By Alexander J. W.
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Extra info for An Example of a Simply Connected Surface Bounding a Region which is not Simply Connected
G. determination of distances by measuring apparent sizes, apparent luminosities, or redshifts. Use of such methods of estimating distances (discussed in the following chapters) allows an observer to construct his world picture at any time 46 Fundamentals of measurement to in his history. The particular advantage of this method of observation is that it can be used out to extremely large distances. Finally, a radar map is the natural picture obtained directly by a radar set as commonly used in aircraft, on ships, in airport control towers, etc.
What condition should Tsatisfy to avoid confusion between different echo pulses? Modify your program to print out also the relative speed of approach of the UFO as determined by the echo pulses received from it. Ensure your program prints out a special warning message if the speed determination for the UFO appears to violate a special relativity condition. What might be an appropriate phrasing of this warning message? Conclusion We have now determined methods for measuring the fundamental quantities (time, distance, simultaneity) needed as a basis for all other kinematic measurements, and have done this taking the limiting nature of the speed of light into account.
27b). However, the travel time from P to Q is shortest on the ring road and longest on the road through the city centre. The map represents accurately the different possible paths from P to Q, but not the different times it will take to travel on these routes; the shortest travel time from the initial to the final points is associated with the path that looks longest on the map. This gives us a good analogy to the spacetime situation represented in Fig. 26c. One can crudely understand the sign of the effect in that case by remembering the example of the observer watching a clock from a tram, which suggests that the nearer to the speed of light a clock moves relative to an observer A, the slower it will appear to him that it is running.
An Example of a Simply Connected Surface Bounding a Region which is not Simply Connected by Alexander J. W.