The next email is now under construction (not yet sent).
The underlying theory requires the solution of differential equations involving functions of a quaternionic variable, quaternionic Fourier expansions and quaternionic phase transformations.
Perhaps the inner automorphism of the quaternion algebra DO NOT correspond to the isometries of space-time BUT SOLELY TO the existence of the combined spin-isospin structure, a derivative of a function. “The harmonic property implicit in class H implies in the possibility that the quaternion quantum fields and states can be represented in terms of quaternionic Fourier expansions, something that is required to represent the quaternion wave packets.”
Third email: Wednesday, January 16, 2019
Dear Prof. Dr. Steve Adler:
I know that I am a nobody from nowhere special, but my questions are genuine and nobody seems to be able to answer these questions about our infinitesimal universe (Notations 1 to 64).
In 1994 you were writing what eventually became a book, Quaternionic Quantum Mechanics and Quantum Fields, (Oxford University Press, 1995). So, we are moved to ask, “What has quaternionic quantum mechanics done to further our common insight? Has it moved us beyond the open questions in big bang cosmology?” Please excuse me if my questions seem too direct or offensive.
References and resources:
JULY 16-27, 2018: IAS PiTP, From Qubits to Spacetime. Speakers included: Scott Aaronson – University of Texas at Austin, Ahmed Almheiri – Institute for Advanced Study, Atish Dabholkar – International Centre for Theoretical Physics, Trieste, Italy, Thomas Faulkner – University of Illinois, Daniel Harlow – Massachusetts Institute of Technology, Matthew Headrick – Brandeis University: Quantum entanglement and the geometry of spacetime, Juan Maldacena – Institute for Advanced Study, Douglas Stanford – Institute for Advanced Study, Leonard Susskind – Stanford University, Aron Wall – Stanford University, Edward Witten – Institute for Advanced Study
The algebraic consistency of spin and isospin at the level of an unbroken SU(2) gauge theory suggests the existence of an additional angular momentum besides the spin and isospin and also produces a full quaternionic spinor operator. The latter corresponds to a vector boson in space-time, interpreted as a SU(2) gauge field. The existence of quaternionic spinor fields implies in a quaternionic Hilbert space and its necessary mathematical analysis. It is shown how to obtain a unique representation of a quaternion function by a convergent positive power series. See HARMONICITY. See: M. F. Atiah, Geometry of the Yang-Mills Fields. Academia Nazionale dei Licei, Scuola Normale Superiore, Pisa (1979).
Second email: Saturday, September 29, 2018, 12:13 AM
Dear Prof. Dr. Steve Adler:
You had an early advantage over most of us having grown up on “The Secret of Light,” but we all eventually learned that we do not really know the boundaries of physics.
So, I ask in your light of history and of the PiTP, From Qubits to Spacetime, is it reasonable to consider Max Planck’s simple definition of time when we talk about the interiority of the space-time?
Rather surprisingly Planck’s more simple formulation actually computes well with experimental results. And, if base-2 notation is applied to Planck Time, of course, it computes well within every notation, not just at one second. It is defined by light! There is a small variable as each quantity is multiplied by 2. Yet, it appears to remain within .001% of the laboratory-defined speed of light throughout all 202 notations from Planck Time to the current time or age of the currently expanding universe,the Now.
By inserting the other base units along this scale of the universe, the data sets become more challenging, yet the simple correspondence between length and time tells a profound story. The correspondence with mass and charge, though stretching the imagination, still retains a deep logic and continuity.
Might you comment? Just nonsense?
PS. You may remember that this work started in a New Orleans high school geometry class where we chased Zeno’s paradox to the Planck Wall and then asked, “What else can we do?”
Related links: https://81018.com/c/
Chart of numbers: https://81018.com/chart/ (see line 10)
A little background story: https://81018.com/home
First email: Wednesday, Apr 26, 2017, 4:26 PM
Dear Prof. Dr. Steve Adler:
In December 2011 with my favorite geometry classes, we followed Zeno inside the tetrahedron to find the octahedron and four half-sized tetrahedrons (by dividing all the edges by 2 then connecting up those new vertices). We continued with our simple progression. Besides ending up with an enormous number of parts, within 45 steps we were near the limits of CERN-labs measurements, somewhere around the size of the Fermion. We continued our base-2 divisions, on paper and in theory back to the Planck base units in just 67 additional steps. The next day we multiplied our original objects by 2; and in just over 90 steps, we were up around the Age of the Universe.
We had tiled and tessellated the universe with octahedral-tetrahedral clusters and had a terrific little chart of everything, everywhere throughout all time.
Of course, it was a bit of silliness. Or is it?
We weren’t sure. For three years we search around for something like it and only found Kees Boeke’s work from 1957. My old friend, Phil Morrison (MIT) loved Boeke’s work. Without any clear criticisms, we started putting it up within its own site on the web and today, I beg people to tell us where we have gone wrong. We are just high school people.
Are the first 67 notations the matrix or Frank Wilczek’s grid? Is this the domain of pointfree geometries (Whitehead)?
I would be perfectly delighted to hear from you no matter how harsh your criticisms. Thank you.
Open question: Is big bang cosmology still the best model?