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On Motion

On Motion. Bernd Schmeikal Wiener Institute for Social Science Documentation and Methodology (WISDOM) 10th International Conference of Numerical Analysis and Applied Mathematics, 19-25 September, 2012, Kypriotis Hotels and Conference Center, Kos, Greece. Cockeyed theories – QM & QED.

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On Motion

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  1. On Motion Bernd Schmeikal Wiener Institute for Social Science Documentation and Methodology (WISDOM) 10th International Conference of Numerical Analysis and Applied Mathematics, 19-25 September, 2012, Kypriotis Hotels and Conference Center,Kos, Greece

  2. Cockeyed theories – QM & QED • Since 1926 we are seduced to give up our common sense in order to understand motion at the atomic level. • Since more than 50 years we accept, nobody can understand QED, least QCD. • Comparing QCD with QED Feynman assured “the quarks have an additional type of polarization that is not related to geometry”.

  3. when we were young Feynman took it for granted, “you are not going to be able to understand it”. His students could not understand it, because, as he said, “I don’t understand it”. Thirringoften mentioned the “unessential constants” at the right hand term of a formula. He meant the light velocity and Planck’s constant, but could have meant just as well the mass and charge, as we jiggle around the complexity of ways and the contributions of the coupling constant . We did not have a good mathematical way to describe the theory of QED. We could not include coupling distances close to zero. Calibration of constants is a still greater problem in QCD as was shown for example by some studies at the Max Planck Institute in Aachen.

  4. How to go on • Physicists often say, let us stay in close contact with empirical reality and let’s not get lost in mathematical details. • May be we need a good double-entry bookkeeping of both quantum events and geometric realities, • and some unifying insight.

  5. two levels of reality • quantum • metric

  6. two questions • The past is gone • where? • Where are past events now? • how many?

  7. two answers • into the present. • Whatever moves, is moving in presence • They are in the presence. • Some that we are aware of and others we do not realize.

  8. The past is in the present nowhere else!

  9. the present • is the platform of change • means life • is contact • is interaction • involves chaos • decomposes the orientation

  10. + a grade 4 Iterant element + – – • quad location, • polarized string, • constituent of quaternion • synchronous detemporalized image • Parsed compass • quaternion location • multivector in geometric algebra • quark density component • Iterants were introduced by Louis H. Kauffman

  11. + + +  +   two iterants representing strings with invisible grade difference +   + …+   …+ = [+1, 1,+1, 1] + = [+1, 1, 1, +1] +   …+ …

  12. +  + + +   + +    +  touch and compare +     + …+ …+ …+ + + +   + …+ … … [+  + ][+  + ]=[+ + ] e24 e124 = e1

  13. shift and identify • ; Result Result is Result is

  14. iterants • form iterant algebras • and reflexive domains

  15. With iterants • we construct real associative algebras with familiar algebraic properties • Including temporal shift operators • Consider the smallest case of iterant algebras to the order 2. The 2nd order time shift is  satisfying • [a, b] = [b, a] and 2=Id

  16. What is an iterant apart from its defining sequence ? • It is an eigenform. For example order 2: [+1, 1]… +1, 1, +1, 1, +1, 1, +1, 1, … is an eigenform of the equation • = • Does it have a fixpoint?

  17. fixpoint •  • We are used to the interpretation . But it can just as well be interpreted as iterant views multiplied with time-shift operators:

  18. Introduce two temporal shift operators • Definition 1: quad-locations are fourfold locations given by iterant views of the form . • Definition 2: of time shift operators. Sequences are iterated by iteration time which satisifies with and by tangle-time, a period-2 iterant time shift satisfying with

  19. and the following three terms • and let them act on iterants and define satisfy the multiplication table of the quaternions. We can verify , and so on.

  20. touch can bring about iteration time

  21. Theorem:

  22. derive the rank 2 motion group • there is a Group with a fixed point • every group element as an element of must have the general form • every group element transforms elements by conjugation just like in a spin group: . • generators of the Lie algebra of the group should be unitary. • group elements are calculated from the algebra by an exponential map. • generators of the group algebra should satisfy commutation relations of some form of .

  23. generators of ; ; ; ; ; ; ;

  24. generators of ; ; ; ; ; ; ;

  25. Consider the idempotent • not primitive in the Minkowski algebra and the isospin Both are elements in . For any natural number we verify the identities and Clifford number represents a swap. The color space can now be decomposed into two ideals with main involuted , and spaces and .

  26. represent Cartan subalgebra and color space • Swap property implies, both and are isomorphic with the Clifford algebra - the double ring of real numbers. So the decomposition is • for • Color space can be spanned either by its orthogonal primitive idempotents or by its base units. by the following quadruples: • ; ; • ;

  27. See the analogy • between quad-locations and the -representations of the base units of . Due to the peculiar construction of the iterant algebra, we can identify iterant views with units having different grades: a spatial unit, a space-time area, a space-time volume: • ; ;

  28. Heisenberg uncertainty or causality amending? • Consider the bivector in the space-time algebra: • and the transformation carried out by a flavour rotation • It carries a vector to a directed space-time area such that we have the identity • .

  29. There are many events under the lightlike ones, that is, events from space-like neigh­bourhoods of x that in SR are supposed to be unable to exercise any causal influence on the worldline associated with . In the first quadrant where , with no division by zero we would have • In order that location 2 be space-like separated from the observer, we should expect which results in • For meters we obtain a limit of equal . For times there are effects from future events.

  30. Also if we change side, that is, we turn from, say, over to , things can change significantly as we compensate time-reversion. Take for example both turning negative and of orders m. Then we had • The further we go into the nuclear domain the more weightily the causality violation. • For distances of 0,772 meters future effects involve a time intervall as large as seconds which is the currently estimated age of the universe.

  31. Literatur • Louis H. Kauffman, REFLEXIVITY, EIGENFORM AND FOU,NDATIONS OF PHYSICS, http://homepages.math.uic.edu/~kauffman/Kauffman@uic.edu • H. L. Kauffman. Eigenforms and Eigenvalues - Cybernetics and Physics, on the occasion of the 100st birthday of Heinz von Foerster, Dec 2011, congress paper (private communication) • Schmeikal, B. On Motion, unpublished paper, 2012

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