arXiv subjects
Publications and source records attributed to Alejandro Jenkins.
We propose an explanation of the title of Prof. James Moriarty's treatise_Dynamics of an Asteroid_, a scientific work mentioned by Sherlock Holmes in_The Valley of Fear_ and prominently featured in Guy Ritchie's 2011 film_Sherlock Holmes: A Game of Shadows_. Our views on the subject differ from those expressed in Isaac Asimov's "The Ultimate Crime".
After Isaac Newton was knighted by Queen Anne in 1705 he adopted an unusual coat of arms: a pair of human tibiae crossed on a black background, like a pirate flag without the skull. After some general reflections on Newton's monumental scientific achievements and on his enigmatic life, we investigate the story of his coat of arms. We also discuss how its simple design illustrates the concept of chirality, which would later play an important role in the philosophical arguments about Newton's conception of space, as well as in the development of modern chemistry and particle physics.
When a real fluid is expelled quickly from a tube, it forms a jet separated from the surrounding fluid by a thin, turbulent layer. On the other hand, when the same fluid is sucked into the tube, it comes in from all directions, forming a sink-like flow. We show that, even for the ideal flow described by the time-reversible Euler equation, an experimenter who only controls the pressure in a pump attached to the tube would see jets form in one direction exclusively. The asymmetry between outflow and inflow therefore does not depend on viscous dissipation, but rather on the experimenter's limited control of initial and boundary conditions. This illustrates, in a rather different context from the usual one of thermal physics, how irreversibility may arise in systems whose microscopic dynamics are fully reversible.
We express the position of the Sun in the sky as a function of time and the observer's geographic coordinates. Our method is based on applying rotation matrices to vectors describing points on the celestial sphere. We also derive direct expressions, as functions of date of the year and geographic latitude, for the duration of daylight, the maximum and minimum altitudes of the Sun, and the cardinal directions to sunrise and sunset. We discuss how to account for the eccentricity of the earth's orbit, the precessions of the equinoxes and the perihelion, the size of the solar disk, and atmospheric refraction. We illustrate these results by computing the dates of "Manhattanhenge" (when sunset aligns with the east-west streets on the main traffic grid for Manhattan, in New York City), by plotting the altitude of the Sun over representative cities as a function of time, and by showing plots ("analemmas") for the position of the Sun in the sky at a given hour of the day.
In the early 18th century, J. E. E. Bessler, known as Orffyreus, constructed several wheels that he claimed could keep turning forever, powered only by gravity. He never revealed the details of his invention, but he conducted demonstrations (with the machine's inner workings covered) that persuaded competent observers that he might have discovered the secret of perpetual motion. Among Bessler's defenders were Gottfried Leibniz, Johann Bernoulli, Professor Willem 's Gravesande of Leiden University (who wrote to Isaac Newton on the subject), and Prince Karl, ruler of the German state of Hesse-Kassel. We review Bessler's work, placing it within the context of the intellectual debates of the time about mechanical conservation laws and the (im)possibility of perpetual motion. We also mention Bessler's long career as a confidence man, the details of which were discussed in popular 19th-century German publications, but have remained unfamiliar to authors in other languages.
Physicists are very familiar with forced and parametric resonance, but usually not with self-oscillation, a property of certain dynamical systems that gives rise to a great variety of vibrations, both useful and destructive. In a self-oscillator, the driving force is controlled by the oscillation itself so that it acts in phase with the velocity, causing a negative damping that feeds energy into the vibration: no external rate needs to be adjusted to the resonant frequency. The famous collapse of the Tacoma Narrows bridge in 1940, often attributed by introductory physics texts to forced resonance, was actually a self-oscillation, as was the swaying of the London Millennium Footbridge in 2000. Clocks are self-oscillators, as are bowed and wind musical instruments. The heart is a "relaxation oscillator," i.e., a non-sinusoidal self-oscillator whose period is determined by sudden, nonlinear switching at thresholds. We review the general criterion that determines whether a linear system can self-oscillate. We then describe the limiting cycles of the simplest nonlinear self-oscillators, as well as the ability of two or more coupled self-oscillators to become spontaneously synchronized ("entrained"). We characterize the operation of motors as self-oscillation and prove a theorem about their limit efficiency, of which Carnot's theorem for heat engines appears as a special case. We briefly discuss how self-oscillation applies to servomechanisms, Cepheid variable stars, lasers, and the macroeconomic business cycle, among other applications. Our emphasis throughout is on the energetics of self-oscillation, often neglected by the literature on nonlinear dynamical systems.
We propose a new framework for multi-field inflation in which a nearly constant potential energy is maintained during inflation before decreasing rapidly, in a manner analogous to a classical top spinning upright for a long time before falling down. We provide the simplest realization of such dynamics as a well-controlled, weakly-coupled effective field theory with a global shift symmetry. Nonperturbative quantum gravitational effects, which break global symmetries, are suppressed in this model. Primordial gravitational waves may be within experimental reach.
Many experimenters, starting with Ernst Mach in 1883, have reported that if a device alternately sucks in and then expels a surrounding fluid, it moves in the same direction as if it only expelled fluid. This surprising phenomenon, which we call "Machian propulsion," is explained by conservation of momentum: the outflow efficiently transfers momentum away from the device and into the surrounding medium, while the inflow can do so only by viscous diffusion. However, many previous theoretical discussions have focused instead on the difference in the shapes of the outflow and the inflow. Whereas the argument based on conservation is straightforward and complete, the analysis of the shapes of the flows is more subtle and requires conservation in the first place. Our discussion covers three devices that have usually been treated separately: the reverse sprinkler (also called the inverse, or Feynman sprinkler), the putt-putt boat, and the aspirating cantilever. We then briefly mention some applications of Machian propulsion, ranging from microengineering to astrophysics.
Unless the scale of electroweak symmetry breaking is stabilized dynamically, most of the universes in a multiverse theory will lack an observable weak nuclear interaction. Such "weakless universes" could support intelligent life based on organic chemistry, as long as other parameters are properly adjusted. By taking into account the seemingly-unrelated flavor dynamics that address the hierarchy of quark masses and mixings, we show that such weakless (but hospitable) universes can be far more common than universes like ours. The gauge hierarchy problem therefore calls for a dynamical (rather than anthropic) solution.
In this essay we review the central difficulty in formulating a viable quantum field theory in which gravity is emergent at low energies, rather than mediated by a fundamental gauge field. The Weinberg-Witten theorem forbids spin 2 massless modes from carrying Lorentz covariant stress-energy. In General Relativity the stress-energy is not covariant because it violates a gauge symmetry, but a gravitational theory without fundamental spin 2 gauge invariance must either lack a stress-energy operator or have a non-relativistic graviton. The latter option is incompatible with the principle of equivalence, though such theories are not necessarily ruled out at low energies.
We summarize the results of previous research on the constraints imposed on quark masses by the anthropically-motivated requirement that there exist stable nuclei with the right charge to form complex molecules. We also mention an upper bound on the mass of the lightest lepton, derived from the requirement that such nuclei be stable against electron capture.
We investigate worlds that lie on a slice through the parameter space of the Standard Model over which quark masses vary. We allow as many as three quarks to participate in nuclei, while fixing the mass of the electron and the average mass of the lightest baryon flavor multiplet. We classify as "congenial" worlds that satisfy the environmental constraint that the quark masses allow for stable nuclei with charges one, six, and eight, making organic chemistry possible. Whether a congenial world actually produces observers depends on a multitude of historical contingencies, beginning with primordial nucleosynthesis, which we do not explore. Such constraints may be independently superimposed on our results. Environmental constraints such as the ones we study may be combined with information about the a priori distribution of quark masses over the landscape of possible universes to determine whether the measured values of the quark masses are determined environmentally, but our analysis is independent of such an anthropic approach. We estimate baryon masses as functions of quark masses and nuclear masses as functions of baryon masses. We check for the stability of nuclei against fission, strong particle emission, and weak nucleon emission. For two light quarks with charges 2/3 and -1/3, we find a band of congeniality roughly 29 MeV wide in their mass difference. We also find another, less robust region of congeniality with one light, charge -1/3 quark, and two heavier, approximately degenerate charge -1/3 and 2/3 quarks. No other assignment of light quark charges yields congenial worlds with two baryons participating in nuclei. We identify and discuss the region in quark-mass space where nuclei would be made from three or more baryon species.
We show that the signs of the leading irrelevant interactions for Dirac fermions are constrained by the analytic structure of the S-matrix. If Regge behavior obtains, negative signs indicate the presence of higher-spin bound states that spoil the convergence of the dispersion integrals and drive the corresponding operators relevant. For nucleon-nucleon scattering, the negativity of some of the low-energy interactions signals the presence of a spin-1 bound state: the deuteron. We connect the divergence of the dispersion integral to the "Sommerfeld enhancement" of the cross-section for low-energy scattering. We also discuss how this illuminates potential pitfalls in using perturbative methods to understand the dependence of the low-energy nuclear interaction on the masses of the light quarks. Finally, we suggest the possibility of applying similar reasoning to the current-current operators in the electroweak effective lagrangian, where no bound states spoil convergence of the dispersion relations.
We propose a simple method for identifying operators in effective field theories whose coefficients must be positive by causality. We also attempt to clarify the relationship between diverse positivity arguments that have appeared in the literature. We conjecture that the superluminal perturbations identified in non-positive effective theories are generally connected to instabilities that develop near the cutoff scale. We discuss implications for the ghost condensate, the chiral Lagrangian, and the Goldstone bosons of theories with spontaneous Lorentz violation.
We review the interpretation of gauge invariance as a mathematical redundancy required in a relativistic description of forces mediated by massless spin-1 and spin-2 particles. In this context we also review the Weinberg-Witten theorem and its implications. This leads us to consider a class of models in which long-range interactions are mediated by Goldstone bosons of spontaneous Lorentz violation. Since the Lorentz symmetry is realized non-linearly in the Goldstones, these models could evade the Weinberg-Witten theorem and the need for gauge invariance. In the case of gravity, the broken symmetry would protect the theory from having non-zero cosmological constant, while the compositeness of the graviton could provide a solution to the perturbative non-renormalizability of gravity. We also consider the phenomenology of spontaneous Lorentz violation by a vector VEV and the experimental limits thereon. We find the general low-energy effective action of the Goldstones of this kind of symmetry breaking minimally coupled to gravity. We compare this to the ghost condensate that has been proposed as a model for gravity in a Higgs phase. We then summarize the cosmological constant problems and show that models in which a scalar field causes super-acceleration of the universe generally exhibit instabilities. We discuss how the equation of state evolves in a universe where the dark energy is caused by the ghost condensate. We comment on the anthropic argument for a small cosmological constant and how it is weakened if the inflaton self-coupling varies over the landscape of possible universes. Finally, we discuss the reverse sprinkler, a problem in elementary fluid mechanics that had eluded a definitive treatment for decades.
Lorentz-violating operators involving Standard Model fields are tightly constrained by experimental data. However, bounds are more model-independent for Lorentz violation appearing in purely gravitational couplings. The spontaneous breaking of Lorentz invariance by the vacuum expectation value of a vector field selects a universal rest frame. This affects the propagation of the graviton, leading to a modification of Newton's law of gravity. We compute the size of the long-range preferred-frame effect in terms of the coefficients of the two-derivative operators in the low-energy effective theory that involves only the graviton and the Goldstone bosons.
We briefly review the history and current status of models of particle interactions in which massless mediators are given, not by fundamental gauge fields as in the Standard Model, but by composite degrees of freedom of fermionic systems. Such models generally require the breaking of Lorentz invariance. We describe schemes in which the photon and the graviton emerge as Goldstone bosons from the breaking of Lorentz invariance, as well as generalizations of the quantum Hall effect in which composite excitations yield massless particles of all integer spins. While these schemes are of limited interest for the photon (spin 1), in the case of the graviton (spin 2) they offer a possible solution to the long-standing UV problem in quantum linear gravity.
The anthropic principle has been proposed as an explanation for the observed value of the cosmological constant. Here we revisit this proposal by allowing for variation between universes in the amplitude of the scale-invariant primordial cosmological density perturbations. We derive a priori probability distributions for this amplitude from toy inflationary models in which the parameter of the inflaton potential is smoothly distributed over possible universes. We find that for such probability distributions, the likelihood that we live in a typical, anthropically-allowed universe is generally quite small.