829 research outputs found
General Relativity from Causality
We study large families of theories of interacting spin 2 particles from the
point of view of causality. Although it is often stated that there is a unique
Lorentz invariant effective theory of massless spin 2, namely general
relativity, other theories that utilize higher derivative interactions do in
fact exist. These theories are distinct from general relativity, as they permit
any number of species of spin 2 particles, are described by a much larger set
of parameters, and are not constrained to satisfy the equivalence principle. We
consider the leading spin 2 couplings to scalars, fermions, and vectors, and
systematically study signal propagation in all these other families of
theories. We find that most interactions directly lead to superluminal
propagation of either a spin 2 particle or a matter particle, and interactions
that are subluminal generate other interactions that are superluminal. Hence,
such theories of interacting multiple spin 2 species have superluminality, and
by extension, acausality. This is radically different to the special case of
general relativity with a single species of minimally coupled spin 2, which
leads to subluminal propagation from sources satisfying the null energy
condition. This pathology persists even if the spin 2 field is massive. We
compare these findings to the analogous case of spin 1 theories, where higher
derivative interactions can be causal. This makes the spin 2 case very special,
and suggests that multiple species of spin 2 is forbidden, leading us to
general relativity as essentially the unique internally consistent effective
theory of spin 2.Comment: 31 pages, 4 figures, 1 table. V2: Some clarifications on EFT
breakdown and comparison to GR. Updated to resemble version published in JHE
Trapping and Cooling a mirror to its quantum mechanical ground state
We propose a technique aimed at cooling a harmonically oscillating mirror to
its quantum mechanical ground state starting from room temperature. Our method,
which involves the two-sided irradiation of the vibrating mirror inside an
optical cavity, combines several advantages over the two-mirror arrangements
being used currently. For comparable parameters the three-mirror configuration
provides a stiffer trap for the oscillating mirror. Furthermore it prevents
bistability from limiting the use of higher laser powers for mirror trapping,
and also partially does so for mirror cooling. Lastly, it improves the
isolation of the mirror from classical noise so that its dynamics are perturbed
mostly by the vacuum fluctuations of the optical fields. These improvements are
expected to bring the task of achieving ground state occupation for the mirror
closer to completion.Comment: 5 pages, 1 figur
Using a Laguerre-Gaussian beam to trap and cool the rotational motion of a mirror
We show theoretically that it is possible to trap and cool the rotational
motion of a macroscopic mirror made of a perfectly reflecting spiral phase
element using orbital angular momentum transfer from a Laguerre-Gaussian
optical field. This technique offers a promising route to the placement of the
rotor in its quantum mechanical ground state in the presence of thermal noise.
It also opens up the possibility of simultaneously cooling a vibrational mode
of the same mirror. Lastly, the proposed design may serve as a sensitive
torsional balance in the quantum regime.Comment: New cavity design, reworked title; to appear in Phys. Rev. Let
The Origin of Power-Law Emergent Scaling in Large Binary Networks
In this paper we study the macroscopic conduction properties of large but
finite binary networks with conducting bonds. By taking a combination of a
spectral and an averaging based approach we derive asymptotic formulae for the
conduction in terms of the component proportions p and the total number of
components N. These formulae correctly identify both the percolation limits and
also the emergent power law behaviour between the percolation limits and show
the interplay between the size of the network and the deviation of the
proportion from the critical value of p = 1/2. The results compare excellently
with a large number of numerical simulations
Degeneracies when T=0 Two Body Matrix Elements are Set Equal to Zero and Regge's 6j Symmetry Relations
The effects of setting all T=0 two body interaction matrix elements equal to
a constant (or zero) in shell model calculations (designated as ) are
investigated. Despite the apparent severity of such a procedure, one gets
fairly reasonable spectra. We find that using in single j shell
calculations degeneracies appear e.g. the and
states in Sc are at the same excitation energies; likewise the
I=,,9 and 10 states in Ti. The
above degeneracies involve the vanishing of certain 6j and 9j symbols. The
symmetry relations of Regge are used to explain why these vanishings are not
accidental. Thus for these states the actual deviation from degeneracy are good
indicators of the effects of the T=0 matrix elements. A further indicator of
the effects of the T=0 interaction in an even - even nucleus is to compare the
energies of states with odd angular momentum with those that are even
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