Episode 42: The Lorentz Transformation - The Mechanical Universe

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Recommends robphy · 2020-05 · Physics Stack Exchange · on “What if a light clock travels perpendicular to mirrors that make up the clock?”

The question describes the " Longitudinal Light Clock ", versus the more common " transverse light clock " found in many textbooks. @Drew 's diagram is correct. Although, in the answers by @Drew and @thermomagnetic condensed boson and others, "length-contraction" is highlighted to account for time-dilation, its probably be better to highlight the "invariance of the square-interval" via the invariance of the area of the triangle (more generally, causal diamond). This area invariance follows from the determinant of the Lorentz boost transformation being equal to 1. Additionally, the eigenvectors of the Lorentz boost preserve the edges to lie along the light cone. Some details of this idea and

Recommends T.Mellin · 2026-01 · Physics Stack Exchange · on “Is space-time one object or does it describe the relationship between space and time?”

I still find these older Caltech animations and explanations helpful in visualizing the simplified model of spacetime you seem to be attempting to describe (i.e., "visualizing time" along a vertical axis while the other two axes represent two spatial dimensions): Episode 42: The Lorentz Transformation - The Mechanical Universe (19:53 onwards) [this video] For a mathematical and historical development of the concept of spacetime—starting with a discussion of simultaneity—the entire video would be helpful.

Cites Eduard · 2025-12 · Physics Stack Exchange · on “Misunderstanding the lorentz transformation”

I do understand the math part of the transformation, but I have a problem understanding why exactly there will be a "triangle" (to say it simply). Pretty much all the textbooks and videos describe this in the same way, and if you are not sure about what I mean exactly, please watch this video [this video] (skip at 12:16) Let's say we are standing on the ground, and there is a man with a laser standing on a moving platform (with fairly large speed) with a mirror at the top. The man goes from -x to +x. We are standing exactly at the x=0, y=0 point. Once the man's x-y coordinates become the same (get in front of us basically), he shoots up a light beam in the y direction. Every explanation would say