lec11.pdf - Scott Hughes 15 March 2005 Massachusetts...

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Scott Hughes 15 March 2005 Massachusetts Institute of Technology Department of Physics 8.022 Spring 2005 Lecture 11: Spacetime: Introduction to Special Relativity Preamble: The vast majority of material presented in this course consists of subjects that are challenging, but that I am convinced every 8.022 student can — and should! — learn well. Special relativity is the only exception to this rule. The material that we will begin covering today (and that we will conclude on Thursday) is, in my experience, by far the most confusing subject that we cover all term. Further, it is not strictly necessary to learn this material inside and out in order to understand and excel in 8.022. You may wonder, given this, why we are bothering to study it at all. The reason is that special relativity “explains” the magnetic field: what we find at the end of all of this is that magnetic forces are nothing but electric forces viewed in another frame of reference. Magnetic fields are just electric fields “in drag”, so to speak. Conceptually, this is an extremely important point: even if you do not fully grasp the details of where many of the formulas we are about to derive come from, I firmly believe every 8.022 student should understand what magnetic forces “look like” in different frames of reference. The punchline of this preamble is that you should not be too worried if 8.022’s discussion of special relativity makes your brain hurt. Those of you who take more physics courses will encounter these concepts several more times; if you don’t quite get it now, you will have plenty of chances to get it later 1 . Try to get the flavor of what is happening now, and practice manipulating these formulas, even if it is not 100% clear what is going on. 11.1 Principles of special relativity Special relativity depends upon two postulates: 1. The laws of physics are the same in all frames of reference. 2. The speed of light is the same in all frames of reference. These postulates beg the question — what is a frame of reference? A frame of reference (more properly an inertial frame of reference) is any set of coordinates that can be used to describe a non-accelerating observer. In the following discussion we will compare measure- ments in two frames of reference: a station, and a train that is moving through this station in the x direction with constant speed v . 11.2 Time dilation These postulates have consequences that are rather amazing. In particular, it means that inertial observers in different frames of reference measure different intervals of time between 1 I studied special relativity in 4 separate courses as an undergrad; I honestly can’t say I really knew what I was doing until about halfway through the third time. Even then, the fourth study was useful to me.
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