 Substructures, Virtual Levels, and Hyperspaces 
In the new approach, our definitions and assumptions immediately drive us to a picture of an infinite set of nested levels of
substructures in the virtual state. That is, anyone component (scalar or vector) in one level of virtual state has an infinite number of even finer virtual components, one level more subtle.
AND THAT IS WHAT PARTICLE PHYSICS AND
QUANTUM MECHANICS ALREADY REVEAL ABOUT THE STRUCTURE OF PHYSICAL REALITY.
So these definitions and assumptions now provide the basis for a new vector mathematics that is in accord with, and fitted to, modern
physical observations.
We have a picture such that any observable scalar
or vector contains a virtual substructure (virtual level 1). Any scalar or vector in virtual level 1
also contains a finer virtual substructure, in virtual level 2. And so on ad infinitum.
Each succeedingly finer level of virtual state can be modeled as a hyperdimension (higher spatial dimension) as I pointed out in Appendix 1 to my book,
The Excalibur Briefing.^{30}
Thus this approach immediately ties into hyperdimensional or
hyperspatial theory  such as Elizabeth Rauscher's 8dimensional theory^{31}
and C. Muses's hypernumber theory.^{32}
The new definitions and assumptions are far richer than what is
allowed by tensors, though there are many similarities. Muses's work, however, essentially can encompass most of these definitions and concepts, except the distinct types of vectors are not so clearly delineated in his theory (at least to my comprehension of it.)
His theory does provide a nested, hyperdimensional structure of time, however, and thus allows "scalar" waves in the hyperspatial structure of time
 in other words, observably "scalar" waves in the virtual state structure of spacetime, or pure Tesla waves, or simply "time" waves.
These are the bare notes;
from this approach, already new (proprietary) mechanisms and exact specifications to make scalar waves  in essentially whatever quantity and degree desired
 appear to have been successfully accomplished by my close colleagues.
The new approach is real and it leads to a new physics. And I
believe that the very beginnings of the new physics are already working on the laboratory bench.
Nikola Tesla discovered the most essential features of the new electromagnetics over eighty years ago and was simply suppressed for his efforts. Now, although it has been eighty years in the
reborning, Tesla electromagnetics is once again loose in the Western world.
This time, let us hope that it fares better at the hands of
orthodox science and large financial control groups than it did for Nikola Tesla.
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