ProtoQuant.com

V. Conclusions

In 1990 Freeman J. Dyson published an old Feynman vision of the connection between Dynamics and Electrodynamics [7]. The publication immediately triggered a host of comments and fundamental approaches to the problem of gauge fields in general, thus proving the fecundity of old ideas. It is our opinion that the novelty of this approach rests upon conceiving the coordinates as integrals of motion to which we apply the formalism of Poisson parentheses, rather than means of Space or Space-Time location. Anyway, one of the main criticisms directed to this approach is that it leads naturally to only a half of the Maxwell equations, the other half requiring more elaborate assumptions, basically connected with the so-called minimal coupling.

The present work answers the same problem as raised by the Feynman connection between Dynamics and Electrodynamics, with the difference that here we preserve the passive classical role of coordinates as parameters of location. The emphasis is then placed upon a generalization of the metric, whereby the symmetric part of the metric tensor is manifestly unknown. In this connection, our results are not singular. First of all, there is a feeling that the metric is not essential for the theory of gravitation [9], inasmuch as it has originally been introduced from the necessity to correlate measurements with clocks and rods, and thus it outlived its usefulness. We might then ask for a meaning to produce a metric tensor anyway, not just as a mean to represent gravitation. The present work suggests such a way. The manner of suggestion brings us to a second citation [10] whereby the metric field is explicitly declared secondary, while the electromagnetic field is fundamental. In this respect our work only changes the emphasis: the electromagnetic field is formally fundamental, in the sense mentioned above, namely that any environmental influence upon a body must be represented as such, regardless of its nature.

Finally we note that the invariantive spirit allows us to conceive as classical topological effects otherwise assigned to quantum realm, like the Aharonov-Bohm effect. In spite of the current academically endorsed interpretation, our opinion is that this effect shows that we have a lot more to understand about the Classical, rather than Quantum, Physics.

Pages: 1 2 3 4 5 6 7