# Unit 3 - Physics 225 Relativity and Math Applications...

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Physics 225 Relativity and Math Applications Spring 2010 Unit 3 The Interval, Causality, and Proper Time N.C.R. Makins University of Illinois at Urbana-Champaign © 2010

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Physics 225 3.2 3.2
Physics 225 3.3 3.3 z STATIONARY observers measure ( x,t ) MOVING observers measure ( x ,t ) speed v x y y x z event Unit 3: The Interval, Causality, and Proper Time Last week, we introduced the Lorentz transformation : the master equations which allow us to transform space-time events from one intertial reference frame to another. The equations are simple … you just have to remember the conventions : the unprimed coordinates refer to our chosen “stationary” frame the primed coordinates refer to the “moving” frame the + x and + x directions points in the direction-of-motion of the moving frame relative to the stationary one All of this is summarized in the equations and figure below. with ! = v c and = 1 1 " # 2 Also remember one of our findings from last week: the inverse Lorentz transformation, which translates from the primed (moving frame’s) coordinates back to the unprimed (stationary frame’s) coordinates, is easily obtained by simply reversing the sign of β . Here’s some new jargon for you: a Lorentz transformation is often called a Lorentz boost . (“Boost” as in “booster rockets”, as in “jumping onto a moving ship”. ) Today, we’ll derive a new measure of the “distance” between two events: it’s called the interval and it is a Lorentz invariant quantity. Next, we’ll consider what it means, and introduce the concept of proper time . Finally, we’ll examine the fundamental concept of causality and see how it can be preserved in the strange world of relativity. But first, let’s take a break from our wacky physics to ponder something more general … Δ t = γ ( Δ t Δ x / c ) Δ x = ( Δ x Δ t c ) Δ y = Δ y Δ z = Δ z

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Physics 225 3.4 3.4 Exercise 3.1: The Scientist’s Toolkit As a scientist or engineer, much of your job will be perfoming calculations, and using calculations performed by others. You do plenty of that in your classes of course . .. but there’s a difference. In classroom exercises, the correct answer is known … in the real world, it isn’t! It’s your responsibility to make sure your work is correct and the consequences may be dire indeed if it isn’t. Experienced scientists develop of sort-of “sixth sense” for when an error appears in their calculations: they are constantly (almost subconsciously) checking their work against their physical intuition. Here’s the secret: Knowing what the answer will roughly look like before you start. That’s the physical intuition part.
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Unit 3 - Physics 225 Relativity and Math Applications...

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