- #1
Foppe Hoekstra
- 41
- 2
- TL;DR Summary
- Is an isosceles triangle after being accelerated still an isosceles triangle to every observer?
Two astronauts, Neil and Michael, visit a solid not revolving planet. They mount a jet engine on this planet to get it turning around its axis. Before starting the engine they put three dots on the surface with the help of an isosceles triangle, which measures 1 by 1 meter. Two dots are placed (1 meter apart) in line with the engines thrust: pointing out the east-west-leg. A third dot is placed 1 meter north of the first dot, together pointing out the north-south-leg. So the isosceles triangle fits perfectly between the three dots.
Then they start the engine, Neil remains on the planet and Michael boards the spaceship to watch the accelerating planet from a stationary place above the surface of the planet.
After a while, when the planet has reached a constant revolving speed, Neil checks whether the dots on the surface of the planet still correspond with the isosceles triangle, and so they do.
To Michael however, things behave a little different. The surface of the planet has gained a speed in east direction and according to Lorentz transformations it should contract in that direction. But to please Ehrenfest, the surface of the planet will be stretched to compensate the east-west-length contraction (so the radius of the planet will hold). The east-west-leg of the loose isosceles triangle however, is not subjected to Ehrenfest and so it will show length contraction to observer Michael in the stationary spaceship, whereas the east-west-dots still have their 1 meter distance, according to Michael.
So Neil reports to Earth that the triangle still fits the dots, whereas Michael reports to Earth that the triangle does not fit the dots anymore. Who are we to believe?
Then they start the engine, Neil remains on the planet and Michael boards the spaceship to watch the accelerating planet from a stationary place above the surface of the planet.
After a while, when the planet has reached a constant revolving speed, Neil checks whether the dots on the surface of the planet still correspond with the isosceles triangle, and so they do.
To Michael however, things behave a little different. The surface of the planet has gained a speed in east direction and according to Lorentz transformations it should contract in that direction. But to please Ehrenfest, the surface of the planet will be stretched to compensate the east-west-length contraction (so the radius of the planet will hold). The east-west-leg of the loose isosceles triangle however, is not subjected to Ehrenfest and so it will show length contraction to observer Michael in the stationary spaceship, whereas the east-west-dots still have their 1 meter distance, according to Michael.
So Neil reports to Earth that the triangle still fits the dots, whereas Michael reports to Earth that the triangle does not fit the dots anymore. Who are we to believe?