相关论文: K-calculus in 4-dimensional optics

We argue that the construction of spacetime is personal, specific to each observer, and requires combining aspects of both discovery and creation. What is usually referred to as the block universe then emerges by noting that part of the…

Dual of K-frames in a right quaternionic Hilbert space has been recently introduced and studied by Ellouz[1]. In this paper, we study duals of K-frames and prove a characterization of a K-dual in terms of the canonical K-dual of a K-frame…

A holistic view of the cosmological appearance and development of space is obtained by studying space as a spherically closed surface of a 4-sphere in a zero energy balance between motion and gravitation. Such an approach re-establishes…

In this paper, it is shown why Lorentz Transformation implies the general case where observed events are not necessarily in the inertia frame of any observer but assumes a special scenario when determining the length contraction and time…

The k-calculus was advanced by Hermann Bondi as a means of explaining special relativity using only simple algebra [1]. Bondi's argument was placed in the context of classical electrodynamics. In this paper it is placed in context of…

We present a novel derivation of both the Minkowski metric and Lorentz transformations from the consistent quantification of a causally ordered set of events with respect to an embedded observer. Unlike past derivations, which have relied…

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…

It is demonstrated that the measured spatial separation of two objects, at rest in some inertial frame, is invariant under space-time transformations. This result holds in both Galilean and Special Relativity. A corollary is that there are…

Hardy's theorem states that the hidden variables of any realistic theory of quantum measurement, whose predictions agree with ordinary quantum theory, must have a preferred Lorentz frame. This presents the conflict between special…

A modern re-visitation of the consequences of the lack of an intrinsic notion of instantaneous 3-space in relativistic theories leads to a reformulation of their kinematical basis emphasizing the role of non-inertial frames centered on an…

In the Special Theory of Relativity space and time intervals are different in different frames of reference. As a consequence, the quantity 'velocity' of classical mechanics splits into different quantities in Special Relativity, coordinate…

The Lorentzian length of a timelike curve connecting both endpoints of a classical computation is a function of the path taken through Minkowski spacetime. The associated runtime difference is due to time-dilation: the phenomenon whereby an…

In \cite{2} it was shown that Einstein's special theory of relativity and Maxwell's field theory have mathematically equivalent dual versions. The dual versions arise from an identity relating observer time to proper time as a contact…

The mathematical treatment and graphical representation of Special Relativity (SR) are well established, yet carry deep implications that remain hard to visualize. This paper presents a new graphical interpretation of the geometry of SR…

One potentially realistic specification for devices designed with transformation optics is that they operate with high precision in curved space-time, such as Earth orbit. This raises the question of what, if any, role does space-time…

The mechanics of an oriented point (point with "spin") based on 3D and 4D Frenet equations is considered. In such mechanics there is an opportunity to describe formally any physical trajectory of a particle with own rotation. We use…

We generalise the notions of supersymmetry and superspace by allowing generators and coordinates transforming according to more general Lorentz representations than the spinorial and vectorial ones of standard lore. This yields novel…

The conventional discussion of apparent distortions of space and time in Special Relativity (the Lorentz-Fitzgerald Contraction and Time Dilatation) is extended by considering observations of : (i) moving objects of limited lifetime in…

It is shown that Euclidean electrodynamics is the exact 4-dimensional analogue of 3-dimensional magnetostatics. This concept is related to a 4-dimensional generalization of the cross product between two vectors where the only essential…

The presentation makes use of geometric algebra, also known as Clifford algebra, in 5-dimensional spacetime. The choice of this space is given the character of first principle, justified solely by the consequences that can be derived from…