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On Solutions to the Nonlinear Phase Modification of the Schrödinger Equation
, 1999
"... We present some physically interesting, in general nonstationary, onedimensional solutions to the nonlinear phase modification of the Schrödinger equation proposed recently. The solutions include a coherent state, a phasemodified Gaussian wave packet in the potential of harmonic oscillator whose ..."
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Cited by 5 (5 self)
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We present some physically interesting, in general nonstationary, onedimensional solutions to the nonlinear phase modification of the Schrödinger equation proposed recently. The solutions include a coherent state, a phasemodified Gaussian wave packet in the potential of harmonic oscillator whose strength varies in time, a free Gaussian soliton, and a similar soliton in the potential of harmonic oscillator comoving with the soliton. The last of these solutions suggests that depending on the assumptions concerning the characteristic size of the oscillator there may exist an energy level in the spectrum of harmonic oscillator not predictable by the linear theory. The free solitonic solution could be thought of as a model for a particle representation in the waveparticle duality embodied in the quantum theory. It is found that the physical size of this particle is equal to its Compton wavelength. The solitonic solutions exist only for the negative coupling constant for which the Gaussian wave packets must be larger than some critical finite size if their energy is to be bounded, i.e., they cannot be pointlike objects. Electronic address:
Why the Quantum Must Yield to Gravity
"... After providing an extensive overview of the conceptual elements – such as Einstein’s ‘hole argument ’ – that underpin Penrose’s proposal for gravitationally induced quantum state reduction, the proposal is constructively criticised. Penrose has suggested a mechanism for objective reduction of quan ..."
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Cited by 3 (1 self)
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After providing an extensive overview of the conceptual elements – such as Einstein’s ‘hole argument ’ – that underpin Penrose’s proposal for gravitationally induced quantum state reduction, the proposal is constructively criticised. Penrose has suggested a mechanism for objective reduction of quantum states with postulated collapse time τ = ¯h/∆E, where ∆E is an illdefinedness in the gravitational selfenergy stemming from the profound conflict between the principles of superposition and general covariance. Here it is argued that, even if Penrose’s overall conceptual scheme for the breakdown of quantum mechanics is unreservedly accepted, his formula for the collapse time of superpositions reduces to τ → ∞ (∆E → 0) in the strictly Newtonian regime, which is the domain of his proposed experiment to corroborate the effect. A suggestion is made to rectify this situation. In particular, recognising the cogency of Penrose’s reasoning in the domain of full ‘quantum gravity’, it is demonstrated that an appropriate experiment which could in principle corroborate his argued ‘macroscopic ’ breakdown of superpositions is not the one involving nonrotating mass distributions as he has suggested, but a Leggetttype SQUID or BEC
Quantum, consciousness and panpsychism: a solution to the hard problem
"... We analyze the results and implications of the combination of quantum and consciousness in terms of the recent QSC analysis. The quantum effect of consciousness is first explored. We show that the consciousness of the observer can help to distinguish the nonorthogonal states under some condition, wh ..."
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We analyze the results and implications of the combination of quantum and consciousness in terms of the recent QSC analysis. The quantum effect of consciousness is first explored. We show that the consciousness of the observer can help to distinguish the nonorthogonal states under some condition, while the usual physical measuring device without consciousness can’t. The result indicates that the causal efficacies of consciousness do exist when considering the basic quantum process. Based on this conclusion, we demonstrate that consciousness is not reducible or emergent, but a new fundamental property of matter. This provides a quantum basis for panpsychism. Furthermore, we argue that the conscious process is one kind of quantum computation process based on the analysis of consciousness time and combination problem. It is shown that a unified theory of matter and consciousness should include two parts: one is the complete quantum evolution of matter state, which includes the definite nonlinear evolution element introduced by consciousness, and the other is the psychophysical principle or corresponding principle between conscious content and matter state. Lastly, some experimental suggestions are presented to confirm the theoretical analysis of the paper. Key words: quantum process, consciousness, distinguish the nonorthogonal states, causal efficacies of consciousness, fundamental property of matter, panpsychism, quantum computation, definite
Quantum evolution in spacetime foam grqc/9911002
, 1999
"... In this work, I review some aspects concerning the evolution of quantum lowenergy fields in a foamlike spacetime, with involved topology at the Planck scale but with a smooth metric structure at large length scales, as follows. Quantum gravitational fluctuations may induce a minimum length thus intr ..."
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In this work, I review some aspects concerning the evolution of quantum lowenergy fields in a foamlike spacetime, with involved topology at the Planck scale but with a smooth metric structure at large length scales, as follows. Quantum gravitational fluctuations may induce a minimum length thus introducing an additional source of uncertainty in physics. The existence of this resolution limit casts doubts on the metric structure of spacetime at the Planck scale and opens a doorway to nontrivial topologies, which may dominate Planck scale physics. This foamlike structure of spacetime may show up in lowenergy physics through loss of quantum coherence and modedependent energy shifts, for instance, which might be observable. Spacetime foam introduces nonlocal interactions that can be modeled by a quantum bath, and lowenergy fields evolve according to a master equation that displays such effects. Similar laws are also obtained for quantum mechanical systems evolving according to good real clocks, although the underlying Hamiltonian structure in this case establishes serious differences among both scenarios. Contents.—