Related papers: What is missing from Minkowski's "Raum und Zeit" l…
Minkowski space serves as a framework for the theoretical constructions that deal with manifestations of relativistic effects in physical phenomena. But neither Minkowski himself nor the subsequent developers of the relativity theory have…
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…
For over a century Minkowskian spacetime has dominated discussions of space contraction and time dilation within special relativity. Brown and Pooley have called into question both the assumptions of Minkowski and the effects his presumed…
The article is a tribute to Hermann Minkowski leading from his geometry of numbers to an attempt at using Finsler geometry for a break of Lorentz invariance.
Understanding the nature of time remains a key unsolved problem in science. Newton in the Principia asserted an absolute universal time that {\it `flows equably'}. Hamilton then proposed a mathematical unification of space and time within…
A simple visual representation of Minkowski spacetime appropriate for a student with a background in geometry and algebra is presented. Minkowski spacetime can be modeled with a Euclidean 4-space to yield accurate visualizations as…
The picture of space-time that Minkowski created in 1907 has been followed by two important developments in physics not contained in the original picture: general relativity and quantum mechanics. We will argue that the use of concepts of…
The special theory of relativity has fundamentally changed our views of space and time. The relativity of simultaneity in particular, and the theory of relativity as a whole, still presents significant difficulty for beginners in the…
Quantum theory and relativity are the pillar theories on which our understanding of physics is based. Poincar\'e invariance is a fundamental physical principle stating that the experimental results must be the same in all inertial reference…
In this essay, dedicated to the one hundredth anniversary of Hermann Minkowski's talk "Space and Time", I argue that physicists should face the issue of the reality of spacetime and worldtubes of physical objects for two reasons. First,…
The positive and negative energy modes of a field theory in $\kappa$-Minkowski/$\kappa$-Poincar\'e noncommutative spacetime have very different symmetry properties. This can be understood geometrically by considering that they span two…
In 1908, Minkowski put forward the idea that invariance under what we call today the Lorentz group, $GL(1,3, {\bf R})$, would be more meaningful in a four-dimensional space-time continuum. This suggestion implies that space and time are…
Minkowski space is a physically important space-time for which the finding an adequate holographic description is an urgent problem. In this paper we develop further the proposal made in hep-th/0303006 for the description as a duality…
The book presents ideas by H. Poincare and H. Minkowski according to those the essence and the main content of the relativity theory are the following: the space and time form a unique four-dimensional continuum supplied by the…
With special relativity, we seem to be facing a conundrum. It is a very well-tested theory; in this way, the Minkowski spacetime must be "capturing" essential features of space and time. However, its geometry seems to be incompatible with…
Broadly speaking, twistor theory is a framework for encoding physical information on space-time as geometric data on a complex projective space, known as a twistor space. The relationship between space-time and twistor space is non-local…
The $\rho$-Minkowski space-time, a Lie-algebraic deformation of the usual Minkowski space-time is considered. A star-product realization of this quantum space-time together with the characterization of the deformed Poincar\'e symmetry…
The starting point of this work is the principle that all movement of particles and photons must follow geodesics of a 4-dimensional space where time intervals are always a measure on geodesic arc lengths. The last 3 coordinates (alpha =…
In asymptotically Minkowski space-times, one finds a surprisingly rich interplay between geometry and physics in both the classical and quantum regimes. On the mathematical side it involves null geometry, infinite dimensional groups,…
These are expanded notes for a short series of lectures, presented at the University of Luxembourg in 2017, giving an introduction to some of the ideas of supersymmetry and supergeometry. In particular, we start from some motivating facts…