General Covariance

Definition

General covariance is a fundamental principle in Einstein's theory of gravity, known as general relativity. It states that the laws of physics must take the same form in all coordinate systems, regardless of their state of motion or orientation. This principle is a cornerstone of general relativity, as it allows for the description of gravity as a consequence of the curvature of spacetime.

5 Must Know Facts For Your Next Test

1. General covariance allows for the description of gravity as a consequence of the curvature of spacetime, rather than a force acting between objects.
2. The principle of general covariance is a generalization of the principle of special relativity, which states that the laws of physics are the same in all inertial (non-accelerating) reference frames.
3. General covariance is achieved by formulating the laws of physics using tensors, which are mathematical objects that transform in a specific way under changes of coordinate systems.
4. The field equations of general relativity, which describe the relationship between the curvature of spacetime and the distribution of matter and energy, are generally covariant.
5. General covariance is a key aspect of the Einstein equivalence principle, which states that the laws of physics are the same for all freely falling observers, regardless of their motion or the gravitational field they are in.

Review Questions

• Explain how the principle of general covariance is a generalization of the principle of special relativity.
  • The principle of special relativity states that the laws of physics are the same in all inertial (non-accelerating) reference frames. The principle of general covariance generalizes this idea by stating that the laws of physics must take the same form in all coordinate systems, regardless of their state of motion or orientation. This allows for the description of gravity as a consequence of the curvature of spacetime, rather than a force acting between objects. The principle of general covariance is a key aspect of Einstein's theory of general relativity, which provides a unified description of gravity as a geometric property of spacetime.
• Describe the role of tensor calculus in achieving general covariance in general relativity.
  • Tensor calculus is a mathematical framework used in general relativity to describe physical quantities and their transformations under changes of coordinate systems. Tensors are mathematical objects that transform in a specific way under changes of coordinate systems, allowing for the formulation of the laws of physics in a generally covariant manner. By expressing the laws of physics using tensors, the principle of general covariance is achieved, ensuring that the laws of physics take the same form in all coordinate systems. This is a crucial aspect of Einstein's theory of general relativity, as it enables the description of gravity as a consequence of the curvature of spacetime.
• Explain how the principle of general covariance is related to the Einstein equivalence principle and the description of gravity in general relativity.
  • The principle of general covariance is closely linked to the Einstein equivalence principle, which states that the laws of physics are the same for all freely falling observers, regardless of their motion or the gravitational field they are in. This principle, combined with the principle of general covariance, allows for the description of gravity as a consequence of the curvature of spacetime, rather than a force acting between objects. By formulating the laws of physics using generally covariant tensors, general relativity provides a unified description of gravity as a geometric property of spacetime, where the presence of mass and energy distorts the fabric of spacetime, leading to the observed gravitational effects. This shift in the conceptual understanding of gravity is a fundamental aspect of Einstein's theory of general relativity.

Related terms

Coordinate Invariance: The idea that the laws of physics should be independent of the choice of coordinate system used to describe them.

Spacetime Curvature: The distortion of the fabric of spacetime caused by the presence of mass and energy, which is the basis for the gravitational force in general relativity.

Tensor Calculus: A mathematical framework used in general relativity to describe physical quantities and their transformations under changes of coordinate systems.