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location Baltimore, MD (USA)
age 24
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2nd year graduate student at Johns Hopkins University in Physics. I'm primarily interested in particle theory and mathematical physics. I have some interest in pure mathematics, especially geometry and topology, and outside of particle physics in other fields including cosmology, topologically protected phases in condensed matter physics, and information theory.

I haven't had much time for this site recently. It's rather difficult to use this site to ask research questions, and it seems there are many people here who are capable of and willing to answer the basic questions which are very common here. If someone starts a new research-level Q&A site about physics (either on SE or elsewhere) I'd be interested in participating.


Oct
17
comment Hopf Algebras in Quantum Groups
The keyword to look for here is Tannaka-Krein duality (e.g. on nLab), a natural extension of Pontryagin duality. Perhaps someone else here is capable of giving some simple explanation of it, but I don't think I can do better than what's already on nLab or Wikipedia.
Jul
24
comment Is speed of light and sound rational or irrational in nature?
I'm not sure in what sense a system with $c=\pi$ would have "very complicated and perhaps even inconsistent behavior under Lorentz transformations". A Lorentz transformation is simply a linear map on $\mathbb R^4$ preserving the quadratic form $(ct)^2-x^2-y^2-z^2$. Even leaving $c$ as a formal parameter, the theory is exactly what we teach in introductory courses. One can just as easily rescale $t$ such that $c=1$ or $c=\pi$ or any other positive real number; the same theorems in dimensional analysis ensure these are all equiconsistent.
Feb
21
comment How can stars make up 0.5% of whole universe?
Minor terminology quibble: neutrinos aren't baryonic matter. They are, however, ordinary matter.
Dec
3
comment Operator-state correspondence in QFT
I'm not saying that we never do things like this in physics, but that it isn't exactly what is meant by "local" (at least to me). For example, in the standard Penrose diagram for Minkowski space, past timelike infinity is mapped to a single point, but if you want to talk about local processes occurring in a neighborhood of that point you really have to blow it up to resolve that. There's also a technical issue as to in what sense the limits converge. On AdS this would be a whole different story of course, but in flat space it doesn't make much sense to regard past infinity as a single point.
Dec
3
comment Operator-state correspondence in QFT
@Axion I agree with Prahar's comment. Perhaps another way to say this is that in a CFT, 0 is literally a point, in that we can compute correlation functions between fields at 0 and other points. In an ordinary QFT, past infinity isn't such a thing. The idea of contracting past infinity to a single point seems inherently nonlocal, in that if I send two wave packets back in time in opposite directions in flat space, I expect them to be getting farther away from each other, not converging to the same point...
Sep
25
comment How to deal with the notation of a function $f$ vs its value $f(x)$ in Physics?
Are you familiar with the implicit function theorem? Many of the "functions" you describe are probably better understood by mathematicians as relations, which can be converted locally into functions via this if you need to do so.
Sep
22
comment How deep can my knowledge of particle physics go without the maths?
"Physics, by definition, is the subset of Mathematics which pertains to our universe." I disagree with this. There's plenty more to physics than just pure math. I tend to agree more with Vladimir Arnold that the containment is in the other direction: "Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap."
Sep
8
comment What are the physical dimensions (units) of the elements in a Hilbert space of a QM system?
@REX Thanks for catching that. I've now corrected it. I make silly typos like that all the time.
Feb
12
comment What are the justifying foundations of statistical mechanics without appealing to the ergodic hypothesis?
@josephf.johnson As for your answer, I haven't yet had a chance to read it, unfortunately. This question has not had any activity for the better part of a year, and the answers do a pretty good job at least at the level I was looking for, so to be honest I had totally forgotten about it. Your answer seems to be at a more advanced level and does explain things in more detail. I appreciate it, even if I don't get a chance to look at it any time soon.
Feb
12
comment What are the justifying foundations of statistical mechanics without appealing to the ergodic hypothesis?
@josephf.johnson Alas, while I used the words "justifying foundations," I must admit that particular turn of phrase is not my own, and I can't comment on the intent contained therein. The title of this question was copied from a question posed on the Area 51 proposal of the now-defunct Theoretical Physics site. I agree with you that the phrase "justifying foundations" is a bit strange, but it seemed imprudent to copy the idea for the question but change the title; instead I tried as best I could to maintain the intent of the original asker and cited the location which I had found it.
May
16
comment Does dark energy affect asymptotic freedom?
It seems to me the idea you are talking about is the Big Rip Hypothesis. In this scenario, quarks do eventually de-hadronize and quark confinement fails. As far as I know the idea is a bit out of favor, but not ruled out for our universe.
May
4
comment Will a stone thrown in space move forever?
I didn't -1, but this answer has issues even if it is technically correct. For me, black holes are incompatible with the OP's statement that "gravity is equal zero" (admittedly poorly phrased, but the idea is to ignore gravity, i.e. work in Minkowski Spacetime). Answering the question in a GR context is also tricky because of strange things like closed timelike geodesics, making both "forward" and "forever" difficult to define. But the basic idea is that "this is mostly still true in general relativity once we make sense of what that even means" which I think you mostly captured.
Apr
26
comment If randomness doesn't exist, how come the universe isn't a perfect sphere with predictable distribution of matter?
Back to probability, I don't think there should be a consistent notion of a "random pick from [0,1]" in the way you are claiming. Such a thing is an abuse of language, as are random bit sequences. A Vitali set isn't an event, so there's no reason to expect it to have a probability. I don't see any paradox with that. It is true that this notion of probability and the physical one are somewhat different, but I don't see a problem with that. If you want to continue this discussion, let's move it to chat, because it's become entirely irrelevant to the topic of the question.
Apr
26
comment If randomness doesn't exist, how come the universe isn't a perfect sphere with predictable distribution of matter?
It is definitely not true that any ring I am interested in is countable; take for instance $\mathbb{C}^n$ with the direct product. Most of the explicit examples I'm interested in could be dealt with by countable choice, but for both categorical and practical reasons it it's far easier to just deal with all rings.
Apr
25
comment If randomness doesn't exist, how come the universe isn't a perfect sphere with predictable distribution of matter?
I don't totally understand what you mean, and I definitely like AC (otherwise how will I know that my rings have maximal ideals?). Personally, I'm of the opinion that random numbers/sequences are essentially abuse of language, but if I translate what you are saying into my language then I think what you call 'pure randomness' is what I would just call randomness, which in my book is a fundamentally physical (i.e. nonmathematical) concept. But in any case I don't think there's any more need for discussion of it here.
Apr
25
comment If randomness doesn't exist, how come the universe isn't a perfect sphere with predictable distribution of matter?
@Anixx I don't see how the two are asking the same question. They seem different both in focus and in the OPs' levels of understanding. I believe that the standard test is something like 'if the answers on a previous question would also constitute complete answers to this question'. If I take, say, Joe's answer on that question and apply it here, it doesn't seem to answer this question or be at an appropriate level.
Apr
25
comment If randomness doesn't exist, how come the universe isn't a perfect sphere with predictable distribution of matter?
This is a nice answer. It addresses the heart of the question succinctly, though my answer is more in depth on some tangential issues.
Apr
25
comment If randomness doesn't exist, how come the universe isn't a perfect sphere with predictable distribution of matter?
Also, I'm not sure what the phrase "pure randomness" means. What makes a particular distribution purely random by your definition?
Apr
25
comment If randomness doesn't exist, how come the universe isn't a perfect sphere with predictable distribution of matter?
Nowhere that I can find did the OP say he wanted a jargon-free answer. Even if he did, a certain level of jargon is useful to know, and most of it was clearly explained. I've added an explanation for the particular phrase in question.
Apr
24
comment Angular Momentum Addition Theorem - Sanity Check
Yes. If you pick $j_1$ to be the larger of the two then it's unnecessary.