World Science Scholars
22.12 How can each observer say the other’s clock runs slow?
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Emilio Sanchez Suarez
Hi, Marius, I can’t follow your writing and question. Please specify the Problem’s number you are referring to.
Marius Smallegoor
Hi Emilio, it's not a problem or excercise but it is the demo in the video in 22.12. Professor Green puts the 65 at Gracie's clock at the finish (George's perspective). I would think it has to be placed at Gracie's clock at the start. I would think that Gracie’s clock at the moment of the start and at the startplace in George’s perspective reads 0. So Gracie's clock at the moment of the start and at the finishplace because of asynchronious clocks should read : (156* 12/13C) / C2 = -144 (Clocks must lag behind)......
Emilio Sanchez Suarez
Good morning, Marius Try to use the Space Time axes George (x,t) and Gracie (x’,t’) or in other words, World Lines (t,t’) and Now Lines (x,x’). I find much better understanding using them. For better explanation, while George remains at the Start line, he has a friend (Peter) at the Finish Line. Both of them have clocks in sync. When Gracie’s World Line (x’=0) crosses the Peter’s World Line (x=156 lt.min), the Now Line of Gracie is (t’=65 min) and the Now Line of Peter and George is (t=169min). The “Problem” starts when Gracie makes numbers, without using the Space Time diagram: The Now Line of Gracie (t’=65 min) crosses the World Line of George (x=0) at (t=25 min). Thinking twice now, she sees her Now Line (t’=0) while crossing the George’s World Line (x=0) at (t=0), crosses the Peter’s World Line (x=156lt.min) at (t=144 min) and solve the problem making 25+144 =169 min! But if she were using the Space Time diagram, she would see that her Now Line (t’=65min) also crosses the World Line of Peter (x=156 lt.min) at (t = 169 min)
Marius Smallegoor
Hi Emilio, thanks for your reaction. Today I was making a walk and I suddenly realized that Gracie's clock at the startplace has moved to the finishplace after t'=65 min. So that's why that clock must read 65, it's the same clock that read 0 at the startplace at the moment of the start! Quite obvious but I missed it. I will look into worldlines and now lines, I never used them before.
Emilio Sanchez Suarez
Space Time is good thought to enjoy the daily walks. I still remember my bike walks in Eindhoven in the summer 1968, when working as a Student Volontair in Philips!
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