of the conductor. This can also be written in terms of electric quantities (voltage
current resistance) and with units of measure (volts amps ohms).MODERN PHYSICS AND MATHEMATICS
What is modern physics?
In contrast to classical physics—although there are overlapping topics—modern
physics includes relativistic mechanics, atomic, nuclear and particle physics, and
quantum physics.How did Albert Einsteinuse mathematics?
German-born American theoretical physicist Albert Einstein (1879–1955) is recog-
nized as one of the greatest physicists of all time, but he was also a notable mathe-
matician. In 1905 he developed the special theory of relativity, mathematically demon-
strating that two observers moving at great speeds with respect to one another will
experience different time intervals and measure lengths differently, that the speed of
light is the “speed limit” for all objects having mass, and that mass and energy are
equivalent.
By around 1915, Einstein completed a mathematical formulation of a general the-
ory of relativity, this time adding gravitational effects to determine curvature of a
time-space continuum. He further tried to discover a unified field theory, which would
combine gravity, electromagnetism, and subatomic phenomena under one set of
rules, but he, and no one since, has ever found such a theory. (For more about Albert
Einstein, see “History of Math.”)What is relativity?
Relativity refers to the idea that the velocity of an object can be determined only rela-
tive to the observer. For example, if a fly moves around the inside of a car at about 1
mile per hour, inside the car’s frame of reference, the fly is moving at 1 mile per hour.
But if the car goes past you at 65 miles per hour, it will appear as if the fly is traveling
at 66 miles per hour, not 1 mile per hour. In other words, it’s all a matter of reference,
and it’s “relative” to your viewpoint.
What new ideas came out of Einstein’s (and others’) study of relativity? He showed
that space and time could no longer be viewed as separate, independent entities, form-
ing a four-dimensional continuum called space-time(also written as spacetime). It is
not easy to verbally explain the intricacies of Einstein’s theory. The best way to inter-
pret his works is with the use of formulations from certain mathematical branches,
such as tensor calculus (for more about tensors, see “Mathematical Analysis”). But
280 such complex equations are beyond the scope of this book.