Physics

Physics investigates matter, motion, and interactions by building mathematical models and testing their consequences against observations. A physical law supplies a relation; a model specifies the objects, conditions, and approximations used to apply it. Classical mechanics, electromagnetism, thermodynamics, and quantum mechanics organize different aspects of these investigations. Their usefulness comes from turning measurements into predictions that can be checked and refined.

Consider a simple pendulum: how does its oscillation period change when its length changes? For small amplitude, the ideal model gives $T_0=2\pi \sqrt{\ell /g}$, where $g$ is gravitational acceleration. Taking $g=9.81m/{\mathrm{s}}^2$ as the model parameter, a one-metre pendulum has predicted period $2.0061\mathrm{s}$. Increasing its length to four metres gives $4.0121\mathrm{s}$: quadrupling the length doubles the period. The point mass cancels from the equation, so changing it alone does not change this model's answer.

The prediction identifies a mechanism and a way to challenge it. The small-angle approximation replaces $\sin \theta$ by $\theta$; the full ideal equation predicts a longer period at large amplitude. At $60^{\circ }$, its period is about $1.07318T_0$, already a $7.3\%$ change. Measurements at such amplitudes can reveal the limit of the approximation, while appreciable drag requires a damped pendulum. These distinctions are developed in simple pendulum and dimensional analysis. The small-amplitude model is also derived in Ling, Sanny and Moebs, University Physics, pendulums.

Several different experiments can become one calculation. Nondimensionalization rewrites the pendulum equation using $\tau =t\sqrt{g/\ell }$, leaving $d^2\theta /d{\tau }^2+\sin \theta =0$. All lengths share that dimensionless equation; the amplitude remains a parameter. Similarly, conservation laws and symmetry reveal features that many models share. This is one source of the subject's beauty: a compact relation can organize a large range of phenomena.

The connection to evidence remains essential when a model is elegant. In his introductory lectures, Richard Feynman emphasizes testing proposed relations by experiment and using idealizations whose accuracy depends on the conditions. ^[ref] A discrepancy can motivate a better measurement, a better approximation, or a different physical model; the mathematical calculation and the empirical assessment are both part of the explanation.

Institutional publisher of open teaching materials.

First author of the 2012 study of computed tomography-based attenuation correction in positron emission tomography/computed tomography bone imaging.^[ref]

Researcher in magnetic resonance imaging instrumentation.^[ref]

Researcher in positron emission tomography and combined PET/computed tomography imaging.^[ref]

International collaboration that evaluates particle properties and publishes the Review of Particle Physics. Official site: pdg.lbl.gov

Institutional author of electronic-component data sheets.

Coauthor of Spin dependent transport: GMR & TMR by Alain Schuhl and Daniel Lacour.

Coauthor of Spin dependent transport: GMR & TMR by Alain Schuhl and Daniel Lacour.

MIT lists the instructor of Organic Optoelectronics lecture notes by Vladimir Bulović as Vladimir Bulovic.

Author named on Lecture Notes for Quantum Matter by Steven H. Simon.

Lecturer named on the cover of Quantum Optical Communication lecture 6 by Jeffrey H. Shapiro.

Institutional author of the instrument and adaptive-optics documentation cited below. www.eso.org

Institutional collaboration producing the Geant4 simulation toolkit and its reference manuals. Official website: geant4.web.cern.ch

The scientific collaboration operating the L3 experiment.