scholarly journals The Heisenberg Indeterminacy Principle in the Context of Covariant Quantum Gravity

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1209
Author(s):  
Massimo Tessarotto ◽  
Claudio Cremaschini

The subject of this paper deals with the mathematical formulation of the Heisenberg Indeterminacy Principle in the framework of Quantum Gravity. The starting point is the establishment of the so-called time-conjugate momentum inequalities holding for non-relativistic and relativistic Quantum Mechanics. The validity of analogous Heisenberg inequalities in quantum gravity, which must be based on strictly physically observable quantities (i.e., necessarily either 4-scalar or 4-vector in nature), is shown to require the adoption of a manifestly covariant and unitary quantum theory of the gravitational field. Based on the prescription of a suitable notion of Hilbert space scalar product, the relevant Heisenberg inequalities are established. Besides the coordinate-conjugate momentum inequalities, these include a novel proper-time-conjugate extended momentum inequality. Physical implications and the connection with the deterministic limit recovering General Relativity are investigated.

1995 ◽  
Vol 04 (01) ◽  
pp. 105-113 ◽  
Author(s):  
V. PERVUSHIN ◽  
T. TOWMASJAN

We show that the first principles of quantization and the experience of relativistic quantum mechanics can lead to the definition of observable time in quantum cosmology as a global quantity which coincides with the constrained action of the reduced theory up to the energy factor. The latter is fixed by the correspondence principle once one considers the limit of the “dust filled” Universe. The “global time” interpolates between the proper time for dust dominance and the conformal time for radiation dominance.


1993 ◽  
Vol 08 (09) ◽  
pp. 1629-1635 ◽  
Author(s):  
IAN H. REDMOUNT ◽  
WAI-MO SUEN

The simple physics of a free particle reveals important features of the path-integral formulation of relativistic quantum theories. The exact quantum-mechanical propagator is calculated here for a particle described by the simple relativistic action proportional to its proper time. This propagator is nonvanishing outside the light cone, implying that spacelike trajectories must be included in the path integral. The propagator matches the WKB approximation to the corresponding configuration-space path integral far from the light cone; outside the light cone that approximation consists of the contribution from a single spacelike geodesic. This propagator also has the unusual property that its short-time limit does not coincide with the WKB approximation, making the construction of a concrete skeletonized version of the path integral more complicated than in nonrelativistic theory.


2020 ◽  
Vol 35 (21) ◽  
pp. 2050114
Author(s):  
M. Bauer ◽  
C. A. Aguillón ◽  
G. E. García

The problem of time in the quantization of gravity arises from the fact that time in Schrödinger’s equation is a parameter. This sets time apart from the spatial coordinates, represented by operators in quantum mechanics (QM). Thus “time” in QM and “time” in general relativity (GR) are seen as mutually incompatible notions. The introduction of a dynamical time operator in relativistic quantum mechanics (RQM), that follows from the canonical quantization of special relativity and that in the Heisenberg picture is also a function of the parameter [Formula: see text] (identified as the laboratory time), prompts to examine whether it can help to solve the disfunction referred to above. In particular, its application to the conditional interpretation of time in the canonical quantization approach to quantum gravity is developed.


2001 ◽  
Vol 56 (1-2) ◽  
pp. 67-75 ◽  
Author(s):  
Daniel M. Greenberger

Abstract It is shown that the generally accepted statement that one cannot superpose states of different mass in non-relativistic quantum mechanics is inconsistent. It is pointed out that the extra phase induced in a moving system, which was previously thought to be unphysical, is merely the non-relativistic residue of the "twin-paradox" effect. In general, there are phase effects due to proper time differences between moving frames that do not vanish non-relativistically. There are also effects due to the equivalence of mass and energy in this limit. The remedy is to include both proper time and rest energy non-relativis-tically. This means generalizing the meaning of proper time beyond its classical meaning, and introduc­ ing the mass as its conjugate momentum. The result is an uncertainty principle between proper time and mass that is very general, and an integral role for both concepts as operators in non-relativistic physics.


Symmetry ◽  
2018 ◽  
Vol 10 (7) ◽  
pp. 287 ◽  
Author(s):  
Claudio Cremaschini ◽  
Massimo Tessarotto

Space-time quantum contributions to the classical Einstein equations of General Relativity are determined. The theoretical background is provided by the non-perturbative theory of manifestly-covariant quantum gravity and the trajectory-based representation of the related quantum wave equation in terms of the Generalized Lagrangian path formalism. To reach the target an extended functional setting is introduced, permitting the treatment of a non-stationary background metric tensor allowed to depend on both space-time coordinates and a suitably-defined invariant proper-time parameter. Based on the Hamiltonian representation of the corresponding quantum hydrodynamic equations occurring in such a context, the quantum-modified Einstein field equations are obtained. As an application, the quantum origin of the cosmological constant is investigated. This is shown to be ascribed to the non-linear Bohm quantum interaction of the gravitational field with itself in vacuum and to depend generally also on the realization of the quantum probability density for the quantum gravitational field tensor. The emerging physical picture predicts a generally non-stationary quantum cosmological constant which originates from fluctuations (i.e., gradients) of vacuum quantum gravitational energy density and is consistent with the existence of quantum massive gravitons.


Author(s):  
رضوان جمال الأطرش ◽  
نجوى نايف شكوكاني

        الملخّص      هدف هذا البحث إبراز إمكانية التأثر العملي بأسلوب التعليل في القرآن الكريم، ومحاولة البحث في تطبيقاته في واقع العملية التعليمية من العالم والمتعلم، بحيث لم يقتصر على الدراسة اللغوية أو الأصولية النظرية؛ وخصوصاً بعد التعريف بهذا الأسلوب وأدواته وأهميته وبيان اللوازم الخاصة للعالم والمتعلم للتأثر به، وقد تم ذلك من خلال استخدام المنهج الاستقرائي بتتبع أعمال العلماء في ذلك وتم رصد أقوال المفسرين فيما يتعلق بالأساليب البيانية وآيات التعليل ووجوه الإعجاز القرآني، ومن ثم استُخدم المنهج التحليلي لإثبات ذلك الأثر وإثبات وجود إشارات وأدلة على مظاهر التأثر؛ واستنتاج حقيقة إمكانية استمرارية البحث في كل أدوات وآيات ومواضيع ذلك الأسلوب بنفس الطريقة التي تمّ طرحُها، مما يثري هذا المجال، ويفتح العقول ويدفعها للنظر والتدبر والبحث في آي القرآن، وفي كل المناحي، منطلقةً من فكر التجديد، والإفادة من مستجدات العصر وعلومه ضمن ضوابط العقيدة الغراء والشرع الحنيف. الكلمات المفتاحية: أسلوب التعليل، أدوات أسلوب التعليل، التدبر، التعليم التقليدي، أثر.  Abstract This study intends to highlight the possible practical impact of the principles of argumentation found in the Qur’an. The study attempts to apply the principles on the actual education process of the scholars and students without limiting it to linguistic studies or theoretical principles. This was done after introducing the principles of reasoning, its tools, its importance, and disclosing the special requirements for the scholars and students in order to be influenced by the latter principles.  The work used inductive method to track the works of the scholars on the subject and observe the opinions of the Qur’an-commentators in relation to principles of explanation, verses of argument, and aspects of Qur’anic Inimitability. Analytical method was used to establish the impacts of the Qur’anic arguments; to prove the presence of signs and evidences for the manifestation of the impacts; and to make the continuity of this research possible in all the tools, verses and topics related to the principles of Qur’anic argument. Among those things that enrich this work is that it opens the minds, and pushes it to ponder and study the verses of the Qur’an. For every direction it becomes the starting point for the innovative thinking, and benefit for the new age and its sciences while maintaining the harmony with the principles of creed and the true SharÊ‘ah. Keywords: Principles of Argumentation, Tools of Argumentation Principles, Thinking, Traditional Education, Effect.


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