16.7. Length Contraction#
The hallmark of the Second Postulate is that the speed of light is constant for all inertial observers. Since a speed is a length divided by a time and if time intervals are not invariant, then maybe space intervals as observed by different observers might be odd as well. That’s in fact the case.
Without going into the more gritty details, we can reason our way to the next odd result predicted by Einstein’s 1905 paper. Here’s the result. Let’s imagine a length, \(L_A\)–say a meter stick–on that, now famous train…the Away frame. Then Couch Guy alongside the tracks would measure a length, \(L_H\) to be:
Since \(\gamma >1\) then the Home frame would see lengths to be shorter than measured in the Away frame. Times longer, and lengths shorter. It’s a strange universe.
This is called Length Contraction. Here’s what the airport folks would see incorporating both of our strange relativistic behaviors: Traveler Man appears to Couch People to be shrunk along the direction of motion with a clock that they claim runs slower than Traveler Guy would claim.
Please study example 2 🖋 📓
Please answer question 6 📺