Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Curving Space, Effective Gravity and Simultaneous Measurements   We present a way of understanding the curvature of space-time, the basic
philosophy being that the (linear) geometry of any space is determined by the
(linear) functionals on the algebra(s) of any fields defined on the space. It
is known that quantum states or hypothetical measurements on a quantum system
may be regarded as unit or normalized positive (or non-degenerate to be more
generic) linear functionals on a $C^\ast$-algebra which contains the variable
events (or variables to be brief) that describe the dynamics of the quantum
system. We consider linear projection geometry and differential calculus on a
$C^\ast$-algebra $\mathcal{A}$ by means of the positive linear functionals
$\mathcal{A}^\ast$ on $\mathcal{A}$. The analysis is done with the help of
linear projections based on a version of the Cauchy-Schwarz inequality. We
mention the relation between uncertainties or errors involved in the
simultaneous measurement of more than one statistical or quantum variable. We
also attempt to obtain Einstein's theory of the gravitational field by analytic
continuation.

29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys