Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Probing Mach's principle   The principle of least action in its original form \'a la Maupertuis is used
to explain geodetic and frame-dragging precessions which are customarily
accounted for a curved spacetime by general relativity. The obtained least-time
equations of motion agree with observations and are also in concert with
general relativity. Yet according to the least-time principle, gravitation does
not relate to the mathematical metric of spacetime, but to a tangible energy
density embodied by photons. The density of free space is in balance with the
total mass of the Universe in accord with Planck's law. Likewise, a local
photon density and its phase distribution are in balance with mass and charge
distribution of a local body. Here gravitational force is understood as an
energy density difference that will diminish when the oppositely polarized
pairs of photons co-propagate from the energy-dense system of bodies to the
energy-sparse system of the surrounding free space. Thus when the body changes
its state of motion, the surrounding energy density must accommodate the
change. The concurrent resistance in restructuring of the surroundings,
ultimately involving the entire Universe, is known as inertia. The all-around
propagating energy density couples everything with everything else in accord
with Mach's principle.

24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
1
The categories of this paper are: cs