the search for the fundamental unifying theory of quantum gravity
one of the key question is
how should space time we describe a very small scale as small as the planks
can tend to the my study five made
space time be described as a continuous manifold
as general relativity with to do this
for space time be described as a discrete structure
as may be something we would indicate
i mean quantum gravity cog editing their entrenched caps on both sides of the scratch
and both of could argue
now the message in this paper
is that both maybe right
space time could be simultaneously continuous and discrete
in mathematical the exactly the same way to information
can be simultaneously continuous and discrete
the fact that information can be simultaneously continuous and discrete
the top of information
and the corresponding mathematics
is in use every modern signal processing and communication engineer
for example
a continuous signal such as music signal
might be completely two
by attitudes
at discrete points continuous information of course has to process some special property
if it is to be equivalent to the screen
and that special property
is band limitation
in this case here
it means that the music signal
cannot have anyway things smaller than some fine minimal
in this case the contains signal
is then completely determined everywhere
from a set of attitudes samples
which have been taken at an average i think that is at most
half of my
thanks for the
it has been shown in previous work
that was a coffee as well
back then attention
mainly in the fall of natural kind of attacks k
here you paper
it is explicitly show that not only
e
well with space time can be compared to the limited but also speech timing so
could be confirmed that number and therefore
simultaneously in continuous and discrete
this provides
instead of two methods of mathematical tools that could be of interest
twenty one working frequency work
for example
discrete series of gravity could be given continuous representation for example to study the number
of how continuously for the right
but also continuous series of random variable discrete representations for example for the purpose of
america
apart from new mathematical tools from new technical tools is there any new is the
coding gain
well it turns out
that's
in this new framework
"'cause" which requires additional interpretation
could be sure
can also be viewed
as being a local modulation of the density of degrees of freedom in space-time
this means that
the interaction
being the integral over the reach a scalar
is actually hardly the integral intensity of degrees of freedom and therefore in a finite
volume
it is just the overall
number of decrease
the fact that the added an action can actually be reformulated information theoretic terms in
this way
i think is yet another indication that perhaps or the laws of nature can be
reformulated information thirty to
and maybe they should all be formulated in information theoretic terms signal to make probably
after their extreme circumstances for example in classical physics
where
the traditional notions
such as the distance for a time interval around that lose operational maybe
in all circumstances we don't even know how we could measure them
in principle
and yet
even in this extreme conditions
it is always possible to quantify how much information goes into process and how much
information comes not
therefore
and then
it would appear that the
motion of vq
is more robust and therefore have more fundamental
then the traditional notions such that links for a mass
or time
maybe due unit of it is more fundamental than the geneva meet the unigram or
something
well i open questions that
so far this work has been done only for scalar filters on space time is
that have you can see
the study of the original signature space time and interacting series was five is really
on the very beginning
this means that there is this one interesting work to be done