D F Bartlett 2004 Metrologia 41 S115 doi:10.1088/0026-1394/41/5/S02
Analogies between electricity and gravity
D F Bartlett
Show affiliationsThis is a brief history of physical analogies that begins at the time of Coulomb. Then it was universally believed that gravity, electricity and magnetism all obeyed Newton's inverse square law. The current era—dominated by quantum mechanics, general relativity, strings and inflationary cosmology—is clearly more complex. A new analogy may be helpful. Evidence is given that, in the non-relativistic limit, electricity is described by a Proca potential 
e satisfying the equation ∇2e − k02e = −ρe/
0 and gravity by a Helmholtz potential m satisfying ∇2m + k02m = 4πGρm. In both equations k0 is a proposed universal constant, whose value is about 2 π(20/R0), where R0 is the distance from the solar system to the centre of the Milky Way. Relativistic treatments are also given.
- Corrections were made to equations (3) and (4) in this article on 22 September 2004. The corrected electronic version is identical to the print version.
- PACS
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95.35.+d Dark matter (stellar, interstellar, galactic, and cosmological)
- Subjects
- Dates
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Issue 5 (October 2004)
Received 23 March 2004
Published 16 September 2004
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Analogies between electricity and gravity
D F Bartlett 2004 Metrologia 41 S115
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