Physics

These programme notes were written for a production of "Hapgood" at the Hampstead Theatre, London in December 2015. I thank Sir Tom Stoppard for helpful suggestions.

The knuckleball is perhaps the most enigmatic pitch in baseball. Relying on the presence of raised seams on the surface of the ball to create asymmetric flow, a knuckleball's trajectory has proven very challenging to predict compared to other baseball pitches, such as fastballs or curveballs. Previous experimental tracking of large numbers of knuckleballs has shown that they can move in essentially any direction relative to what would be expected from a drag-only trajectory. This has led to speculation that knuckleballs exhibit chaotic motion. Here we develop a relatively simple model of a knuckleball that includes quadratic drag and lift from asymmetric flow which is taken from experimental measurements of slowly rotating baseballs. Our models can indeed exhibit dynamical chaos as long In contrast, models that omit torques on the ball in flight do not show chaotic behavior. Uncertainties in the phase space position of the knuckleball are shown to grow by factors as large as 10 6 over the flight of the ball from the pitcher to home plate. We quantify the impact of our model parameters on the chaos realized in our models, specifically showing that maximum Lyapunov exponent is roughly proportional to the square root of the effective lever arm of the torque, and also roughly proportional to the initial velocity of the pitch. We demonstrate the existence of bifurcations that can produce changes in the location of the ball when it reaches the plate of as much as 1.2 m for specific initial conditions similar to those used by professional knuckleball pitchers. As we introduce additional complexity in the form of more faithful representations of the empirical asymmetry force measurements, we find that a larger fraction of the possible initial conditions result in dynamical chaos.

A Dyson Sphere is a hypothetical structure that an advanced civilization might build around a star to intercept all of the star's light for its energy needs. One usually thinks of it as a spherical shell about one astronomical unit (AU) in radius, and surrounding a more or less Sun-like star; and might be detectable as an infrared point source. We point out that Dyson Spheres could also be built around white dwarfs. This type would avoid the need for artificial gravity technology, in contrast to the AU-scale Dyson Spheres. In fact, we show that parameters can be found to build Dyson Spheres suitable --temperature- and gravity-wise-- for human habitation. This type would be much harder to detect.

Land-based beacons, information laden probes sent into our solar system, and more distal communication nodes have each been proposed as the most likely means by which we might be contacted by ET. Each method, considered in isolation from ET's point of view, has limitations and flaws. An overarching galactic communication architecture that tethers together probes, nodes, and land bases is proposed to be a better overall solution. From this more efficient construct flows several conclusions: (a) Earth has been thoroughly surveilled, (b) Earth will be contacted in due course, (c) SETI beyond half the distance that Earth's EM has reached (~35-50 LY) is futile, and (d) the very quiescence of the galaxy paradoxically implies that that Drake's N = many, and that there is a system of galactic governance. Search strategies are proposed to detect the described probe-node-land base communications pathway.

Almost all SETI searches to date have explicitly targeted stars in the hope of detecting artificial radio or optical transmissions. It is argued that extra-terrestrials (ET) might regard sending physical probes to our own Solar System as a more efficient means for sending large amounts of information to Earth. Probes are more efficient in terms of energy and time expenditures; may solve for the vexing problem of Drake's L factor term, namely, that the civilization wishing to send information may not coexist temporally with the intended recipient; and they alleviate ET's reasonable fear that the intended recipient might prove hostile. It is argued that probes may be numerous and easier to find than interstellar beacons.

Finding life on other worlds is a fascinating area of astrobiology and planetary sciences. Presently, over 3500 exoplanets, representing a very wide range of physical and chemical environments, are known. Tardigrades (water bears) are microscopic invertebrates that inhabit almost all terrestrial, freshwater and marine habitats, from the highest mountains to the deepest oceans. Thanks to their ability to live in a state of cryptobiosis, which is known to be an adaptation to unpredictably fluctuating environmental conditions, these organisms are able to survive when conditions are not suitable for active life; consequently, tardigrades are known as the toughest animals on Earth. In their cryptobiotic state, they can survive extreme conditions, such as temperatures below -250°C and up to 150°C, high doses of ultraviolet and ionising radiation, up to 30 years without liquid water, low and high atmospheric pressure, and exposure to many toxic chemicals. Active tardigrades are also resistant to a wide range of unfavourable environmental conditions, which makes them an excellent model organism for astrobiological studies. In our study, we have established a metric tool for distinguishing the potential survivability of active and cryptobiotic tardigrades on rocky-water and water-gas planets in our solar system and exoplanets, taking into consideration the geometrical means of surface temperature and surface pressure of the considered planets. The Active Tardigrade Index (ATI) and Cryobiotic Tardigrade Index (CTI) are two metric indices with minimum value 0 (= tardigrades cannot survive) and maximum 1 (= tardigrades will survive in their respective state). Values between 0 and 1 indicate a percentage chance of the active or cryptobiotic tardigrades surviving on a given exoplanet.

I will report below on a few examples of raving and insane (or maybe utterly genial) sentences that can be found in famous and otherwise admirable books of physics, because I genuinely believe it is amusing.

Little has been published regarding whether and how sound suppressors impact bullet flight, including velocity, bullet yaw, and drag. These parameters were compared for four different bullets fired from a .300 Winchester Magnum under four different muzzle conditions (no device and three different suppressors). While effects were not observed in all cases, results indicate that sound suppressors can have the effect of reducing bullet yaw and drag significantly, and can also have small effects on muzzle velocity. Results further suggest that bullets with a propensity to yaw demonstrate significant reductions in yaw and drag when shot through a two stage symmetric suppressor versus unsuppressed or with a conventional mouse-hole/K-baffle design.

At some point in the future, if mankind hopes to settle planets outside the Solar System, it will be crucial to determine the range of planetary conditions under which human beings could survive and function. In this article, we apply physical considerations to future exoplanetary biology to determine the limitations which gravity imposes on several systems governing the human body. Initially, we examine the ultimate limits at which the human skeleton breaks and muscles become unable to lift the body from the ground. We also produce a new model for the energetic expenditure of walking, by modelling the leg as an inverted pendulum. Both approaches conclude that, with rigorous training, humans could perform normal locomotion at gravity no higher than 4 g Earth .

In 1936, Albert Einstein wrote a brief article where he suggested the possibility that a massive object acted as a lens, amplifying the brightness of a star. As time went by, this phenomenon, known as gravitational lensing, has become a powerful research tool in astrophysics. The simplest and symmetrical expression of a gravitational lens is known as Einstein ring. This model has recently allowed the measurement of the mass of a star, the white dwarf Stein 2051 B. The purpose of this work is to show an accessible and uptodate introduction to the effect of gravitational lensing, focused on the Einstein ring and the measurement of the mass of Stein 2051 B. The intended audience of this article are non-graduate students of physics and similar fields of study, and requires only basic knowledge of classical physics, modern physics, algebra and trigonometry.