Environmental Engineering Reference
In-Depth Information
1
Space, Time and Motion
1.1 DEFINING SPACE AND TIME
If there is one part of physics that underpins all others, it is the study of motion.
The accurate description of the paths of celestial objects, of planets and moons,
is historically the most celebrated success of a classical mechanics underpinned
by Newton's laws
1
. The range of applicability of these laws is vast, encompass-
ing a scale that extends from the astronomical to the microscopic. We have come
to understand that many phenomena not previously associated with motion are in
fact linked to the movement of microscopic objects. The absorption and emission
spectra of atoms and molecules arise as a result of transitions made by their con-
stituent electrons, and the random motion of ensembles of atoms and molecules
forms the basis for the modern statistical description of thermodynamics. Although
atomic and subatomic objects are properly described using quantum mechanics, an
understanding of the principles of classical mechanics is essential in making the
conceptual leap from continuous classical systems with which we are most familiar,
to the discretised quantum mechanical systems, which often behave in a manner
at odds with our intuition. Indeed, the calculational techniques that are routinely
used in quantum mechanics have their roots in the classical mechanics of particles
and waves; a close familiarity with their use in classical systems is an asset when
facing problems of an inherently quantum mechanical nature.
As we shall see in the second part of this topic, when objects move at speeds
approaching the speed of light classical notions about the nature of space and
time fail us. As a result, the classical mechanics of Newton should be viewed as a
low-velocity approximation to the more accurate relativistic theory of Einstein
2
.To
look carefully at the differences between relativistic and non-relativistic theories
