2,986 reputation
817
bio website about.me/danieldf
location Providence, RI
age 38
visits member for 3 years, 9 months
seen Feb 22 '13 at 21:12

Feb
2
comment How could spacetime become discretised at the Planck scale?
@qftme: i didn't mean to bury you in refs, sorry if i gave that impression. But your questions were so 'open ended' that i didn't know a better way to address them (but to point you towards more comprehensive papers).
Feb
2
comment Give a description of Loop Quantum Gravity your grandmother could understand
@Marek: that's exactly right: the term "loops" come precisely from this decomposition in terms of Ashtekar variables and how they relate to Wilson loops, etc. In this sense, i think it's very fitting that both, String Theory and LQG, hinge on the same object: flux algebras. ;-) (Glad to be back! :-)
Nov
25
comment Can special relativity be deduced from $E=mc^2$?
@David: I had the low speed expansion in mind when i made the comment above — of course, the case where $p = 0$ is contained in this expansion. ;-)
Nov
23
comment Introductions to discrete space-time
@mtrencseni: Yup. But, i think you can understand CDTs as a Discrete Differential Geometry endowed with a Causal Structure. So, in the sense of "reducing to the basics", i think it'd be best to understand what it means to discretize geometrical objects (eg, Diff Forms), and then add causality to the mix.
Nov
23
comment Why is it hopeless to view differential geometry as the limit of a discrete geometry?
@dmckee @Hans: Discrete Differential Geometry is the name of the game — there's much that can be done.
Nov
23
comment Why is it hopeless to view differential geometry as the limit of a discrete geometry?
@Hans: when you say that $\hbar\rightarrow 0$ recovers classical mechanics, i objected, correct? So, i provided a link to explain the tip of the iceberg behind my objection.
Nov
23
comment Why is it hopeless to view differential geometry as the limit of a discrete geometry?
@Hans: you can look for decoherence in quantum mechanics and also Bose-Einstein condensates, etc.
Nov
23
comment Why is it hopeless to view differential geometry as the limit of a discrete geometry?
@dmckee: i just saw the other question... it would have been nice to know this beforehand though, ie, it would have been nice to have had this information in the question, so we're not lost. Thanks for the 'heads up'. :-)
Nov
17
comment How does gravity escape a black hole?
@Nogwater: Even though DavidZ already answered, i just want to offer my 2¢: things that happen inside a black hole (eg, mass increase) affect the curvature of spacetime, and this can be measured from the outside. You can choose to understand this via the Holographic Principle, but you don't necessarily need to: it's vanilla Differential Geometry (and Topology).
Nov
16
comment How does gravity escape a black hole?
@MarkE: I could open my magic toolbox and talk about holonomies and their relation with orbits in GR (ie, with closed geodesics). And, by mapping the holonomies of a space you can get information about its curvature. So, if you're orbiting a black hole, you can gather all the information about its curvature. (That's why i made that comment about global properties of spaces: they are very non-intuitive.)
Nov
16
comment How does gravity escape a black hole?
@MarkE: only if you were God. Look, the bottom-line is that we're dealing with classical GR, and not Quantum Gravity nor its effects. And, within the framework of classical GR, it's simply not possible for you to change any of the properties (charge, mass, angular momentum) of a black hole from the inside of it. A black hole is simply a "sink" of gravitational fields.
Nov
16
comment How does gravity escape a black hole?
The thing to note is that curvature is not something that lives only inside the Black Hole: this is a property of spacetime as a whole, and that's what counts. Global, topological, properties are very non-intuitive things. ;-)
Nov
16
comment How does gravity escape a black hole?
If "The Hand of God" (and we're <a href="en.wikipedia.org/wiki/… talking about Maradona</a> here ;-) did something like this, and we were only thinking about classical GR, we can say the following: it would be possible to measure such change, in the sense that the curvature of spacetime would change and we'd be able to see that the black hole got more massive this way (the curvature increased).
Nov
15
comment What are some approaches to discrete space-time used in modern physics?
@Amir: i perfectly understood your question (5). If you check the link i sent, you'll see that things such as "Planck Volume" and "Planck Time" exist and are well defined (and have a numerical value, as per your wish). So, in this sense, a notion of "spacetime atom" does exist, even if it's vague. To make it precise, it will of course depend on the particular theory you have at hand.
Nov
15
comment Is a “third quantization” possible?
(continuing…) This geometrical meaning is given by noting that Curvature is really the relevant quantity in this game. The question, then, is the following: What would you get if you did what you want? Fine, you go ahead and quantize again… what kinds of structures do you get? What do they represent? I hinted at this in my answer above…
Nov
15
comment Is a “third quantization” possible?
@Tobias: But why would you do that? More importantly, which object would you get if you did that? Let me try to make a long story short, amputated: the Jacobi Metric is given by $\tilde{g}_E = \sqrt{2 (E - V(q))}$, where $V$ is the Potential energy for your system (be it particles, fields, etc). Once you re-write your Lagrangian in terms of Jacobi's metric, you map the Hamiltonian flow into the Geodesic one. The bottom line is that the eqs of motion, now, have a very clear geometrical meaning. (continues…)
Nov
14
comment Suggested reading for renormalization (not only in QFT)
Just a couple of more links that i think can come in pretty handy, given the above comments: <a href="dx.doi.org/10.1016/0003-4916(81)90072-5">Dimensional Analysis in field theory</a> and Renormalization as Dimensional Analysis — worth checking out. ;-)
Nov
13
comment Are the physical laws scale-dependent?
@j.c.: you're correct, on both counts: i did have something else in mind; and the $\epsilon$-expansion is very good thing to keep in mind. ;-)
Nov
13
comment Are the physical laws scale-dependent?
It's very hard to find non-trivial solutions to the Renormalization Group eqs; in the end of the day, they are the ones that end up determining how a certain phenomenon in a given scale will behave in another. But, i'm not sure i'd go as far as saying "never"… but it is pretty hard.
Nov
13
comment Are the physical laws scale-dependent?
@Sklivvz: this is far from being a matter of opinion: there are macroscopic quantum effects: Bose-Einsein condensates being a good example.