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:
“The very presence of guilt, let alone its tenacity, implies imbalance: Something, we suspect, is getting more of our energy than warrants, at the expense of something else, we suspect, that deserves more of our energy than we’re giving.”
—Melinda M. Marshall (20th century)
“The Settlement ... is an experimental effort to aid in the solution of the social and industrial problems which are engendered by the modern conditions of life in a great city. It insists that these problems are not confined to any one portion of the city. It is an attempt to relieve, at the same time, the overaccumulation at one end of society and the destitution at the other ...”
—Jane Addams (1860–1935)
“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)
“Mothers seem to be in subtle competition with teachers. There is always an underlying fear that teachers will do a better job than they have done with their child.... But mostly mothers feel that their areas of competence are very much similar to those of the teacher. In fact they feel they know their child better than anyone else and that the teacher doesn’t possess any special field of authority or expertise.”
—Sara Lawrence Lightfoot (20th century)
“... the first reason for psychology’s failure to understand what people are and how they act, is that clinicians and psychiatrists, who are generally the theoreticians on these matters, have essentially made up myths without any evidence to support them; the second reason for psychology’s failure is that personality theory has looked for inner traits when it should have been looking for social context.”
—Naomi Weisstein (b. 1939)