Energy Conditions in Classical Field Theory
Einstein's theory of General Relativity amounts to a description of the relationship between the curvature of space-time, on the one hand, and the distribution of matter throughout space-time on the other. This precise details of this relationship are determined by the Einstein equations
.
Here, the Einstein tensor describes the curvature of space-time, whilst the energy-momentum tensor describes the local distribution of matter. ( is a constant.) The Einstein equations express local relationships between the quantities involved—specifically, this is a system of coupled non-linear second order partial differential equations.
A very simple observation can be made at this point: the zero-point of energy-momentum is not arbitrary. Adding a "constant" to the right-hand side of the Einstein equations will effect a change in the Einstein tensor, and thus also in the curvature properties of space-time.
All known classical matter fields obey certain "energy conditions". The most famous classical energy condition is the "weak energy condition"; this asserts that the local energy density, as measured by an observer moving along a time-like world line, is non-negative. The weak energy condition is essential for many of the most important and powerful results of classical relativity theory—in particular, the singularity theorems of Hawking et al.
Read more about this topic: Quantum Inequalities
Famous quotes containing the words energy, conditions, classical, field and/or theory:
“Long before Einstein told us that matter is energy, Machiavelli and Hobbes and other modern political philosophers defined man as a lump of matter whose most politically relevant attribute is a form of energy called “self-interestedness.” This was not a portrait of man “warts and all.” It was all wart.”
—George F. Will (b. 1941)
“My dear young friend ... civilization has absolutely no need of nobility or heroism. These things are symptoms of political inefficiency. In a properly organized society like ours, nobody has any opportunities for being noble or heroic. Conditions have got to be thoroughly unstable before the occasion can arise.”
—Aldous Huxley (1894–1963)
“The basic difference between classical music and jazz is that in the former the music is always greater than its performance—Beethoven’s Violin Concerto, for instance, is always greater than its performance—whereas the way jazz is performed is always more important than what is being performed.”
—André Previn (b. 1929)
“A field of water betrays the spirit that is in the air. It is continually receiving new life and motion from above. It is intermediate in its nature between land and sky.”
—Henry David Thoreau (1817–1862)
“No theory is good unless it permits, not rest, but the greatest work. No theory is good except on condition that one use it to go on beyond.”
—André Gide (1869–1951)