Related papers: Space and time as containers, Space divisibility, …

Some ideas aimed to understand that time is one-dimensional are briefly reviewed. Some attempts to construct theories in varieties with more spatial and temporal components are presented. It is discussed, from the epistemological point of…

Physics relies on mathematical spaces carefully matched to the phenomena under study. Phase space in classical mechanics, Hilbert space in quantum theory, configuration spaces in field theory all provide representations in which physical…

In spacetime physics, we frequently need to consider a set of all spaces (`universes') as a whole. In particular, the concept of `closeness' between spaces is essential. However, there has been no established mathematical theory so far…

Most of us think we know some basic facts about how time works. The facts we believe we know are based on a few intuitions about time, which are, in turn, based on our conscious waking experiences. As far as I can tell, these intuitions…

The concept of the space-time as emerging in the world phase transition, vs. a priori existing, is put forward. The theory of gravity with two basic symmetries, the global affine one and the general covariance, is developed. Implications…

Over the last decade a growing number of quantum-gravity researchers has been looking for opportunities for the first ever experimental evidence of a Planck-length quantum property of spacetime. These studies are usually based on the…

I present an analysis of the physical assumptions needed to obtain the metric structure of space-time. For this purpose I combine the axiomatic approach pioneered by Robb with ideas drawn from works on Weyl's "Raumproblem". The concept of a…

The often-asked question whether space-time is discrete or continuous may not be the right question to ask: Mathematically, it is possible that space-time possesses the differentiability properties of manifolds as well as the ultraviolet…

Two questions are investigated by looking successively at classical mechanics, special relativity, and relativistic gravity: first, how is space related with spacetime? The proposed answer is that each given reference fluid, that is a…

This paper puts forward a broad critical analysis of the concept of physical time. Clock effect is conceived as a consequence of the variation of the gravitational or pseudo gravitational potential, and it is remarked that only some real…

The essay is devoted to the problem of time in the context of quantum cosmology, which acquires a philosophical level to date. At an example of the minisuperspace model, we show that this problem is illusive in the sense that it does not…

In this review we present the problem of time in quantum physics, including a short history of the problem and the known objections about considering time a quantum observable. The need to deal with time as an observable is elaborated…

In quantum mechanics time usually appears as classical parameter which means that it is treated as being essentially different from spatial coordinates that are represented by operators. On the other hand, relativity theory demands to treat…

What is the shape of space in a spacetime? One way of addressing this issue is to consider edgeless spacelike submanifolds of the spacetime. An alternative is to foliate the spacetime by timelike curves and consider the quotient obtained by…

In this paper I argue that the fundamental aspect of our notion of time is that it defines an order relation, be it a total order relation between configurations of the world or just a partial order relation between events. This position is…

With the theory of special relativity, time has been linked with space into a four-dimensional space-time from which a basic question must be asked: can space be really transformed into time and vice-versa? The response is affirmative if…

This review consists of two parts. The first part establishes certain astrophysical bounds on the smoothness of classical spacetime. Some of the best bounds to date are based on the absence of vacuum Cherenkov radiation in ultrahigh-energy…

It is a widespread belief that results like G\"odel's incompleteness theorems or the intrinsic randomness of quantum mechanics represent fundamental limitations to humanity's strive for scientific knowledge. As the argument goes, there are…

The existence of a global time is often taken for granted but should instead be considered as a matter of investigation. By using the tools of global Lorentzian geometry I show that, under physically reasonable conditions, the impossibility…

There are competing schools of thought about the question of whether spacetime is fundamentally either continuous or discrete. Here, we consider the possibility that spacetime could be simultaneously continuous and discrete, in the same…