Historical research guide · 0314 · 1999
Polarizable-Vacuum (PV) representation of general relativity
H. E. Puthoff
In one minute
Hal Puthoff presents a way to express general relativity without curved-space tensors. Building on Wilson and Dicke, the polarizable-vacuum picture treats empty space as a dielectric medium: a position-dependent dielectric constant K carries the gravitational effects. Near a mass K grows; in his formalism light’s underlying speed is c divided by K, clocks run slower, length scales shrink and effective mass rises. Puthoff writes the interval in terms of K and recovers the standard isotropic metric. With an exponential K derived from a Lagrangian, he calculates gravitational redshift, starlight bending and Mercury’s perihelion advance at standard values, then extends the calculation to charged masses. He calls it a metric-engineering approach, while limiting this paper to spherical cases rather than gravitational radiation or frame-dragging.
Connection
Chapter 4 treats the metric as something you build rather than something you inherit, and this paper hands over the handle: change the permittivity and permeability of the vacuum and you have changed the metric locally, because the speed of light is a property of the medium and not of light. That is the same knob chapters 2 and 3 turn when they treat the zero-point field as the substrate that matter, inertia and gravity come out of.
From the source
General relativity can be represented without curved-space tensors by treating the vacuum as a polarizable medium whose dielectric constant K varies with position, so that a single scalar function carries every gravitational effect the paper considers.Section 2, Equation 3; Section 6, Discussion
Observational limits require the fine-structure constant to stay fixed, and that constraint forces the permittivity and permeability of the vacuum to change together — each scaling as K — so the impedance of free space is preserved, the weak equivalence principle survives, and the underlying velocity of light becomes c divided by K.Section 2A, Equations 4 to 7
Where the vacuum is more polarizable, self-energy falls as one over the square root of K, effective mass rises as K to the power three halves, emitted frequencies redshift, clock intervals lengthen as the square root of K, and every fundamental length measure — the Bohr radius, the classical electron radius, the Compton wavelength — shrinks as one over the square root of K; there is therefore no such thing as a perfectly rigid rod.Sections 2B and 2C, Equations 8 to 13; summary Table
Because the measuring rods and the clocks are distorted by the same K as the light they measure, the locally measured speed of light renormalises from its underlying value of c divided by K back to exactly c, so the polarizable-vacuum formalism preserves the universal constancy of the locally measured light speed.Section 2C, Equations 14 and 15
Written in terms of K the infinitesimal interval takes the standard metric-tensor form of an isotropic coordinate system, and with the exponential solution for K derived from a Lagrangian in which the dielectric constant is a variable function of space and time, the three classical tests of general relativity — redshift, light bending and the perihelion advance — come out at the accepted values, with the charged-mass case reproducing the Reissner-Nordstrom result.Section 2D, Equations 17 to 19; Section 3; Sections 4A and 5, Equations 47 to 64
Puthoff hands the method on as unfinished business: the treatment is confined to spherically symmetric cases, gravitational radiation and frame-dragging are not addressed, and he asks that every extension be cross-referenced against conventional general-relativistic results to confirm that the polarizable-vacuum route introduces no spurious ones.Section 6, Discussion
The way in
https://arxiv.org/abs/gr-qc/9909037How to cite it
H. E. Puthoff (1999) Polarizable-Vacuum (PV) representation of general relativity arXiv:gr-qc/9909037