2,426 reputation
11332
bio website berkeley.academia.edu/…
location Berkeley, CA
age 25
visits member for 3 years, 8 months
seen Dec 23 at 23:12

Currently a graduate student in mathematics at the University of California - Berkeley.

Previously obtained a MASt. in Applied Mathematics from the University of Cambridge (2013), and a B.S. in Mathematics and a B.A. in Physics from the University of Chicago (2012).


Nov
30
comment Fast and slow modes, and the vanishing of certain diagrams during re-normalization
"Within a perturbative RG scheme, by which I mean the expansion parameter remaining small all the way to the fixed point and at the fixed point, engineering scaling dimension is enough to prove the irrelevance of the $\phi ^6$ vertex." ---- How do I actually go about proving this statement? With a proof of this, I believe my question will be completely answered. (Also, am I correct in presuming that this is not specific to $\phi ^6$, but is also true for general $\phi ^{2n}$ with $n\geq 3$?)
Nov
30
comment Fast and slow modes, and the vanishing of certain diagrams during re-normalization
In particular, am I correct in saying that we can ignore the diagram I am worried about, not because it vanishes, but because its contribution is irrelevant? On another note, how does one relate this to "momentum conservation"? Is the meaning of this just that one cannot produce vertices with an odd number of slow modes?
Nov
30
comment Fast and slow modes, and the vanishing of certain diagrams during re-normalization
How do we know a priori that vertices of the form $\phi ^{2n}$ with $n\geq 3$ will be irrelevant. Once again, don't we actually need to complete the re-normalization procedure to verify this precisely? Sure, one can do dimensional analysis and obtain that the 'engineering degree' suggests that they will be irrelevant, but to actually prove this expectation is correct, do we not have to do the full re-normalization procedure?
Nov
30
comment Fast and slow modes, and the vanishing of certain diagrams during re-normalization
"Clearly, $E$ cannot be odd since $V$ and $I$ are positive integers." ---- Sure, but what about, e.g., $E=6$. For example, consider a diagram with two $\phi _{\text{s}}^3\phi _{\text{f}}$ vertices with the two $\phi _{\text{f}}$ legs contracted. This yields a diagram with $6$ external slow legs, no? In fact, it is this specific diagram which I have been struggling to show vanishes for the past couple of days now.
Nov
30
comment Fast and slow modes, and the vanishing of certain diagrams during re-normalization
"However, $\phi _s^3$ vertex is not generated because there is no process in a $\phi ^4$ theory that can produce a $\phi ^3$ vertex." ---- I feel as if this argument is circular . . . Part of what we would like to show is that, after a RG transformation, we do not generate any new terms in the action (at least to the order we are working). It is conceivable that we could generate a $\phi ^3$ term after re-normalization, in which case the theory obviously could produce a $\phi ^3$ vertex. Am I seriously mis-understanding something?
Nov
26
comment How is it that Quantum entanglement does not let you transmit infomation?
Also, this: wikiwand.com/en/Quantum_decoherence
Nov
26
comment How is it that Quantum entanglement does not let you transmit infomation?
Also, I don't think collapse is truly instantaneous. As a matter of fact, I don't think the notion that it be instantaneous even really makes sense. How would one show, experimentally, that this is instantaneous? You can measure again as fast as you can immediately after your first measurement, but there will always be a non-zero amount of time between these measurements. One would need to show that the correlation between the two measurements increased as we decreased the time between the measurements . . . but Heisenberg says that this cannot happen for the uncertainty will diverge!
Nov
26
comment How is it that Quantum entanglement does not let you transmit infomation?
I wouldn't really say this is in agreement with relativity. More like it doesn't disagree with relativity. In particular, there is no hard speed limit here. All this says is that you can't transmit information instantaneously, but this argument doesn't show that you can't send it faster than the speed of light.
Nov
25
comment All geodesics are inextendable?
Well, then I would ask what they did in the comments: what do you mean by in-extendable? My definition would imply that a geodesic defined on all of $\mathbb{R}$ is automatically in-extendable.
Nov
25
comment Do bad clocks measure proper time?
I'm also not sure if I understand your question regarding how to measure the metric. I am not an experimentalist, so I could only be able to give a "in principle" answer to this. I am also un-familiar with this five-point curvature detector.
Nov
25
comment Do bad clocks measure proper time?
Well, quite honestly, I had never even heard the term "bad clock" until I read this question. I think it's safe to say that, unless otherwise stated, if someone says "clock" they mean "good clock". With this assumption, then all three quotes are correct and they would not retract their claims.
Nov
24
comment Do bad clocks measure proper time?
In particular, in general, no single observer can measure the entire space-time metric everywhere. You can only measure the space-time metric locally.
Nov
24
comment Do bad clocks measure proper time?
I'm afraid I will not be able to explain how one can measure the metric in an understandable way without being able to draw a diagram, but the basic idea is one that comes up in a derivation of length-contraction/time-dilation. Briefly, you send a light beam to a point you want to determine the distance to (after you've placed a perfect mirror there), and by measuring the time (proper time, according to you) it takes to get back to you, you can determine the distance to that point. It's not quite this simple in curved space-time, but that's the basic idea.
Nov
24
comment Do bad clocks measure proper time?
By definition, bad clocks do not measure proper time. The argument I gave should show that this is equivalent to 'making the world-lines of free particles locally look curved'.
Nov
22
comment Work-Energy theorem vs conservation of mechanical energy?
Sure, but this is not the integral of $-kx$, it is the integral of $-kx(s)$ with respect to s.
Nov
21
comment Work-Energy theorem vs conservation of mechanical energy?
How do you get that result for the integral? It should not be the case that $x(s)=s$. Remember, the spring itself is moving as well, so it should be the case that $s\geq x(s)$.
Nov
14
comment A question from Schwinger's particles, sources and fields monograph
I am confused. In some places you write $\phi ^\mu$ and in others you write simply $\phi$. Is there a scalar field $\phi$ and a vector field $\phi ^\mu$?
Nov
14
comment Calculating the Sun's emitted power in a wavelength range?
See wikiwand.com/en/Stefan%E2%80%93Boltzmann_law#/… . I believe this calculation is very similar to what you would like to do.
Nov
14
comment Which renormalisation techniques are available for 3+1 QED?
You should probably distinguish between re-normalization and regularization. Pauli-Villars is a method of regularization. Two other ones that come to mind are dimensional regularization and the usual cut-off regularization.
Nov
12
comment Momentum conservation in an electromagnetic system?
Well, I honestly don't know why you would need to do this. Perhaps I misunderstand your question. I thought that you took note of the fact that momentum was not conserved, and was confused as to why that was not the case. And the reason of course is because we are applying a non-zero net force to the system. As a 'sanity check', I suppose you could actually calculate the change in momentum of those three things to verify that it does indeed come out to $f\Delta t$, but given that it's so tedious to do so, I don't know why you would want to do that.