Uncertainty: Einstein, Heisenberg, Bohr, and the Struggle for the Soul of Science, by David Lindley (Doubleday, 2007), is as much a history as an explanation.  It recounts events and individuals involved in the discovery of the uncertainty principle in quantum physics, known otherwise as the Heisenberg principle.  The book is a relatively short (some 240 pages) and cogent narrative of the history of physics in the nineteenth and twentieth centuries, mainly from around 1820 to 1935.  It illustrates the collaborative nature of science, especially of physics, and how major discoveries are usually the result of contributions over time by many individuals, with one or two leading figures providing the key insights that bring clarity to a particular issue.  In this regard the book is similar to the much longer, more complicated, but still excellent Black Holes and Time Warps: Einstein's Outrageous Legacy, by physicist Kip Thorne. 

Uncertainty primarily concerns the development of quantum physics and more specifically of the uncertainty principle.  This principle made clear the true nature of the quantum world and its distinctiveness from the world of Newtonian physics.  Newtonian physics holds that the universe must function according to strict laws and principles that enable scientists to predict with precision the movements and behaviors of objects as small as atoms and as large as planets, stars, and galaxies.  Quantum physics, informed by the uncertainty principle, views the universe as subject at a subatomic level to a certain unpredictability.  The behavior of subatomic particles becomes a matter of statistical probability, not of exact behavior and measurement. 

Certain seemingly impossible and paradoxical principles come into play.  For instance, science can measure the velocity of a photon but not its exact location.  Or, science can measure the location of a photon but not its velocity.  Newtonian physics would argue that it should be possible to measure both, while quantum physics argues that it is impossible to measure both.  There are other aspects of unpredictability: for instance, science can explain the process of radioactivity, how an atom splits and emits particles that are detected as radiation.  However, it cannot predict when a particular atom will split or why it splits at a particular moment.  This apparent randomness and unpredictability are characteristics of the quantum world.

Some predicted that science would end when Heisenberg and others defined a principle that described the limitations of science’s ability to measure and define precisely certain basic phenomena.  Einstein in particular was deeply bothered and could never accept uncertainty, though he could see the sense of it.  One of the purposes of this book is to show how the Heisenberg principle did not bring an end to science at all.