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The purpose of this paper is to show that the mathematics of quantum mechanics (QM) is the mathematics of set partitions (which specify indefiniteness and definiteness) linearized to vector spaces, particularly in Hilbert spaces. That is,…
The main results for the two-dimensional quantum gravity, conjectured from the matrix model or integrable approach, are presented in the form to be compared with the world-sheet or Liouville approach. In spherical limit the integrable side…
Recently, it is shown that, the quantum effects of matter are well described by the conformal degree of freedom of the space-time metric. On the other hand, it is a wellknown fact that according to Einstein's gravity theory, gravity and…
A new idea of quantum gravity is developed based on {\it Gravitational Complementary Principle}. This principle states that gravity has dual complement features: The quantum and classical aspects of gravity are complement and absolutely…
A quantum mechanics representation based on position ($\vec{r}$), linear momentum($\vec{p}$) and energy($E$) eigenvalues is presented here. A set of equations, explicitly independent on wave function, was derived relating these observables.…
Five fundamental scales of mass follow from holographic limitations, a self-similar law for angular momentum and the basic scaling laws for a fractal universe with dimension 2. The five scales correspond to the observable universe,…
A phenomenology for the deep spatial geometry of loop quantum gravity is introduced. In the context of a simple model, an atom of space, it is shown how purely combinatorial structures can affect observations. The angle operator is used to…
We review our recent work on quantum foundations of quantum mechanics, quantum field theory and quantum gravity (formulated as metastring theory) and various implications for the problems of dark matter and dark energy. The first point…
We study the quantum contributions to the classical cosmological constant in a quantum gravity theory for GR with matter on a piecewise linear spacetime corresponding to a triangulation of a smooth manifold. We use the effective action…
We show that in complete agreement with classical mechanics, the dynamics of any quantum mechanical wave packet in a linear gravitational potential involves the gravitational and the inertial mass only as their ratio. In contrast, the…
Amidst all candidates of physics beyond the Standard Model, string theory provides a unique proposal for incorporating gauge and gravitational interactions. In string theory, a four-dimensional theory that unifies quantum mechanics and…
We elaborate an interpretation of quantum physics founded on the hypothesis that quantum particles are conceptual entities playing the role of communication vehicles between material entities composed of ordinary matter which function as…
Quantum entanglement between several particles is essential for applications like quantum metrology or quantum cryptography, but it is also central for foundational phenomena like quantum non-locality. This leads to the problem of…
The self-gravitating systems are formed by particles interacting through gravity. They describe structure formation in the universe. As a consequence of the long range interaction of gravity, they are inhomogeneous even at thermal…
If time has three dimensions, how does a particle move? This paper demonstrates that quantum physics naturally emerges from a framework of three-dimensional time. We present the equations governing the motion of 0-spin, 1-spin, and 1/2-spin…
Relational particle models are of value in the absolute versus relative motion debate. They are also analogous to the dynamical formulation of general relativity, and as such are useful for investigating conceptual strategies proposed for…
Physicists believe, with some justification, that there should be a correspondence between familiar properties of Newtonian gravity and properties of solutions of the Einstein equations. The Positive Mass Theorem (PMT), first proved over…
In this study, we explore the field of physics through the lens of fractional dimensionality. We propose that space is not confined to integer dimensions alone, but can also be understood as a superposition of spaces that exist between…
A model of matter-coupled gravity in two dimensions is quantized. The crucial requirement for performing the quantization is the vanishing of the conformal anomaly, which is achieved by tuning a parameter in the interaction potential. The…
A new method involving the effective wave function is used to define the mass of a particle in a standard five-dimensional extension of general relativity. The mass is inversely proportional to the magnitude of the scalar field of the extra…