Time dilation (25-10)

Question 1 of 4

Question

Speed of light in a vacuum

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Question

Speed of $S′$ relative to $S$

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Question

Time interval between two events as measured in frame $S'$ , in which those events occur at the same place.

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Question

Time interval between the same two events as measured in frame $S$

{"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!