4,253 research outputs found

### Large scale density perturbations from a uniform distribution by wave transport

It has long been known that a uniform distribution of matter cannot produce a
Poisson distribution of density fluctuations on very large scales $1/k > ct$ by
the motion of discrete particles over timescale $t$. The constraint is part of
what is sometimes referred to as the Zel'dovich bound. We investigate in this
paper the transport of energy by the propagation of waves emanating {\it
incoherently} from a regular and infinite lattice of oscillators, each having
the same finite amount of energy reserve initially. The model we employ does
not involve the expansion of the Universe -- the scales of interest are all
deeply sub-horizon -- but the size of regions over which perturbations are
evaluated far exceed $ct$, where $t$ is the time elapsed since the start of
emission (it is assumed that $t$ greatly exceeds the duration of emission). We
find that to lowest order, when only wave fields $\propto 1/r$ are included,
there is exact compensation between the energy loss of the oscillators and the
energy emitted into space, which means $P(0)=0$ for the power spectrum of
density fluctuations on the largest scales. This is consistent with the
Zel'dovich bound. To the next order when near fields $\propto r^{-2}$ are
included, however, $P(0)$ settles at late times to a positive value that
depends only on time, as $t^{-2}$ (the same applies to an energy non-conserving
term). Even though this effect looks like superluminal energy transport, there
is no violation of causality because the two-point function vanishes completely
for $r>t$ if the emission of each oscillator is truncated beyond some duration.
The result calls to question any need of enlisting cosmic inflation to seed
large scale density perturbations. When applied to fast radio bursts --
uniformly distributed transients (to lowest order) that repeat at other
locations -- the result supports Hoyle's hypothesis of constant energy
injection.Comment: 17 pages, 38 equations, 2 appendices, final edited proof version,
JCAP in pres

### A microscopic derivation of Special Relativity: simple harmonic oscillations of a moving space-time lattice

The starting point of the theory of Special Relativity$^1$ is the Lorentz
transformation, which in essence describes the lack of absolute measurements of
space and time. These effects came about when one applies the Second Relativity
Postulate to inertial observers. Here I demonstrate that there is a very
elegant way of explaining how exactly nature enforces Special Relativity, which
compels us to conclude that Einstein's great theory has already revealed
quantization of space and time. The model proposes that microscopically the
structure of space-time is analogous to a crystal which consists of lattice
points or `tickmarks' (for measurements) connected by identical `elastic
springs'. When at rest the `springs' are at their natural states. When set in
motion and used to measure objects at rest, however, the lattice effectively
vibrates in a manner described by Einstein's theory of the heat capacity of
solids, with consequent widening of the `tickmarks' because the
root-mean-square separation now increases. I associate a vibration temperature
$T$ with the speed of motion $v$ via the fundamental postulate of this theory,
viz. the relation $\frac{v^2}{c^2} = e^{-\frac{\epsilon}{kT}}$ where $\epsilon$
is a quantum of energy of the lattice harmonic oscillator. A moving observer
who measures distances with such a vibrating lattice obtains results which are
precisely those given by the Lorentz transformation. Apart from its obvious
beauty, this approach provides many new prospects in understanding space and
time. For example, a consequence of the model is that space-time, like mass,
can in principle be converted to energy.Comment: 7 pages, 1 figur

### Hubble redshift and the Heisenberg frequency uncertainty: on a coherence (or pulse) time signature in extragalactic light

In any Big Bang cosmology, the frequency $\omega$ of light detected from a
distant source is continuously and linearly changing (usually redshifting) with
elapsed observer's time $\delta t$, because of the expanding Universe. For
small $\delta t$, however, the resulting $\delta\omega$ shift lies beneath the
Heisenberg frequency uncertainty. And since there {\it is} a way of telling
whether such short term shifts really exist, if the answer is affirmative we
will have a means of monitoring radiation to an accuracy level that surpasses
fundamental limitations. More elaborately, had $\omega$ been `frozen' for a
minimum threshold interval before any redshift could take place, i.e. the light
propagated as a smooth but {\it periodic} sequence of wave packets or pulses,
and $\omega$ decreased only from one pulse to the next, one would then be
denied the above forbiddingly precise information about frequency behavior. Yet
because this threshold period is {\it observable}, being $\Delta t \approx
1/\sqrt{\omega_0 H_0} \sim$ 5 -- 15 minute for the cosmic microwave background
(CMB), we can indeed perform a check for consistency between the Hubble Law and
the Uncertainty Principle. If, as most would assume to be the case, the former
either takes effect without violating the latter or not take effect at all, the
presence of this characteristic time signature (periodicity) $\Delta t$ would
represent direct verification of the redshift phenomenon.Comment: 9 pages, 18 equations, 1 figure. Paper overhauled. A much simpler
interpretation of the CMB Fourier transform in terms of the Uncertainty
Principle is availabl

### Exclusion of standard $\hbar\omega$ gravitons by LIGO observation

Dyson (2013) argued that the extraordinarily large number of gravitons in a
gravitational wave makes them impossible to be resolved as individual
particles. While true, it is shown in this paper that a LIGO interferometric
detector also undergoes frequent and {\it discrete} quantum interactions with
an incident gravitational wave, in such a way as to allow the exchange of
energy and momentum between the wave and the detector. This opens the door to
another way of finding gravitons. The most basic form of an interaction is the
first order Fermi acceleration (deceleration) of a laser photon as it is
reflected by a test mass mirror oscillating in the gravitational wave,
resulting in a frequency blueshift (redshift) of the photon depending on
whether the mirror is advancing towards (receding from) the photon before the
reflection. If e.g. a blueshift occurred, wave energy is absorbed and the
oscillation will be damped. It is suggested that such energy exchanging
interactions are responsible for the observed radiation reaction noise of LIGO
(although the more common way of calculating the same amplitude for this noise
is based on momentum considerations). Most importantly, in each interaction the
detector absorbs or emits wave energy in amounts far smaller than the standard
graviton energy $\hbar\omega$ where $\omega$ is the angular frequency of the
gravitational wave. This sets a very tight upper limit on the quantization of
the wave energy, viz. it must be at least $\approx 10^{11}$ times below
$\hbar\omega$, independently of the value of $\omega$ itself.Comment: This final version was published on 17 August, 2018 by CQG as a
Letter to the Edito

### Topological phases in the non-Hermitian Su-Schrieffer-Heeger model

We address the conditions required for a $\mathbb{Z}$ topological
classification in the most general form of the non-Hermitian
Su-Schrieffer-Heeger (SSH) model. Any chirally-symmetric SSH model will possess
a "conjugated-pseudo-Hermiticity" which we show is responsible for a quantized
"complex" Berry phase. Consequently, we provide the first example where the
complex Berry phase of a band is used as a quantized invariant to predict the
existence of gapless edge modes in a non-Hermitian model. The chirally-broken,
$PT$-symmetric model is studied; we suggest an explanation for why the
topological invariant is a global property of the Hamiltonian. A geometrical
picture is provided by examining eigenvector evolution on the Bloch sphere. We
justify our analysis numerically and discuss relevant applications.Comment: 8 pages (PRB, in press

### Harmonically dancing space-time nodes: quantitatively deriving relativity, mass, and gravitation

The microscopic structure of space and time is investigated. It is proposed
that space and time of an inertial observer $\Sigma$ are most conveniently
described as a crystal array $\Lambda$, with nodes representing measurement
`tickmarks' and connected by independent quantized harmonic oscillators which
vibrate more severely the faster $\Sigma$ moves with respect to the object
being measured (due to the Uncertainty Principle). The Lorentz transformation
of Special Relativity is derived. Further, mass is understood as a localized
region $\Delta \Lambda$ having higher vibration temperature than that of the
ambient lattice. The effect of relativistic mass increase may then be
calculated without appealing to energy-momentum conservation. The origin of
gravitation is shown to be simply a transport of energy from the boundary of
$\Delta \Lambda$ outwards by lattice phonon conduction, as the system tends
towards equilibrium. Application to a single point mass leads readily to the
Schwarzschild metric, while a new solution is available for two point masses -
a situation where General Relativity is too complicated to work with. The
important consequence is that inertial observers who move at relative speeds
too close to $c$ are no longer linked by the Lorentz transformation, because
the lattice of the `moving' observer has already disintegrated into a liquid
state.Comment: 13 pages, 3 figure

### Relativity as the quantum mechanics of space-time measurements

Can a simple microscopic model of space and time demonstrate Special
Relativity as the macroscopic (aggregate) behavior of an ensemble ? The
question will be investigated in three parts. First, it is shown that the
Lorentz transformation formally stems from the First Relativity Postulate (FRP)
{\it alone} if space-time quantization is a fundamental law of physics which
must be included as part of the Postulate. An important corollary, however, is
that when measuring devices which carry the basic units of lengths and time
(e.g. a clock ticking every time quantum) are `moving' uniformly, they appear
to be measuring with larger units. Secondly, such an apparent increase in the
sizes of the quanta can be attributed to extra fluctuations associated with
motion, which are precisely described in terms of a thermally agitated harmonic
oscillator by using a temperature parameter. This provides a stringent
constraint on the microscopic properties of flat space-time: it is an array of
quantized oscillators. Thirdly, since the foregoing development would suggest
that the space-time array of an accelerated frame cannot be in thermal
equilibrium, (i.e. it will have a distribution of temperatures), the approach
is applied to the case of acceleration by the field of {\it any} point object,
which corresponds to a temperature `spike' in the array. It is shown that the
outward transport of energy by phonon conduction implies an inverse-square law
of force at low speeds, and the full Schwarzschild metric at high speeds. A
prediction of the new theory is that when two inertial observers move too fast
relative to each other, or when fields are too strong, anharmonic corrections
will modify effects like time dilation, and will lead to asymmetries which
implies that the FRP may not be sustainable in this extreme limit.Comment: 17 pages, 3 figure

### Has inflation really solved the problems of flatness and absence of relics?

Among the three cosmological enigma solved by the theory of inflation, {\it
viz.} (a) large scale flatness, (b) absence of monopoles and strings, and (c)
structure formation, the first two are addressed from the viewpoint of the
observed scales having originated from very small ones, on which the density
fluctuations of the curvaton and relics are {\it inevitably} of order unity or
larger. By analyzing strictly classically (and in two different gauges to
ensure consistency) the density evolution of the smoothest possible
pre-inflationary component -- thermal radiation -- it is found that the O(1)
statistical fluctuations on the thermal wavelength scale present formidable
obstacles to the linear theory of amplitude growth by the end of inflation.
Since this wavelength scale exited the horizon at an early stage of inflation,
it severely limits the number of e-folds of perturbative inflation. With more
e-folds than $\approx 60$ there will be even larger fluctuations in the
radiation density that ensures inflation keeps making `false starts'. The only
`way out' is to invoke a super-homogeneous pre-inflationary fluid, at least on
small scales, adding to the fine-tuning and preventing one from claiming that
inflation simply `redshifts away' all the relic inhomogeneities; {\it i.e} the
theory actually provided no explanation of (a) or (b), merely a tautology.Comment: MNRAS in press (9 journal pages, 1 appendix); minor changes at proofs
stage. Final versio

### The outermost gravitationally bound orbit around a mass clump in an expanding Universe: implication on rotation curves and dark matter halo sizes

Conventional treatment of cold dark matter halos employs the
Navarro-Frenk-White (NFW) profile with a maximum radius set at $r=r_{200}$,
where the enclosed matter has an overdensity of 200 times the critical density.
The choice of $r=r_{200}$ is somewhat arbitrary. It is not the collapsed
(virial) radius, but does give $r \sim$ 1 Mpc for rich clusters, which is a
typical X-ray size. Weak lensing measurements, however, reveal halo radii well
in excess of $r_{200}$. Is there a surface that places an absolute limit on the
extension of a halo? To answer the question, we derived analytically the
solution for circular orbits around a mass concentration in an expanding flat
Universe, to show that an outermost orbit exists at $v/r = H$, where $v$ is the
orbital speed and $H$ is the Hubble constant. The solution, parametrized as
$r_2$, is independent of model assumptions on structure formation, and {\it is
the radius at which the furthest particle can be regarded as part of the bound
system}. We present observational evidence in support of dark matter halos
reaching at least as far out as $r=r_2$. An interesting consequence that
emerges concerns the behavior of rotation curves. Near $r=r_2$ velocities will
be biased low. As a result, the mass of many galaxy groups may have been
underestimated. At $r=r_2$ there is an abrupt cutoff in the curve, irrespective
of the halo profile. An important cosmological test can therefore be performed
if velocity disperion data are available out to 10 Mpc radii for nearby
clusters (less at higher redshifts). For Virgo it appears that there is no such
cutoff.Comment: Shortened to satisfy ApJL page limit. Re-submitted. First version
contains serious error due to cancellation of lowest order Hubble effect in
the Lab. 2nd order effect is genuine, and is presented her

### Proving the conservation of surface brightness during the strong and weak lensing of light by an isothermal sphere

An analytical proof of the conservation of surface brightness during the
strong and weak lensing of light by a singular isothermal sphere is provided.
It is shown that the movement of asymptotic rays provide room for precisely the
extra solid angle claimed by the magnification of the centrally passing rays.
Previous claim of a violation of this conservation law, leading to a problem
over the COBE all sky CMB flux, is hereby withdrawn.Comment: Research note (for pedagogical purpose

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