the only justification for the einstein velocity addition law appeared to be its empirical adequacy, so that the intrinsic beauty and harmony in einstein addition remained for a long timea mystery to be conquered. accordingly, the aim of this expository article is to present(i) the einstein relativistic vector addition,(ii) the resulting einstein scalar multiplication,(iii) the einstein relativ...

We present some basic facts concerning simultaneity in both special and general relativity. We discuss Weyl’s proof of the consistence of Einstein’s synchronization convention and consider the general relativistic problem of assigning a time function to a congruence of timelike curves. 1 Simultaneity in special relativity In special relativity the possibility of synchronizing distant clocks so ...

In a new theory, local Lorentz invariance is a low-energy symmetry which no longer holds when a fermion energy E is well above 1 TeV. Here we find that the modified E(p) relation is consistent with observation, and is in fact nearly the same as in Einstein relativity. On the other hand, there is a strong modification of the fermion equation of motion and propagator at ultrahigh energy, which sh...

This paper describes a method for the detection of tracking of elongated structures that is robust under changes of scale and orientation. This method is based on extending the concept of scale invariant natural interest points to include elongated ridge structures. An operator is proposed that directly detects ridge points and provides an estimation of their elongation and orientation. A track...

This paper introduces a novel method for constructing and selecting scale-invariant object parts. Scale-invariant local descriptors are first grouped into basic parts. A classifier is then learned for each of these parts, and feature selection is used to determine the most discriminative ones. This approach allows robust part detection, and it is invariant under scale changes—that is, neither t...

We discuss a rigorous foundation of the pure scale relativity theory for a one-dimensional space variable. We define several notions as ‘‘representation’’ of a continuous function, scale law and minimal resolution. We define precisely the meaning of a scale reference system and space reference system for non-differentiable one-dimensional manifolds. 2002 Elsevier Science Ltd. All rights reserved.

There are several perspectives which have motivated the work. One of the most important is that of "linguistic relativity". This paper definitely falls in the tradition started by Herder (1772), continued by Humboldt (1836), Boas (1911), Sapir (1921), Whorf (1956), Weissgerber (1953), Kainz (1946), and Leise (1975), to mention only a few of the historically important contributors to the investi...

This paper presents some ideas which might assist teachers incorporating special relativity into an introductory physics curriculum. One can define the proper-time/velocity pair, as well as the coordinate-time/velocity pair, of a traveler using only distances measured with respect to a single “map” frame. When this is done, the relativistic equations for momentum, energy, constant acceleration,...