Chapter 25. Time dilation (25-10)

Question

OAF0ADXbjZ8glkC9J5nP/DKmPD34rS8DzPgTBBVOKHPgAcApqTiRDGH0jgxQ/NOQfbVejSUThop5sQBTQTBSiET87YzmdHISqOja4/M5v/siqGEhjAKjReP6u+PhCZsX4oU43Z29CscHDIA5TATjRw==
{"title":"Time interval between two events as measured in frame S', in which those events occur at the same place.","description":"Correct!","type":"correct","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"10,16,12,16\"},{\"shape\":\"poly\",\"coords\":\"144,22\"},{\"shape\":\"rect\",\"coords\":\"155,14,179,50\"}]"} {"title":"Speed of S′ relative to S","description":"Incorrect","type":"incorrect","color":"#ffff00","code":"[{\"shape\":\"rect\",\"coords\":\"234,112,274,156\"}]"} {"title":"Speed of light in a vacuum","description":"Incorrect","type":"incorrect","color":"#00ff00","code":"[{\"shape\":\"rect\",\"coords\":\"238,184,266,217\"}]"} {"title":"Time interval between the same two events as measured in frame S","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"30,57,52,96\"}]"}

Question

USBvyHRBdEnF6sVsYWEZ3yeRGnaxjPzV29zoYCC3y1d46C7mHw+ufw==
{"title":"Time interval between two events as measured in frame S', in which those events occur at the same place.","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"10,16,12,16\"},{\"shape\":\"poly\",\"coords\":\"144,22\"},{\"shape\":\"rect\",\"coords\":\"155,14,179,50\"}]"} {"title":"Speed of S′ relative to S","description":"Correct!","type":"correct","color":"#ffff00","code":"[{\"shape\":\"rect\",\"coords\":\"234,112,274,156\"}]"} {"title":"Speed of light in a vacuum","description":"Incorrect","type":"incorrect","color":"#00ff00","code":"[{\"shape\":\"rect\",\"coords\":\"238,184,266,217\"}]"} {"title":"Time interval between the same two events as measured in frame S","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"30,57,52,96\"}]"}

Question

bPc1Yg7xoR7yKjhmbmrt4oWiBz5cnkvqFSFY9UDw4ZQ=
{"title":"Time interval between two events as measured in frame S', in which those events occur at the same place.","description":"Incorrect","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"10,16,12,16\"},{\"shape\":\"poly\",\"coords\":\"144,22\"},{\"shape\":\"rect\",\"coords\":\"155,14,179,50\"}]"} {"title":"Speed of S′ relative to S","description":"Wrong","type":"incorrect","color":"#ffff00","code":"[{\"shape\":\"rect\",\"coords\":\"234,112,274,156\"}]"} {"title":"Speed of light in a vacuum","description":"Correct!","type":"correct","color":"#00ff00","code":"[{\"shape\":\"rect\",\"coords\":\"238,184,266,217\"}]"} {"title":"Time interval between the same two events as measured in frame S","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"30,57,52,96\"}]"}

Question

diRVLePwgeLsMpTf9a3UFtWfiG03092Um8hInIpwNZ1Z28skDd8AbAQfE3pXIe7unZP66C2LZns40wTqEDOJ7h/PbgQyb7JC
{"title":"Time interval between two events as measured in frame S', in which those events occur at the same place.","description":"Incorrect","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"10,16,12,16\"},{\"shape\":\"poly\",\"coords\":\"144,22\"},{\"shape\":\"rect\",\"coords\":\"155,14,179,50\"}]"} {"title":"Speed of S′ relative to S","description":"Wrong","type":"incorrect","color":"#ffff00","code":"[{\"shape\":\"rect\",\"coords\":\"234,112,274,156\"}]"} {"title":"Speed of light in a vacuum","description":"Incorrect","type":"incorrect","color":"#00ff00","code":"[{\"shape\":\"rect\",\"coords\":\"238,184,266,217\"}]"} {"title":"Time interval between the same two events as measured in frame S","description":"Correct!","type":"correct","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"30,57,52,96\"}]"}

Review

An observer in \(S\) moving relative to the clock measures a time interval \(\Delta{t}\) for one tick of the light clock. An observer in \(S'\) who is at rest with respect to the clock measures the time interval for one tick to be \(\Delta{t_{\mathrm{proper}}}\), regardless of whether the observer and clock are moving with respect to some other observer. Equation 25-10 shows that \(\Delta{t}\) and \(\Delta{t_{\mathrm{proper}}}\) are not equal: An observer in the \(S\) frame sees time running at a different rate than an observer in the \(S'\) frame. This is astounding!