**Part I**

- Source: The spacetime world, loedel’s spacetime diagram: Applications of physics (UMAP modules in undergraduate mathematics and its application), Publisher: COMAP, Inc. (January 1, 1993).
- “Spacetime diagrams of various types provide geometric constructions equivalent to the Lorentz transformation between uniformly moving reference frames. The best-known and one of the oldest spacetime diagrams is the Minkowski construction… Although the Minkowski diagram is particularly useful for treating such problems as the Twin Paradox, it is complicated by the necessity of using different scales along the two sets of spacetime axes. A much simpler geometric method was presented in 1948 by Enrique Loedel. [Loedel’s paper, Aberración Relatividad, published in
*Anales de la Cientifica Argentina*145 (Jan. 1948), attracted little attention in the scientific community until the same method was independently presented by Henri Amar in the*American Journal of Physics*23, 487 (Nov. ’55).]” - “… unprimed X and CT axes represent positions and times as determined by an observer O, while axes labeled X’ and CT’ represent the corresponding spacetime coordinates as determined by O’. This second observer is fixed at the origin of an x’y’z’ space reference frame which moves uniformly along the common direction of increasing X and X’.”
- “In Loedel’s spacetime diagram, both sets of axes are tilted. This feature, which allows primed and unprimed axes of the spacetime diagram to be drawn to the same scale, is the principal advantage of this type of diagram. Figure 2 shows how the axes of the Loedel diagram are arranged.
- A
traces an observer’s path through spacetime. The**worldline****CT**and**CT’**axes are the worldlines of two observers: O and O’. -
connect all simultaneous events and establish chronological order in a given reference frame.**Lines of simultaneity** - A Loedel diagram preserves the essential content of Einstein’s theory of special relativity.
- In the next diagram, the vertical CT:CT’ and the perpendicular, horizontal
**X:X’**lines represent two observers at rest with respect to each other.

- “Spacetime diagrams of various types provide geometric constructions equivalent to the Lorentz transformation between uniformly moving reference frames. The best-known and one of the oldest spacetime diagrams is the Minkowski construction… Although the Minkowski diagram is particularly useful for treating such problems as the Twin Paradox, it is complicated by the necessity of using different scales along the two sets of spacetime axes. A much simpler geometric method was presented in 1948 by Enrique Loedel. [Loedel’s paper, Aberración Relatividad, published in

- The following nine diagrams represent two observers in motion with respect to each other at different velocities.

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- Table of Nine
/**sin α = β = v**calculations:**c**