Via Dmitry Podolsky, a series of YouTube videos from Stanford encompassing an entire course by Lenny Susskind on general relativity. I didn’t look closely enough to figure out exactly what level the lectures are pitched at, but it looks like a fairly standard advanced-undergrad or beginning-grad introduction to the subject. (For which I could recommend an excellent textbook, if you’re interested.) This is the first lecture; there are more.

It’s fantastic that Stanford is giving this away. I don’t worry that it will replace the conventional university. The right distinction is not “people who would physically go to the lectures” vs. “people who will just watch the videos”; it’s between “people who can watch the videos” and “people who have no access to lectures like this.” And Susskind is a great lecturer.

Oh, awesome!
I’ve been watching Susskind’s lectures already, I started with Quantum Mechanics.. I’ve been waiting for the entire General Relativity series to up.Very cool.

http://ryandickherber.com/ Ryan Dickherber

Then there are these quantum field theory lectures by Sidney Coleman at Harvard:

He’s clearly a good lecturer too, and as a bonus, you get to watch him smoke.

Sili

I hope the following lectures pick up. This introduction ended up feeling like 90 minutes wasted.

On the up-side, I guess that means I haven’t forgotten as much as I feared.

(A propos your book – is it possible to buy it in installments? (And didn’t you raffle away some for the Donors Choose charity drive?))

Sam Gralla

You can see just from the still-frame that he’s clearly teaching Newtonian gravity, not general relativity. That explains why Stanford would give these videos away so cheaply!

By the way, Sean, could you please recommend some text(s) on cosmology that could serve as a follow-up for your book and cover both earlier (inflation and all that) and more recent (dark matter, dark energy, quintessence, multiverse, etc.) developments? It doesn’t have to be a book, some good lecture notes would do just as well. Many thanks in advance!

http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

Researcher, there are a lot of good cosmology books out there, and some less-good ones. Also, cosmology is a big field, and you have to make choices about what to cover and what to leave out. Scott Dodelson’s book has become a standard reference for people interested in the CMB and large-scale structure. Steven Weinberg’s book is, as you might expect, extremely good, but he derives everything himself from scratch, so the notation isn’t always the most standard. Beyond that, I would recommend looking into specific books to find one that matches what you’re looking for.

Toiski

It’s interesting to hear that the inside of a hollow sphere would have no gravitational field resulting from the mass of the sphere (I think that’s what he’s saying at the end). I’ll have to do the math myself one of these days, although I dread the integrals involved…
Couldn’t you make the argument that for a sufficiently large hollow sphere, sufficiently near its inner surface, the flat earth approximation would work equally as well as for the case on the outside?
On a side note, I recall a Tarzan book from my youth that involved a hollow earth and people living on the inner surface. it seemed perfectly logical to me at the time, that gravity would be stronger at the inner surface and zero at the center.

EDIT: I listened to it again, and now I’m even more confused. Damn it all.
Oh, and just to put things into perspective, I’m an undergrad student at Helsinki University of Technology, and the only physics courses I’ve completed are the basic ones.

Toiski

I had 3 seconds left on the editing timer when I realised… If you move the opposite surface away by enlarging the hollow sphere, the force it exerts per unit area decreases as 1/(r²) but the total area (and thus the mass, and total force) increases as r², right? Am I even on the right track?

http://Interestingrelativityparadox uncle sam

Thanks. GR is also supposed to be able to handle EM fields in conjunction with gravity, but there’s some loose ends IMHO. Consider the following: a tunnel is drilled through the Earth, and we let a charged body Q (can be macroscopic, not a “particle”) fall from one side to the other in SHM. It is moving like a charge in an antenna, and EM fields in any fixed vicinity change and these changes must propagate at c. Hence, even if there is some gravitational distortion of the EM waves, Q must effectively “radiate” and carry off energy.

If Q was an ordinary charge in an antenna (yeah, usually electrons but charged bodies must radiate too) we’d put in work fighting the radiative reaction, f_rad = 2kq^2v.dot.dot/c^3. However, Q is in free fall – it “doesn’t know” physically that it is falling, so how can a reaction force apply? I know, there are tidal fields, but the whole thing gets complicated. In order to get “actual” (!?) v.dot.dot instead of “felt” v dot dot (which is always zero), we must take v.dot.dot = (dg/dr)(dr/dt) = [gradient of g]*v. So Q has to sense its velocity relative to the planet. That brings up sticky questions of “relative to what”? I mean, what if the substance of the body Q oscillated in flowed like protoplasm, then what?

Some author said the charge does indeed act according to (dg/dr)(dr/dt), but that has more problems on top of what I noted above. That formula works OK in free fall. But a charge moved at constant speed on an elevator inside (or outside) a planet will have a reaction force, but then it shouldn’t be radiating. Any scoop on this? Sean?

http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

You have to solve Maxwell’s equations in curved spacetime. There’s a temptation to appeal to the Principle of Equivalence and say “the particle is in free fall, it’s not accelerating” but that’s not right. The P of E only applies in “small regions of spacetime,” and the setup of the problem demands that you consider large regions of spacetime. In particular, the wavelength of radiation is of the same order as the length scale over which the gravitational field is changing.

In short: there’s nothing paradoxical and there are no loose ends, but to actually solve the problem requires a lot of work solving Maxwell’s equations in curved spacetime.

Sam Gralla

Toiski,

Try making the argument in electromagnetism for a charged sphere (hint: use gauss’ law). The argument is the same in Newtonian gravity. You’ll have to wait until you get to the Schwarzshild solution to make the argument in general relativity.

Haelfix

Maybe its just me, but my experience over the years shows a large number of visibly superior GR lecturers relative to quantum mechanics or field theory lecturers.

Most major universities have a great GR course, and subpar quantum courses.

You have to search long and hard for a Sydney Coleman equivalent.

Bean

Susskind’s lectures are a fantastic resource. I like to watch them while I’m working out. The Gen Rel ones are particularly good

Love the lectures, but true to God, I will find the two or three stupid kids that stall the class with their non-questions and slap them. “Can you say the dark force is a relative force?” What in God’s name are you even trying to say? What is the point of that intervention?

I thought we only had these in Political Sciences and that real science class were exempted of such classroom trolls, but it’s worst than anything I’ve ever seen.

And you can see the professor getting irritated. There’s no such thing as a stupid question, as long as it’s a question. If you’re trying to show off the very little you know, if you’re speaking just to hear the sound of your voirce and have the feeling of actively participating in class, if you’re trying to prove the professor wrong, it’s not a question, even if you put an question mark at the end. So shut up, please just shut up.

uncle sam

OK, thanks Sean but I wouldn’t be able to do that calculation! So could I ask if that solution involves a reaction force that is the same as if there was no gravity? still don’t get how a local self-interaction (what creates the self-force) can be correlated to the overall field. There is, after all, a difference between calculating a force directly from its causes, and inferring what it “must be” to get a desired result. I figure GR would calculate the self-force the latter way (as a sort of circular argument) from assuming it would be the needed value, since Maxwell’s equations AFAICT don’t tell us directly what self-force should be on a charge.

Also, do you know who first worked this sort of thing out? Thanks, if you have time.

http://www.davidnataf.com David Nataf

Sean,

Any plan on a 2nd edition of your spacetime book?

http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

David, nope, sorry.

uncle sam, I have no idea how to do the calculation (not that I’ve tried) nor who has done it. All I know is that arguments from the Principle of Equivalence that lead to purported puzzles are misguided.

GR

uncle sam,

If you have access to it,

A. Kovetz, G.E. Tauber, American J. Physics, 37(4) 382-385 (1969) has a pretty good treatment of the problem. It is complicated, though, and it seems a paper or two about it (reaching different conclusions…) appear every few years.

GR: I’ve noticed this “reaching different conclusions” about too many offbeat topics of physical speculation. Why should competent authors reach different conclusions, if we have the wherewithal to know how to find the right answer? It happens with radiations issues (gravity as noted; problems with self-force in general such as Schott energy, averaging, runaway, etc.), the stressed extended body in SRT (right-angle lever paradox, with wrangling for decades in Nuovo Cimento and AJP about whether the “von Laue Energy current” is appropriate versus internal torques, how best to find conservation of angular momentum in the case of Thomas Precession, etc.) and of course the old “4/3 paradox” about EM mass.

Clearly, IMHO that means some things haven’t been fully hashed out properly and that physics isn’t “finished” even not counting traditional frontier areas like ultimate particle theory and ur-cosmology. Take another look at my “complaints” and see if anything impresses you.

Sam Gralla

There are no “problems with self-force in general”. In classical physics bodies move according to coupled Maxwell and matter equations, and you can derive lorentz force and self-force as approximations to that motion. There are no runaway solutions in a proper derivation.

Jdhuey

I was about mid-way through Susskind’s _The Cosmic Landscape_ when I listened to this lecture (this is the first time I’ve heard his voice). Now, when I’m reading, I’m hearing his ‘voice’ in my head. Tres cool.

They are very well produced but also very technical. I wasn’t able to truly follow them, but I probably could have had I come armed with pen and paper.

Count Iblis

Uncle sam, in your problem General Relativity is not important, the Newtonian treatment of gravity yields almost the exact answer. The reason why a naive appication of the equivalence principle gives you the wrong answer, is because if the equivalence principle were to apply, the boundary conditions for the fields at infinity would necessarily have to be different.

So, if you consider an electron at rest in some inertial frame and then you switch to an accelerating frame, then in that accelerating frame, the electron is accelerating in the opposite direction, but it is not emitting any radiation. Now, compare the electromagnetic fields of this accelerating electron in the non-inertial accelerating frame to the electromagnetic fields of an electron that is accelerated in an inertial frame which we know will radiate electromagnetic waves.

In the latter case, you know that the fields are given as an integral over the charge and current densities at the retarded time, which then gives you radiation fields that fall of as 1/r at large distances. But in the former case, you simply have the Coulomb field that falls off as 1/r^2 at large distances which remains the case if you switch to the accelerating frame.

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Cosmic Variance

Random samplings from a universe of ideas.

About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson.
Here are some of his favorite blog posts, home page, and email: carroll [at] cosmicvariance.com .

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