Speaker
Description
The velocity triangle is a graphical construct for solving various problems of the Lorentz
Transform in special relativity. This construct assumes that all matter travels at the speed of
light in four-dimensional space, defining the direction of that travel as the local time axis.
Relative velocity results from a difference of direction, through the Brehme velocity angle beta,
the sine of which equals v/c. The Lorentz Transform, expressed trigonometrically using beta,
shows that relative motion is the projection of the passage of time in one reference frame onto
the temporal and spatial axes as time varying components with velocity v/c. The trigonometric
expression and the velocity triangle reveal that the Lorentz Transform has an axis of symmetry
for which ct1=ct2 and x1=-x2, which allows quick graphical solution of any combination ct, x into
another reference frame.
The velocity triangle is of my own development, though it is similar to the Brehme diagram
developed by Robert Brehme of Wake Forest University in 1964, with whom I had several
conversations before his passage. The main difference between the Brehme diagram and the
velocity triangle is that the orthogonality of the spatial and temporal axes are maintained, along
with equal units of measure in both reference frames, allowing the measurement of an event by
three or more reference frames to be depicted on the same chart. No other Lorentzian time-
space diagram supports this, as all distort the units of measure and orthogonality of one or both
reference frames.
The axis of symmetry is wholly original to my work.
