Interferometry Whittaker scalar potential

Whittaker s early work [27,28] is the precursor [4] to twistor theory and is well developed. Whittaker showed that a scalar potential satisfying the Laplace and d Alembert equations is structured in the vacuum, and can be expanded in terms of plane waves. This means that in the vacuum, there are both propagating and standing waves, and electromagnetic waves are not necessarily transverse. In this section, a straightforward application of Whittaker s work is reviewed, leading to the feasibility of interferometry between scalar potentials in the vacuum, and to a trouble-free method of canonical quantization. 

X. Scalar Interferometry and Canonical Quantization from Whittaker s Potentials... 

An important by-product of the development in this chapter (Section X) is the possible existence of scalar interferometry, which is interferometry between structured scalar potentials, first introduced by Whittaker [27,28] and that can be defined in terms of B<3 This is a type of interferometry that depends on physically meaningful potentials that can exist self-consistently, as we have argued, only in a non-singly connected 0(3) vacuum, because potentials in the nonsingly connected U(l) vacuum are assumed to be unphysical. 

X. SCALAR INTERFEROMETRY AND CANONICAL QUANTIZATION FROM WHITTAKER S POTENTIALS... 

This result is consistent with Whittaker s main conclusion [27,28], that the scalar potential is structured and physical in the vacuum, leading to the possibility of interferometry between different scalar potentials, without the presence of fields. To reinforce this conclusion, we can differentiate Eq. (484)... 

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