ech@spuxll.UUCP (Ned Horvath) (06/09/84)
Question: could one build a bigger-than-one-light-second object that "flashed" with a period less than a second? As viewed from SOMEWHERE? Sure; to take a trivial example, place yourself at the center of an arbitrarily large shell, and make a BIG flash at an arbitrary frequency. The reflections off the shell will appear to come from all directions simultaneously. The upper bound on size based on frequency is based on the assumption that one is NOT at any such privileged position with respect to the periodic system; given that there is a large number of (pulsars, quasars, you name it) that exhibit the periodic behavior, the suggestion that one is at some privileged position for ALL of them is absurd. So, throw that out. Contrived examples, at least as gedanken experiments, can always be had. The argument goes 1. We assume that we are viewing a single periodic system in each case, and 2. In order for a physical system to display any sort of behavior the various "parts" must be able to interract, and 3. No interraction can propagate at more than the speed of light. You don't have to accept ANY of these assumptions; the contrived example with the shell, for example, violates assumption 2, i.e. that the various parts of the shell are interracting. If you are willing to accept the first two assumptions as reasonable, and the speed of light limit (an axiom of relativity, by the way, not a theorem!), then the argument yields a (very crude) upper bound on the size of the system. Does that help? =Ned=
matt@oddjob.UChicago.UUCP (Matt Crawford) (06/10/84)
Yes, a system can be made to flash with period P and still be larger than c*P, but only certain observers will see the flashing. As an example consider a square sheet which emits from all points with an intensity that varies periodically with a period P = 1 second. Let the square have an edge of length L = (10 sec) * c = 3*10^9 meters. Let an observer be located a distance d from the center of the square on a line perpendicular to the square. The points on the square farthest from the observer are the corners, at a distance d' = d + L^2/4d + ... . This can be made arbitrarily close to d make making d sufficiently larger than L. To have d'-d < (0.1 sec)*c it suffices to make d > (250 sec)*c = 7.5*10^10 meters. Under these conditions, if the square switches between full intensity and zero intensity with a period of 1 second, the observer will see the pulsation, but with the transition from bright to dark smeared out over a tenth of a second. Consider another observer the same distance from the center of the square but 30 degrees off the perpendicular. The center of the edge nearest to this observer is (247.54 sec)*c away while the center of the farthest edge is (252.54 sec)*c away. This difference of five seconds of light travel time (a bit more for the far corners) will cause the observer not to see simultaneous pulsation but an average brightness, unless the observing instruments are sufficiently powerful to discern the bands of light and dark. Increasing the distance of the second observer will not reduce the time difference to less than 5 seconds. Diagram: (distances in light-seconds) | <- 250 -> 10 |-------------------------------O 1st observer | O 2nd observer If the object is spherical the ideas are the same, except that there are NO positions outside the sphere from which all points on the surface of the sphere are arbitrarily close to being equidistant. ___________________________________________________________ Matt University ARPA: crawford@anl-mcs.arpa Crawford of Chicago UUCP: ihnp4!oddjob!matt