Physics
Scientific paper
Jan 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994phdt........17r&link_type=abstract
Thesis (PH.D.)--STANFORD UNIVERSITY, 1994.Source: Dissertation Abstracts International, Volume: 55-10, Section: B, page: 4417.
Physics
Schiff'S Conjecture, Gravity
Scientific paper
A conjecture, due originally to Schiff and amplified by Thorne, Lee, and Lightmann, states that the universality of free fall of test bodies is only possible if the underlying field theory of matter is universally coupled, that is, if gravity influences matter only by modifying the metric and connection that enter the matter field Lagrangian. To check this conjecture I have investigated the constraints on the matter field Lagrangian imposed by IFP2, the requirement that test bodies not only follow universal world lines, but that these world lines are geodesics of a metric. The (classical) motion of stable bound states of a quantum field theory of matter coupled to a classical background metric and, weakly, to an arbitrary collection of classical non-metric "gravitational fields" was found. IFP2 holds for these bound states (= test bodies) if and only if the currents that couple to the non-metric gravitational fields integrate to zero over the bound states. An attempt was made to find all solutions to this requirement, i.e., all couplings to non-metric gravity allowed by IFP2. The condition is too difficult to solve in its original quantum form. Therefore, classical field theory was considered instead, with bound solutions which are static in their rest frames playing the role of test bodies. In a 1 + 1 dimensional toy model all couplings allowed by IFP2 were found. In 3 + 1 dimensions many specific types of allowed couplings to non-metric gravity were found, showing that IFP2 does not imply universal coupling and a fortiori that Schiff's conjecture is not strictly correct. However, the counter-examples seem unreasonable as physical theories. A possibly realistic coupling to an antisymmetric tensor gravitational field was found, but it may be trivial as a counter-example to Schiff's conjecture. Byproducts of this work are (1) a mathematically precise definition of the "test body limit", (2) several clearly defined versions of the "Equivalence Principle", of different strengths, and (3) an efficient method for calculating the motion of test bodies from a Lagrangian field theory of matter in a nearly metric gravitational field is derived.
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