Related papers: The Time-Energy Principle in Algebraic Geometry
We give a short review of known exact inequalities that can be interpreted as "energy-time" and "frequency-time" uncertainty relations. In particular we discuss a precise form of signals minimizing the physical frequency-time uncertainty…
We give a brief account of the description of the standard model in noncommutative geometry as well as the thermal time hypothesis, questioning their relevance for quantum gravity.
The temporal Bell inequalities are derived from the assumptions of realism and locality in time. It is shown that quantum mechanics violates these inequalities and thus is in conflict with the two assumptions. This can be used for…
Even though irreversibility is one of the major hallmarks of any real life process, an actual understanding of irreversible processes remains still mostly semiempirical. In this paper we formulate a thermodynamic uncertainty principle for…
By collecting both quantum and gravitational principles, a space-time uncertainty relation $(\delta t)(\delta r)^{3}\geqslant\pi r^{2}l_{p}^{2}$ is derived. It can be used to facilitate the discussion of several profound questions, such as…
The problem of time operator in quantum mechanics is revisited. The unsharp measurement model for quantum time based on the dynamical system-clock interaction, is studied. Our analysis shows that the problem of the quantum time operator…
We have previously presented a version of the Weak Equivalence Principle for a quantum particle as an exact analog of the classical case, based on the Heisenberg picture analysis of free particle motion. Here, we take that to a full…
Quantum Geometrodynamics with intrinsic time development and momentric variables is presented. An underlying SU(3) group structure at each spatial point regulates the theory. The intrinsic time behavior of the theory is analyzed, together…
I consider in this book a formulation of Quantum Mechanics. Usually QM is formulated based on the notion of time and space, both of which are thought a priori given quantities or notions. However, when we try to define the notion of…
We proved that the uncertainty relation fits in with many-particle system and the equality of the relation corresponds to the thermodynamic equilibrium state, the inequality of the relation corresponds to the thermodynamic non-equilibrium…
Incorporating time into thermodynamics allows addressing the tradeoff between efficiency and power. A qubit engine serves as a toy model to study this tradeoff from first principles, based on the quantum theory of open systems. We study the…
The aim of this work is to review the concepts of time in quantum mechanics and general relativity to show their incompatibility. We show that the absolute character of Newtonian time is present in quantum mechanics and also partially in…
We review the present status of gauge theories built on various quantum space-times described by noncommutative space-times. The mathematical tools and notions underlying their construction are given. Different formulations of gauge theory…
The generalized uncertainty principle of string theory is derived in the framework of Quantum Geometry by taking into account the existence of an upper limit on the acceleration of massive particles.
The algebras of non-relativistic and of classical mechanics are unstable algebraic structures. Their deformation towards stable structures leads, respectively, to relativity and to quantum mechanics. Likewise, the combined relativistic…
Time plays different roles in quantum mechanics and gravity. These roles are examined and the problems that the conflict in the roles presents for quantum gravity are briefly summarised.
Understanding the electron clock and the role of complex numbers in quantum mechanics is grounded in the geometry of spacetime, and best expressed with Spacetime Algebra (STA). The efficiency of STA is demonstrated with coordinate-free…
The time-energy uncertainty relation is discussed for a relativistic massless particle. The Lorentz-invariant uncertainty relation is obtained between the root-mean-square energy deviation and the scatter of registration time. The…
We study the behaviour of a nonrelativistic quantum particle interacting with different potentials in the spacetimes of topological defects. We find the energy spectra and show how they differ from their free-space values.
In this article, we present a heuristic derivation of the on-shell equation of the Lorentzian classicalized holographic tensor network in the presence of a non-zero mass in the bulk spacetime. This derivation of the on-shell equation is…