Welcome to the web site of Dr. Mark P. Silverman, Jarvis Professor of Physics at Trinity College. I am a physicist whose scientific interests and contributions fall broadly in the areas of quantum physics, atomic & nuclear physics, optics & electromagnetism, and gravitation. I am also a teacher who has developed humane and effective educational methods for teaching science at all levels of instruction. At this site you can find books and papers in which I discuss my scientific research and educational experiments. More about me »

New Book

A Certain Uncertainty

Cambridge University Press 2014 - ISBN-13: 978-1107032811

A Certain Uncertainty cover

This book examines randomness, chance, and uncertainty in matters pertaining to fundamental questions of physics as well as to issues that are likely to affect readers in personal ways. Among the topics discussed are controversial issues concerning the decay of radioactive nuclei, predictability of the stock market, safety of commercial aircraft, accelerating rise in Earth’s temperature, interpretation of medical tests, detection of drug use to enhance athletic performance, and more. The book helps develop proficiency in the use of probability and statistics to understand a multiplicity of physical processes. Read more »

Recent Work

The Half-Life of Radioactive Nuclei

Estimating the half-life of an unstable nucleus from just two measurements does not give an accurate result. However, a histogram of a large number of two-point estimates leads to a nearly perfect Cauchy distribution centred at the true value.

See: M P Silverman, “Theory of nuclear half-life determination by statistical sampling”, Europhysics Letters 105 (2014) 22001 p1-p5. doi: 10.1209/0295-5075/105/22001

Probability of Half-Life Estimate

Rising Temperatures and Urban Heat Stress

The Earth’s surface temperature is increasing. However, measurements of subterranean temperature variations, which are largely insensitive to the vicissitudes of weather, indicate that the rate of temperature rise in cities can far outpace the rate of global or regional warming.

See: M P Silverman, “Statistical analysis of subsurface diffusion of solar energy with implications for urban heat stress”, Journal of Modern Physics, 5 (2014) 751-762, published online

Variation of Temperature with Time and Depth

Recurrent Patterns in Random Events

The common perception (see Wikipedia) of randomness is that it is devoid of all order, pattern, or predictability. However, that is a misperception. It is precisely the existence of patterns of recurrence that characterise a random process and serve usefully in many ways, among which is to test the randomness of quantum events.

See: M P Silverman, “Numerical Procedures for Calculating the Probabilities of Recurrent Runs”, Open Journal of Statistics 4 (2014) 122-131, published online

Variation of Temperature with Time and Depth


I am available for lecturing on a variety of topics related to my research of which the following are some examples. Also, see Lectures for more details.

  • The strange behaviour of quantum particles
  • New directions in electron microscopy and interferometry
  • Do radioactive nuclei decay randomly?
  • Seeing through turbid media with polarised light
  • Quantum stabilisation of stellar black holes
  • A radical hypothesis: Are crowds wise?
  • A warning from the weather under ground: Solar energy diffusion and urban heat stress


A Certain Uncertainty And Yet It Moves More Than One Mystery Waves and Grains Probing The Atom A Universe of Atoms Quantum Superposition