# To understand relativity you really need a lot of

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To understand relativity, you really need a lot of time going through examples (numerically). In this lab and the next we will compare a number of examples in Galilean and Special relativity. For the purposes of this lab, we restrict ourselves to motion along a single direction (along the x-axis).
Special Relativity 72 GALILEAN RELATIVITY Galilean relativity is based upon our everyday experience, using the Newtonian notions of space and time. That is, we assume that time is the same for all observers. If we have two reference frames(denoted by xand x’) with the primed () moving at velocity urelative to the unprimed frame, the velocities of an observed object are related via: v = v’ + u (So here, assume that the unprimed observer is “at rest” and the primed observer is “moving” - this is the difference in the sign compared to what we had before.) Assuming that at t=0, x’=x (i.e., at t=0 our observers are at the same place), the coordinate transformationof an object is related via: Figure 1. Frame S is moving with velocity v in the x-direction. After a period of time thas elapsed, Frame S’ denotes the new position of frame S.
Special Relativity 73 LORENTZ TRANSFORMATIONS For the transformations in special relativity (called “Lorentz transformations”) we need a specific factor, gamma (γ): The relationship between proper time and proper length and the time and length in a boosted frame (along the direction of motion) is simple: The above set of equations expresses the effects of time dilation(i.e. a clock in a moving frame will be observed to run slow) and length contraction(i.e. the length of an object in a moving frame will appear to have shortened (contracted) in the direction of motion.) More generally, coordinates between one reference frame and another can be calculated (these coordinates are
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