Introduction to General Relativity and Cosmology: Newton-Einstein Gravity (for educated, intelligent beginners)

Preface: Based on understandings acquired during my research, over the years I have evolved an approach to teaching the subject. During the years 2002 – 2013 I gave several series of lectures to undergraduate physics-majors, under the rubric of the Society of Physics Students at NYU, and to graduate and undergraduate students at Ben Gurion University.

Prerequisites: The lecture-series was designed for physics students who have taken at least two college semesters of physics with calculus, and some vector calculus, but have never taken any differential geometry.

The book-version has been reconfigured as an ebook accompaniment to the lectures.

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For the student-viewer of the course: The first video is an optional 3-minute slide-show presentation of the what the course will cover (and it includes some photos of Einstein’s original papers). If you wish, you can skip right to lecture 1.

You can also read more about the topics covered in the lectures – with many additional diagrams, examples, solved problems, and references to interesting textbooks – in the accompanying eBook  manuscript (which can be ordered via Amazon or directly):

Warped Spacetime, the Einstein Equations, and the Expanding Universe 

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The first lecture stands on its own, and viewing it will give a nice very basic idea of a fundamental feature of general relativity (GR) and its relation to gravity. The second lecture will provide a deeper insight. Later lectures extend the theory, and are appropriate for undergraduate physics and engineering majors.

Lecture 1

Galilean relativity (Section A of Lecture 1) : It is imperative that before starting general relativity, one have at least a light familiarity with Galilean relativity. This video presents in just 6 minutes all you will need on the topic as background to the GR course (and so even students who are familiar with the subject should watch this). It also contains the Table of Contents for Lecture 1.

Note: Galileo and others showed that an object does not need input to maintain motion, except to counter friction, wind resistance etc. Running and being on a horse requires constant exertion to maintain the same speed, but this is a red herring. And even a smooth car and plane ride require constant engine input, but gliding on ice requires less; indeed, uniform motion in outer space requires no input….we conclude that all uniform motion is indistinguishable, only relative motion is absolute, and so understanding inertia leads to Galilean relativity.

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You are strongly urged to interact with the next segment (which is Section B of Lecture 1) by trying to answer the challenges I pose, while pausing the video. This segment is a transitional step between Galilean and Einsteinian theory; it introduces a new concept, which will be very fundamental, giving it a non-standard name:

After viewing the video, you may wish to read Chapter 2 of the accompanying eBook manuscript, which extends the ideas presented here, and has various interesting diagrams as well as quotes from Maxwell’s work in which he presents the relevant ideas.

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You will have satisfaction in guessing the answers to the challenges posed in the next segment. This 30-minute video will begin your introduction to the heart of the matter.

After viewing the video, you may wish to read Chapter 3 of the accompanying eBook manuscript, which extends the ideas presented here, and has various interesting diagrams as well as relevant quotes from the writings of Newton and Einstein.

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Background material about the lectures: There are many qualitative (non-mathematical) books describing the ideas of GR to lay readers with some science background, and many texts suited to mathematically-sophisticated physics graduate students.  Here the special challenge was to construct a mini-course for those who are somewhere between the two categories mentioned above, for whom material already exists. In other words, exploiting the knowledge and mathematical techniques which physics undergraduates have acquired by their 3rd & 4th year in the BA program, but not more than that. Doing so required recasting the advanced-math treatment in standard texts into a mathematical/physical language familiar to undergraduates; this was accomplished by exploiting somewhat-unexpected similarities between Newtonian gravity theory and GR uncovered during my research.

The first few hours of the Youtube playlist is taken from lectures delivered in 2013. Additional videos are being added, taken from the more extensive lecture series in previous years, which covered more ground and presents more intermediate and advanced material, but is nevertheless also geared for physics undergraduates.

‘Enrichment’ lectures on General Relativity: Most of the lectures were given as an optional non-credit introduction to the subject, though on at least one occasion the final grade of an actual credit-bearing course included attending the lectures and solving a problem on the final exam taken from the lecture material.

Videos of some of the more recent lectures can be seen on my Youtube channel (see below), with some videos of the older lectures to come.

Ranking and review of the lectures: There are about 11,000 views for the videos on my physics channel. Googling “top lecture video introduction general relativity” (or substitute ‘best’ for ‘top’) leads right to my Youtube lectures. They are also featured on physicsdatabase.com (in June 2015 they were banner-features); that site also lists them as one of three lecture-videos and seven texts recommended for beginners to learn GR calling the original three lectures “a great overview to the ideas of GR … recommended for beginners”. Recently I partially-edited and uploaded several lectures with intermediate-level material continuing where the original three left off, and have begun working on editing the more advanced material.

Future plans: The intent is to create a complete undergraduate “introduction to GR” course, possibly to be marketed via services such as Coursera etc, or offered for credit via online universities with myself as guiding-instructor.

My textbook: The lectures were to a large extent based on my text:  “Warped Spacetime, the Expanding Universe & the Einstein Equations” (or google just “Warped Spacetime & the Einstein Equations”). The book contains far more material than do the lectures, and has many diagrams, examples, exercises, solved problem and extensive references. A newer version is being prepared as a lecture-companion (rather than a formal textbook), following the order of presentation of the material in the video series, and meant to be sold as an ebook to those who appreciated the lecture-videos.

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