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Notation: our Lorentz metric is diag (+++−) 1. μ,v, λ,…=0,1,2,3 are space-time indices; α,β,λ,…=0, 1, 2, 3, 5 are sphere space indices.x 0=t, x 5=λ in the flat case (3). Units:c=1.
N. B. Conformalpoint transformations of space-time are included in this formalism as the special case of null spheres: λ=0. Although many workers consider only these, this is not correct and fruitful physically in our opinion (see ref. (3)).R. L. Ingraham: inLectures in Theoretical Physics, Vol.13 (Boulder, Colo., 1971). In particular, the present theory of inertial e.m. motion is excluded.
R. L. Ingraham: inLectures in Theoretical Physics, Vol.13 (Boulder, Colo., 1971).
Note that even for flat space-time angle space has constant curvature ≠0. We mean the extra uneven curvature caused by mass-energy.
R. L. Ingraham:Proc. Nat. Acad. Sci.,41, 165 (1955);Phys. Rev.,101, 1411 (1956).
By integrating outx ′o (note that the step function picks out the roott ret<t of the delta-function), one easily sees that this reduces to the usual expressions,e.g.,W. Panofsky andM. Phillips:Classical Electricity and Magnetism, eqs. (13.24), (13.25) (Cambridge, Mass., 1955).
R. L. Ingraham:Nuovo Cimento,9, 886 (1952).
L. Infeld andA. Schild:Rev. Mod. Phys.,21, 408 (1949).
Formally this decomposition is the same as that first obtained in the Kaluza 5-dimensional unified field theory,Th. Kaluza:Sitz. Preuss. Akad. Wiss., 966 (1921);O. Klein:Zeits. Phys.,37, 895 (1926);46, 188 (1927).
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Ingraham, R.L. Electromagnetism as an inertial force. Lett. Nuovo Cimento 7, 846–850 (1973). https://doi.org/10.1007/BF02725401
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DOI: https://doi.org/10.1007/BF02725401