57,602 reputation
481195
bio website
location New York City
age 41
visits member for 3 years, 2 months
seen 5 hours ago

I do not participate on this site any longer, except to respond to comments regarding my own text, if that text is unavailable in another form. I do not accept the political moderation atmosphere here, it is not compatible with open science. I participate at physicsoverflow.org.


Aug
9
revised what co-operates with a Super Symmetry Transform
added 1308 characters in body
Aug
9
awarded  Yearling
Aug
9
comment Does the Banach-Tarski paradox contradict our understanding of nature?
@WetSavannaAnimalakaRodVance: This is basically everyone's motivation. But to learn it, all you need is to understand the Skolem theorem (which is very simple and intuitive) and the Godel completeness theorem (which is important for other reasons, it's the deduction theorem in logic, it's also the essence of the first Turing complete computer ever defined, in hindsight). The demonstration that the uncountable ordinals are not absolute is simply from noting that all the models of an axiom system can be countable. It means that you don't need to take the uncountable ordinals seriously.
Aug
2
comment What is currently incomplete in M-theory?
@MitchellPorter: Yes, it's a little string theory in type II analogs, but how does it reproduce the M-theory in holographic detail? This is the open question. It's because these theories are so ill understood, they are not like N=4 gauge theory, you don't know how the holography works here.
Aug
1
awarded  Good Question
Aug
1
awarded  Necromancer
Jul
28
comment Why regularization?
The approximations for symbolic differentiation are no different--- you can represent a function as a sum of wavelets, and differentiate "symbolically", it's no different. The analytic representation is a text string, and doesn't represent it any less discretely than a bunch of doubles on a grid, except it may be a more efficient countable structure. You don't prefer different approximation scheme, you define the derivative as the thing they have in common--- that's the limit. Same in field theory, the field theory is that universal limiting thing different approximations have in common.
Jul
28
comment What is currently incomplete in M-theory?
There's a lot more to do, but it seems people are pretty stuck at the moment. The last major breakthrough was the M2 brane CFT by Schwartz and co, and I haven't followed the last few years. The Lagrangian is not exactly what you are after, you want to know the scattering amplitudes--- it's not from a local Lagrangian density in string theory. The scattering amplitudes are only well defined in certain backgrounds, where there is a known CFT dual. The general formulation is lacking, and it probably requires a major new idea.
Jul
27
comment What is currently incomplete in M-theory?
@dimension10: Not completely, because it's defined around a flat background. All the solutions are in a fixed background, either AdS or flat, or some other supersymmetric background. You can't describe deSitter spaces, or backgrounds that interpolate between different finite-energy-density states, like Simeon Hellerman's 26 dimensional bosonic string cosmology, going to a standard string theory. Is it completely consistent non-perturbatively? That's what a non-perturbative formulation should answer. The Matrix theory and AdS/CFT are only valid as finite-number-of-particles over solvable vacuum
Jul
27
comment AdS/CFT correspondence and M-theory
@Dimension10: It's not necessary to beat people up, just explain the mistake. It's already at -1.
Jul
27
comment What is currently incomplete in M-theory?
@Dimension10: Matrix theory can reproduce M5 branes, opaquely. I just mean that there is a little-string theory living on 5-branes which, on general AdS/CFT principles, is supposed to be dual to the gravitational theory near the branes, and it is ill understood what the theory is in M-theory, as opposed to type II string theory, or how the duality works properly. It's something that was just barely sorted out for the M2 branes, and it is useful for knowing the stuff that's consistent in M-theory beyond the classical supergravity limit, we don't have strings to probe M-theory with, only branes.
Jul
27
comment Why are the even and odd Regge trajectories degenerate?
Oh that's interesting! This might be because the glue is larger than the quark, so it's a large N thing. But I don't have intuition for the left-hand cut arising from exchange force, I'll need to think about it before accepting. Already upvoted, I'll get back to it at some point. Thank you.
Jul
25
comment Does the Banach-Tarski paradox contradict our understanding of nature?
This relates ZFC to ZFC-powerset by reflection, and ZFC-powerset is related to ZFC-powerset-infinity by reflection of the same type--- it's iterating a model-theoretic consistency statement as many times as ZFC-powerset-infinity has ordinals. ZFC-powerset-infinity is Peano Arithmetic (equiconsistently), which is a reflection of a different kind, over the integers, of primitive recursive arithmetic, and is completely well understood since the 1930s (with some more progress in the 1970s), it's described by the simple ordinal epsilon-naught. People were brainwashed that Godel killed Hilbert.
Jul
25
comment Does the Banach-Tarski paradox contradict our understanding of nature?
I should say that all of this is predicated on the idea that you can translate the axiom systems to describe countable structures. One way you can do this is by replacing the powerset axiom of set theory with the axiom "every cardinal has a set of larger cardinality", which is equivalent to V=L powerset. You can then, if you have a good handle on ZFC-powerset describe ZFC from this, by adding one more level of reflection, since all that is happening in ZFC is that you get a tower of models of weaker systems as long as the minimal model of ZFC-powerset has countable ordinals.
Jul
25
comment Does the Banach-Tarski paradox contradict our understanding of nature?
The thing that is false in such a scheme is the absoluteness of uncountable ordinals--- so there would be no "aleph1" all you would talk about would just be the representation of aleph-1 in a countable model, so it would be a countable ordinal. The finite computations are more fundamental than sets, in the sense that the properties of computation are absolute and independent of axiom systems, the axioms are only important to the degree they describe computation. "Constructivist" usually means intuitionist logic, and I don't care about this as much, I care about finishing up Hilbert's program.
Jul
24
awarded  Necromancer
Jul
23
awarded  Self-Learner
Jul
23
comment What happened to David John Candlin?
The first email wasn't rude at all, I was just trying to know if it's the guy. Once I knew it was him, I asked the fellow about priority, you know, who was cribbing who, and the fellow I was talking to thought I was completely out of line talking that way.
Jul
23
comment What happened to David John Candlin?
I just wanted people to know. Do what you want, it doesn't matter, but I am pretty sure he doesn't want to be bothered. I don't know why, I never talked to him. He might not be well, I don't know.
Jul
23
awarded  Revival