scholarly journals Approaching space-time through velocity in doubly special relativity

2004 ◽  
Vol 70 (12) ◽  
Author(s):  
R. Aloisio ◽  
A. Galante ◽  
A. F. Grillo ◽  
E. Luzio ◽  
F. Méndez
2003 ◽  
Vol 12 (02) ◽  
pp. 299-315 ◽  
Author(s):  
J. KOWALSKI-GLIKMAN ◽  
S. NOWAK

Doubly Special Relativity (DSR) theory is a recently proposed theory with two observer-independent scales (of velocity and mass), which is to describe a kinematic structure underlining the theory of Quantum Gravity. We observe that there are infinitely many DSR constructions of the energy–momentum sector, each of whose can be promoted to the κ-Poincaré quantum (Hopf) algebra. Then we use the co-product of this algebra and the Heisenberg double construction of κ-deformed phase space in order to derive the non-commutative space–time structure and the description of the whole of DSR phase space. Next we show that contrary to the ambiguous structure of the energy momentum sector, the space–time of the DSR theory is unique and related to the theory with non-commutative space–time proposed long ago by Snyder. This theory provides non-commutative version of Minkowski space–time enjoying ordinary Lorentz symmetry. It turns out that when one builds a natural phase space on this space–time, its intrinsic length parameter ℓ becomes observer-independent.


2005 ◽  
Vol 20 (20n21) ◽  
pp. 4925-4940 ◽  
Author(s):  
M. DASZKIEWICZ ◽  
K. IMIŁKOWSKA ◽  
J. KOWALSKI-GLIKMAN ◽  
S. NOWAK

In this paper we recall the construction of scalar field action on κ-Minkowski space–time and investigate its properties. In particular we show how the coproduct of κ-Poincaré algebra of symmetries arises from the analysis of the symmetries of the action, expressed in terms of Fourier transformed fields. We also derive the action on commuting space–time, equivalent to the original one. Adding the self-interaction Φ4 term we investigate the modified conservation laws. We show that the local interactions on κ-Minkowski space–time give rise to six inequivalent ways in which energy and momentum can be conserved at four-point vertex. We discuss the relevance of these results for Doubly Special Relativity.


1991 ◽  
Vol 32 (7) ◽  
pp. 1788-1795 ◽  
Author(s):  
Daniel Zerzion ◽  
L. P. Horwitz ◽  
R. I. Arshansky

2008 ◽  
Vol 660 (3) ◽  
pp. 267-274 ◽  
Author(s):  
Pierre Gosselin ◽  
Alain Bérard ◽  
Hervé Mohrbach ◽  
Subir Ghosh

2013 ◽  
Vol 23 ◽  
pp. 373-378
Author(s):  
PETR JIZBA ◽  
FABIO SCARDIGLI

We show how a Brownian motion on a short scale can originate a relativistic motion on scales larger than particle's Compton wavelength. Special relativity appears to be not a primitive concept, but rather it statistically emerges when a coarse graining average over distances of order, or longer than the Compton wavelength is taken. Our scheme accommodates easily also the doubly special relativistic dynamics. A previously unsuspected, common statistical origin of the two frameworks is brought to light for the first time.


2021 ◽  
Vol 19 (4) ◽  
pp. 01-14
Author(s):  
Meriama Hansali Mebarki

The reinforcement sensitivity theory lacks basic sources of any human experience :time, place, and learning contexts that have shaped the reinforcement; therefore I have assumed a missing link in Gray's framework based on special relativity relying on the «what, where, and when of happenning»? as major resources of human conscious experience, which under punishment or reward exceed the sensitivity to pleasant or unpleasant stimuli transcending therefore the Weber law, that's why I called it: Psychological Space-Time Reinforcement Sensitivity “PSTRS” axis. The lasts explains BAS and BIS systems sensitivity to reinforcement across the cognitive space-time continuum of episodic memory, and not only across the two great dimensions of fear/anxiety and defensive distance of the McNaughton & Corr model of 2004. So, based on the disruption of the high-sensitivity information processing system in the brain, the four-dimensional conscious experience is distorted by its underlying sources and context. Thus, one of the timedominating records prevents the individual from overcoming the present., such in depression, obsessive compulsive disorder and post-traumatic stress disorder (psychological sensitivity to the past). These temporal records clearly lose their sequence and associative nature in dissociative symptoms due to the disruption of the most important milestone on which Einstein's physics was based. Consequently, psychological space-time reinforcement sensitivity supposes that psychological disorders can be interpreted according to the laws of special relativity (acceleration / deceleration), but this seems more complicated when it comes to mental disorders where the self is disturbed on its spatio-temporal axis as observed in schizophrenia. Schizophrenia looks like a three-componements disorder characterized by a disruption of the experience of time, place and self, which could be asummed up as a “self space-time disturbance". Notably schizophrenic patients appear losing the ability to gather in a dynamic way these componements, as if the world seemed missig the gestalt characteristic or fragmented. The past felt like an inevitable destiny inhibits the direction towards the future; sometimes disorient the self to the point of feeling lost, as if the psychological time slows down to the point of feeling separated from the « now » the physical time. So are we dealing with an Euclidian space? The article attempts to provide a non-traditional interpretation of mental disorders by including general relativity in psychological studies, based on the neurobiological bases involved in the spatio-temporal processing of the conscious experience in the quantum brain.


2019 ◽  
pp. 265-284
Author(s):  
Steven J. Osterlind

This chapter provides the context for the early twentieth-century events contributing to quantification. It was the golden age of scientific exploration, with explorers like David Livingstone, Sir Richard Burton, and Sir Ernest Shackleton, and intellectual pursuits, such as Hilbert’s set of unsolved problems in mathematics. However, most of the chapter is devoted to discussing the last major influencer of quantification: Albert Einstein. His life and accomplishments, including his theory of relativity, make up the final milestone on our road to quantification. The chapter describes his time in Bern, especially in 1905, when he published several famous papers, most particularly his law of special relativity, and later, in 1915, when he expanded it to his theory of general relativity. The chapter also provides a layperson’s description of the space–time continuum. Women of major scientific accomplishments are mentioned, including Madame Currie and the mathematician Maryam Mirzakhani.


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