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Physics
Special and General Relativity
Calculate Proper Time for Two Events in Special Relativity
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[QUOTE="pervect, post: 6052382, member: 14402"] Let me try an overview which might allow you to answer your own question. Start off with the idea that events are points on a space-time diagram. One draws two events on said diagram. This is where I'm currently getting stuck, because I don't understand the verbal description of the problem, it's ambiguously worded. Then one draws a straight line that passes through both events. If the interval between the two events is timelike, then line on the space-time diagram connecting the two events is the woldline of some observer, a worldline moving at some physically possible velocity. THen the invariant interval (length of the line) is just the amount of time that a clock traversing the worldline would record in moving from one event to the other along the straight line. Sometimes, though, the worldline won't be timelike separated. This happens when the events are outside of the "light cones" of each other. I'm not sure if the phrase "light cones" is familiar or not, if not I can explain more, I suppose. It's a very useful concept in special relativity, though, and quite common, so I hope it's familar to you. Noting in special relativity can move faster than light, so if the two events are far enough apart in space, there is no light ray that could connect them. We say that the events are "space-like separated" in that case. There is a third case, where a light beam can just reach from one event to the other. In that case, the invariant interval between the two points is always zero. In the case where the two events are space-liek separated, there will be some frame of reference where both events happen at the same time. This may not be obvious, I can discuss this point in more detail if there is some interest. For this idea to make sense, one needs to realize that "at the same time" in special relativity is observer-dependent, there is no universal notion of "at the same time". This is called the relativity of simultaneity, and it's a common source of confusion about special relativity. Then the space-like interval between the two events that are space-like separated is given by the distance between the two events in a frame of reference where the two events happen at the same time. A space-time diagram would help here too, to demonstrate that this is possible. I have stated that there is an obsever who regards both events as simultaneous this without proof at the moment, I am uncertain if it'd be helpful to explain this point in more detail. My inclination is to wait for a question about this issue, because perhaps I'm not answering the question you really wanted to ask. I will say that if you can draw light cones of both events on the space-time diagram, which requires familiarity with both space-time diagrams and light-cones, it's not hard to construct the worldline of the observer who regards the events as simutaneous. [/QUOTE]
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Calculate Proper Time for Two Events in Special Relativity
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