World Science Scholars
22.12 How can each observer say the other’s clock runs slow?
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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!
Luke Gurbin
Given a certain frame of reference, and the "stationary" observer described earlier, if a second observer accompanied the "moving" clock, each of the observers would perceive the other's clock as ticking at a slower rate than their own local clock, due to them both perceiving the other to be the one that is in motion.
John Lee Farnsworth Sr
In frame 3 you state that gracie's clock starts at 144, but start moment should all be zero because there is no relative motion yet.
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