Einstein's Field Equation? What did he mean by Field?

Question

Chassical physics indicates a field to be the ratio of Force to Mass,and that they call it a Gravity Field. Are there any differences in defining a Field?

Is the Gravitational constand G really constant or is it a function of a Universal time multiplied by C^3 divide by mass of Universe?Is that what auniversal field is about?

Answer 1

Einstein's Field Theory predicts that space and time may be warped by objects with large masses.

Answer 2

In physics, the word "field" just means that you assign a mathematical entity to each point in space.

The mathematical entity can be a number, a vector, a tensor, or perhaps even an entire geometric space.

In Newtonian gravity, the gravitational field is a number (a scalar) that gives the gravitational potential.

In classical electromagnetism, the electric field is a vector, that points in a direction and has a size.

In Einsteinian gravity, the gravitational field is a tensor, which is a sort of matrix that must transform in a particular way with geometric changes.

Almost all modern physical theories, including quantum mechanics and string theory, are field theories. This is often a problem, because there are an infinity of mathematical entities in each small volume of space and this can lead to mathematical difficulties with infinite quantities.

Answer 3

This destroys the beauty of the field equations, which attribute the source of curvature entirely to matter as represented by the stress-energy tensor. And in fact the constant is not even necessary, because it is perfectly possible to include an equivalent term as part of the stress-energy tensor, representing the vacuum value of some quantum field; this is the basis of inflationary cosmology....

Answer 4

Tensors are a device of differential geometry. Crudely, tensors, as utilized regularly realtivity, are gadgets of values which outline coordinate adjustments at the same time as the gap is curved (has curved axes.somewhat than straightforward immediately line x,y,x axes). They enable you to calculate the elements of a vector in a curved coordinate gadget, given the coordinates in yet another curved coordinate gadget. once you've time and some maths heritage (somewhat calculus), I somewhat propose the Stanford lectures through Leonard Susskind. the maths (inclusive of tensors) is advanced in the course of the lectures. The third one contained in the sequence introduces tensors, so try gazing it - hyperlink lower than.