Theoretical Principles

Einstein spent the end of his career in a fruitless pursuit of a mathematical formulation that would unify the theories of electromagnetism and gravitation. His search was motivated by a simple proposition: the known interactions appear to occur simultaneously, and therefore there should be a mathematical description that allows us to calculate all of the effects at once. The challenge comes in developing a theory that conforms to mathematical transformations that correspond to assumed equivalences between physical systems (known as invariances in the jargon).

For example, in developing General Relavitity, Einstein observed that a man standing in a constantly accelerating elevator cannot prove that he is not standing on a planet. Since a light beam piercing the side of the elevator would appear to curve minutely as it traversed the elevator, this must mean that the beam would also follow a curved path in a gravitational field.

Remarkable mathematical consequences were evolved by Einstein from such simple postulates. That those consequences were validate by physical measurement is a testament to the importance of such postulates in guiding theoretical developments.

The mathematical constrains evolved from physical invariances are essential guides to the development of new theories. They constrain the imagination, guiding theorists away from magical thinking.

Among the most important of the guiding principles of modern particle theory are the following:

There are certain mathematical constraints that were adopted in achieving a successful unification. These include:

Neither of these last two assertions is directly falsifiable.