Pressure, Potentials, And
Field Theories in Physics
You are already familiar with the physics of forces, and you understand that an object can only be
accelerated if a force acts on it.
We have however avoided the fundamental questions of exactly
how one object places a force upon an other object.
You may respond, "How silly,
a force is
placed upon an object when another object pushes or pulls it."
But there are forces for which the
bodies do not need to be in contact, for example, gravity where it is possible for one planet to
attract another even though the two are separated by a very large distance.
This "action at a
distance" has stymied many of the great minds, and the full understanding of this problem has
come only within the last forty years.
Unlike other theories, it is not the work of an isolated
genius, but is the culmination of centuries of work by many people.
The question we will answer is how can one object place a force upon another without any
apparent contact between the two whatsoever?
Something must go between the two objects to
carry the force, and we'll call it the field.
We will direct our attention from the forces to the fields
Note that this raises the level of abstraction considerably, but you should not forget
that the reason for obtaining the field is to find the force.
Always ask your self, "Now that I have
found this field,
what force would this field place upon my system."
This course is the study of
classical field theories.
What properties must the fields have, and how do we describe these field?
It turns out, as you will see, that classical field theories do not fundamentally answer the question
posed because one cannot touch or feel a classical electric field.
More importantly, the
electromagnetic fields are not conserved at all!
They can be created and destroyed.
Well, if they
cannot be seen or felt and they are not conserved, do they exist?
Might they be nothing more than
a mathematical trick?
There is no way yet devised to tell whether the classical electromagnetic fields in fact do exist, but
in any case, the question is not relevant because a modern theory with the unwieldy name of
Quantum Electrodynamics (referred to as QED) has combined field theory, relativity, and quantum
mechanics into a powerful theory that agrees with experiment to 14 decimal places!
In QED the
electric and magnetic field are combined to form discreet packets or quanta called photons.
photons sometimes behave as particles and they can be seen and counted by machines.
under special circumstances,
it is possible for the human eye to "see" one photon.
In relativity mass and energy are equivalent, and it is possible, therefore, to create mass from
photons, and conversely, to annihilate matter and antimatter to produce photons.
This is done
Classical Fluids, Chapter 1
quite easily in modern particle accelerators.
Relativity gives us a general conservation law called