Your perplexity with the artist's rendition (commissioned, on Nov.30, 2009, by the European Southern Observatory), and with its caption, may perhaps be resolved through consideration of Nikodem J. Poplawski's "cosmology with torsion", which has been developed from his Feb. 2009 paper "Radial moti...
I know I’m a bit out of the field, but that really doesn’t look like anything close to a reasonable
@KyleKanos I don't think he's a troll. I believe he's sincere, and has good intentions. He does like a lot of fringe stuff, but as far as I can tell, he's not pushing stuff that's definitely contrary to mainstream physics.
Re your point on the last of the OP's two secondary questions, vis-a-vis the ESO's press release at eso.org/public/news/eso0946, do you feel it likelier that its astrophysicists made some computational errors re "escape velocity" as described in the Wikipedia link you've made, or that you yourself might not have taken adequate account of such details as the effect of whatever media the plasma jet might've been traversing on the velocity of its particles, with respect to the condensation which Kshitiz Sharma had been considering as a possibility? — Edouard19 hours ago
@PM2Ring only instance of "Kshitiz Sharma" is a cricketer
@KyleKanos I think it's understandable. OP was just randomly bringing up names and papers all willy-nilly. They aren't exactly clear with their communication.
@KyleKanos He seemed to really want to talk about universes starting inside black holes, so when there was a question about black holes and galaxy creation, he just went for it.
yeah, the whole "local universe" thing confused the crap out of me. like no where does anyone mention anything about a universe being zapped into being...
Nor does anything in the article even remotely imply it's happening inside a black hole. It seems to be quite explicit that it's talking about events outside a black hole.
From Linear map, the sixth example:
The translation $x \rightarrow x+1$ is not a linear transformation. Why?
What about $x \rightarrow x +dx$? Is this translation a linear transformation?
Does it matter if the transformation is not linear?
Why is this question getting such a great response? The examples are pulled from wikipedia, but they are essentially just worked examples of showing if a transformation is linear or not
Added my vote. This is completely a math question, and even the answers are just math based. Closest thing to physics in an answer is someone mentioning that linearity is often used in physics/engineering.
@AaronStevens When I see answers like that, 9 times out of 10 I just zone out and don't bother reading them. I like having math to help support a point; but I'm not a fan of people describing things mostly with formulas and only a couple words to chain them together.
@JMac Sometimes I enjoy the mathematical derivations, so I can tolerate them :) It depends on the context and how well the reasoning flows between the equations.
@AaronStevens I don't mind derivations, I just like them with at least sentences in between the formulas. I need both to understand things well. I can usually follow paragraphs of explanation; but I have trouble following line after line of formula unless there are decent explanations with it.
@JMac Oh for sure. On this site you definitely don't want that. I think the better answers usually skip the math and get to the final result. If an answer has too much math then I would say it most likely is answering an off-topic homework question :)
I find it worse when it's done on questions that clearly aren't supposed to be homework. Like someone asks a conceptual question, and then the answerer just presents a series of algebraic manipulations to arrive at some conclusion about the concepts. Thankfully there isn't too much of that.
@AaronStevens : In hindsight, I agree that it is strictly speaking a math question, although I didn't thought about that when I answered. From OP's style, I got the impression that OP came to the question while studying physics. E.g. OP never made mathematically precise what $dx$ is supposed to mean.
Gravity isn't Yang-Mills theory in the narrow sense – well, except for equivalences such as AdS/CFT or Matrix theory that imply that a quantum gravitational theory is fully equivalent to a gauge theory living in a different space (e.g. in AdS/CFT, on the boundary of the AdS space).
However, grav...
@JMac Since my comments about hot vs cold are kind of unsatisfying, I wrote something really quick and dirty to plot up the total heat transfer as a function of Reynolds number and temperature
Color is in log space, dark is less heat transferred, light is more heat transferred
So if you follow the curves, cold water that is moving can out-perform hot water that is not moving as much. In a pretty non-linear way, but it's possible to find combinations of moving water where faster + colder is better than slower + hotter
For example, stagnant boiling water is just as effective as just-above-freezing water at Re $10^5$. And just-above-freezing water at $10^6$ outperforms boiling water for all Re $< 0.5 \times 10^3$ or so
Some caveats -- I was lazy and assumed viscosity and Prandtl number are linear between 0 and 100. They probably aren't, but to get an idea of why it's possible that faster+colder >> slower+hotter it seemed fine enough.
And the Nusselt correlations come from correlations for a circular cylinder. Different shapes have different correlations.
@tpg2114 Nice. I do think the wording is still a bit awkward though. I wouldn't consider it a paradox to say hot water running slower than cold water transfers less heat, that's somewhat expected. The wording in your answer seemed to somewhat imply (by omission) that you were talking about streams with the same flow. That's what I was really having trouble accepting.
@JMac Ah, fair enough. I think for most people without a physics background, like OP, saying that cold moving water is better than a big bowl of boiling water is a paradox though
There is an inflection point in the curves though, where cooler water is better than hotter at similar flow rates, but I'd have to go back and put in the real thermo/transport properties to point out exactly where that happens
From Linear map, the sixth example:
The translation $x \rightarrow x+1$ is not a linear transformation. Why?
What about $x \rightarrow x +dx$? Is this translation a linear transformation?
Does it matter if the transformation is not linear?
