Speaker
Prof.
Sjinji Mukohyama
(Yukawa Institute for Theoretical Physics, Kyoto University)
Description
The Lorentzian metric structure used in any field theory
allows one to
implement the relativistic notion of causality and to define
a notion
of time dimension. In this talk we investigate the
possibility that at
the microscopic level the metric is Riemannian, i.e., locally
Euclidean, and that the Lorentzian structure, that we
usually consider
as fundamental, is in fact an effective property that
emerges in some
regions of a four-dimensional space with a positive definite
metric.
In such a model, there is no dynamics nor signature flip
across some
hypersurface; instead, all the fields develop a Lorentzian
dynamics in
these regions because they propagate in an effective metric.
It is
shown that one can construct a decent classical field theory for
scalars, vectors, and spinors in flat spacetime. It is then
shown that
gravity can be included but that the theory for the effective
Lorentzian metric is not general relativity but of the covariant
Galileon type. The constraints arising from stability, the
equivalence
principle, and the constancy of fundamental constants are
detailed and
a phenomenological picture of the emergence of the
Lorentzian metric
is also given. The construction, while restricted to
classical fields
in this article, offers a new view on the notion of time.
