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02_Special_Relativity

02_Special_Relativity - Physics 160 Principles of Modern...

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Physics 160 Principles of Modern Physics (Spring 2008) Laboratory session #2 Special Relativity Simulation INTRODUCTION While the mathematics of special relativity consist of relatively simple algebraic manipulations, identifying which relativistic effects need to be taken into account takes practice. And knowing the relevant effect is insufficient if you are not certain which reference frame is considered “proper”. For example, the formula for length contraction has two different distances and you need to know which one is the proper distance. Today's exercises will give you an opportunity to visualize relativistic effects as well as practice calculating, graphing and explaining them. This experiment uses a simulation program called Spacetime, which graphically illustrates the results of Lorentz transformations. Open it by going to the Start menu Programs Physics 160 Spacetime Simulator . Press [Enter] twice (and click “ignore” if an error message comes up regarding the COM2 port). Press any key to dismiss the banner announcing the program and its authors. The program will open to its highway mode. This mode provides snapshots along a "cosmic superhighway" consisting of various horizontal lanes in which objects travel at different speeds. Objects in the middle of the screen lie at rest in the median strip of the highway. Objects lying above the median strip move to the right; the farther above the median strip, the faster they move. Objects in the topmost lane move at the speed of light; only light pulses can occupy this lane. Objects below the median strip move to the left; the farther below the strip the faster they move. The vertical axis scale is in terms of ß = v c and the corresponding γ = 1 1- β 2 , but these scales are non-linear so they accentuate effects at higher β . One way to view the screen is as a stop-action movie of objects moving along the highway shown from the perspective of an observer standing on the median. At any instant you view only one frame of the movie. Initially, the only object on the highway is a digital clock at x =0. Time can be advanced forward or backward in increments of 0.01, 0.10, or 1.00 time units, using the keypad as shown in the diagram below. Try advancing the time and seeing that the clock reading changes accordingly. Return to t =0. Note that the num-lock mode must be turned off in order to use the keypad to advance the time. EXERCISE 1: LENGTH CONTRACTION “Moving rods shrink” is the abbreviated statement of length contraction. To see how this works, place a rod on the highway by pressing the [R]-key. A white cross will appear at the center of the median. You can move the rod to a different lane (i.e. different velocity as seen by the observer in the median) using the up and down arrow keys. You can also place it at different spatial locations using the right and left arrow keys. The values for ß
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Physics 160 Laboratory, Spring 2006 Session 2: Special Relativity Simulation 2 and x are shown at the bottom of the screen. Once you have decided where you want to locate the rod, press [Enter].
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