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.

Textbook version: The book-version has been reconfigured as an ebook accompaniment to the lectures. Read the Preface to the book here.

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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 the first section of lecture 1. Non-physics science-majors might prefer to first watch a more introductory-level and briefer series of videos.

If you enjoyed a video, please 'like' it, and also leave a comment, it's much appreciated. If you have criticisms which will assist me in improving the comprehensibilty(not the sound, speed and other technical issues) let me know, please! And if you attended any of these lectures (at NYU & BGU), and enjoyed watching the video, please do write to me. air1@nyu.edu

After seeing the videos on this playlist, go to the next one, about the Newtonian gravity field equaiton, and the Einstein field equaiotn for curved spacetime which we construct heuristically based on it. And also see the Cosmology playlist refererred to below.

This playlist's lecture series (especially after lecture 3) is meant for physics majors [for beginners (lec1,2),for science/physics majors(lec1-10)]. An alternate version appropriate for those who have a background in science but were not physics majors is: "Cosmology and the big bang theory, with an introduction to Einstein's General Relativity: for science majors"https://www.youtube.com/playlist?list=PLxxDwhhhmLZuaArmuR...

However I strongly encourage anyone interested in the subject to watch lectures 1 & 2 below (less than 2 hours total)

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The first lecture on this playlist 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. (The lectures were given to the NYU Society of Physics Students.) . CONTENT OF LECTURES 1&2:

Everyone knows that GR is about spacetime curvature. But why? And what does spacetime curvature really mean anyway. And what does it have to with gravity, and with 'relativity'?

Lecture 1 (sections A-E): All uniform motion is indistinguishable, only relative motion is absolute, and so understanding inertia leads to Galilean relativity. Einstein's sophisticated and audacious understanding of the essence of Galilean relativity and Newtonian gravity leading to his extension of the notion of 'relativity', a deeper understanding of gravity, and the intimate relationship between these two. (1 hr)

Lecture 2 (sections I-V): How this understanding leads to a model based on 'spacetime', and to the notion of a 'geometry of spaceitme' - specifically a model of gravity as ''spacetime curvature". (1 hr)

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How a deep understanding of inertia & gravity (Lecture 1) reveals the existence of spacetime curvature (lecture 2)

Why the spacetime curvature underlying gravity is time-warping (lecture 4?); why this type of warping is considered 'stretching' (lecture 5).

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Lecture 1:" RANIP": Einstein teaches us:

How two can grow apart without either one moving.

The whole is more than the sum of the parts

"Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth." - Arthur Conan Doyle/Sherlock Holme; Lewis Carroll: Why, sometimes I've believed as many as six impossible things before breakfast.

Two contradictory opinions can both be right (anecdote of Rabbi)

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Much of the playlist will present an Einsteinian view of newtonian gravity, ie a curved spacetime model of Newtonian gravity, and then only later on, a full GR theory contianing spatial curvature, FRW cosmology, etc.

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: Note that all of lecture 1 is based purely on Newtonian physics, there's no mention at all of spacetime nor of geometry.

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.

For all the videos: The amount of time allotted to reading the text 'slides' is v approx, so you can choose to freeze the video to read them...

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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.

Note re video #7: When I say that Einstein did not want to abandon his model, he kept the idea that particles are in an inertial state, and introduced warping to explain for the anomalous relative acceleration between inertial particles, it is not meant to be historically accurate, he didn't actually think exactly along those lines, but I feel that nevertheless it's a good way of understanding his theory.

After learning GR in depth, and rigorously, and as it is understood today with the benefit of 100 years of clarifying discussions and mathematical development, it can be interesting to investigate Einstein's own path to GR 100 years ago, but it was a long tortuous path, with many detours and mistakes along the way. [Actually, it's a subject on its own, with specialists debating this or that point of what he actually meant, and most physicists do not really want to learn how he did it since their goal is to understand the theory he eventually invented and how it was later made more rigorous, rather than caring about how HE happened to come to the theory.]

After viewing these videos, you may wish to read Chapters 1-3 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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NOW TO LECTURES 2 & 3: