Relation between Observers and Effects of Number Valuation in Science
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
This paper is a small step towards the goal of constructing a coherent theory of physic and mathematics together. It is based on two ideas, the localization of mathematical systems in space or space time, and the separation of the concepts of number from number value. The separation of number from number value along with the freedom of choice of number values at different points of space or space time enables the introduction of a space or space time dependent number valuation field. The presence of a location dependent number value field affects theoretical descriptions of many physical and geometric quantities. A simple geometric example is worked out in detail, that of the length of a path. The localization of mathematical systems and the separation of number from number value or meaning both emphasize the role of observers. The separation of number from number value shows the role of observers in that value or meaning are conscious observer related concepts. Nothing, including numbers, has value or meaning to an unconscious observer. The localization of mathematical systems also shows the role of observers in that the mathematics that is potentially available to an observer is that at the same position as is the observer. This represents the mathematical knowledge that can reside in an observers brain. As an observer moves in space or space time, the mathematical knowledge potentially available to the observer is the collection of mathematical systems at the same location as the observer. It is hoped that this work, which was begun in 2010, will lead to a better understanding of the relation between the foundations of mathematics and physics, and the role that observers play in this relation.
Abstract
This paper is a small step towards the goal of constructing a coherent theory of physic and mathematics together. It is based on two ideas, the localization of mathematical systems in space or space time, and the separation of the concepts of number from number value. The separation of number from number value along with the freedom of choice of number values at different points of space or space time enables the introduction of a space or space time dependent number valuation field. The presence of a location dependent number value field affects theoretical descriptions of many physical and geometric quantities. A simple geometric example is worked out in detail, that of the length of a path. The localization of mathematical systems and the separation of number from number value or meaning both emphasize the role of observers. The separation of number from number value shows the role of observers in that value or meaning are conscious observer related concepts. Nothing, including numbers, has value or meaning to an unconscious observer. The localization of mathematical systems also shows the role of observers in that the mathematics that is potentially available to an observer is that at the same position as is the observer. This represents the mathematical knowledge that can reside in an observers brain. As an observer moves in space or space time, the mathematical knowledge potentially available to the observer is the collection of mathematical systems at the same location as the observer. It is hoped that this work, which was begun in 2010, will lead to a better understanding of the relation between the foundations of mathematics and physics, and the role that observers play in this relation.
참고문헌 (23)
- R. Omnes, "Wigner’s Unreasonable Effectiveness of Mathematics", Revisited, Foundations of Physics, 41, pp.1729~1739 (2011)
- A. Plotnitsky, "On the reasonable and unreasonable effectiveness of mathematics in classical and quantum physics", Foundations of Physics, 41, pp.466~491 (2011)
- E. Wigner, "Symmetries and Reflections", pp.222~237 (1966), Indiana Univ. Press
- P. Benioff, "Towards a Coherent Theory of Physics and Mathematics", Foundations of Physics, 32, pp.989~1029 (2002)
- P. Benioff, "Towards a coherent theory of physics and mathematics: the theory-experiment connection", Foundations of Phys, 35, pp.1825~1856 (2005)
- I. Montvay, "Quantum fields on a lattice" (1994), Cambridge University Press
- C. N. Yang, "Conservation of Isotopic Spin and Isotopic Gauge Invariance", Phys. Rev, 96, pp.191~195 (1954)
- Shapiro, S., "Spectrum Series, Mathematical Association of America", pp.157~178 (2008)
- J. Barwise, "Handbook of Mathematical Logic", pp.5~46 (1977), North-Holland Publishing Co
- H. J. Keisler, "Handbook of Mathematical Logic", pp.47~104 (1977), North-Holland Publishing Co
- P. Benioff, "New Gauge Field from Extension of Space Time Parallel Transport of Vector Spaces to the Underlying Number Systems", International Journal of Theoretical Physiocs, 50, pp.1887~1907 (2011)
- P. Benioff, "Intech open access publisher" (2012)
- P. Benioff, "Fiber bundle description of number scaling in gauge theory and geometry", Quantum Studies: Mathematics and Foundations, 2, pp.289~313 (2015)
- P. Benioff, "Effects of a scalar scaling field on quantum mechanics", Quantum Information Processing, 15(7), pp.3005~3034 (2016)
- M. Czachor, "Relativity of arithmetics as a fundamental symmetry of physics", Quantum Studies: Mathematics and Foundations, 3, pp.123~133 (2016)
- M. Czachor, "Dark energy as a manifestation of nontrivial arithmetic", Int. J. Theor. Phys, 56, pp.1364~1381 (2017)
- H. A. Smith, "Alone in the Universe", American Scientist, 99(4), pp.320~ (2011)
- F. Bezrukov, "The standard model Higgs boson as the infl aton", Physics Letters B, 659, pp.703~706 (2008)
- I. Zlatev, "Quintessence, Cosmic Coincidence, and the Cosmological Constant", Physical Review Letters, 82(5), pp.896899~ (1999)
- M. Rinaldi, "Higgs dark energy", Classical Quantum Gravity, 32 (2015)
- P. W. Higgs, "Broken Symmetries and the Masses of Gauge Bosons", Phys. Rev. Lett, 13(16), pp.508~ (1964)
- M. Saravani, "Dark matter from spacetime nonlocality", Physical Review D, 92, pp.103504~ (2015)
- Miao Li, "Dark energy, a brief review", Frontiers of Physics, 8, pp.828~846 (2013)