Is a tensor a scalar?
Is a tensor a scalar?
In fact tensors are merely a generalisation of scalars and vectors; a scalar is a zero rank tensor, and a vector is a first rank tensor. The rank (or order) of a tensor is defined by the number of directions (and hence the dimensionality of the array) required to describe it.
Who explained the scalar theory?
In 1979, R. Wagoner proposed a generalization of scalar–tensor theories using more than one scalar field coupled to the scalar curvature. JBD theories although not changing the geodesic equation for test particles, change the motion of composite bodies to a more complex one.
Is gravity a scalar field?
Newtonian gravitation is a scalar theory in which the gravitational interaction is described by a gravitational scalar field or potential \varPhi , that satisfies a Poisson equation. It is complemented by Newton’s second law of mechanics for the trajectories of particles moving in the gravitational potential \varPhi .
What is a scalar theory?
In theoretical physics, scalar field theory can refer to a relativistically invariant classical or quantum theory of scalar fields. A scalar field is invariant under any Lorentz transformation. The only fundamental scalar quantum field that has been observed in nature is the Higgs field.
Are all scalars tensors?
However, all scalars are not tensors and all tensors of rank 0 are scalars. The same applies to vectors, dyads or triads. A vector dyad product results in a dyad which would make it possible to alter the direction of a vector and also an increase from rank1 to rank2 tensor.
Why is gravity scalar?
Physical Science 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.
What is tensor quantity?
A tensor is a quantity, for example a stress or a strain, which has magnitude, direction, and a plane in which it acts. Stress and strain are both tensor quantities. In real engineering components, stress and strain are 3-D tensors.
Is energy a scalar field?
In physics, scalar fields often describe the potential energy associated with a particular force. The force is a vector field, which can be obtained as a factor of the gradient of the potential energy scalar field.
Who invented tensors?
0. Born on 12 January 1853 in Lugo in what is now Italy, Gregorio Ricci-Curbastro was a mathematician best known as the inventor of tensor calculus.
What is a scalar tensor theory in physics?
In theoretical physics, a scalar–tensor theory is a field 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 .
What is an example of a tensor field?
An example of a tensor field is the stress tensor field in a stressed body, used in continuum mechanics . In physics, forces (as vectorial quantities) are given as the derivative (gradient) of scalar quantities named potentials.
Is gravity a scalar-tensor theory?
Hence, string theory predicts that the actual theory of gravity is a scalar–tensor theory rather than general relativity. However, the precise form of such a theory is not currently known because one does not have the mathematical tools in order to address the corresponding non-perturbative calculations.
Can a universal scalar field be directly coupled to a gravitational field?
The coupling of a universal scalar field directly to the gravitational field gives rise to potentially observable effects for the motion of matter configurations to which gravitational energy contributes significantly.