Video Lectures, introduction to General Relativity and Cosmology: Newton-Einstein Gravity (for educated, intelligent beginners). Guide to playlist https://www.youtube.com/playlist?list=PLn_5Sx_ThgDGLVOal214TLTuWO2PA_xZt avi rabinowitz

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.

Overview of Youtube course "Introduction to General Relativity for beginners" (& for physics majors)

by Avi Rabinowitz

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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Introductory General Relativity: Einstein's beautiful& magical recasting of Newtonian Gravity: A.beginner B.science/physics student.Not Dummy Tutorial

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...

Galilean inertia

by Avi Rabinowitz

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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.

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Lecture 1,Section B (BTW: I know the sound on most of the Playlist videos is not great. Sorry)
“Section C" : Note re all the videos: To the student-viewer:: Do you think my adding explanatory text improves them or makes them worse?
Amazing! See how far we get without speaking at all about spacetime or about geometry! (we introduce those in the next lecture, #2)
Appendix

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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:

Lecture 2 Section I [Note to advanced viewers: Lecture 2 introduces the Connection& Riemann levels of geometry; we avoid 'Metric' until lecture 8] :
Lecture 2, Section II: We present Newtonian gravity in terms of r(t), and thereby formulate a sort of NeoNewtonian gravity theory.
We introduce the notion of "spacetime" rather than 'space+time', in the context of inertia, and in the next video we'll continue on to grravity.
Newtonian gravity as a theory of 'warped' spacetime. (Presenting R.A.N.I.P. = Relative acceleration of neighboring inertial particles.)
We finally get to 'curvature' (not just generic 'warping'), and curvature ofSpacetime itself (rather than of lines in spacetime).Next is the Appendix.
This video and the next 4 (47 minutes total) overlap; they are about the very important topics of RANIP, geodesic deviation& intrinsic curvature.
2/5 (R.A.N.I.P. = Relative acceleration of neighboring inertial particles)
Hi! Please send me feedback if you watched any video on my playlist, your comments are valuable to me: air1@nyu.edu
Review: The time-warping model deals only with the possibly-spurious acceleration/Connection level; we need a tidal/Rieman-level theory.
The last of the 5.
Five videos (total:~ 27 minutes)presenting a more sophisticated version of the EP (Equivalence principle)and of Einstein's model of Newtonian gravity.
Summary of the model.
A longer summary of the model
Lect #3.In this lecture (in Part III) we arrive at spacetime curvature via an alternate route than in lecture 2. All throughout we will showcase the role of time. Besides being fundamental in its own right, this time-explicit material is also preparation for lecture 6 which actually goes so far as to base the spacetime curvature underlying Newtonian gravity on a time-effect and so is appropriately titled 'Time-warping'.
Part II of lecture #3
Part III of lecture #3

A few videos supplementing and reviewing the previous material
- We'll develop Newtonian theory in terms of space+time diagrams, e.g r(t) rather than spatial trajectories. We know an inertial r(t) is a straight line

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Order of the topics in the GR lecture-vidoes on Youtube:

Newtonian gravity:

A: Acceleration

1. Gravity as an acceleration field on the medium, so that Newtonian gravity acceleration-field equaiton is: a = -GM/r2

2. Gravity as a field of the curvature of the graph r(t), which can be called "the worldline", so that Newtonian gravity field equaiton is: r..(t) = "worldline curvature" = -GM/r2.

B: Tidals:

Because in free fall frame r.. = 0 , we need to go to a theory of tidals, so we get the Newtonian tidal field equaiotn div r..(t) = 0 in vacuum [where the tidals are expressed in terms of the accelerations, ie: r..', (1/r) r.., (1/r) r..].

C: Potential:

After we see that the whole theory is accounted for, I introduce the potential, which gives the energy equation etc, and we see it is additional, gives nice structure and properties, but adds nothing truly new.

GR:

A: Similarly: without metric at all at first, only connection,

In calculus we know the second derivative is curvature: r(t) is the flat spacetime 'worldline', and for r(t) the 2nd derivative r..(t) is the curvature of the worldline, so Newtonian gravity theory is basically: free fall worldline curvature= r..(t)= GM/r2

In GR we see the free fall particle as not accelerating.

one postulates that free fall particles have geodesic worldlines, whether the spacetime is warped in the presence of matter (for Newtonian cases we don;t need to say 'matter-energy'), and free fall worldlines are geodesics of the warped spacetime - we re-write the Newtonian gravitational acceleraiton equaiotn as: r..(t) - GM/r2 = 0 and it is the geodesic equaiotn, where - GM/r2 is the Gamma, ie the conneciotn.

Said in a different way: in the Newtonian regime the geodesic equaiotn reduces to d2r/dt2 = Gamma rtt , which in Newtonian gravity is the acceleration equaiotn

the observer standing on Earth watching the free fall particle sees it has acceleraiton, but it is the observer's accleeration, the free fall particle has zero accelration: the Earth-observer's worldline is curved, and that curvature is his accleeration, and it is exactly the amount of the acceelration between him and the free fall particle, whoever is considered to be accelerating,. The free fall particle's equaiotn is the geodesic equaiton, saying that its worldline curvature is zero, and it vanishes due to the correciton facotr in the geodesic equaiotn, the Gamma, so that amount is exactly the acceleration as seen from the Earth-stationary viewpoint.

Notice that just as the conneciotn vanishes at every point, but the derivative (RIemann) doe snot, so too free fall acceleration vanishes but its derivative, tidal aceelration, doe snot.

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We can use the geodesic equaiotn to find an equaiotn of the free fall worldline, which gives us the 4-acceleration (the geodesic equaiotn says this acceleraiton is 0, ie the worldline curvature = 0) and thus we can relate it to the Newtonian gravity equaiotn for the acceleraiotn of a free particle (in Newtonian gravity the interpretaiton is that a free fall particle has acceleraiton Gamma, rather than Gamma being a correction factor in the equaiton: acceleration = 0

BTW: The sum of the quantities set to 0 in the geodesic equaiotn is the 4-acceleration, that's the vector, it is basically the worldine curvature, which is zero for a free fall particle (the Gama is a correction factor designed to make the sum zero)

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B: Riemann.

C: Then I ask about a "third tier" of the structure (which turns out to be ‘metric’). I make the point that the r(t) graph's importance does not at all imply that there is meaning to the "distance between points in the (r,t) plane (unless they are along one of the axii). We know there is a space metric, we know there is a time metric, but is there a spacetime metric!?

Introducing the concept of a spaceimte metric: relevant material in the videos::

1. Less than two minutes: https://www.youtube.com/watch?v=XdvPsTE_As8&index=104&list=PLn_5Sx_ThgDGLVOal214TLTuWO2PA_xZt

2. Less than 3 minutes, but it includes part of a few classes and reviews, so there is some duplication:https://www.youtube.com/watch?v=4piqtxtJlgc&index=117&list=PLn_5Sx_ThgDGLVOal214TLTuWO2PA_xZt

3. Less than 3 minutes: https://www.youtube.com/watch?v=ZsGtJqp3vI0&index=110&list=PLn_5Sx_ThgDGLVOal214TLTuWO2PA_xZt&t=116s

4. 3.25 minutes: https://www.youtube.com/watch?v=07gMB5kdQ4A&index=112&list=PLn_5Sx_ThgDGLVOal214TLTuWO2PA_xZt

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And now to Lectures 4-10

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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 3^rd & 4^th 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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