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Understand the importance of events within Special Relativity, and the distinction between events and their coordinates in a particular frame; and appreciate why we have to define very carefully the process of measuring distances and times, and how we go about this.
In , we used the axioms ofto obtain the Lorentz transformation. That allowed us to describe events in two different frames in relative motion. That part was rather mathematical in style. Now we are going to return to the physics, and describe motion: velocity, acceleration, momentum, energy and mass.
We are now able to deduce the Lorentz transformation, relating two inertial frames. We examine three paradoxes, namely the famous twins paradox, the pole-in-the-barn paradox, and the so-called Bell's spaceships paradox. We also take another look at the relationship with electromagnetism.
We look at the immediate consequences of the two axioms, and discover, qualitatively and then quantitatively, the phenomena of length contraction and time dilation.
We survey relativity's contact with experiment and observation, briefly discussing the classical tests of SR and of GR, and including a discussion of the famous 1919 Dyson-Eddington observations of the bending of starlight during the solar eclipse. In the latter, we look at the historical and social pressures on the scientists involved, and what effect these have on the processes of theory choice.
Inwe saw how observers could make measurements of lengths and times in frames which are in relative motion, and reasonably disagree about the results – the phenomena of length contraction and time dilation. In , we were able to put numbers to this and derive a quantitative relation, Eq. (), between the duration of a ‘tick’ of the light clock as measured in two frames. We want to do better than this, and find a way to relate the coordinates of any event, as measured in any pair of frames in relative motion. That relation – a transformation from one coordinate system to another – is the Lorentz transformation (LT). The derivation inhas a lot in common with the account given in .
Many short gamma-ray bursts (GRBs) originate from binary neutron star mergers, and there are several theories that predict the production of coherent, prompt radio signals either prior, during, or shortly following the merger, as well as persistent pulsar-like emission from the spin-down of a magnetar remnant. Here we present a low frequency (170–200 MHz) search for coherent radio emission associated with nine short GRBs detected by the Swift and/or Fermi satellites using the Murchison Widefield Array (MWA) rapid-response observing mode. The MWA began observing these events within 30–60 s of their high-energy detection, enabling us to capture any dispersion delayed signals emitted by short GRBs for a typical range of redshifts. We conducted transient searches at the GRB positions on timescales of 5 s, 30 s, and 2 min, resulting in the most constraining flux density limits on any associated transient of 0.42, 0.29, and 0.084 Jy, respectively. We also searched for dispersed signals at a temporal and spectral resolution of 0.5 s and 1.28 MHz, but none were detected. However, the fluence limit of 80–100 Jy ms derived for GRB 190627A is the most stringent to date for a short GRB. Assuming the formation of a stable magnetar for this GRB, we compared the fluence and persistent emission limits to short GRB coherent emission models, placing constraints on key parameters including the radio emission efficiency of the nearly merged neutron stars (
$\epsilon_r\lesssim10^{-4}$
), the fraction of magnetic energy in the GRB jet (
$\epsilon_B\lesssim2\times10^{-4}$
), and the radio emission efficiency of the magnetar remnant (
$\epsilon_r\lesssim10^{-3}$
). Comparing the limits derived for our full GRB sample (along with those in the literature) to the same emission models, we demonstrate that our fluence limits only place weak constraints on the prompt emission predicted from the interaction between the relativistic GRB jet and the interstellar medium for a subset of magnetar parameters. However, the 30-min flux density limits were sensitive enough to theoretically detect the persistent radio emission from magnetar remnants up to a redshift of
$z\sim0.6$
. Our non-detection of this emission could imply that some GRBs in the sample were not genuinely short or did not result from a binary neutron star merger, the GRBs were at high redshifts, these mergers formed atypical magnetars, the radiation beams of the magnetar remnants were pointing away from Earth, or the majority did not form magnetars but rather collapse directly into black holes.
In this chapter, I am going to introduce the two axioms of Special Relativity. These axioms are, to an extent, the only new physics introduced in this text: once I have introduced them and made them plausible, the rest of our work is devoted to examining their consequences, and the way in which they change the physics we are already familiar with.
Therecently discovered massive binary system Apep is the most powerful synchrotron emitter among the known Galactic colliding-wind binaries. This makes this particular system of great interest to investigate stellar winds and the non-thermal processes associated with their shocks. This source was detected at various radio bands, and in addition the wind-collision region was resolved by means of very-long baseline interferometric observations. We use a non-thermal emission model for colliding-wind binaries to derive physical properties of this system. The observed morphology in the resolved maps allows us to estimate the system projection angle on the sky to be
$\psi \approx 85^\circ$
. The observed radio flux densities also allow us to characterise both the intrinsic synchrotron spectrum of the source and its modifications due to free–free absorption in the stellar winds at low frequencies; from this, we derive mass–loss rates of the stars of
$\dot{M}_\mathrm{WN} \approx 4\times10^{-5}\;\mathrm{M}_\odot\,\mathrm{yr}^{-1}$
and
$\dot{M}_\mathrm{WC} \approx 2.9\times10^{-5}\;\mathrm{M}_\odot\,\mathrm{yr}^{-1}$
. Finally, the broadband spectral energy distribution is calculated for different combinations of the remaining free parameters, namely the intensity of the magnetic field and the injected power in non-thermal particles. We show that the degeneracy of these two parameters can be solved with observations in the high-energy domain, most likely in the hard X-rays but also possibly in
$\gamma$
-rays under favourable conditions.
This compact yet informative Guide presents an accessible route through Special Relativity, taking a modern axiomatic and geometrical approach. It begins by explaining key concepts and introducing Einstein's postulates. The consequences of the postulates – length contraction and time dilation – are unravelled qualitatively and then quantitatively. These strands are then tied together using the mathematical framework of the Lorentz transformation, before applying these ideas to kinematics and dynamics. This volume demonstrates the essential simplicity of the core ideas of Special Relativity, while acknowledging the challenges of developing new intuitions and dealing with the apparent paradoxes that arise. A valuable supplementary resource for intermediate undergraduates, as well as independent learners with some technical background, the Guide includes numerous exercises with hints and notes provided online. It lays the foundations for further study in General Relativity, which is introduced briefly in an appendix.
Recent ground-based deep observations of the Universe have discovered large populations of massive quiescent galaxies at
$z\sim3\!-\!5$
. With the launch of the James Webb Space Telescope (JWST), the on-board Near-Infrared Spectrograph (NIRSpec) instrument will provide continuous
$0.6\!-\!5.3\,\unicode{x03BC}\,\mathrm{m}$
spectroscopic coverage of these galaxies. Here we show that NIRSpec/CLEAR spectroscopy is ideal to probe the completeness of photometrically selected massive quiescent galaxies such as the ones presented by Schreiber et al. (2018b, A&A, 618, A85). Using a subset of the Schreiber et al. (2018b, A&A, 618, A85) sample with deep Keck/MOSFIRE spectroscopy presented by Esdaile J., et al. (2021b, ApJ, 908, L35), we perform a suite of mock JWST/NIRSpec observations to determine optimal observing strategies to efficiently recover the star formation histories (SFHs), element abundances, and kinematics of these massive quiescent galaxies. We find that at
$z\sim3$
, medium resolution G235M/FL170LP NIRSpec observations could recover element abundances at an accuracy of
${\sim}15\%$
, which is comparable to local globular clusters. Mimicking ZFOURGE COSMOS photometry, we perform mock spectrophotometric fitting with Prospector to show that the overall shape of the SFHs of our mock galaxies can be recovered well, albeit with a dependency on the number of non-parametric SFH bins. We show that deep high-resolution G235H/FL170LP integral field spectroscopy with a
$S/N\sim7$
per spaxel is required to constrain the rotational properties of our sample at
$>\!2\sigma$
confidence. Thus, through optimal grism/filter choices, JWST/NIRSpec slit and integral field spectroscopy observations would provide tight constraints to galaxy evolution in the early Universe.