Soviet Physics: Landau & Lifshitz on General Relativity
On Dec 26, 2004, at 7:19 PM, Jack Sarfatti wrote:
Look at sections 84 & 97 in Landau & Lifshitz Classical Theory of Fields.
BTW Landau & Lifshitz from the Soviet Era, in spite of Lysenko, is still probably the best course, even today in 2004, in "classical" theoretical physics including the earlier versions of quantum field theory. Better than Weinberg because it is closer to observation and even in the English translations the explanations are generally very clear. Better than MTW in some respects.
Also in 82:
"in the general theory of relativity it is impossible in general to have a system of bodies which are fixed relative to one another. This result essentially changes the very concept of a system of reference in the general theory of relativity, as compared to its meaning in the special theory. In the latter we meant by a reference system a set of bodies at rest relative to one another in unchanging relative positions. Such systems of bodies do not exist in the presence of a variable gravitational field, and for the exact determination of the position of a particle in space we must, strictly speaking, have an infinite number of bodies which fill all space like some sort of 'medium'. Such a system of bodies with arbitrarily running clocks fixed on them constitutes a reference system in the general theory of relativity."
Paul you cannot improve on Landau & Lifshitz, they have covered all the real ground on the classical foundations.
"In connection with the arbitrariness of the choice of reference system, the laws of nature must be written in the general theory of relativity in a form which is appropriate to any four dimensional system of coordinates (or, as one says, in 'covariant' form). This, of course, does not imply the physical equivalence of all these reference systems (like the physical equivalence of all inertial reference systems in the special theory)."
Now Hal Puthoff's PV is not generally covariant in this sense as Hal's coworker at IAS Austin, Michael Ibison, has written explicitly. This is basically why Hal's theory is almost universally rejected by all the Top Guns in spacetime physics down to almost the last man standing. Hal is basically using the fixed background of special relativity in his action principle with the variable "dielectric" whose controlled variation is much too small for the practical metric engineering of Warp, Wormhole and Weapon (from C^3 to W^3) anyway. That is not how to Make Star Trek real. PV is not the "Right Stuff" to reach for the stars and beyond.
Note BTW that Landau & Lifshitz explicitly say that non-Cartesian CS are only for "noninertial reference frames" on p. 228 "Thus, in a noninertial system of reference, the square of the interval appears as a quadratic form of a general type in the coordinate differentials, that is, it has the form
ds^2 = gikdx^idx^k
... Thus, when we use a noninertial system, the four-dimensional coordinate system ... is curvilinear."
Now there is no way to make such a non-inertial system of reference as an approximation to "an infinite number of bodies which fill all space like some sort of 'medium'. Such a system of bodies with arbitrarily running clocks fixed on them constitutes a reference system in the general theory of relativity" without non-gravity forces. That is, in a purely gravitational universe noninertial systems of reference do not exist! Actually gravity is not a fundamental field at all. It cannot exist without the electromagnetic field to give it its light cones. Indeed it also needs quantum theory to emerge as a macro-quantum coherence effect.