The Schrödinger Equation of the Hilbert Hyper Space

Yehuda Roth

Oranim Academic College, Kiryat Tivon, Israel.

DOI: 10.4236/jmp.2013.42023                

Abstract

Quantum measurement requires an observer to prepare a specific macroscopic measuring device from various options. In previous papers we redefined this observer role through a new concept: the observer determination, that is, the observer’s unique selection between the various measurement-devices. Unlike the measurement itself that is rationalized as dictated by nature, we presented the observer determination as a selection that cannot be disputed since it can neither be measured nor proven to be true or false. In general, we suggest that every action or decision made by the observer is eventually an output of some measurement. The apparently contradiction between the observer free determination and the deterministic measurement output was solved by extending the Hilbert space into a Hyper Hilbert space that is a space with hierarchy. In that frame the so called free selection of the observer determination in a certain level turns out to be a deterministic measurement output in the next higher level of the hierarchy. An important role of the conventional Hilbert space is played by the Schr?dinger equation. It determines a basis of stationary states. In this paper we define the Schr?dinger equation that corresponds with the various levels and we show that each level can be characterized by a unique time scale. We also show how various levels can be synchronized. We believe that this hyperspace level represents a certain level in the physics of consciousness and therefore a level unique time scale can contribute to the time perception of the mind.

Keywords

Hilbert Hyperspace; Observer Determination; Levels Hierarchy

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Y. Roth, “The Quantum Observer’s Consciousness,” EPL (Europhysics Letters), Vol. 82, No. 1, 2008, Article ID: 10006. doi:10.1209/0295-5075/82/10006
[2]	Y. Roth, “The Observer Determination,” International Journal of Theoretical Physics, Vol. 51, No. 12, 2012, pp. 3847-3855 doi:10.1007/s10773-012-1270-z
[3]	A. Sorli and I. Sorli, “Consciousness as a Research Tool into Space and Time,” Electronic Journal of Theoretical Physics, Vol. 6, No. 6, 2005, pp. 1-6.
[4]	H. P. Stapp, “The Hard Problem: A Quantum Approach,” Journal of Consciousness Studies, Vol. 3, No. 3, 1996, pp. 194-210.
[5]	http://arxiv.org/abs/quant-ph/9505023v2
[6]	C. Rovelly, “Relational Quantum Mechanics,” International Journal of Theoretical Physics, Vol. 35, No. 8, 1996, pp. 1637-1678. doi:10.1007/BF02302261
[7]	J. R. Searle, “The Rediscovery of the Mind,” MIT Press, Cambridge, 1992.
[8]	B. Baars, “The Conscious Access Hypothesis: Origins and Recent Evidence,” Oxford University Press, Oxford, 2001.
[9]	A. Bassi, “Dynamical Reduction Models: Present Status and Future Developments,” Journal of Physics: Conference Series, Vol. 67, No. 1, 2007, Article ID: 012013. doi:10.1088/1742-6596/67/1/012013
[10]	A. Bassi and D. G. M. Salvetti, “The Quantum Theory of Measurement within Dynamical Reduction Models,” Journal of Physics A: Mathematical and Theoretical, Vol. 40, No. 32, 2007, pp. 8959. doi:10.1088/1751-8113/40/32/011
[11]	S. L. Adler and A. Bassi, “Collapse Models with Non-White Noises,” Journal of Physics A: Mathematical and Theoretical, Vol. 40, No. 50, 2007, pp. 15083-15098. doi:10.1088/1751-8113/40/50/012