Invariance of Physical Laws
Imagine: You wake up inside a room with no windows and one locked door (you checked). You cannot see outside. Looking around you see a table with a number of items on it: a desk lamp (plugged in and turned on), a tennis ball, a bunch of string, a pitcher of water and a cup, a candle, a box of matches, and a music player with headphones. A skateboard and a wooden stool are also in the room.
The music player has a sign on it saying “Turn on for instructions,” so you do. You are told that you are in a specially designed vibration-proof and noise-proof train car on a set of straight and level train tracks. Your task is to use one or more of the items in the room, perhaps in combination with each other, to determine whether the train car is stationary or is moving on the tracks. There is a thirty-minute time limit for your test (or tests), and destroying or modifying the walls, floor, or ceiling of the car is not permitted.
Can you think of some creative ways to use the items that might indicate whether you are moving? (Spoiler alert: The principle of relativity asserts that there is no way for you to tell whether the train car is moving. So once you think of some creative ways that might seem to be able to tell you whether you are moving, think about why they fail to do so. If you have a car, you might even try some experiments in it while it is stationary and while it is moving, with a friend driving, not yourself!)
Consider two railway stations. One of them is exactly 25 kilometers to the east of the main railway station, and the other is exactly 25 kilometers to the west of the main station. (The tracks between them are straight and the ground is level, so the distances are straight-line distances.) Outline at least two methods by which you can make sure that the clocks at each outlying station are exactly synchronized with the clock at the main station.