Polarizable vacuum

In essence, Dicke and Puthoff proposed that the presence of mass alters the electric permittivity and the magnetic permeability of flat spacetime, ε_o and μ_o respectively by multiplying them by a scalar function, K:

${\displaystyle \varepsilon _{0}\to \varepsilon =K\varepsilon _{0}\;;\;\mu _{0}\to \mu =K\mu _{0}}$

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

${\displaystyle ds^{2}=-{\frac {1}{\kappa ^{2}}}dt^{2}+\kappa ^{2}\,(dx^{2}+dy^{2}+dz^{2})}$

where ${\displaystyle \kappa ^{2}=K}$ 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

${\displaystyle \kappa =\exp(m/r)=1+m/r+O\left({\frac {1}{r^{2}}}\right)}$

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.

Puthoff himself has apparently offered various characterizations of his proposal, which has been variously characterized as

• an attempt to reformulate general relativity in terms of a purely formal analogy with the propagation of light through an optical medium,
• an attempt to replace general relativity with a scalar theory of gravitation featuring formal analogies with Maxwell's theory of electromagnetism,
• an attempt to unify gravitation and electromagnetism in a theory of electrogravity,
• an attempt to provide a physical mechanism for how spacetime gets curved in general relativity, which suggests (to Puthoff) the possibility of "metric engineering" for such purposes as spacecraft propulsion (see Breakthrough Propulsion Physics Program).

PV has origins in more mainstream work by such physicists as Robert Dicke, but in current parlance the term does appear to be most closely associated with the speculations of Puthoff. The claims have not been accepted in mainstream physics.

Mainstream physicists agree that PV is

1. not viable as a unification of gravitation and electromagnetism
2. not a "reformulation" of general relativity,
3. not a viable theory of gravitation, since it violates observational and theoretical requirements.

Antecedents of PV and more recent related proposals include the following:

1. A proposal in 1921 by H. A. Wilson to reduce gravitation to electromagnetism by pursuing the formal analogy between "light bending" in metric theories of gravitation and propagation of light through an optical medium having a spatially varying refractive index. Wilson's approach to a unified field theory is not considered viable today.
2. An attempt (roughly 1960-1970) by Robert Dicke and Fernando de Felice to resurrect and improve Wilson's idea of an optical analogue of gravitational effects. If interpreted conservatively as an attempt to provide an alternative approach to GTR, rather than as work toward a theory unifying electromagnetism and gravitation, this is not an unreasonable approach, although most likely of rather limited utility.
3. The 1967 proposal of Andrei Sakharov that gravitation might arise from underlying quantum field theory effects, in a manner somewhat analogous to the way that the (simple) classical theory of elasticity arises from (complicated) particle physics. This work is generally regarded as mainstream and not entirely implausible, but highly speculative, and most physicists seem to feel that little progress has been made.
4. In a series of papers, Bernard Haisch and Alfonso Rueda have proposed that the inertia of massive objects arises as a "electromagnetic reaction force", due to interaction with the so-called zero point field. According to mainstream physics, their claims rest upon incorrect computations using quantum field theory.
5. Recent work, motivated in large part by the discoveries of the Unruh effect, Hawking radiation, and black hole thermodynamics, to work out a complete theory of physical analogues such as optical black holes. This is not work toward a unified field theory, but in another sense can be regarded as work towards an even more ambitious unification, in which some of the most famous effects usually ascribed to general relativity (but actually common to many metric theories of gravitation) would be seen as essentially thermodynamical effects, not specifically gravitational effects. This work has excited great interest because it might enable experimental verification of the basic concept of Hawking radiation, which is widely regarded as one of the most revolutionary proposals in twentieth century physics, but which in its gravitational incarnation seems to be impossible to verify in experiments in earthly laboratories.
6. The 1999 proposal by Keith Watt and Charles W. Misner of a scalar theory of gravitation which postulates a stratified conformally flat metric of the form ${\displaystyle ds^{2}=-\exp(2\,\phi )+\exp(-2\phi )(dx^{2}+dy^{2}+dz^{2}}$, given with respect to a Cartesian chart, where φ satisfies a certain partial differential equation which reduces in a vacuum region to the flat spacetime wave equation ${\displaystyle \Box \phi =0}$. This is a "toy theory", not a fully fledged theory of gravitation, since as Watt and Misner pointed out, while this theory does have the correct Newtonian limit, it disagrees with the result of certain observations.

• Induced gravity (for Sakharov's proposal)
• Maxwell's equations in curved spacetime
• Electromagnetic stress-energy tensor

• Visser, Matt (2005). "Analog Gravity". Living Reviews in Relativity. Archived from the original on 2005-12-31. Retrieved 2006-06-02.
• Ibison, M. (2003). "Investigation of the polarizable vacuum cosmology". arXiv:astro-ph/0302273.
• Watt, Keith & Misner, Charles (10 Oct 1999). "Relativistic Scalar Gravity: A Laboratory for Numerical Relativity". arXiv:gr-qc/9910032.
• Puthoff, H. E. (2002). "Polarizable-Vacuum (PV) representation of general relativity". Foundations of Physics. 32 (6): 927–943. doi:10.1023/A:1016011413407. S2CID 118146080. arXiv eprint
• de Felice, F. (1971). "On the gravitational field acting as an optical medium". General Relativity and Gravitation. 2 (4): 347–. Bibcode:1971GReGr...2..347D. doi:10.1007/BF00758153. S2CID 115547188.
• Dicke, R. H. (1957). "Gravitation without a principle of equivalence". Reviews of Modern Physics. 29 (3): 363–376. Bibcode:1957RvMP...29..363D. doi:10.1103/RevModPhys.29.363.
• Wilson, H. A. (1921). "An electromagnetic theory of gravitation". Physical Review. 17 (1): 54–59. Bibcode:1921PhRv...17...54W. doi:10.1103/PhysRev.17.54.