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So, if there was a clock reading 12 noon at the hub of the wheel, the clock leading the motion would be before 12 noon (spoke bending up, and the clock trailing the motion would be after 12 noon (spoke also bending up). So the spokes would tend to delay and cluster at the top of the wheel and pass quickly around the bottom!!!? Interesting 🙂
Clocks in motion run slow, objects in motion are Lorentz contracted, time is dilated. All this was ok. It has taken me several days to absorb the maths supporting the concept that clocks moving away from the observer run slow whilst those moving toward the observer run fast – my brain must be running away from me!
Clocks in motion run slow, objects in motion are Lorentz contracted, time is dilated. All this was ok. It has taken me several days to absorb the maths supporting the concept that clocks moving away from the observer run slow whilst those moving toward the observer run fast – my brain must be running away from me!
It took me a while to scrape the rust off my basic math skills in order to follow the presentation. A few days later I realised that using the value of 1 for the hypotenuse on the x’ y’ axes provides a template that can be scaled up to solve a translation problem – once we are given a value for the angle of rotation (theta), and the coordinates to be translated . . . but it was a slow, grinding process that only resolved at 3am after several days and nights of careful consideration 🙂
When I wrote this (late at night) I assumed that George was looking out from the front of the train at the approaching mountain! From this perspective the mountain would exhibit that peculiar lensing, tunnel vision aspect, but be otherwise geometrically stable…? However, from a carriage window the view of passing scenery would be subject to Lorentz contraction and the mountain would appear to be the same height but steeper – more of a climbing/skiing challenge! But the snow would not fall off.