What is mathematical physics?
Mathematical physics uses the concepts of statistical mechanics and quantum field
theory. But it is not the same as theoretical physics. Mathematical physics studies
physics on a more abstract and meticulous level. Theoretical physics entails less math-
ematics than mathematical physics and has more to do with experimental physics. But
like many fields of science, defining mathematical physics is not easy. For example,
still another definition of modern mathematical physics states that it entails all areas
of mathematics other than classical mathematical physics.CLASSICAL PHYSICS AND MATHEMATICS
How is mathematicsused in physics to describe motion?
Everything in the universe is in motion, from the rotating Earth to subatomic parti-
cles. Motion in physics is described mainly through mathematics, including speed,
velocity, acceleration, momentum, force (something that changes the state of rest or
motion of an object), torque (when a force causes rotation or twisting around a pivot
point), and inertia (a body at rest remains at rest, and a body in motion remains in
motion, until acted upon by an outside force).
Unlike what most people think, speed and velocity are not the same. Speed is the
rate at which something moves; velocity is speed in a certain direction. Speed is also
called a scalar quantity, described by the following formula: speed distance/time.
For example, if you drive 200 miles in 2 hours, and your speed is constant, your aver-
age speed is 200/2, or 100 miles per hour. On the other hand, velocity is known as a
vector quantity (for more about vectors, see “Mathematical Analysis”). That gives
velocity both speed and direction—and that leads directly to acceleration.
When an object’s velocity changes, we say that it accelerates. Acceleration—also a
vector like velocity—is represented as the change in velocity divided by the time it
276 takes for the change to occur. We define the formula for acceleration—or the change in
What are some physics fields that rely heavily on mathematics?
A
lmost every field of physics—especially modern physics—relies heavily on
mathematics. For example, mathematics is needed to understand the con-
cepts of acceleration, velocity, and gravitational forces. Statistical mechanics
also uses an intense amount of mathematics. And it is impossible to comprehend
quantum mechanics without a good knowledge of mathematics. In fact, the sub-
ject of quantum field theory is one of the most mathematically rigorous and
abstract areas of the physical sciences.