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

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Physics 225 3.2 3.2
Background image of page 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
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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.
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 15

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

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online