Phys 3250: Topics in Relativity Instructor: Dr. Spencer Buckner Office: SSC B-326 Office Hours: MWF 10:15 – 11:30am and MWThF 2:30 – 4:00pm or by appointment Email: [email protected] Website: www.apsu.edu/physics/buckners Class Meeting Time: Friday 12:20 – 1:15pm Class Meeting Place: SSC B-310 Textbooks Schaum’s Outline for Modern Physics by Ronald Gaurteau & William Savin

Supplemental materials from Exploring Black Holes by Wheeler and Taylor. Not a required book. Won’t be used until the last few weeks of class. Grading

Exams………45% A…90 – 100% Homework…30% B…80 – 89% Project………20% C…70 – 79% Participation…5% D…60 – 69% F…<60% Exams

There will be three exams during the semester. The exam will be handed out in-class on Friday and due in the D2L Dropbox by 12:01 PM (noon) the following Monday. The exams will consist of a number of numerical problems similar to the homework and at least one essay question. The exam dates are: Friday September 18 Friday October 16 Friday December 4 Homework Homework will be assigned each week and will be due the following week. Most problems will be out of the Schaum’s Outline for Modern Physics but additional supplemental problems from other sources may be assigned. Solutions to the homework will be posted in the class D2L shell within a day or two of the due date.

First Homework Set: Schaum’s Outline Chapter 1 Supplementary Problems #1.11, 1.13, 1.17, 1.18, 1.19 & 1.20 The assignment is also posted at http://www.apsu.edu/physics/buckners/relativity- homework-assignments.php Project There will be one project on a topic in relativity, either special or general, during the semester. The results of the project will be presented orally via Zoom sometime during the week of December 4 - 10. A project abstract (prestract?), worth 10% of the project grade, will be due Friday October 16. The Need for Relativity 1 c  0 0 First published in a four part paper by James Clerk Maxwell between 1861 and 1862. Maxwell showed that light was an electromagnetic wave whose propagation speed was equal to the inverse square root of the product of the two fundamental constants in his equations. Question: What is the medium through which light travels? The Luminiferous Aether? The Need for Relativity II

Performed in 1887 by Albert Michelson and Edward Morley at Case Western Reserve University to detect the motion of Earth through the luminiferous aether

Watch YouTube video on Michelson-Morley experiment The Need for Relativity III To account for the null results of Michelson and Morley, one proposal was that electricity & magnetism should use a Lorentz transformation rather than a Galilean transformation. Problem is, while Maxwell’s equations are invariant under a Lorentz transformation, Newton’s equations aren’t. Plus, Maxwell’s equations gave a speed of propagation of the dp electromagnetic force: the speed of F  light. There was no propagation speed inherent in Newton’s equations dt for gravity or forces in general. Galilean Transformations are simple addition and subtraction

ux u x  v

uy u y

uz u z This doesn’t work for the electromagnetic force and Maxwell’s Equations. It works fine for Newtonian mechanics and the gravitational force Hints on the homework

ux u x  v

uy u y

uz u z The Need for Relativity IV

The orbit of Mercury wasn’t what it was supposed to be. The perihelion of Mercury's orbit precesses by just over 574 arcseconds per century. Perturbations due to the other planets and the oblateness of the Sun could account 531 arcsecond per century. The other 43 arcseconds per century could not be explained using Newtonian physics. Colored Card Question

The null results of Michelson and Morley A) proved there was no luminiferous aether. B) proved that the Earth dragged the luminiferous aether with it as it moved through space. C) proved that, when dealing with light, velocities required a Lorentz transformation rather than a Galilean transformation. D) didn’t prove anything other than there was something wrong with physics. Another Colored Card Question The precession of the perihelion of Mercury was evidence that A) the planet was dragging the luminiferous aether with it and thus slowing its motion. B) the force of the Sun’s gravity on Mercury was stronger than it should be due to its proximity to the Sun. C) Newton’s law of gravity was wrong and no longer useful anywhere. D) due to its high orbital speed, a Lorentz transformation for velocity was required to get the correct orbit. 5-Minute Essay My name is ______.

I am a (sophomore, junior, senior).

My major is ______. (include concentration, if you have one)

I am taking Topics in Relativity because I want to learn ______.

When I graduate I want to ______.