# Minkowski vs Loedel

1. Dec 19, 2013

### phyti

This is in response to the closed thread "perspective on Relativity and length contraction"
The Loedel drawing is a special case for a symmetrical situation with two observers sharing their relative speed equally. This method is common in many expositions of SR, though not labelled as such. Since the setup is symmetrical, the results are not surprising, but more like a 'self fullfilling prophecy'. The Minkowski drawing is far more flexible in analyzing the general case, and more informative in demonstrating reciprocal observations with different speeds for two observers.

This is the Minkowski version of the Loedel drawing.

Begin with a spacetime drawing with U as a reference (left). Green and Red are moving in ide
ntical ships in opposite x directions. As the ships pass each other, R in the center of his ship, records the time for the G ship to pass, as indicated by the two circles.
The purple diagonal from B (back of red ship) at Ut = t to Ut = t' is the graphical equivalent of transforming the time from U to R, i.e. it's a scaling factor.

The initial conditions:
U measures ship speed v as .577 (c=1)
U measures ship rest length as 12
U calculates 1/γ for v as .817.
U calculates moving ship length as .817*12 = 9.80.

R records the G ship passing from 3.47 to 10.41 or 6.94 time units.
R measures the speed of G as .866.
R calculates the length of the G ship as .866*6.94 = 6.01
R calculates 1/γ for v = .866 as .500.
R calculates the length of the G ship as .500*12 = 6

By symmetry G makes the same measurements and calculations as R.

The right portion is R's perception of events.

View attachment 64928

Last edited: Mar 9, 2014