Dear Prof. Kripov,

                               I have tried to use Fractal Geometry to analyse stock exchange digital displays as part of the Econophysics system and I have by using mainly Shroedinger type factorization been able to String Theoretically model stock exchange prototypes using Indian Stock Market experiments. You can for e.g. take a look at my Haag's Theorem paper on my RG page. My son Sandipan Mallick who is an undergraduate researcher has also built Physical Chemical Analysis into the Engineering EconoPhysics model prototypes. So Geometry is very much in consonance with Quantum Mechanics. I have also two Theoretical Physics papers on Reservoir Engineering of Coal Mines and Stock Markets using geometry with the Arrow of Time postulate made explicit, on my RG page. Special Relativity is very geometric and Euclidean Geometric also I think. Earl Chair Prof. Dr. SKM QC EPS Fellow (In) MRES MES MAICTE 

Dear prof. Soumitra K Mallick,

Thank you your imformation. But I misunderstood what were objects for which you used fractal geometry. How do you use the fractals, e.g. to prove that the triangle angles sum is close to 180?

Thank you

Dear Prof. Khripov,

                                  Since I am modelling machine systems where digital quantities are the outputs like say LED or LCD displays partitioning of sets or material particles like say the compounds we have developed through physical chemical analysis (Sandipan doesn't have any published paper as yet but if we are called to make any presentation we have a joint presentation ready which is still a mixture of theoretical physics, Econophysics and physcial chemical analysis (c/o Sandipan )). This substitutes for Chromodynamics by using crystallographic engineering to some extent and electronic circuits using String Theoretic Differentiation and integration by using what we have called Dbranes String Theory and M(Econophysics) Theory. We have established that this necessarily generates a Higgs Englert Bosonic Field because of being able to use free electrons hence tachyonic condensation is possible by spacetime dynamics even at close to room temperatures in Dynamic Edgeworth Boxes which conserve Arrow of Time hence substitute for Shroedinger Closed Cat Boxes with individual electrons so the Lie Algebra groups can be used as the space medium algebra. This is still however what is called in Economic Sciences Hedonic Model, dependant heavily on model parameters but there are four Laws of Econophysics which have been developed which is satisfied by all these experimental systems, I think can be showed. We have worked this out for Stock Market systems with electrical energy inputa and stock market indices and of course stock market  trading actions (information flows ) as output. Ratios are an important calculation using Debroglie, Planck and Maxwell calculations and infinity cancellations for which Geometry atleast fractal algebraic geometry (simple and simplectic) works.  So to repeat there are a number of points of applications of Geometric calculations and group theories. Earl Chair Prof. Dr. SKM QC EPS Fellow (In) MES MRES MAICTE

Maybe this helps to find answers to your question:

H.J.Schmidt:

Axiomatic Characterization of Physical Geometry

Springer Lecture Notes in Physics 111 (1979)

http://link.springer.com/book/10.1007%2F3-540-09719-8

Schmidt's work can be considered as kind of physical pre-theory for the axioms of Euclidean geometry. 

Dear  Karl G. Kreuzer,

This is very interesting. But the textbook is not free at Springer site. I would be very appreciate if you could send me the pdf or give the emails of authors or other physicists who could send me even a part of it. Maybe it is in some articles? In Russia I simply can not find this book in libraries. It is a pity!

Thank you for an advance,

Anatoly Khripov

Hello Anatoly. I do not understand why the axioms of Euclidean geometry would not apply to Classical Mechanics. The theorems of Euclidean geometry are deduced from postulates and axioms of Euclidean geometry and are used in the formulation and application of classical mechanics. Classical mechanics has enormous application in physics and engineering. It works very well. So I would have to conclude that these axioms or postulates do apply to classical mechanics and the real world. I think that mathematical physicists have tried to create a more physical geometry. This is tackled in Quantum Gravity where the geometry of space-time is linked to quantum fluctuations at the Planck Length. This theory states that the continuity of space breaks down at this distance scale. Also, there is the Twistor theory by Roger Penrose based on 4-dimensional complex space that "generates" space-time. But here, some continuity in geometry has to be assumed.  

David Hilbert started a project that targeted an axiomatic foundation of physics that is based on geometry. Also Garret Birkhoff and John von Neumann started a project that started with a relational structure that is based on a small set of 25 axioms and that straightforward extends to a structure in which dynamic geometric data emerge that have an Euclidean signature. This all happened in the first few decades of the twentieth century.

The physicists did not take theses attempts very seriously and proceeded with the spacetime geometry that emerges from Maxwell equations and from the concept of the photon as an EM wave that acts as an information carrier. That decision has made physics far more complicated than necessary, because an Euclidean space progression structure offers far more compact and more comprehensible formulas. After walking a century long in the wrong direction it becomes difficult to correct this misleading direction. However from a mathematical point of view the Euclidean structure makes more sense,

http://arxiv.org/abs/1101.5690

Dear Hans van Leunen,

Could you give these old references by D Hilbert, Garret Birkhoff and John von Neumann?

Thank you for an advance!!!

Anatoly,

Google for Hilbert's foundation of physics in order to find a series of articles about this project of David Hilbert.

Google for "quantum logic" and von Neumann in order to find articles about this lattice and its consequences and the original paper.

Personally, I use this orthomodular lattice as the foundation of my model of physical reality.

http://vixra.org/abs/1603.0021

Dear E. J. Zampino,

You confuse the reason (axiom) and the consequence (theorem) in your message. If the theorem is true it does not mean at all that the axioms on which the theorem is based are true.

Physicists are very afraid of fantasies and for that reason they invented a version of the "scientific method" which requires that every significant physical statement must be verifiable by corresponding experiments. This attitude encounters two dilemmas. The first is that every experiment requires a theory that supports the set-up of the experiment and a theory that supports the interpretation of the results of the experiment. The second dilemma is that not all physical items are accessible to observation.

One of these items is the fact whether dynamic geometry must have an Euclidean structure. The problem here is that observation plays an essential role in the this question. The transfer of information plays a fundamental role in the selection of the models. Thus it is possible to develop a completely self-consistent model of physical reality that uses a spacetime structure, which has a Minkowski signature. However it is as well possible to develop a completely self-consistent model of the same physical reality that features a Euclidean signature. The difference between the two models will be the complexity of the description.  The Euclidean version will deliver the most compact and most simple formulas. The main trend in current physics is to select the spacetime version that has a Minkowski signature. This choice has been taken by the way that physical theories were developed in the last two centuries. The essential decisions were made by scientists that guided this development.

Physics did not develop in a rational way. It is strongly colored by its history.

These facts become apparent when Maxwell equations are compared to the partial differential equations that hold in quaternionic function space. The first set applies spacetime with Minkowski signature. The second set uses a strict Euclidean signature. The first set applies coordinate time where the second set applies proper time. In quaternionic number space proper time can be played by the real parts of the quaternions, while coordinate time is played by quaternionic distance.