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What does $AB$ mean in the paper On the Electrodynamics of Moving Bodies?

Physics Asked by Pro Q on April 15, 2021

When reading through the paper "On the Electrodynamics of Moving Bodies" by Albert Einstein, my friends and I were confused by some of the notation used and how to interpret it.

On page 3, there is the following equation:

$$frac{2AB}{t’_A-t_A}=c$$

Previously, $A$ and $B$ were defined to be points in space.

So what does $AB$ mean?

Is it multiplication? If so, are we to think of the two points as being vectors? If so, are we computing the dot product, the cross product, or some other version of multiplication of two vectors?

Note: I think we figured it out, so I wanted to post here with a self-answered question in case it helps future people who are also trying to read it. (Also, we may be wrong, so please submit answers that improve understanding!)

One Answer

We believe $AB$ is meant to be a distance, namely, the length of the line segment $overline{AB}$.

This seems to make sense given our intuitive definition of the "speed" of something. Since speed is usually computed as $distance/time$, it makes sense that $2AB$ would be the distance of travelling from one clock to the other clock and back, and the time would be the time when it arrives back at the first clock minus the time that it left the first clock.

However, it's still unclear why Einstein wrote $2AB$ rather than $2|overline{AB}|$ or something to that extent. Is this just a usual physics notation, that two points next two one another signify the magnitude of a line segment?

Correct answer by Pro Q on April 15, 2021

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