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In essence, Dicke and Puthoff proposed that the presence of mass alters the electric permittivity and the magnetic permeability of flat spacetime, εo and μo respectively by multiplying them by a scalar function, K:
εo→ε = Kεo, μo→μ = Kμo
arguing that this will affect the lengths of rulers made of ordinary matter, so that in the presence of a gravitational field the spacetime metric of Minkowski spacetime is replaced by
where is the so-called "dielectric constant of the vacuum". This is a "diagonal" metric given in terms of a Cartesian chart and having the same stratified conformally flat form in the Watt-Misner theory of gravitation. However, according to Dicke and Puthoff, κ must satisfy a field equation which differs from the field equation of the Watt-Misner theory. In the case of a static spherically symmetric vacuum, this yields the asymptotically flat solution
The resulting Lorentzian spacetime happens to agree with the analogous solution in the Watt-Misner theory, and it has the same weak-field limit, and the same far-field, as the Schwarzschild vacuum solution in general relativity, and it satisfies three of the four classical tests of relativistic gravitation (redshift, deflection of light, precession of the perihelion of Mercury) to within the limit of observational accuracy. However, as shown by Ibison (2003), it yields a different prediction for the inspiral of test particles due to gravitational radiation.
However, requiring stratified-conformally flat metrics rules out the possibility of recovering the weak-field Kerr metric, and is certainly inconsistent with the claim that PV can give a general "approximation" of the general theory of relativity. In particular, this theory exhibits no frame-dragging effects. Also, the effect of gravitational radiation on test particles differs profoundly between scalar theories and tensor theories of gravitation such as general relativity. LIGO is not intended primarily as a test ruling out scalar theories, but is widely expected to do so as a side benefit once it detects unambiguous gravitational wave signals exhibiting the characteristics expected in general relativity.
Ibison has considered a "cosmological solution" of PV, analogous to the Friedmann dust solution with flat orthogonal hyperslices in general relativity, and argues that this model is inconsistent with various observational and theoretical constraints. He also finds a rate of inspiral disagreeing with observation. The latter result disagrees with that of Watt and Misner, whose Lorentzian manifold differs from PV in the case of cosmology.
It is widely accepted that no scalar theory of gravitation can reproduce all of general relativity's successes, contrary to Puthoff's claims. It might be noted that De Felice uses constitutive relations to obtain a susceptibility tensor which lives in spatial hyperslices; this provides extra degrees of freedom which help make up for the degree of freedom lacking in PV and other scalar theories.
Read more about this topic: Polarizable Vacuum
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