@_youhadonejob tweeted this textbook picture with the amusing and sardonic comment “Little girl in this textbook is 5 m tall”.

I liked @jim_henderson60’s take on this when he tweeted: “You see. Physics helps us all grow tall.”

But then I started thinking, what if the 5 m measuring stick was in an inertial frame moving past Lottie’s inertial frame at a substantial fraction of light speed? (In my head, I named the girl “Lottie”, although “Alice” would be more in the more usual tradition of SR* pedagogy, I guess.)

The illustration could represent that single instant at which both ends of the 5 m ruler were precisely opposite Lottie’s head and feet as its inertial frame whizzed by hers…

A quick calculation indicated that Lorentz length contraction could indeed account for the relative measurements on the illustration if *v* = 0.97*c*

Of course, Lorentz length contraction is a two way street. From the 5 m ruler’s inertial frame, length contraction would make Lottie appear even shorter than her compact 1.2 m. Given that *v* = 0.97*c*, I calculate that she would appear only 0.29 m tall.

Correction: not *appear. *She would genuinely *be *only 0.29 m tall when viewed from that inertial frame, just as the 5 m rule would genuinely be only 1.2 m long when viewed from Lottie’s inertial frame.

We live in an universe where everything is indeed *relative*. However, for most of us that takes a fair amount of getting used to…

*SR = special relativity. My brain is currently too small to handle GR (general relativity).

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paulmartin42March 5, 2018 / 5:49 amHmm What is Lottie doing. Is she in a lift ?

Is it a simple typo …

e=mc2andallthatMarch 5, 2018 / 10:08 pmProbably a typo!