Fields on the horizon

Fields. It’s time to bring them home. Fields are at the foundation of everything. Even consciousness. We need them in our endeavours.

… But I’ll keep on waitin’ ’til you return.
I’ll keep on waiting until the day you learn
You can’t be happy while your heart’s on the roam.
You can’t be happy until you bring it home,
Home to the greenfields and me once again.

So were singing Brothers Four. We have also our own brothers four – The Four Quaternions. And we need to study fields related to their action.
Fields are everywhere. Look

The Origins of the Field Concept in PhysicsErnan McMullin*

The term, ‘‘field,’’ made its first appearance in physics as a technical term in the mid-nineteenth century.But the notion of what later came to be called a field had been a long time in gestation. Early discussions of magnetism and of the cause of the ocean tides had long ago suggested the idea of a ‘‘zone of influence’’ surrounding certain bodies. Johannes Kepler’s mathematical rendering of the orbital motion of Mars encouraged him to formulate what he called ‘‘a true theory of gravity’’ involving the notion of attraction. Isaac Newton went on to construct an eminently effective dynamics, with attraction as its primary example of force. Was his a field theory? Historians of science disagree. Much depends on whether a theory consistent with the notion of action at a distance ought qualify as a ‘‘field’’ theory.Roger Boscovich and Immanuel Kant later took the Newtonian concept of attraction in new directions.It was left to Michael Faraday to propose the ‘‘physical existence’’ of lines of force and to James Clerk Maxwell to add as criterion the presence of energy as the ontological basis for a full-blown ‘‘fieldtheory’’ of electromagnetic phenomena.Key words:Johannes Kepler; Isaac Newton; Roger Boscovich; Immanuel Kant;Michael Faraday; magnetism; gravity; field theory.


International Institute of Biophysics, ehem.Raketenstation, Kapellener Str., D-41472 Neuss, Germany, and Future Science & Medicine, Gotlandstr.7, D-10439 Berlin, Germany
Published in: Beloussov, L.V., Popp, F.A., Voeikov, V.L., and Van Wijk, R., (eds.): Biophotonics and Coherent Systems. Moscow University Press, Moscow 2000, pp.1-25.
Due to recent advances in several disciplines, the basic features of a holistic biophysics are now emerging. It is proposed that the postulates for such a field must include that it will be based on the intrinsic holism of quantum theory and the properties of macroscopic quantum effects, that it should include the principles of nonlocality, nonseparability, and interconnectedness, that it will be based on a field picture of reality and the organism, and finally must include consciousness.
The paper attempts to show why field models are appropriate tools for the holistic modeling of the organism, proposes a hierarchy of regulation systems based on fields, gives a review of field models proposed in biology, biophysics, consciousness research and social science, and discusses the possible role of fields in bridging the mind-body gap.
Finally, a discussion of the perspectives that may be opened up for biophysics by some recently proposed extensions of electromagnetic theory leads the author to suggest a role for the physical vacuum in the organism.

But we are not going to travel that far. Not yet. For now we will need the concept of a vector field. Vector fields are at the basis of “differential geometry”.

Vector field of wind velocity

Vector fields are at the basis of “continuous groups of symmetries”. Vector fields are needed for understanding the famous laws of conservation of energy, momentum, angular momentum, electric charge ….

So we will start to talk about them, as we will need them for understanding the Dzhanibekov effect through geometry. That was Einstein’s dream, to understand everything through geometry, and through fields. True, at some point he started to doubt if such a project is viable. What if all is discrete? What if there is no continuity? But then – what would be the connecting principle?

But, for now, we will introduce vector fields. First with complex numbers, then with quaternions, then ….. who knows where we will end?