Frame of Reference in VS .NET

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Frame of Reference
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A frame of reference is more or less a fancy way of saying coordinate system. In our thought experiments, however, we do more than think in mathematical terms and would like to imagine a way that a frame of reference could really be constructed. This is done by physically constructing a coordinate system from measuring rods and clocks. Local clocks are positioned everywhere within the frame and can be used to read off the time of an event that occurs at that location. You might imagine that you have 1-m long measuring rods joined together to form a lattice, and that there is a clock positioned at each point where rods are joined together.
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Clock Synchronization
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One problem that arises in such a construction is that it is necessary to synchronize clocks that are physically separated in space. We can perform the synchronization using light rays. We can illustrate this graphically with a simple spacetime diagram (more on these below) where we represent space on the horizontal axis and time on the vertical axis. This allows us to plot the motion of
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Special Relativity
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reflected light ray returns to clock 1 at time t2
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reflected at clock 2, at time t'
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emitted light ray Time of emission, t1
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Fig. 1-1. Clock synchronization. At time t1 , a light beam is emitted from a clock at the origin. At time t , it reaches the position of clock 2 and is re ected back. At time t2 , the re ected beam reaches the position of clock 1. If t is halfway between the times t1 and t2 , then the two clocks are synchronized.
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objects in space and time (we are of course only considering one-dimensional motion). Imagine two clocks, clock 1 located at the origin and clock 2 located at some position we label x1 (Fig. 1-1). To see if these clocks are synchronized, at time t1 we send a beam of light from clock 1 to clock 2. The beam of light is re ected back from clock 2 to clock 1 at time t2 , and the re ected beam arrives at the location of clock 1 at time t1 . If we nd that t = 1 (t1 + t2 ) 2
then the clocks are synchronized. This process is illustrated in Fig. 1-1. As we ll see later, light rays travel on the straight lines x = t in a spacetime diagram.
Inertial Frames
An inertial frame is a frame of reference that is moving at constant velocity. In an inertial frame, Newton s rst law holds. In case you ve forgotten, Newton s rst
Special Relativity
F y F' y'
x' z'
Fig. 1-2. Two frames in standard con guration. The primed frame (F ) moves at velocity v relative to the unprimed frame F along the x-axis. In prerelativity physics, time ows at the same rate for all observers.
law states that a body at rest or in uniform motion will remain at rest or in uniform motion unless acted upon by a force. Any other frame that is moving uniformly (with constant velocity) with respect to an inertial frame is also an inertial frame.
Galilean Transformations
The study of relativity involves the study of how various physical phenomena appear to different observers. In prerelativity physics, this type of analysis is accomplished using a Galilean transformation. This is a simple mathematical approach that provides a transformation from one inertial frame to another. To study how the laws of physics look to observers in relative motion, we imagine two inertial frames, which we designate F and F . We assume that they are in the standard con guration. By this we mean the frame F is moving in the x direction at constant velocity v relative to frame F. The y and z axes are the same for both observers (see Fig. 1-2). Moreover, in prerelativity physics, there is uniform passage of time throughout the universe for everyone everywhere. Therefore, we use the same time coordinate for observers in both frames. The Galilean transformations are very simple algebraic formulas that tell us how to connect measurements in both frames. These are given by t =t, x = x + vt, y=y, z=z (1.10)
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