Unit 2 - Physics 225 Relativity and Math Applications...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Physics 225 Relativity and Math Applications Spring 2010 Unit 2 The Lorentz Transformation N.C.R. Makins, George Gollin 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 2.2 2.2
Background image of page 2
2.3 2.3 Unit 2: Special Relativity Formalized: the Lorentz Transformation The Axioms of Special Relativity Today we will be formalizing our study of Special Relativity (SR). To kick things off, there’s nothing more formal than a precise statement of the Axioms of Special Relativity : 1. The Principle of Relativity : All inertial frames are totally equivalent for the performance of all physical expts. 2. The Universality of the Speed of Light : The speed of light in vacuum is the same for all inertial observers, regardless of the motion of the source. Every formula and physical consequence of special relativity is derivable from those two axioms. How do we know they’re true? Experiment. No experiment to date has found any discrepancy with SR, and that’s the only definition of “true” that we have for anything in science. We worked with axiom #2 last week. We were tacitly using axiom #1 but we didn’t really discuss it. Think about the Principle of Relativity for a moment. Here’s another way of expressing it which might make its meaning more clear: There is no experiment which can distinguish between a stationary frame and one that is moving at constant velocity. Thus, there is no such thing as an absolute “stop”. If you say an object is “stopped” or “stationary” without any further information, your statement is meaningless. An object can be stopped relative to another object (hence “relativity”!), but not in any absolute sense. Key concepts: space-time events and reference frames The only quantitative features of special relativity we've seen so far are the rates at which moving clocks slow down and moving objects shrink. This week we’ll incorporate those effects into the full-blown mathematical framework of special relativity, which is the Lorentz transformation . The Lorentz transformation tells us how events in space-time transform from one reference frame to another. What do we mean by “ reference frame ”? The idea is simple: it's just a coordinate system in which all our clocks and rulers are at rest, and all our clocks are synchronized. It is simply the coordinate system in which one observer measures positions and times. What do we mean by “ space-time event ”? An event is just an occurrence, like a rocket launch from Cape Canaveral, or you pouring your morning cup of coffee. The thing is: an event occurs somewhere in space and somewhere in time. The great lesson of SR is that space and time must be treated together . If I asked you where you poured your cup of coffee, you’d probably say “at my kitchen table”. But relativity demands that we never ignore the time portion. A complete description of the event, in your reference frame, would be: “I poured my cup of coffee at my kitchen table at 8:30 am.” If you poured another cup of coffee at 8:50 am, that would be a
Background image of page 3

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

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

This note was uploaded on 10/06/2011 for the course PHYS 225 taught by Professor Makins during the Spring '10 term at University of Illinois, Urbana Champaign.

Page1 / 12

Unit 2 - Physics 225 Relativity and Math Applications...

This preview shows document pages 1 - 4. Sign up to view the full document.

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