Speculation on delta E delta t >=.5 hbar, Retarded Time and a Charge at Rest

 In quantum mechanics, the use of Heisenberg’s uncertainty relationship delta E delta t >= hbar/2 to qualitatively describe virtual particles in forces is well-known. (1) In 1898 and 1890,  Lienard and Wiechart made use of retarded time (2)(3) when solving the problem of a moving/accelerating charge. At first, these two ideas seem separate.

   We try to argue here, however, that the two should be related, at least qualitatively. We consider the case of a charge at rest and argue that signals moving at the speed of c should travel from the charge Q at the origin to a point r, but should also move back. These signals would seem to be linked to energy and momentum, but do not seem to obey Newtonian mechanics. In other words, there seem to be energy fluctuations and energy may disappear from near the charge, move at speed c to some point and then disappear there and move back to the origin. These fluctuations seem to already exist in the case of a charge at rest, but are developed in more detail for an accelerating charge in (4). As a result, we argue that retarded time in electromagnetism is linked with quantum energy fluctuations. We note that the use of a retarded time is consistent with special relativity and so argue that special relativity and quantum mechanics are directly linked.