85 research outputs found
Measurement of Time-of-Arrival in Quantum Mechanics
It is argued that the time-of-arrival cannot be precisely defined and
measured in quantum mechanics. By constructing explicit toy models of a
measurement, we show that for a free particle it cannot be measured more
accurately then , where is the initial kinetic
energy of the particle. With a better accuracy, particles reflect off the
measuring device, and the resulting probability distribution becomes distorted.
It is shown that a time-of-arrival operator cannot exist, and that approximate
time-of-arrival operators do not correspond to the measurements considered
here.Comment: References added. To appear in Phys. Rev.
The Hypothesis of Locality and its Limitations
The hypothesis of locality, its origin and consequences are discussed. This
supposition is necessary for establishing the local spacetime frame of
accelerated observers; in this connection, the measurement of length in a
rotating system is considered in detail. Various limitations of the hypothesis
of locality are examined.Comment: LaTeX file, no figures, 14 pages, to appear in: "Relativity in
Rotating Frames", edited by G. Rizzi and M.L. Ruggiero (Kluwer Academic
Publishers, Dordrecht, 2003
Optimal Quantum Clocks
A quantum clock must satisfy two basic constraints. The first is a bound on
the time resolution of the clock given by the difference between its maximum
and minimum energy eigenvalues. The second follows from Holevo's bound on how
much classical information can be encoded in a quantum system. We show that
asymptotically, as the dimension of the Hilbert space of the clock tends to
infinity, both constraints can be satisfied simultaneously. The experimental
realization of such an optimal quantum clock using trapped ions is discussed.Comment: 4 pages, revtex, 1 figure, revision contains some new result
Time-Frequency Transfer with Quantum Fields
Clock synchronisation relies on time-frequency transfer procedures which
involve quantum fields. We use the conformal symmetry of such fields to define
as quantum operators the time and frequency exchanged in transfer procedures
and to describe their transformation under transformations to inertial or
accelerated frames. We show that the classical laws of relativity are changed
when brought in the framework of quantum theory.Comment: 4 page
Measurement of the space-time interval between two events using the retarded and advanced times of each event with respect to a time-like world-line
Several recent studies have been devoted to investigating the limitations
that ordinary quantum mechanics and/or quantum gravity might impose on the
measurability of space-time observables. These analyses are often confined to
the simplified context of two-dimensional flat space-time and rely on a simple
procedure for the measurement of space-like distances based on the exchange of
light signals. We present a generalization of this measurement procedure
applicable to all three types of space-time intervals between two events in
space-times of any number of dimensions. We also present some preliminary
observations on an alternative measurement procedure that can be applied taking
into account the gravitational field of the measuring apparatus, and briefly
discuss quantum limitations of measurability in this context.Comment: 17 page
On the Precision of a Length Measurement
We show that quantum mechanics and general relativity imply the existence of
a minimal length. To be more precise, we show that no operational device
subject to quantum mechanics, general relativity and causality could exclude
the discreteness of spacetime on lengths shorter than the Planck length. We
then consider the fundamental limit coming from quantum mechanics, general
relativity and causality on the precision of the measurement of a length.Comment: 5 pages, to appear in the proceedings of the 2006 International
School of Subnuclear Physics in Erice and in ''Young Scientists'' online-only
supplement of the European Physical Journal C-Direct (Springer
On Di\'osi-Penrose criterion of gravity-induced quantum collapse
It is shown that the Di\'osi-Penrose criterion of gravity-induced quantum
collapse may be inconsistent with the discreteness of space-time, which is
generally considered as an indispensable element in a complete theory of
quantum gravity. Moreover, the analysis also suggests that the discreteness of
space-time may result in rapider collapse of the superposition of energy
eigenstates than required by the Di\'osi-Penrose criterion.Comment: 5 pages, no figure
From computation to black holes and space-time foam
We show that quantum mechanics and general relativity limit the speed
of a simple computer (such as a black hole) and its memory space
to \tilde{\nu}^2 I^{-1} \lsim t_P^{-2}, where is the Planck time.
We also show that the life-time of a simple clock and its precision are
similarly limited. These bounds and the holographic bound originate from the
same physics that governs the quantum fluctuations of space-time. We further
show that these physical bounds are realized for black holes, yielding the
correct Hawking black hole lifetime, and that space-time undergoes much larger
quantum fluctuations than conventional wisdom claims -- almost within range of
detection with modern gravitational-wave interferometers.Comment: A misidentification of computer speeds is corrected. Our results for
black hole computation now agree with those given by S. Lloyd. All other
conclusions remain unchange
Quantum evolution according to real clocks
We characterize good clocks, which are naturally subject to fluctuations, in
statistical terms. We also obtain the master equation that governs the
evolution of quantum systems according to these clocks and find its general
solution. This master equation is diffusive and produces loss of coherence.
Moreover, real clocks can be described in terms of effective interactions that
are nonlocal in time. Alternatively, they can be modeled by an effective
thermal bath coupled to the system.Comment: RevTeX 3.01, 6 page
Time Uncertainty in Quantum Gravitational Systems
It is generally argued that the combined effect of Heisenberg principle and
general relativity leads to a minimum time uncertainty. Most of the analyses
supporting this conclusion are based on a perturbative approach to
quantization. We consider a simple family of gravitational models, including
the Einstein-Rosen waves, in which the (non-linearized) inclusion of gravity
changes the normalization of time translations by a monotonic energy-dependent
factor. In these circumstances, it is shown that a maximum time resolution
emerges non-perturbatively only if the total energy is bounded. Perturbatively,
however, there always exists a minimum uncertainty in the physical time.Comment: (4 pages, no figures) Accepted for publication in Physical Review
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