Gravitation by Charles W Misner; Kip S Thorne; John Archibald Wheeler

By Charles W Misner; Kip S Thorne; John Archibald Wheeler

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16) we see now that M X.. 20) -2-X C such that this term and, furthermore, the higher-order radiation corrections can be neglected. W. 3) taking radiative back-reaction into account. In a letter to Heisenberg, Pauli (1933) wrote that, in discussions with Peierls, he had formulated the following objection to this procedure. A charged test body can be brought into a very large opaque box. The repulsion of the box as well as the energy absorbed by the walls of the box can be measured arbitrarily exactly.

In particular, one cannot perform field measurements by an electron showing radiative back reaction, as was done by Landau and Peierls. Measurement in Quantum Gravity 29 For a measurement arrangement one has to realize classical bodies with an arbitrarily high accuracy. The main argument for this standpoint is given by the statement that a consideration of the atomic structure of the measurement body is not adequate to a measurement of pure fields because it transfers the discussion to the level of the amalgamation of quantumelectrodynamics and atomic matter theory.

Before continuing the measurement discussion, we shall consider here one aspect of this problem by discussing gauge invariance and its breaking in the covariant quantization approach (see BIeyer and Borzeszkowski, 1984). The covariant quantization of the gravitational field uses the functional integral formulation of quantum field theory (DeWitt, 1964; Faddeev and Popov, 1973). 24) where g#v denotes the Riemannian metric of the spacetime manifold. The Lagrangian density is given by the Ricci scalar Lgrav = R.

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