Scalar-tensor theory

In theoretical physics, a scalar–tensor theory is a theory that includes both a scalar field and a tensor field to represent a certain interaction. For example, the Brans–Dicke theory of gravitation uses both a scalar field and a tensor field to mediate the gravitational interaction.

Modern physics tries to derive all physical theories from as few principles as possible. In this way, Newtonian mechanics as well as quantum mechanics are derived from Hamilton's principle of least action. In this approach, the behavior of a system is not described via forces, but by functions which describe the energy of the system. Most important are the energetic quantities known as the Hamilton function and the Lagrangian function. Their derivatives in space are known as Hamilton density and Lagrange density. Going to these quantities leads to the field theories.

Modern physics uses field theories to explain reality. These fields can be scalar, vectorial or tensorial. For them:

Scalars are numbers, quantities of the form f(x), like the temperature. Vectors are more general and show a direction. Tensors (degree 2) are a wider generalization, the best known example of which are matrices (that can give equation systems). Higher order tensors are found for example in the deformation theory and in General Relativity.

In physics, forces (as vectorial quantities) are given as the derivative (gradient) of scalar quantities named potentials. In classical physics before Einstein, gravitation was given in the same way, as consequence of a gravitational force (vectorial), given through a scalar potential field, dependent of the mass of the particles. Thus, Newtonian gravity is called a scalar theory. The gravitational force is dependent of the distance r of the massive objects to each other (more exactly, their centre of mass). Mass is a parameter and space and time are unchangeable.

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