Events in VS .NET

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Events
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An event is anything that can happen in spacetime. It could be two particles colliding, the emission of a ash of light, a particle just passing by, or just anything else that can be imagined. We characterize each event by its spatial location and the time at which it occurrs. Idealistically, events happen at a single
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Special Relativity
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mathematical point. That is, we assign to each event E a set of four coordinates (t, x, y, z).
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The Interval
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The spacetime interval gives the distance between two events in space and time. It is a generalization of the pythagorean theorem. You may recall that the distance between two points in cartesian coordinates is d= (x1 x2 )2 + (y1 y2 )2 + (z 1 z 2 )2 = ( x)2 + ( y)2 + ( z)2
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The interval generalizes this notion to the arena of special relativity, where we must consider distances in time together with distances in space. Consider an event that occurs at E 1 = (ct1 , x1 , y1 , z 1 ) and a second event at E 2 = (ct2 , x2 , y2 , z 2 ). The spacetime interval, which we denote by ( S)2 , is given by ( S)2 = c2 (t1 t2 )2 (x1 x2 )2 (y1 y2 )2 (z 1 z 2 )2 or more concisely by ( S)2 = c2 ( t)2 ( x)2 ( y)2 ( z)2 (1.11)
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An interval can be designated timelike, spacelike, or null if ( S)2 > 0, ( S)2 < 0, or ( S)2 = 0, respectively. If the distance between two events is in nitesimal, i.e., x1 = x, x2 = x + dx x = x + dx x = dx, etc., then the interval is given by ds 2 = c2 dt 2 dx 2 dy 2 dz 2 (1.12)
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The proper time, which is the time measured by an observer s own clock, is de ned to be d 2 = ds 2 = c2 dt 2 + dx 2 + dy 2 + dz 2 (1.13)
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This is all confusing enough, but to make matters worse different physicists use different sign conventions. Some write ds 2 = c2 dt 2 + dx 2 + dy 2 + dz 2 , and in that case the sign designations for timelike and spacelike are reversed. Once you get familiar with this it is not such a big deal, just keep track of what the author is using to solve a particular problem.
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Special Relativity
The interval is important because it is an invariant quantity. The meaning of this is as follows: While observers in motion with respect to each other will assign different values to space and time differences, they all agree on the value of the interval.
Postulates of Special Relativity
In a nutshell, special relativity is based on three simple postulates. Postulate 1: The principle of relativity. The laws of physics are the same in all inertial reference frames. Postulate 2: The speed of light is invariant. All observers in inertial frames will measure the same speed of light, regardless of their state of motion. Postulate 3: Uniform motion is invariant. A particle at rest or with constant velocity in one inertial frame will be at rest or have constant velocity in all inertial frames. We now use these postulates to seek a replacement of the Galilean transformations with the caveat that the speed of light is invariant. Again, we consider two frames Fand F in the standard con guration (Fig. 1-2). The rst step is to consider Postulate 3. Uniform motion is represented by straight lines, and what this postulate tells us is that straight lines in one frame should map into straight lines in another frame that is moving uniformly with respect to it. This is another way of saying that the transformation of coordinates must be linear. A linear transformation can be described using matrices. If we write the coordinates of frame F as a column vector ct x y z then the coordinates of F are related to those of F via a relationship of the form ct ct x x y = L y z z
(1.14)
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