No, I'm no longer optimistic that anyone will figure out quantum gravity anytime soon. That's why I quit working on it over a decade ago. For more:
What have you changed your mind about: Should I be thinking about quantum gravity?
Yes, the book is nice to read. It teaches you the basics of differential geometry and how this math shows up in the fundamental laws of physics: special relativity, Maxwell's equations, the Yang-Mills equations and general relativity. It also introduces the basic ideas of knot theory and...
I've helped write a few books. Gauge Fields, Knots and Gravity with the physics grad student Javier Muniain is the most popular, since it's an intro to lots of math and physics. Introduction to Algebraic and Constructive Quantum Field Theory with my advisor Irving Segal and Zhengfang Zhou is...
I don't know what Schild's argument is, and I don't really want to know. If it's famous, it's almost certainly right. I just wanted to point out the hole in your apparent "paradox" - someone asked me to help.
It's hopeless to define "parallel" in a curved spacetime, but it makes perfect sense in the Rindler spacetime, and with that definition the opposite sides of a parallelogram in that spacetime have equal length.
I could try to explain all this, but that's unnecessary if all we want is to find...
We reconcile them by noticing that one of your statements is erroneous, namely:
It's impossible to have a parallelogram in flat space for which all four edges are geodesics and two opposite sides have unequal lengths. However, the 'parallelograms' you are talking about - in both the...
This interview has some really wretched line breaks. I believe the technology underlying PhysicsForums requires that you not include carriage returns within a paragraph, if you want to prevent that.
If you could exactly measure the position of a particle, the probability of getting any specific value would be zero, since the measure ## |\psi|^2 d^n x## is absolutely continuous. But of course it's unrealistic to act as if we exactly measure the position of a particle. A somewhat more...
In short, Deligne's theorem applies perfectly well to the tensor category of representations of the Galilean group: it says this tensor category can be seen as consisting of representations of a group. But that's not very surprising!
By the way, the lopsided nature of the analogy is perfectly fine if we take the attitude that string theory - or more precisely SCFTs - is primary and then we're investigating the particle limit. And that's what you were doing. It only becomes an issue if we imagine ourselves trying to treat...
Okay, that makes sense: if you take a finite-dimensional Hilbert space ##\mathcal{H}## and equip with a nice commutative algebra structure, namely a commutative dagger-Frobenius structure, this does two things:
it provides an isomorphism between ##\mathcal{H}## and 'an algebra of functions on a...
What I mean was this. I can easily see how "conformal field theory" is a reasonable answer to "what's a 2d quantum field theory?". But I would never have guessed that "spectral triple" is the answer to "what's a 1d quantum field theory?" I would instead have imagined the answer is "a Hilbert...
That review article is nice. I might have some technical questions/comments, but I'm watching the US presidential debate so right now I can only muster a very simple-minded general question. Roggenkamp and Wendland seem to present a systematic construction that takes us from 2d SCFTs (or...
Typos:
emberrassingly -> embarrassingly
(modul0 8) -> (modulo 8)
conicidence -> coincidence
Those that do are called sigma-model -> Those that do are called sigma-models
I've got a bunch of things to say, but here are three preliminary comments, in order of increasing seriousness:
1) Has...
Steve Wenner:
"Imposing a cutoff" or "regularization" is one way to change the measure to get a convergent integral. This is an important first step. But in making this step, you are led to inaccurate answers to physics questions. This step amounts to pretending that virtual particles with...
I wrote:
For example, consider the magnetic dipole moment of the electron. An electron, being a charged particle with spin, has a magnetic field. A classical computation says that its magnetic dipole moment is
$$ \vec{\mu} = -\frac{e}{2m_e} \vec{S} $$
where ##\vec{S}## is its spin angular...
The questions you raise are a huge amount of fun and a great way to learn physics. I don't know the answer to your question about confinement, but you can answer the question about asymptotic freedom by going here. This gives an approximate formula for the beta function. If we believe this...
Thanks! You may know about this article; it's not about the geodesics just the geometry of the Kerr solution, with a reasonable amount of detail on the 'ring singularity' and the closed timelike curves it gives rise to - those were my main concerns this weekend:
Leonardo Gualtieri and Valeria...
Nice post! There's a typo:
I guess you need something like two pound signs to do math here, not a dollar sign. Also, there are a number of bad line breaks - Wordpress blogs are unforgiving when you hit the carriage return.
What I'd really love to see is a study of orbits in a Kerr metric...
No. Deligne's theorem says, very very roughly, that under certain conditions particles must have some super-group of symmetries. However, for the purposes of this theorem, an ordinary group counts as a special case of a super-group, namely one that has no transformations mixing fermions and...
This question is a bit like "Is there a way to see if a Feynman diagram contains a hydrogen atom?" In quantum field theory a typical history of the world is not a single Feynman diagram but a superposition of many Feynman diagrams. Similarly, we how that in loop quantum gravity a history of...
Yes. Maxwell's equations of electromagnetism are not consistent with pre-special-relativity ideas about how things should look in a moving frame of reference, but that's a separate matter. Newtonian gravitation is perfectly consistent with these ideas. In fact it's the best theory that uses...
In brief: no. It could have some intrinsic energy, but in most familiar quantum field theories (QED, the Standard Model) the energy is assumed to be zero.
Marcus said:
As others have said, it's just a matter of interpretation whether you want to treat the cosmological constant term in Einstein's equations as part of the energy-momentum tensor or just... some other thing, which you're calling "baseline curvature". This decision doesn't affect...
My concept of biology is so broad that it includes biochemistry, neurobiology, ecology and more. The network formalisms I'm developing are so general that they should have some relevance to all of these topics... though of course it'd take expertise to develop any one particular application to...
Here's the relation. A sphere in n-dimensional space can have least one continuous nowhere vanishing vector field if and only if n = 2,4,6,8,... A sphere in n-dimensional space can have (n-1) linearly independent continuous vector fields if n = 1, 2, 4, or 8.
People know, for a sphere of any...