28 research outputs found
Switching quantum reference frames in the N-body problem and the absence of global relational perspectives
Given the importance of quantum reference systems to both quantum and
gravitational physics, it is pertinent to develop a systematic method for
switching between the descriptions of physics relative to different choices of
quantum reference systems, which is valid in both fields. Here, we continue
with such a unifying approach, begun in arxiv:1809.00556, whose key ingredients
is a gravity-inspired symmetry principle, which enforces physics to be
relational and leads, thanks to gauge related redundancies, to a
perspective-neutral structure which contains all frame choices at once and via
which frame perspectives can be consistently switched. Formulated in the
language of constrained systems, the perspective-neutral structure turns out to
be the constraint surface classically and the gauge invariant Hilbert space in
the Dirac quantized theory. By contrast, a perspective relative to a specific
frame corresponds to a gauge choice and the associated reduced phase and
Hilbert space. Quantum reference frame switches thereby amount to a symmetry
transformation. In the quantum theory, they require a transformation that takes
one from the Dirac to a reduced quantum theory and we show that it amounts to a
trivialization of the constraints and a subsequent projection onto the
classical gauge fixing conditions. We illustrate this method in the relational
-body problem with rotational and translational symmetry. This model is
particularly interesting because it features the Gribov problem so that
globally valid gauge fixing conditions are impossible which, in turn, implies
also that globally valid relational frame perspectives are absent in both the
classical and quantum theory. These challenges notwithstanding, we exhibit how
one can systematically construct the quantum reference frame transformations
for the three-body problem.Comment: 22 pages, plus appendice
Dynamics of quantum causal structures
It was recently suggested that causal structures are both dynamical, because
of general relativity, and indefinite, due to quantum theory. The process
matrix formalism furnishes a framework for quantum mechanics on indefinite
causal structures, where the order between operations of local laboratories is
not definite (e.g. one cannot say whether operation in laboratory A occurs
before or after operation in laboratory B). Here we develop a framework for
"dynamics of causal structures", i.e. for transformations of process matrices
into process matrices. We show that, under continuous and reversible
transformations, the causal order between operations is always preserved.
However, the causal order between a subset of operations can be changed under
continuous yet nonreversible transformations. An explicit example is that of
the quantum switch, where a party in the past affects the causal order of
operations of future parties, leading to a transition from a channel from A to
B, via superposition of causal orders, to a channel from B to A. We generalise
our framework to construct a hierarchy of quantum maps based on transformations
of process matrices and transformations thereof.Comment: 13+5 pages, 4 figures. Two appendices added. Published versio
Einstein's Equivalence principle for superpositions of gravitational fields
The Principle of Equivalence, stating that all laws of physics take their
special-relativistic form in any local inertial frame, lies at the core of
General Relativity. Because of its fundamental status, this principle could be
a very powerful guide in formulating physical laws at regimes where both
gravitational and quantum effects are relevant. However, its formulation
implicitly presupposes that reference frames are abstracted from classical
systems (rods and clocks) and that the spacetime background is well defined. It
is unclear if it continues to hold when quantum systems, which can be in a
quantum relationship with other physical systems, are taken as reference
frames, and in a superposition of classical spacetime structures. Here, we
tackle both questions by introducing a relational formalism to describe quantum
systems in a superposition of curved spacetimes. We build a unitary
transformation to the quantum reference frame (QRF) of a quantum system in
curved spacetime, and in a superposition thereof. In both cases, a QRF can be
found such that the metric looks locally minkowskian. Hence, one cannot
distinguish, with a local measurement, if the spacetime is flat or curved, or
in a superposition of such spacetimes. This transformation identifies a Quantum
Local Inertial Frame. We also find a spacetime path-integral encoding the
dynamics of a quantum particle in spacetime and show that the state of a freely
falling particle can be expressed as an infinite sum of all possible classical
geodesics. We then build the QRF transformation to the Fermi normal coordinates
of such freely falling quantum particle and show that the metric is locally
minkowskian. These results extend the Principle of Equivalence to QRFs in a
superposition of gravitational fields. Verifying this principle may pave a
fruitful path to establishing solid conceptual grounds for a future theory of
quantum gravity.Comment: 18 pages main text, 10 pages Appendices, 3 figures. Improved Appendix
G, minor edits throughout the tex