Special relativity in complex vector algebra

نویسنده

  • Garret Sobczyk
چکیده

Special relativity is one of the monumental achievements of physics of the 20th Century. Whereas Einstein used a coordinate based approach [1], which obscures important geometric aspects of this fundamental theory, many coordinate free geometric languages have since been developed. In [2], D. Hestenes showed how the ideas of special relativity can be elegantly expressed in space-time algebra. The purpose of this paper is to examine the fundamental ideas of special relativity in a complex vector-based language that is the natural generalization of the Gibbs-Heaviside vector algebra of 3-dimensional space [3].

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The Principle of Relativity: From Ungar’s Gyrolanguage for Physics to Weaving Computation in Mathematics

‎This paper extends the scope of algebraic computation based on a non standard $times$ to ‎the more basic case of a non standard $+$‎, ‎where standard means associative ‎and commutative‎. ‎Two physically meaningful examples of a non standard $+$ are ‎provided by the observation of motion in Special Relativity‎, ‎from either ‎outside (3D) or inside (2D or more)‎, ‎We revisit the ``gyro''-theory ...

متن کامل

ph ys ic s / 99 09 05 9 v 2 13 O ct 1 99 9 1 I s the Kinematics of Special Relativity incomplete ?

An analysis of composite inertial motion (relativistic sum) within the framework of special relativity leads to the conclusion that every translational motion must be the symmetrically composite relativistic sum of a finite number of quanta of velocity. It is shown that the resulting space-time geometry is Gaussian and the four-vector calculus has its roots in the complex-number algebra, furthe...

متن کامل

Tensors and Special Relativity

While you have probably used tensors of rank 1, i.e vectors, in special relativity, relativity is most efficiently expressed in terms of tensor algebra. General relativity, however, requires tensor algebra in a general curvilinear coordinate system. Before discussing special relativity, it will be useful to introduce some of the mathematics of differential forms in a general curvilinear set of ...

متن کامل

Derivation of Dirac’s Equation from the Evans Wave Equation

The Evans wave equation [1] of general relativity is expressed in spinor form, thus producing the Dirac equation in general relativity. The Dirac equation in special relativity is recovered in the limit of Euclidean or flat spacetime. By deriving the Dirac equation from the Evans equation it is demonstrated that the former originates in a novel metric compatibility condition, a geometrical cons...

متن کامل

What Is Categorical Relativity?

The categorical relativity is a groupoid category of massive bodies in mutual motions. The relative velocity is defined to be the basis-free and coordinate-free binary morphism. In categorical relativity there is no need to distinguish separately the constant relative velocities (special relativity) from the variable accelerated velocities, hence the categorical relativity goes beyond boundary ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008