相关论文: The Meaning of Dimensions

Despite the extraordinary successes the two great bastions of $20^{th}$ century science (Quantum Theory and General Relativity) are troubled with serious conceptual and mathematical difficulties. As a result, further growth of fundamental…

Five dimensional model with extended dimensions investigated. It is shown that four dimensionality of our world is the result of stability requirement. Extra component of Einstein equations giving trapping solution for matter fields…

Have our fundamental theories got time right? Does size really matter? Or is physics all in the eyes of the beholder? In this essay, we question the origin of time and scale by reevaluating the nature of measurement. We then argue for a…

The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a high-dimensional space and concepts are represented by regions in this space. In this…

The fact that in Minkowski space, space and time are both quantized does not have to be introduced as a new postulate in physics, but can actually be derived by combining certain features of General Relativity and Quantum Mechanics. This is…

Several physical concepts, including the concept of time, are clarified herein by taking into account existing experimental data. In addition, the missing links among these physical concepts are established. This allows us to take another…

A rigorous mathematical theory of dimensional analysis, systematically accounting for the use of physical quantities in science and engineering, perhaps surprisingly, was not developed until relatively recently. We claim that this has…

The way we view the reality of nature, including ourselves, depend on consciousness.It also defines the identity of the person, since we know people in terms of their experiences. In general, consciousness defines human existence in this…

Even though the concepts of time and space are basic concepts of physics, they have not been vouchsafed a constructive definition. As to space, this is no wonder because a correct notion of space cannot be formed in the frame of the…

We propose quantum-mechanical systems in which the number of spatial dimensions is promoted to a dynamical quantum variable, making the effective dimension state-dependent. Interestingly, systems of this form can exhibit enhanced symmetries…

In unified field theories with more than four dimensions, the form of the equations of physics in spacetime depends in general on the choice of coordinates in higher dimensions. The reason is that the group of coordinate transformations in…

Conventional thinking says the universe is infinite. But it could be finite and relatively small, merely giving the illusion of a greater one, like a hall of mirrors. Recent astronomical measurements add support to a finite space with a…

The idea that possible configurations of a physical system can be represented as points in a multidimensional configuration space ${\cal C}$ is explored. The notion of spacetime, without ${\cal C}$, does not exist in this theory. Spacetime…

Space and time are central concepts for understanding our World. They are important ingredients at the core of every scientific theory and subject of intense debate in philosophy. Albert Einstein's Special and General theories of Relativity…

The numerical dimension is a numerical measure of the positivity of a pseudo-effective divisor $L$. There are several proposed definitions of the numerical dimension due to Nakayama (2004) and Boucksom et al. (2004). We prove the equality…

We propose a possible answer to one of the most exciting open questions in physics and cosmology, that is the question why we seem to experience four- dimensional space-time with three ordinary and one time dimensions. We have known for…

The implications of string theory for understanding the dimension of uncompactified spacetime are investigated. Using recent ideas in string cosmology, a new model is proposed to explain why three spatial dimensions grew large. Unlike the…

The concept of synthetic dimensions has emerged as a powerful framework in photonics and atomic physics, enabling the exploration of high-dimensional physics beyond conventional spatial constraints. Originally developed for quantum…

The most dramatic developments in theoretical physics in the next millennium are likely to come when we make progress on so far unresolved foundational questions. In this essay I consider two of the deepest problems confronting us, the…

We consider the dimensions of finite type of representations of a partially ordered set, i.e. such that there is only finitely many isomorphism classes of representations of this dimension. We give a criterion for a dimension to be of…