Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Entanglement of quantum clocks through gravity   In general relativity, the picture of spacetime assigns an ideal clock to
each worldline. Being ideal, gravitational effects due to these clocks are
ignored and the flow of time according to one clock is not affected by the
presence of clocks along nearby worldlines. However, if time is defined
operationally, as a pointer position of a physical clock that obeys the
principles of general relativity and quantum mechanics, such a picture is at
most a convenient fiction. Specifically, we show that the general relativistic
mass-energy equivalence implies gravitational interaction between the clocks,
while the quantum mechanical superposition of energy eigenstates leads to a
non-fixed metric background. Based only on the assumption that both principles
hold in this situation, we show that the clocks necessarily get entangled
through time dilation effect, which eventually leads to a loss of coherence of
a single clock. Hence, the time as measured by a single clock is not
well-defined. However, the general relativistic notion of time is recovered in
the classical limit of clocks.

33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
19
The categories of this paper are: eess