Non-relativistic Approach to Gravity as Originating from Vacuum Zero-Point Field van der Waals Forces”

The material contained here is intended to supplement and support the information reported in our article, “On a Stochastic Non-relativistic Approach to Gravity as Originating from Vacuum Zero-Point Field van der Waals Forces,” to be published in Phys. Rev. A. The present material can be obtained from the EPAPS homepage (http://www.aip.org/pubservs/epaps.html) or from ftp.aip.org in the directory /epaps/. The footnotes and reference numbers in this supplementary section refer to references listed at the end of this material, rather than to the reference numbers in the main article. The information provided here is broken up into three subsequent parts. Section II contains additional background on work related to Sakharov’s proposal, on stochastic electrodynamics, and on related work to Puthoff’s gravity proposal. Section III then turns to a detailed analysis on how Ir (b) and Iur (b) can be extracted from I (b) in Eq. (3). We are not aware of such calculations being available elsewhere on the connection between the full, retarded, and unretarded van der Waals expressions, so this material should be of general interest for researchers involved with van der Waals and Casimir interaction calculations. Moreover, the question is examined on what happens if an upper cut-off of wc = ωcR/c is imposed in the integration in Eq. (3). Section IV then contains a discussion on the energy aspects associated with variations of the proposal in Ref. [1]. This analysis provides an intuitively compelling argument as to the unlikelihood of the gravitational attraction being a long range van der Waals type force originating in the very low frequencies of the ZP radiation spectrum. Finally, Sec. V provides some concluding comments.