BACKGROUNDER ON THE GRAND UNIFIED THEORY (GUT) SOME BASIC INFORMATION by E. E. Escultura

Why do problems in mathematics and physics defy solution or resolution for a long time? In mathematics the most famous unsolved problem was the 360-year-old Fermat’s conjecture known as Fermat’s last theorem (FLT) and in physics it was the 200-year-old Laplace or gravitational n-body problem. The author posed this question in 1988 after a 17-year absence from his mathematical career. Given that both problems appear to be very clearly stated he came to the conclusion that the difficulty lies in the inadequacy and other defects of their underlying fields. He then proceeded to first make a thorough critique of the underlying fields of FLT, namely, foundations, number theory and the real number system and he found, among others that the real number system is inconsistent and is, therefore, ill-defined or ambiguous. Consequently, FLT being formulated in it is also ambiguous and cannot be resolved. He proceeded to construct the consistent new real number system on three simple axioms and reformulate FLT in it to make it clear and open to resolution. Indeed, FLT has countably infinite counterexamples in the new real number system.

What has FLT to do with GUT? The first major theorem in its resolution was the characterization of undecidable (unprovable) propositions that says, essentially, that a proposition is unprovable if it is ambiguous, i.e., involves ambiguous or ill-defined concepts. Being “ill-defined” is the negation of “well-defined” and a concept is well-defined if its existence, properties or behavior and relationship with other concepts are specified by the axioms of the given mathematical space. To avoid ambiguity and contradiction (the latter often hides in the former) every concept in a mathematical space must be well-defined and in its construction the choice of the axioms is not complete until this requirement is achieved. When we have two distinct mathematical spaces every concept in one is ill-defined in the other since each mathematical space is well defined only by its axioms. A physical theory is a mathematical space whose axioms are laws of nature. In a mathematical space the axioms are man-made and have nothing to do with the laws of nature.

In the present methodology of physics called quantitative modeling (formerly called mathematical modeling) natural phenomena are described mathematically and a physical problem is modeled by a mathematical problem so that the solution of the latter is attributed to the solution of the physical problem. Reasoning is purely by analogy since there is no causal relation between the physical and mathematical spaces concerned. This is the reason for the existence of long-standing unsolved problems and unanswered fundamental questions of physics like what the basic constituent of matter and the structure of the electron are.

The remedy for this inadequacy of methodology is qualitative or non-quantitative modeling (formerly called dynamic modeling) that explains nature or natural phenomena in terms of the laws of nature. While quantitative modeling describes the appearances of nature mathematically, qualitative modeling explains its internal dynamics and interactions including its appearances in terms of its laws. The former is based on computation, measurement and intuition, the latter on qualitative mathematics, rational thought and analysis. Qualitative mathematics includes the following routine activity of the mathematician or scientist:
Making conclusions, visualizing, abstracting, thought experimenting, engaging in creative activity, intuition, imagination and trial and error to sift out what is more appropriate, negating what is known to gain some insights into the unknown, altering premises to draw out new conclusions, thinking backwards and all other techniques that yield results.

Qualitative modeling alters the task of the scientist from computation and measurement to the search for the laws of nature. It was used for the first time to solve the gravitational n-body problem in 1997. The solution required the discovery of the basic constituent of matter, the superstring. It required 11 laws of nature to accomplish both. They where the initial laws of nature of GUT known as the flux theory of gravitation then.

At present particle physicists are still smashing the nucleus of the atom in search of the basic constituent of matter, the superstring, which has been going on for over half a century. Actually, the superstring has been staring at us since 1811 when Ernest Rutherford discovered the electron. The electron is an agitated superstring. A non-agitated superstring is dark, i.e., its size is less than 10^(-10) meters. It is the basic constituent of dark matter, one of the two fundamental states of matter, the other being visible or ordinary matter. Dark matter is not observable with present technology and is known only by its impact on visible matter. When suitably agitated by cosmic waves the superstring expands to a primum, unit of visible matter such as the electron or positive or negative quark. These three prima are called basic prima because they are constituents of every atom. They are converted from dark matter at staggering rate in the Cosmos and in the cells of living things – plants or animals. In the Cosmos alone the prima form cosmic dust that get entangled into cosmological vortices and collect at their cores at the rate of one star per minute.

References

[1] Escultura, E. E., The solution of the gravitational n-body problem, Nonlinear Analysis, Series A: Theory, Methods and Applications, 30(8), Dec. 1997, 521 – 532.
[2] Escultura, E. E. (1997) Exact solutions of Fermat's equation (Definitive resolution of Fermat’s last theorem, 5(2), 227 – 2254.
[3] Escultura, E. E. (1999) Superstring loop dynamics and applications to astronomy and biology, J. Nonlinear Analysis, 35(8), 259 – 285.
[4] Escultura, E. E. (1999) Recent verification and applications, Proc. 2rd International Conf.: Tools for Mathematical Modeling, St. Petersburg, vol. 4, 74 – 89.
[5] Escultura, E. E. (2001) From macro to quantum gravity, J. Problems of Nonlinear Analysis in Engineering Systems, 7(1), 56 – 78.
[6] Escultura, E. E. (2001) Quantum gravity, Proc. 3rd International Conference on Dynamic Systems and Applications, Atlanta, 201 – 208.
[7] Escultura, E. E. (2001) Turbulence: theory, verification and applications, J. Nonlinear Analysis, 47(2001), 5955 – 5966.
[8] Escultura, E. E. (2001) Vortex Interactions, J. Problems of Nonlinear Analysis in Engineering Systems, Vol. 7(2), 30 – 44.
[9] Escultura, E. E. (2001) Chaos, turbulence and fractal, Indian J. Pure and Applied Mathematics, 32(10), 1539 – 1551.
[10] Escultura, E. E. (2002) The mathematics of the new physics, J. Applied Mathematics and Computations, 130(1), 145 – 169.
[11] Escultura, E. E. (2003) The new mathematics and physics, J. Applied Mathematics and Computation, 138(1), 127 – 149.
[12] Escultura, E. E. (2003) Macro and quantum gravity and the dynamics of cosmic waves, J. Applied Mathematics and Computation, 139(1), 23 – 36.
[13] Escultura, E. E., (2003) Dynamic Modeling and Applications, Proc. 3rd International Conference on Tools for Mathematical Modeling, State Technical University of St. Petersburg, St. Petersburg.
[14] Escultura, E. E., (2004) Problems and Unanswered Questions of physics and their resolution, Nonlinear Analysis and Phenomena, I(1), 1 – 26.
[15] Escultura, E. E., The new real number system and discrete computation and calculus, 17 (2009), 59 – 84.
[16] Escultura, E. E., (2005) Dynamic Modeling of Chaos and Turbulence, Proc. 4th World Congress of Nonlinear Analysts, Orlando, June 30 – July 7, 2004; Nonlinear Analysis, Volume 63, Issue 5-7, 1 November 2005, e519-e532.
[17] Escultura, E. E., (2005). The theory of everything, Nonlinear Analysis and Phenomena, II(2), 1 – 45.
[18] Escultura, E. E., (2006) Foundations of Analysis and the New Arithmetic, Nonlinear Analysis and Phenomena, January 2006.
[19] Escultura, E. E., The Pillars of the new physics and some updates, Nonlinear Studies, 14(3), 2007, 241 – 260.
[20] Escultura, E. E., The physics of the mind, accepted, The Journal of the Science of Healing Outcome.
[21] Escultura, E. E., The cosmology of our universe, submitted, Problems of Nonlinear Analysis in Engineering Systems.
[22] Escultura, E. E., (2007) Dynamic Modeling and the new mathematics and physics, Neural, Parallel and Scientific Computations, 15(4), 2007, 527 – 538.
[23] Escultura, E. E., The grand unified theory, contribution to the Felicitation Volume on the occasion of the 85th birth anniversary of Prof. V. Lakshmikantham: Nonlinear Analysis: TMA, 69(3), 2008, 823 – 831.
[24] Escultura, E. E. The mathematics of the grand unified theory, in pres, Nonlinear Analysis.
[25] Escultura, E. E. Dynamic and mathematical models in physic, Proc. 5th International Conference on Dynamic Systems and Applications, June 30 – July 5, 2007, Atlanta, 164 – 169.
[26] Escultura, E. E. (2004) Dynamic Modeling of Chaos and Turbulence, NA, TBA, 63(5-7), e519 – e532.
[27] Escultura, E. E. The basic concepts and dynamics of quantum gravity with applications, in press, Nonlinear Studies
[28] Escultura, E. E., Qualitative model of the atom, its components and origin in the early universe, in press, Nonlinear Analysis: Real World Applications.