The Quaternion Structure of Space-Time and Arrow of Time

ABSTRACT

In fundamental theories of physics, the dynamical equations all have time inversion invariance. Except for the evolution of some simple system which has realistic inverse processes, but for a slightly more complicated system, the evolution processes are irreversible. This is the problem of arrow of time, which is always warmly debated. In different point of view, we find there may have some conceptual misunderstanding in the controversy: 1) The realization of an inverse process does not mean the time of the system goes backward. 2) The principles of relativity and covariance are the constraints to physical laws, but not constraints to specific solutions. The equations must be covariant, but the solutions are not definitely symmetric. 3) Time is a global property of the universe, which is a measurement of the evolution process of the universe. The internal time of a matter system reflecting its internal evolution speed also takes this cosmic time as a unified background and standard of measurement. 4) The universe has a unified cosmic time*T* and a cosmic space related to this cosmic time. They are objective and absolute. 5) The eigensolution of a spinor is a critical state losing time concept, which responses the interaction of environment with some uncertainty, then the evolution process of the world is not uniquely determined. 6) The non-uniqueness of the evolution process means that the inverse process is absent. So for a world including spinors, the evolution is essentially irreversible. In this paper, according to the widely accepted principles and direct calculations of transformation, we reveal the misunderstandings in the usual controversy, and then give more natural and reasonable explanations for structure of space-time and arrow of time.

In fundamental theories of physics, the dynamical equations all have time inversion invariance. Except for the evolution of some simple system which has realistic inverse processes, but for a slightly more complicated system, the evolution processes are irreversible. This is the problem of arrow of time, which is always warmly debated. In different point of view, we find there may have some conceptual misunderstanding in the controversy: 1) The realization of an inverse process does not mean the time of the system goes backward. 2) The principles of relativity and covariance are the constraints to physical laws, but not constraints to specific solutions. The equations must be covariant, but the solutions are not definitely symmetric. 3) Time is a global property of the universe, which is a measurement of the evolution process of the universe. The internal time of a matter system reflecting its internal evolution speed also takes this cosmic time as a unified background and standard of measurement. 4) The universe has a unified cosmic time

Cite this paper

Y. Gu, "The Quaternion Structure of Space-Time and Arrow of Time,"*Journal of Modern Physics*, Vol. 3 No. 7, 2012, pp. 570-580. doi: 10.4236/jmp.2012.37078.

Y. Gu, "The Quaternion Structure of Space-Time and Arrow of Time,"

References

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[13] G. F. R. Ellis and J.-Ph. Uzan, “c Is the Speed of Light, Isn’t It?” American Journal of Physics, Vol. 73, No. 3, 2005, pp. 240-247. doi:10.1119/1.1819929

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[15] Y. Q. Gu, “The Spinor Connection and Its Dynamical Effects,” arXiv:gr-qc/0610001v3.

[16] Y. Q. Gu, “A Canonical Form for Relativistic Dynamic Equation,” Advances in Applied Clifford Algebras, Vol. 7, No. 1, 1997, pp. 13-24. doi:10.1007/BF03041212

[17] G. F. R. Ellis, “On the Limits of Quantum Theory: Contextuality and the Quantum-Classical Cut,” arXiv:1108.5261.

[18] OPERA Collaboration, “Measurement of the Neutrino Velocity with the OPERA Detector in the CNGS Beam,” arXiv:1109.4897v2.

[19] Y. Q. Gu, “Some Properties of the Spinor Soliton,” Advances in Applied Clifford Algebras, Vol. 8, No. 1, 1998, pp. 17-29. doi:10.1007/BF03041923

[20] Y. Q. Gu, “The Characteristic Functions and Their Typical Values for the Nonlinear Spinors,” arXiv:hep-th/0611210.

[21] Y. Q. Gu, “New Approach to N-body Relativistic Quantum Mechanics,” International Journal of Modern Physics, Vol. A22, 2007, pp. 2007-2020. doi:10.1142/S0217751X07036233

[22] Y. Q. Gu, “A Sensitive Test of Mass-Energy Relation,” arXiv:hep-th/0610189.

[1] S. F. Savitt, “Time’s Arrows Today,” Cambridge University Press, Cambridge, 1995. doi:10.1017/CBO9780511622861

[2] J. L. Lebowitz, “Boltzmann’s Entropy and Time’s Arrow,” Physics Today, Vol. 46, No. 9, 1993, pp. 32-38.

[3] P. M. Harman, “The Natural Philosophy of James Clerk Maxwell,” Cambridge University Press, Cambridge, 1998.

[4] D. Ruelle, “Chance and Chaos,” Princeton University Press, New Jersey, 1991.

[5] D. Albert, “Time and Chance,” Harvard University Press, Cambridge, 2000.

[6] H. D. Zeh, “The Physical Basis of the Direction of Time,” Springer-Verlag, Berlin, 2001.

[7] S. W. Hawking, R. Laflamme and G. W. Lyons, “The Origin of Time Asymmetry,” arXiv:gr-qc/9301017.

[8] J. W. Moffat, “Quantum Gravity, the Origin of Time and Time’s Arrow,” arXiv:gr-qc/9209001.

[9] I. Dincer and Y. A. Cengel, “Energy, Entropy and Exergy Concepts and Their Roles in Thermal Engineering,” Entropy, Vol. 3, No. 3, 2001, pp. 116-149. doi:10.3390/e3030116

[10] G. F. R. Ellis, “On the Flow of Time,” arXiv:0812.0240.

[11] Y. Q. Gu, “Some Subtle Concepts in Fundamental Physics,” arXiv:0901.0309v1

[12] Y. Q. Gu, “Some Paradoxes in Special Relativity and the Resolutions,” Advances in Applied Clifford Algebras, Vol. 21, No. 1, 2011, pp. 103-119. doi:10.1007/s00006-010-0244-6

[13] G. F. R. Ellis and J.-Ph. Uzan, “c Is the Speed of Light, Isn’t It?” American Journal of Physics, Vol. 73, No. 3, 2005, pp. 240-247. doi:10.1119/1.1819929

[14] Y. Q. Gu, “The Vierbein Formalism and Energy-Mo- mentum Tensor of Spinors,” arXiv:gr-qc/0612106.

[15] Y. Q. Gu, “The Spinor Connection and Its Dynamical Effects,” arXiv:gr-qc/0610001v3.

[16] Y. Q. Gu, “A Canonical Form for Relativistic Dynamic Equation,” Advances in Applied Clifford Algebras, Vol. 7, No. 1, 1997, pp. 13-24. doi:10.1007/BF03041212

[17] G. F. R. Ellis, “On the Limits of Quantum Theory: Contextuality and the Quantum-Classical Cut,” arXiv:1108.5261.

[18] OPERA Collaboration, “Measurement of the Neutrino Velocity with the OPERA Detector in the CNGS Beam,” arXiv:1109.4897v2.

[19] Y. Q. Gu, “Some Properties of the Spinor Soliton,” Advances in Applied Clifford Algebras, Vol. 8, No. 1, 1998, pp. 17-29. doi:10.1007/BF03041923

[20] Y. Q. Gu, “The Characteristic Functions and Their Typical Values for the Nonlinear Spinors,” arXiv:hep-th/0611210.

[21] Y. Q. Gu, “New Approach to N-body Relativistic Quantum Mechanics,” International Journal of Modern Physics, Vol. A22, 2007, pp. 2007-2020. doi:10.1142/S0217751X07036233

[22] Y. Q. Gu, “A Sensitive Test of Mass-Energy Relation,” arXiv:hep-th/0610189.