Here’s a collection of things I’ve run across recently that may be of interest:

The Tevatron is doing quite well, with sizable increases in luminosity in recent months. There are some articles telling about this in Fermilab Today, and you can get up to date information about how things are going here. At the moment they’re doing better than their “design” projection, which is meant to be quite optimistic.

On December 1 there will be a live 12 hour webcast called Beyond Einstein, which will feature many different groups and individuals talking about physics.

December 1 will also be the opening of the 23rd Solvay conference in Brussels. These conferences have a very illustrious history. This year the topic is The Quantum Structure of Space and Time, and most of the invited participants will be string theorists. Of the 60 participants there seems to be exactly one physicist from the LQG camp, Abhay Ashtekar. There will also be an event for the public, with talks by string theorists Brian Greene and Robbert Dijkgraaf, and a debate featuring five string theorists and Gerard ‘t Hooft.

Witten has been giving talks about his new work on gauge theory and geometric Langlands. Notes from a talk at Penn last month are on-line, and video from a talk at Rutgers last week should soon appear.

A conference was held earlier this month at Queen Mary College in London entitled From Twistors to Amplitudes, with many interesting talks on using twistor techniques to study gauge theory amplitudes.

There’s a new site called Mixed States which does a good job of aggregating blog entries about physics.

There are all sorts of links relevant to research in number theory at the Number Theory Web.

Robert Wald has an article on teaching general relativity. Until I taught our graduate differential geometry course I hadn’t realized just how tricky the definition of a tangent vector can be. Most of the difficulty with teaching GR has to do with the large amount of sophisticated geometry needed.

This is one of the funnier things I’ve read in a while. It seems that, like all non-string theorists, internet con artists are really stupid.

**Update:** Two recent talks by Alain Connes at the KITP in Santa Barbara are now online. One is entitled Non-Commutative Geometry and Space-Time, the other, discussing his ideas about the Riemann hypothesis, is called Noncommutative Motives, Thermodynamics, and the Spectral Realization of Zeros of Zeta.

http://physicsmathforums.com/showthread.php?t=56

I think the taxpayers aare getting tired of funding String Theory.

Perhaps Hollywood is better suited?

Tied Up & Strung Out: Hollywood String Theory Movie!!! Looking For Extras!!!

FOR IMMEDIATE RELEASE:

ALL TIED UP & STRUNG ALONG, a movie about String Theorists and their expansive theories which extend human ignorance, pomposity, and frailty into higher dimensions, is set to start filming this fall. Jessica Alba, John Cleese, Eugene Levie, Jackie Chan, and David Duchovney of X-files fame have all signed on to the $700 million Hollywood project, which is still cheaper than String Theory itself, and will likely displace less physicists from the academy.

“As contemporary physics is about money, hype, mythology, and chicks,” Ed Witten explained from his offices at the Princeton Institute for Advanced Study, “The next logical step was Hollywood, although I thought Burt Reynolds should play me instead of Eugene Levy.”

Brian Greene, the famous String Theorist who will be played by David “the truth is out there” Duchovney, explained the plot: “String theory’s muddled, contorted theories that lack postulates, laws, and experimentally-verified equations have Einstein spinning so fast in his grave that it creates a black hole. In order to save the world, we String Theorists have to stop reformulating String Theory faster than the speed of light. We are called upon to stop violating the conservation of energy by mining higher dimensions to publish more BS than can accounted for with the Big Bang alone, and I win the Nobel prize for showing that M-Theory is in fact the dark matter it has been searching for.”

Greene continues: “At first my character is reluctant to stop theorizing and start postulating, but when my love interest Jessica Alba is sucked into the black hole, I search my soul and find Paul Davies there, played by John Cleese. I ask him what he’s doing in my soul, and he explains that the answer is contained in the mind of God, which only he is privy too, but for a small fee, some tax and tuition dollars, a couple grants here and there, and an all-expense-paid book tour with stops in Zurich and Honolulu, he can let me in on it. And he shows me God in all her greater glory, as he points out that we can make more money in Hollywood than writing coffee-table books that recycle Einstein, Bohr, Dirac, Feynman, and Wheeler. I am quickly converted, and I agree to turn my back on String Theory’s hoax and save Jessica Alba.”

But it’s not that easy, as standing in Greene’s way is Michio “king of pop-theory-hipster-irony-the-theory-of-everything-or-anything-made-

you-read-this” Kaku, played by Jackie Chan. Kaku beats the crap out of Greene for alomst blowing the “ironic” pretense his salary, benefits, and all-expense paid trips depend on. “WE MUST HOLD BACK THE YOUNG SCIENTISTS WITH OUR NON-THEORIES!! WE MUST FILL THE ACADEMY WITH THE POMO DARK MATTER THAT IS STRING THEORY TO KEEP OUR UNIVERSE FROM FLYING APART, OUR PYRAMID SCHEMES FROM TOPPLING, AND OUR PERPETUAL-MOTION NSF MONEY MACHINE FROM STOPPING!!” Kaku argues as he delivers a flying back-kick, “There can be ony ONE! I WILL be String Theory’s GODFATHER as referenced on my web page!! I have better hair!”

But Greene fights back as he signs his seventeenth book deal to make the hand-waving incoherence of String Theory accessible to the South Park generation, senior citizens, and starving chirldren around the world. “Kaku! Kaku! (pronounced Ka-Kaw! Ka-Kaw! like Owen Wilson did in Bottle Rocket),” Greene shouts. “It is theoretically impossible to build a coffee tables strong enough to support any more coffee-table physics books!!!”

“Time travel is also theoretically impossible, but there’s a helluva lot more money for us in flushing physics down a wormhole. Nobody knows what the #&#%&$ M stands for in M theory ya hand-waving, TV-hogging crank!!! Get it?? Ha Ha Ha! We’re laughing at the public! We’re the insider pomo hipsters! Get with the gangsta-wanksta-pranksta CRANKSTER bling-bling program!!”

How does it all end? Does physics go bankrupt funding theories that have expanded our ignorance from four dimensions into ten, twenty, and thirty dimensions? Do tax payers revolt? Do young physicists overthrow the hand-waving, contortionist bullies and revive physics with a classical renaissance favoring logic, reason, and Truth over meaningless mathematical abstractions? Does Moving Dimensions Theory (MDT) prevail with its simple postulate? We’ll all just have to wait!

But in the meantime, how do you think it will play out?

Will theories with postulates ever be allowed in physics again? Or will the well-funded, tenured pomo String Theory / M-Theory (Maffia-Theory) Priests send their armies of desperate, snarky postdocs and starving graduate students forth to displace and destroy all common sense, logic, reason, and physics in the academy? It must be so–for the greater good of physics, the individual physicist, and thus physics, must be sacrificed.

MDT’s postulate: THE FOURTH DIMENSION IS EXPANDING AT A RATE OF C RELATIVE TO THE THREE SPATIAL DIMENSIONS IN QUANTIZED UNITS OF THE PLANCK LENGTH, GIVING RISE TO TIME AND ALL CLASSICAL, QUANTUM MECHANICAL, AND RELATIVISTIC PHENOMENA.

http://physicsmathforums.com/showthread.php?t=56

How many times are you going to post this spoof.?

It was only funny the first time.

It was only funny the first time.I’m not sure I’d go that far…

How many times are they going to publish the string theory spoof?

How many more coffee table books?

How many more films?

How many more conferences?

How many more millions of dollars to further the postmodern hoax that is string theory?

How many more hoaxters are going to receive tenure for doing absolutely nothing positive for physics?

How does it feel to be famous, to be revered, and yet,

not one iota

of your thought

matters

because it ain’t true.

what does it profit a man

to gain the world

and lose his soul?

so c’mon!

let us in on it!

I think it’s hilarious. Especially with the pictures:

http://physicsmathforums.com/showthread.php?t=56

Peter wrote: “Until I taught our graduate differential geometry course I hadnāt realized just how tricky the definition of a tangent vector can be.”

Much simpler than equivalence classes of paths, derivations, or whatever, is synthetic differential geometry’s idea of a tangent vector as a map from an infinitesimal object into the manifold.

Urs Schreiber discusses SDG and gives references here.

apparently assistant professors at haavard aren’t too bright either.

Peter , Jim Hartle is another non-string theorist whose name appears in the

participants of teh quantum structure of space-time conference.

Shantanu,

I didn’t mean to imply that all except Ashtekar were string theorists, just that Ashtekar is the only LQGer. Besides Hartle, there are also various cosmologists (Linde, Steinhardt, etc.), and various other non-string theorists (Wilczek), or even historians (Peter Galison).

yes you are right. sorry I misundertood your article.

hope the video of the talks are archived

Thanks Peter for the link to Robert Wald’s paper. I like his emphasis on Einstein’s great discovery in GR, p3:

‘Gravity isn’t a force at all, but rather a change in spacetime structure that allows inertial observers to accelerate relative to each other.’

Well done Robert Wald! That is accurate, and emphasises the spacetime fabric of general relativity. General relativity is better tested than string theory. Students should be allowed to know that there is FAR MORE evidence for a spacetime fabric than there is for string theory š

Mega-dittoes on Robert Wald. I didn’t realize until reading the paper that a lot of my hangups in understanding GR are due to my attachment to the Sophmore level Linear Algebra concept of a vector.

Maybe I should do some re-reading. Got nothing else to do while my spacetime fabric is at the cleaners.

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The definition of a tangent vector becomes tricky only in context of modern DG because algebraic techniques are introduced right from the start. The concept itself is nothing that one can’t explain a high school student or even an ancient mathematician of a Pythagorean academia in a pure geometric terms without coordinates or algabraic clutter. With little additional investment of very basic topology it goes as follows:

Start with a sphere S ( in arbitrary dimensions > 0 ) . Draw a line L from the center of S to a point p on S. The hyperplane H orthogonal to L with p in H is the

tangent spaceof S in p. The points q!=p on H are calledtangent vectors.This concept can now be applied to smooth surfaces. First we need a definition of smoothness: let F be a surface of dim n and p a point on F. F is

smoothin p if p is a point in an open set of S ( not a boundary point ) and n-dim spheres S1, S2 exist which suffices the requirements that p is the only common point of S1, S2 and F ( no cusps ). F is smooth iff it is smooth in each point ( it is left to the reader to proof that choosing a certain pair of S1 and S2 is no loss of generality ).In particular a non-intersecting sphere S(p) exists in each point p on a smooth surface F. The tangent bundle is the set of tangent spaces of such spheres in the points p of F.

One thing is missing in the little discussion above. The n-spheres S1 and S2 should be “parallel” i.e. embeddable in an n+1 dim space. Otherwise the tangent-spaces in their common point p would be different.

I took a one-quarter GR class from Bob Wald and didn’t think it was so great. As he mentions in those notes, it was almost all spent on mathematical background. If I remember correctly, he only got to the Schwarzschild solution on the last day of class. Rather than cutting out material, perhaps he could save time if he didn’t write everything out longhand on the blackboard and spend a great deal of time formulating every sentence in the most precise way possible. People are capable of getting all of the details from his book without him spelling it all out on the blackboard, after all. I felt that his class involved very little physics, so for those of us with a solid mathematical background it was largely a waste of time.

Do people really get to grad school at Columbia without knowing what a tangent vector is? This was covered in my first year of undergraduate mathematics (an analysis course, where we learned about calculus on manifolds and differential forms). Granted, not everyone has such a class so early, but surely most well-educated undergrads in mathematics learn some basic things about differential manifolds?

Certainly most grad students at Columbia have seen some geometry and know what a tangent vector is. My comment was from the point of view of teaching this material in a graduate level math class where you want to be able to rigorously prove things. The issue here is how to define a tangent vector intrinsically, not assuming your manifold is embedded in Euclidean space. There are at least three kinds of different definitions you can use:

1. tangent vector = derivation

which is one the algebraic geometers love because it can be expressed algebraically.

2. tangent vector = equivalence class of curves

3. tangent vector = something that transforms correctly under change of coordinates.

Each of these definitions works, and can ultimately be shown to be equivalent. When preparing this material, I was just surprised to realize that rigorously showing this is not completely trivial.

“The issue here is how to define a tangent vector intrinsically, not assuming your manifold is embedded in Euclidean space. There are at least three kinds of different definitions you can use”

Sure. We saw each of these definitions, and proved their equivalence, in that undergrad class I was talking about. And they came up again in at least one other undergrad class I took. So I would have expected graduate students in math to be familiar with this already.

This was covered as one part of the first couple weeks of foundational material in the class, it wasn’t a big part of the course. Graduate classes often go over some of the same material as in undergrad classes, just much faster. Some undergraduate geometry classes don’t really do much intrinsic geometry, so some of our graduate students probably hadn’t seen some of this before.

It’s not

thatunusual for an undergraduate math major to never have seen differential geometry, particularly at a smaller school. Most will have heard about tangent vectors from a differential equations course or just because the idea is in the air, but it’s not unusual to not see it formally.I think the place where starting with manifolds embedded in R^n really pays off is in tensor calculus. Picturing the tangent bundle as the manifold with little vectors attached to it isn’t that hard, but general tensors are sufficiently abstract that the extrinsic point-of-view helps ease the pain.

IsnĀ“t one of the most basic things you learn in math phys class that COORDINATES ARE OF NO PHYSICAL SIGNIFICANCE?

But then it looks physicists (and many diff geometers too) donĀ“t want to do linear algebra without coordinates.

A field is a Christoffel symbol. A tensor is a monstrosity with indices. Wrrrrrrrrrrr. 90% of your IQ wasted! IĀ“ve seen eminent minds fail at the calculus product rule while doing “tensor” calculus. No wonder without abstract tensor product.

Them Christoffel symbols and index notation have their place in computations with concrete coordinates. In general expositions they are more than a superfluous nuisance. O microsoftified math!

Funny thing is I’ve known several physicists who have told me what a revelation it is to realize that you can think about these things in a coordinate-invariant way. I’ve also known mathematicians who have told me it was a revelation to realize they could actually make a choice of coordinates and use them to do calculations.

Seems to me, what one should aim for is understanding what you are trying to calculate in a coordinate invariant way, but also being able when necessary to know how to choose appropriate coordinates and work with them.

A veeery subtle reason for avoiding coordinates/bases where possible: TO MAKE CLEAR WHERE THEY ARE NEEDED. This point is way above almost all math/phys writ I encountered.

Indeed you sometimes need bases in abstract linear algebra. Example: Compute the adjoint of

,

This might occur in computations with (co)differential.

———————-

One more pearl of my wisdoms thrown into this fine black hole:AVOID DIRECTIONAL COVARIANT DERIVATIVES where possible. Otherwise, you will one day get stuck at a Laplacian.Exercise: Formulate the product rule for the induced cov. derivative on the tensor product of vector bundles without using a directional derivative. (Hint: Use the flat map permuting the factors).

==============

Sigh. Last century one of the final drops into my bucket was when I caught myself translating Lichnerowicz & Tachibana stuff (P Petersen, Riem.Geom, Springer GTM 171, Ch. 7.5) into my own calculus. Shortly after I gave up on serious math…

——————-

One of my DaDaistic dreams is writing a book titled THE CALCULUS OF PHYSICS, based on Th. FrankelĀ“s book “The Geometry of Physics”, putting most of his writ into a large appendix titled “Computational Reference”

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