1,182 research outputs found
On a Time Symmetric Formulation of Quantum Mechanics
We explore further the suggestion to describe a pre- and post-selected system
by a two-state, which is determined by two conditions. Starting with a formal
definition of a two-state Hilbert space and basic operations, we systematically
recast the basics of quantum mechanics - dynamics, observables, and measurement
theory - in terms of two-states as the elementary quantities. We find a simple
and suggestive formulation, that ``unifies'' two complementary observables:
probabilistic observables and non-probabilistic `weak' observables.
Probabilities are relevant for measurements in the `strong coupling regime'.
They are given by the absolute square of a two-amplitude (a projection of a
two-state). Non-probabilistic observables are observed in sufficiently `weak'
measurements, and are given by linear combinations of the two-amplitude. As a
sub-class they include the `weak values' of hermitian operators. We show that
in the intermediate regime, one may observe a mixing of probabilities and weak
values. A consequence of the suggested formalism and measurement theory, is
that the problem of non-locality and Lorentz non-covariance, of the usual
prescription with a `reduction', may be eliminated. We exemplify this point for
the EPR experiment and for a system under successive observations.Comment: LaTex, 44 pages, 4 figures included. Figure captions and related text
in sections 3.1, 4.2 are revised. A paragraph in pages 9-10 about non-generic
two-states is clarified. Footnotes adde
Comment on ``Protective measurements of the wave function of a single squeezed harmonic-oscillator state''
Alter and Yamamoto [Phys. Rev. A 53, R2911 (1996)] claimed to consider
``protective measurements'' [Phys. Lett. A 178, 38 (1993)] which we have
recently introduced. We show that the measurements discussed by Alter and
Yamamoto ``are not'' the protective measurements we proposed. Therefore, their
results are irrelevant to the nature of protective measurements.Comment: 2 pages LaTe
Superoscillations and tunneling times
It is proposed that superoscillations play an important role in the
interferences which give rise to superluminal effects. To exemplify that, we
consider a toy model which allows for a wave packet to travel, in zero time and
negligible distortion a distance arbitrarily larger than the width of the wave
packet. The peak is shown to result from a superoscillatory superposition at
the tail. Similar reasoning applies to the dwell time.Comment: 12 page
Sequential weak measurement
The notion of weak measurement provides a formalism for extracting
information from a quantum system in the limit of vanishing disturbance to its
state. Here we extend this formalism to the measurement of sequences of
observables. When these observables do not commute, we may obtain information
about joint properties of a quantum system that would be forbidden in the usual
strong measurement scenario. As an application, we provide a physically
compelling characterisation of the notion of counterfactual quantum
computation
``Weighing'' a closed system and the time-energy uncertainty principle
A gedanken-experiment is proposed for `weighing'' the total mass of a closed
system from within the system. We prove that for an internal observer the time
, required to measure the total energy with accuracy , is
bounded according to . This time-energy uncertainty
principle for a closed system follows from the measurement back-reaction on the
system. We generally examine what other conserved observables are in principle
measurable within a closed system and what are the corresponding uncertainty
relations.Comment: 8 page
Weak measurement takes a simple form for cumulants
A weak measurement on a system is made by coupling a pointer weakly to the
system and then measuring the position of the pointer. If the initial
wavefunction for the pointer is real, the mean displacement of the pointer is
proportional to the so-called weak value of the observable being measured. This
gives an intuitively direct way of understanding weak measurement. However, if
the initial pointer wavefunction takes complex values, the relationship between
pointer displacement and weak value is not quite so simple, as pointed out
recently by R. Jozsa. This is even more striking in the case of sequential weak
measurements. These are carried out by coupling several pointers at different
stages of evolution of the system, and the relationship between the products of
the measured pointer positions and the sequential weak values can become
extremely complicated for an arbitrary initial pointer wavefunction.
Surprisingly, all this complication vanishes when one calculates the cumulants
of pointer positions. These are directly proportional to the cumulants of
sequential weak values. This suggests that cumulants have a fundamental
physical significance for weak measurement
Aharonov-Bohm Type Forces Between Magnetic Fluxons
Forces related to A-B phases between fluxons with
are discussed. We find a type interaction
screened on a scale . The forces exist only when the fluxons are
actually immersed in the region with non vanishing charge density and are
periodic in . We briefly comment on the problem of observing such
forces.Comment: 10 pages, latex, no fi
Trans-Planckian Tail in a Theory with a Cutoff
Trans-planckian frequencies can be mimicked outside a black-hole horizon as a
tail of an exponentially large amplitude wave that is mostly hidden behind the
horizon. The present proposal requires implementing a final state condition.
This condition involves only frequencies below the cutoff scale. It may be
interpreted as a condition on the singularity. Despite the introduction of the
cutoff, the Hawking radiation is restored for static observers. Freely falling
observers see empty space outside the horizon, but are "heated" as they cross
the horizon.Comment: 17 pages, RevTe
Noncommutative quantum mechanics and the Aharonov-Casher effect
In this work a new method is developed to investigate the Aharonov-Casher
effect in a noncommutative space. It is shown that the holonomy receives
non-trivial kinematical corrections.Comment: 8 pages, Plain Tex, to appear in Eur. Phys. J.
Quantum limitations on superluminal propagation
Unstable systems such as media with inverted atomic population have been
shown to allow the propagation of analytic wavepackets with group velocity
faster than that of light, without violating causality. We illuminate the
important role played by unstable modes in this propagation, and show that the
quantum fluctuations of these modes, and their unitary time evolution, impose
severe restrictions on the observation of superluminal phenomena.Comment: RevTeX 4 page
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