QUERY 9 Numerical clock rate difference. Substitute values for the various quantities in equation . Result: To two significant figures, the satellite clock appears to run faster than the Earth clock by approximately 39 000 nanoseconds per day. Give your answer to three significant figures.
Section 2 described the difference in clock rates due only to difference in altitude. We predicted at the end of Section 2 that the full general relativis-tic treatment would lead to a smaller difference in clock rates than the altitude effect alone. Your result for Query 9 verifies this prediction. In the following section we examine some of the other approximations made in the analysis.
A practical aside: When Carroll O. Alley was consulting with those who originally designed the Global Positioning System, he had a hard time convincing them not to apply twice the correction given in equation : first to account for the difference in clock rates at the different altitudes and second to allow for the blue shift in frequency for the signal sent downward from satellite to Earth. There is only one correction; moreover there is no way to distinguish what is the "cause" of this correction. Hear what Clifford Will has to say on the subject, as he describes the difference in rates between one clock on a tower and a second clock on the ground:
A question that is often asked is, Do the intrinsic rates of the emitter and receiver or of the clock change, or is it the light signal that changes frequency during its flight? The answer is that it doesn't matter. Both descriptions are physically equivalent. Put differently, there is no operational way to distinguish between the two descriptions. Suppose that we tried to check whether the emitter and the receiver agreed in their rates by bringing the emitter down from the tower and setting it beside the receiver. We would find that indeed they agree. Similarly, if we were to transport the receiver to the top of the tower and set it beside the emitter, we would find that they also agree. But to get a gravitational red shift, we must separate the clocks in height; therefore, we must connect them by a signal that traverses the distance between them. But this makes it impossible to determine unambiguously whether the shift is due to the clocks or to the signal. The observable phenomenon is unambiguous: the received signal is blue shifted. To ask for more is to ask questions without observational meaning. This is a key aspect of relativity, indeed of much of modern physics: we focus only on observable, operationally defined quantities, and avoid unanswerable questions.
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