References:
G. Sardanashvily, Discrete space-time, Enciclopaedia of Mathematics (Springer)
D.Ivanenko, G.Sardanashvily, Towards a model of discrete space-time, Russ. Phys. J. 21(1978) 1508.
My Scientific Biography
My Scientific Biography
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