Bibipandi said:As I know, Einstein initially tried describe the gravitational interaction as mediated by a scalar field, but he later gave up this idea because it is incompatible with the Principle of Equivalence.I don't know how this idea is incompatible with the Principle of Equivalence. Please help me. Thanks
Yes, but as this article by Brans shows: the natural approach for people who know SR is ofcourse to describe gravity by a Lorentz scalar, and it is this approach which violates the equivalence principle.JustinLevy said:There was classical field theory way before there was quantum field theory. They don't mean "scalar" as in spin-0.
Newton's theory had a scalar gravitational potential. Many tried to make this relativistic, and quickly ran into problems with theory not matching experiment or behaving "reasonably" (orbits weren't stable, and other problems). Nordstom came very "close". Einstein most likely played with these himself to understand what was going on. Ultimately it was a tensor theory that worked.
Sure, they didn't look at it as a "spin-2 field" while working towards the finished goal, but it clearly was a tensor theory and not a scalar theory that was being fleshed out in the end.
Yes, there were problems regarding the most straight forward descriptions with a scalar (ie, just swapping the derivatives in Newton's theory with the d'Alembertian operator).haushofer said:Yes, but as this article by Brans shows: the natural approach for people who know SR is ofcourse to describe gravity by a Lorentz scalar, and it is this approach which violates the equivalence principle.
Not quite.Bibipandi said:Thanks for your suggestion. As I understand, the principle of equivalence states that: in small enough regions of spacetime, the laws of physics reduce to those of special relativity; it is impossible to detect the existence of a gravitational field by means of local experiments. The scalar field describes only the gravitational potential (as stated in Newton's theory of gravitation), not the electromagnetic field (described by tensor field), so the scalar field doesn't satisfy the equivalence principle which requires all kinds of experiment (involving electromagnetic experiments). Am I right?
Scalar fields are mathematical functions that assign a single value to each point in space. They are often used in physics to describe quantities such as temperature or pressure. However, not all physical properties can be described by a scalar field. Some properties, such as direction or orientation, require vector fields for their description.
The main difference between scalar and vector fields is that scalar fields only have magnitude, while vector fields have both magnitude and direction. Scalar fields can be thought of as a single number at each point in space, while vector fields can be thought of as arrows pointing in a specific direction at each point in space.
No, a scalar field cannot be converted into a vector field. Scalar fields and vector fields are fundamentally different types of mathematical objects and cannot be converted into one another. However, certain physical properties can be described by both a scalar field and a vector field, depending on the context.
Vector fields are more complex than scalar fields because they require both magnitude and direction to be fully described. This adds an extra layer of complexity to the mathematical equations used to represent vector fields. Additionally, vector fields have more degrees of freedom and can exhibit more complex behaviors compared to scalar fields.
Examples of physical properties that cannot be described by a scalar field include velocity, electric and magnetic fields, and fluid flow. These properties have both magnitude and direction, which require vector fields for their description. Another example is the orientation of an object, which requires a rotation matrix (a type of vector field) for its description.