Did Einstein’s theorieschange our concept of dimensions?
Yes, our ideas about dimensions changed dramatically thanks to Einstein’s theories,
not to mention the mathematics involved in producing those theories. In particular,
one can’t distinguish space and time as elements in the description of events. Instead,
they are joined in what is called the fourth dimension—also called a four-dimensional
manifold known as space-time (see above).
Although it sounds like something out of the television show Star Trek,in space-
time events in the universe are described in terms of the four-dimensional continuum.
Simply put, each observer locates an event by three spacelike coordinates (positions)
and one timelike coordinate. The choice of the timelike coordinate in space-time is
not unique; hence, time is not absolute but is relative to the observer. The strange
effects go on: In general, events at different locations that are simultaneous for one
observer will not be simultaneous for another observer. (For more information about
dimensions, see “Geometry and Trigonometry.”)
Why was Max Planckimportant to quantum theory?
Quantum theory (or physics) entails the emission and absorption of energy by matter
and the motion of material particles. It is a special situation in which very small quan-
tities are involved. When added to the theory of relativity—in which great speeds are
involved—both form the theoretical basis of modern physics.
One of the most important aspects of quantum theory is the quanta. In 1900 Ger-
man physicist Max Karl Ernst Ludwig Planck (1858–1947) proposed that all forms of
radiation—such as light and heat—come in bundles called quanta. These bundles are
further emitted and absorbed in small, discrete amounts, thus behaving in some situa-
tions like particles of matter. For example, a bundle of light energy is known as light
quanta or photons. Planck devised the equation: Ehv, in which Eis the amount of
energy in a single particle, vis the frequency of the wave, and his the constant now
known as Planck’s constant. 281
MATH IN THE PHYSICAL SCIENCES
What does Einstein’s famous equation Emc^2 signify?
A
mong his other accomplishments, Albert Einstein showed mathematically
that there was a connection between mass and energy: energy has mass, and
mass represents energy. This equation, also called the energy-mass relation, is
expressed as Emc^2 , in which Eis energy, mis mass, and cis the speed of
light. Because cis a very large number, even a very small amount of mass repre-
sents an enormous amount of energy.