Inconsistency, Asymmetry, and Non-Locality: A Philosophical Investigation of Classical Electrodynamics by Mathias Frisch

Author:Mathias Frisch [Frisch, Mathias]
Language: eng
Format: epub
ISBN: 0195172159

end p.107

Third, even in those situations for which initial-value surfaces with approximately zero incoming fields can be found, there are also many spacelike hypersurfaces on which the fields are nonzero that could serve as initial-value surfaces as well, but that do not result in purely retarded fields. For example, we can model a radiating charge by picking an initial-value surface at some time after the charge has begun radiating. In what sense, then, does the condition "apply in most situations"? And, fourth, there seem to be just as many situations as there are situations , for yet another reason: Every spacelike hypersurface can serve both as an initial-value surface for the fields in its future and as a final-value surface for fields in its past. But then it might seem that radiation is not asymmetric after all. While both initial-value and final-value representations are individually asymmetric, radiation as a whole might seem to be symmetric, since every asymmetric representation with zero incoming fields is balanced by one with zero outgoing fields.

We can address the final worry once we realize that there is an additional asymmetry between situations with zero incoming and zero outgoing fields. Many phenomena for which the total field is approximately equal to a sum of retarded fields involve only the retarded fields associated with a small number of sources. By contrast, in situations where the total field is very nearly fully advanced, the total field is (almost) always a sum of advanced fields of a very large number of sources. Roughly—and we will have the opportunity to discuss this in much more detail in later chapters—the electromagnetic field can be zero in a certain region of space at a certain time despite the fact that there were coherently radiating sources in the region's distant past, if there is an absorbing medium in the region's more recent past. And absorbing media are usually modeled as consisting of a very large number of charges that scatter and damp out any incoming field. Thus, regions with approximately zero fields will have either no charged particles in their (recent) past or a very large number. By contrast, such regions may have a small number of charges in their future.

Finally, if we express the puzzle as postulating the existence of spacelike hypersurfaces on which the incoming fields are zero, then the third objection above can be met as well, and the asymmetry of radiation can now be expressed somewhat more precisely, as follows: (RADASYM)There are many situations in which the total field can be represented as being approximately equal to the sum of the retarded fields associated with a small number of charges (but not as the sum of the advanced fields associated with these charges), and there are almost no situations in which the total field can be represented as being approximately equal to the sum of the advanced fields associated with a small number of charges.

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