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Some Preliminary Thoughts
on the Geometric Meaning of Quantum Mechanics (and Relativity)

Paper of a short talk given at Symmetries in Science XVI in Bregenz:

An Introduction to Geometric Algebra with some Preliminary Thoughts on the Geometric Meaning of Quantum Mechanics
IOP Science, Journal of Physics: Conference Series 538 012010 (pdf, 1,27 MB)


Why does time exist?

A somehow sporadic answer is given in the following paper. It's based on an entire geometrization of space and time: If everything is built up from two space-like vectors using the Zehfuss-Kronecker product, there has to be a four-dimensional spacetime. It's not possible to construct a four-dimensional space with only space-like base vectors this way. Thus time has to exist:

Living in a World Without Imaginaries
IOP Science, Journal of Physics: Conference Series 380 012006 (pdf, 709 KB)


How can we travel to infinity?
And how can we travel beyond infinity?

An answer to this question is given in the following poster presentation and papers. The main point of all this of course is: If someone calculates and tells you what happens beyond infinity or before the big bang or beyond the event horizons of black holes, do not believe him unless she or he uses surreal numbers in his calculations. Calculations using real numbers only will (almost automatically and nearly inevitably) be wrong.

 Eine Reise in die Unendlichkeit und über die Unendlichkeit hinaus
DPG Poster 2012 (pdf, 56 KB)   DPG Paper 2012 (pdf, 107 KB)   GDM Paper (pdf, 37 KB)

A travel beyond infinity is a travel into the realm of surreal numbers.


Ramanujan . . .

Bilateral Binomial Theorem, SIAM Problem 03-001
SIAM problem (pdf, 44,61 kB)   SIAM solution (pdf, 68,91 kB)

And please have a look at eq. (2.5) of the paper of Bruce C. Berndt and Wenchang Chu:

Two entries on bilateral hypergeometric series in Ramanujan's lost notebook
Proceedings of the American Mathematical Society,
135 (2007), pp. 129 – 134 (pdf, 128,17 KB)



My father writes Japanese books...
You can find more about his activities at his homepage


And of course there is also an Englisch translation of the German original, written by him together with Hanscarl Leuner and Edda Klessmann:

Guided Affective Imagery with Children and Adolescents
table of contents (pdf, 600 KB)







Kaufe gleichfalls auch Melonen
Und vergiss des Zuckers nicht ...

(Martin Opitz: Carpe Diem)

German version / deutsche Fassung: www.martin-erik-horn.de