The h Bar - 2016-08-15 (page 4 of 5)

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7:00 PM

@JohnDuffield I think it could be an interesting question, what really waves

@ACuriousMind Are you fairly certain e.g. BBS understand group theory? Is their textbook a lie-to-children?

@0celo7 No, that is a different and much sadder issue.

@ACuriousMind : it isn't a lie-to-children. It's a lie. It's downright wrong, as you know full well. Virtual particles only exist in the mathematics of the model, and it is not an insult to call it out.

@peterh : I know what waves.

@JohnDuffield What?

Space.

7:02 PM

@ACuriousMind What gets me about that book is that they use crazy advanced math (Dolbeault complexes, Hodge theory, ...) but never specify if e.g. sets are open. Physicist math truly baffles me.

@JohnDuffield I suppose that depends on how you call it out

@0celo7 Although I do think they understand "group theory" as it is commonly understood among physicists. The issue is that "physicists' group theory" is not really "group theory" :P

@JohnDuffield Wow! It is like a QG thing? But why does it then randomly?

diplomacy is a nice touch

@JohnDuffield You may well say that using virtual particles is wrong from your point of view (and this is one of the rare instances where I actually agree with you). You may not say "She doesn't understand GR or electromagnetism", and your qualms about "censorship" are similarily specious

7:05 PM

@Jim : true enough. Like I said, I'm not a fan. I wouldn't mind so much, but if you say something, what you see is Your comment has been saved and will be visible after blog owner approval. If it's in any way challenging it's never visible.

@ACuriousMind telling lies-to-children in pop-sci articles is like arming afghanistan during the cold war. Very unlikely to ever come back and make life difficult for you later

@peterh : no, it's an electromagnetism thing. Only it isn't quite like what Maxwell said.

@JohnDuffield what does "curved spacetime is inhomogeneous space wherein the inhomogeneity is non-linear" even mean? Why are you using an example of curved space to illustrate curved spacetime, which you claim are radically different? This kind of hand-waiving could be fixed by not being lazy and picking up a hard book tbh

@Jim : do I detect a touch of irony there?

@Jim heh

7:10 PM

@bolbteppa : see what Einstein said.

@0celo7 come on man, just go for it, calculate $\lim_{dx \rightarrow 0} \frac{\sin(x + dx) - \sin(x)}{dx}$

@bolbteppa : and things like this and this.

@JohnDuffield Yeah, Einstein is just describing the "ten functions $g_{\mu \nu}$", why are you not learning about those things he is describing in his passage? You're not even reading him fully, you have to skip and make leaps because you don't understand certain things, "which are amenable to law in the form of differential equations", another question mark eh?

@JohnDuffield modelling light propagation in an inhomogeneous vacuum amounts to determining the metric geometry of the inhomogeneous space around the light, linking to an article like that like it says anything is very strange

@bolbteppa : read what Einstein actually said. I don't make this stuff up. Also see this Baez article: "Similarly, in general relativity gravity is not really a 'force', but just a manifestation of the curvature of spacetime. Note: not the curvature of space, but of spacetime. The distinction is crucial." Space isn't curved where a gravitational field is. Instead it's inhomogeneous.

@JohnDuffield you keep referencing other people's analyses of the math, why can't you learn it and form your own well enough to be able to convince actual professionals? Seems like you use shadow villains like money and establishment to justify laziness of not learning the basic material so you can be an independent thinker and think on your own about the material without referencing random articles

7:18 PM

@bolbteppa : I have and I will.

@JohnDuffield dude that is obvious, I don't know why you're linking hand-waiving explanations of something I can derive and prove for you, why can't you write down the action and derive that fact?

@JohnDuffield What's so evil and scary about, say, this amazon.com/Spacetime-Geometry-Introduction-General-Relativity/… ?

@bolbteppa : you can't derive and prove that space is curved in the room you're in.

Dude there is air and humidity and stuff in the room I'm in curving the space

I've even given you the shortcut to getting a first grasp of the technicalities theoreticalminimum.com/courses

Writing a book on physics when you don't know the math is really something else tbh

@Jim I never understood this bacon thing, why is it so important. Roasting eliminates the danger of infection, which nearly so exist also in the case of cattle meat. Their flavor is so similar, I never could really differentiate them. If something would forbid me to eat pork, it would be absolutely no problem to me. Actually, eating only cattle means that you have to kill fewer life for the same meat.

Does it stem from the belief that the scary math will pervert your clear ideological view? It didn't with Einstein, I mean if anything you could learn all the math up to modern times then read his notebooks and mix his crazy theories in with modern stuff and really do something serious instead of insinuating money skews physicists minds or whatever

7:24 PM

@JohnDuffield You say vacuum fluctuations are like displacement currents in also in time?

At the best of times I've seen you having to link to obscure notebooks to explain something you could explain with a 9 symbol equation, it genuinely seems like the math would help you out and you're just wasting time by not learning it, there's really no reason not to learn the language of the subject you are interested in, it didn't pervert Einstein so there's no reason it'll brainwash you

@bolbteppa : your pencil doesn't fall down because space is curved. I've never insinuated that money skews physicists minds. And I've never refused to learn the maths. Au contraire, I pick through it term by term as per this answer.

@peterh : yes, vacuum fluctuations are minor / chaotic / random displacement currents. In the ripplets-on-the-sea analogy the current is primarily up and down.

@JohnDuffield From your post: "Ricci curvature represents "the amount by which the volume of a geodesic ball in a curved Riemannian manifold deviates from that of the standard ball in Euclidean space"." Why? Can you prove that interpretation from the definition of Ricci curvature, or are you just hoping the sentence you read someone else write is true, because who knows right?

Is it not the antithesis of independent thought to quote sentences describing technical justifiable statements without being able to justify them? Just wondering...

"And note that the stress–energy tensor "describes the density and flux of energy and momentum in spacetime"" WHY?

@peterh Don't ask me. I don't take issue with the idea that others are philosophically opposed to bacon, so long as they don't impose their views on me through means other than reasoning

@bolbteppa : I didn't make that up. It occurs because a concentration of energy "conditions" the surrounding space, this effect diminishing with distance. Stress is directional pressure. I didn't make up the stress-energy tensor either. A gravitational field is akin to a pressure-gradient in space. Like you press outwards. So the volume of a geodesic ball deviates.

7:37 PM

@JohnDuffield .... maybe

@Jim : the trouble with lies to children, is that children grow up believing them. And then they start writing physics papers.

hooray, relativistic mass!

@JohnDuffield You don't seem to understand what I'm saying, you say those interpretations are true using an argument from authority to justify yourself, referencing some links where you quote other people, who knows if they are lying or if money is telling them to say this in some big conspiracy, did Einstein do that? I'm asking can you justify that interpretation for yourself without any assistance using just the precise (mathematical) definition of those terms

If not, is that not the antithesis of independent thinking to copy what others say is true without knowing why?

@bolbteppa I suppose that depends on the reason one copies what they say. An independent thinking may think "gee, if I spend all my time establishing for myself the truth of all the trivial facts I need to use here, I won't have time to do the important stuff I'm here to do. I guess I can reasonably trust the words of experts in the respective fields". Seems like a fairly rational course of action from an independent thinker

@bolbteppa : I understand what you're saying. Just as you understand that what I said about Ricci curvature and the stress-energy tensor etc isn't some "appeal to authority".

It's just physics.

7:46 PM

@JohnDuffield instead of wasting time with this 'paint-equations-by-pictures' approach to math, that is just intrinsically susceptible to error since you're not even aware of the full definition of the things you're using pictures to describe, would you not maybe explore why someone qr.ae/TIMeFS claims Schwinger derived all of Einstein's equations in a quantum context in his book and maybe try to understand the depth of that in a modern context, something ignored in the scary mainstream

@JohnDuffield Dude I have read explanations for that Ricci curvature geodesic ball thing and I still don't understand them, it's in MTW (if I remember correctly) and I still don't understand the derivation of that interpretation despite knowing how to derive Ricci, so no I don't really understand what you're saying, I just appreciate how hard it is to justify that, and yes you are 100% using an appeal to authority, that is obvious and you know this is the antithesis of independent thinking

@Jim yeah I agree, it depends on what you're trying to do, here we have a clear-cut case of someone trying to criticize and deeply understand the material he's talking about without knowing the very first definitions, and actually going off saying other people don't understand the things he says he understands, despite not being able to derive any of the equations and using copy-pasta'd interpretations of technical things that are hard to justify

@Jim : the trouble is that when you compare what the expert in the field says with the Einstein digital papers, you find some significant differences which are not explained. In fact, I'd go so far as to say that some experts in the field appeal to Einstein's authority whilst flatly contradicting the guy.

just to play devil's advocate for a moment. I'd much rather have someone who doesn't fully understand the physics themselves recite the interpretations of a higher authority on the subject than I would have that same person act authoritative on only their own interpretations. Seems like the former case has a higher chance of being accurate with accepted physics

@JohnDuffield the question then becomes, why are we so sure Einstein was correct in his interpretations? Why do we consider his name an effective trump card?

@Jim : because there is no magic. Because it matches our experience elsewhere.

user image

user image

@JohnDuffield whether or not it matches other experience does not rule out magic

after all, M.A.G.N.E.T.S. exist

@Jim : magnets are not magic. I can explain how a magnet works.

There is no magic.

7:58 PM

magnets - Magical Arcane Gadgets Normally Explained Through Science

^ therefore, magic

No magic. No mystery. No mysticism. There's less to it than meets the eye.

@JohnDuffield This may break the current tension

@JohnDuffield are you seriously saying linking to an article that says you can provide some intuitive understanding of a technical derivation is not an argument from authority? You are linking to that article on Ricci and geodesic balls because you have no way of deriving that interpretation, honestly I think you don't know what it means to derive an interpretation like that from the definition.

@Jim Oh, I had almo0st forgotten about those!

Damn magnets

@Jim : maybe. On the other hand, you could just ask me about a mystery.

8:02 PM

answer to every "how does this work?" question

@ACuriousMind we worked so hard to figure out that acronym and you almost forget it? For shame

@Jim Sorry I tried to reply ocelo7.

@bolbteppa : yep.

@Jim sorry :(

@ACuriousMind magnets got you?

I'll make up for it by buying you a better pointy hat

8:07 PM

OK guys, I have to go I'm afraid. Good night.

@JohnDuffield Exactly, at least you finally admit you have to link to articles like that to quote others who say you can do X, Y, Z because you lack the ability to derive that interpretation yourself, that is called being a sheep following the lead of others, going off saying others who've studied the material don't understand it when you have to resort to this high-school essay level of argument is something else

@JohnDuffield "Yes, Schwinger found a natural place for gravity as a spin 2 quantum field. The spin 2 is required because of the complexity of the field equations, as introduced by Einstein in the classical limit.
Yes, the equations are unrenormalizable (if you know what that means) but Schwinger later found a way around that using his source theory, which is also unknown or ignored by most physicists. In fact, in his book "Particles, Sources and Fields", vol. 1, he was able to duplicate all of Einstein's classical results." http://qr.ae/TIMeFS It seems to me like if you did the hard work…

@JohnDuffield Its math should be worked out and it will be probably over the limits of the enthusiast skill level.

@JohnDuffield But it doesn't mean trying it wouldn't be useful :-)

@bolbteppa Theories tend to simplify with time, as the understand grows. Maxwell began with around 20 equations with a lot of mechanical analogy. Now there is only 4.

2, or even 1 if you do geometric algebra ;)

I'll just throw this out there: a spin 2 matrix has 5 entries, Kaluza-Klein mixing of EM and GR uses a 5 entry matrix, coincidence? Nonsense?

@ACuriousMind Oh come now. He said "IMHO".

That was as polite as a person can be while voicing an opinion that someone else doesn't understand a thing.

@DanielSank Saying "In my opinion" doesn't make it less of an insult, and I do not believe this chat should be a place where people with...lacking understanding of physics can come and talk about actual researchers like that.

If I said "Daniel Sank doesn't understand the first thing about quantum mechanics", that wouldn't be appropriate, either.

If a singular instance, I wouldn't be all too worried about this, but this is part of a pattern with JohnDuffield, and I don't think we should be lenient about that.

8:33 PM

@ACuriousMind If you said I don't understand quantum mechanics and gave an example, I think that would be totally fine.

So then we ask, do we require substantiation of opinions for those opinions to be allowed in chat?

I think not.

As for the issue of repeated patterns, I somewhat agree. However, I think JD's real pattern is ignorance, refusal to back up anything he says, and an over-use of poorly disguised acts of moving the goal-posts when he's pressed to do so.

I don't think any of those things are against chat rules. In fact, I think the "ignore" feature is well suited to this case.

I've been using it for months and it's been wonderful.

@DanielSank Well, I didn't say it was against chat rules (else I would have flagged it). But I wanted to state my displeasure that we are allowing the general chat to be used for such statements. There was a period of time where JD was banned from talking about physics in here, and I'm in fact not entirely sure what it adds to the room to have him talk here again.

The power of the ignore feature is limited since I can still see all the people engaging with the ignored person, which is especially confusing if they don't use the reply feature

2

9:26 PM

@ACuriousMind Ignore them too.

9:40 PM

SE chatrooms can be closed, for example the mods have one.

10:07 PM

So, can anyone explain why the Hubble sphere is expanding?

@bolbteppa dude, I don't know how to prove that sin(x)/x limit

@0celo7 Page 2 here web.auburn.edu/holmerr/1617/Textbook/derivsincos-screen.pdf has a picture showing you why $\sin(x) < x < \tan(x)$, this is true by the very definitions of $\sin$ and $\tan$ as opp/hyp, these are the definitions you must use

I'm so dubious they should call me Doubi

From this you easily get $\cos(x) < \frac{\sin(x)}{x} < 1$, again you can even see this inequality by looking at that picture if you think about it, thus $1 = \lim_{x \rightarrow 0} \cos(x) < \lim_{x \rightarrow 0} \frac{\sin(x)}{x} < 1$

easily if you're a PhD analyst!

10:14 PM

haha can you really not see $\sin(x) < x < \tan(x)$ by looking at the picture on page 2?

@ACuriousMind I recall you once tried to ignore me and that lasted all of 5 seconds because of that :)

$\sin(x)$ is the adjacent side of the triangle over the hypoteneuse, but the hypoteneuse is $1$

so?

So can you visualize the blue line in the picture as $\sin(x)$ so far?

I wonder

10:18 PM

@SirCumference As I know, it actually shrinks

Can I compute $$\lim_{x\to 0}\frac{1}{x}\sum_{n=1}^\infty \frac{(-)^nx^{2n+1}}{(2n+1)!}$$ directly?

@peterh If that were the case, then the light cone shouldn't overlap with the Hubble sphere

user image

What is wrong with $\sin(x) < x < \tan(x)$, can you not see it from this picture?

As far as I know, because the radius of the Hubble sphere is increasing, photons emitted by a galaxy that recedes faster than light will eventually find themselves within the Hubble sphere

why was that starred

10:20 PM

@SirCumference Light cone of what?

sad attempt to embarrass me?

@peterh I'm referring to the observable universe

Our light cone

Yo momma so fat she ain't in our light cone 😂😂

Goddammit I starred that

@SirCumference Why they shouldn't overlap? We are in the centre of both.

10:22 PM

@0celo7 if $\sin(x) = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \dots$ then $\frac{\sin(x)}{x} = 1 - \frac{x^2}{3!} + \frac{x^4}{5!} - \dots$ so that $\lim_{x \rightarrow 0} \sin(x) = \lim_{x \rightarrow 0} (1 - \frac{x^2}{3!} + \frac{x^4}{5!} - \dots) = 1$

@peterh I'm sorry, I meant that the light cone shouldn't go beyond the Hubble sphere

@bolbteppa FORGET TRIGONOMETRY

I refuse to use pictures any more

Bourbaki would be disgusted with me

It shouldn't be bigger than the Hubble sphere if the Hubble sphere is shrinking

I shall make them proud

@0celo7 The $(-)^n$ seems to miss something.

10:23 PM

@peterh $(-)^n$ is a perfectly acceptable substitute for $(-1)^n$

@0celo7 Bourbaki uses the complex exponential to show these derivatives

proof?

Go get the books yourself and see

No money

There's nothing wrong with the picture given here at all

10:25 PM

@SirCumference The light cone is so linear only in a flat metric, if there is a curvature, the light cone also curves. And the accelerating expansion is not flat.

I'm poor

Go check your library or get access to the professor's libraries

@0celo7 Uhm, thanks, good to know :-)

@peterh All right, but it still doesn't make sense for the Hubble sphere to be shrinking. If it were, then photons emitted by a superluminally receding galaxy shouldn't ever find themselves within the Hubble sphere, and they would never make it to our eyes

@SirCumference The metric of the acelerated expansion is a tricky one, because its spacelike segments are flat (below measurement precision), but the spacetime isn't.

10:28 PM

It's called logic: If you start from this definition, then you use this method of proof, if you start from that definition, you can use that definition to prove the thing, but you have to link it all together in the end, if you used ratios of sides to define your trig functions, then you use ratios to prove that inequality, it's just algebra man

I'm not using ratios

@SirCumference Exactly this is why we can see only around 80billion ly away.

Ratios are not Rigorous

@peterh What? Of course we can see objects beyond the Hubble sphere

lol

Ratio's are rigorous

10:29 PM

@bolbteppa no

@SirCumference Which ones?

@SirCumference physicsforums.com/threads/…

If you want to make them rigorous, do it without pictures

No picture is rigorous

You just get that it is expanding because the Hubble "constant" is currently decreasing, and the radius of the Hubble sphere is proportional to the inverse of the Hubble constant

Physics terminology is amazing

10:31 PM

@peterh Here's a good illustration

user image

@0celo7 Can you not see how to prove the inequality in that picture using arc length

A curved line is longer than a straight line

@bolbteppa holy shit

PICTURES ARE NOT PROOF

Notice how there are areas outside of the Hubble sphere that are still within the light cone

I don't think you understand the concept then, because the picture just represents algebraic ratios

Although in math, the structure constants of an orthonormal frame are not constant usually

10:33 PM

Use your power series definition then, I gave you a proof of the limit above from power series

Good luck proving $\sin^2(x) + \cos^2(x) = 1$ using those power series

Or $\sin(a+b) = \dots$

@bolbteppa I think that's easy.

@bolbteppa that too

I don't, proof?

Prove Euler's formula

@peterh If you need any more evidence, read this paper

arxiv.org/pdf/astro-ph/0310808v2.pdf

once you have the power series, you can prove Euler

from that, all of trig should follow.

10:36 PM

> The teardrop shape of our past light cone in the top panel of Fig. 1 shows why we can observe objects that are receding superluminally. Light that superluminally receding objects emit propagates towards us with a local peculiar velocity of c, but since the recession velocity at that distance is greater than c, the total velocity of the light is away from us (Eq. 20).

Not very bourbaki-like to use complex numbers to prove things in a completely different domain, the domain of real numbers

> However, since the radius of the Hubble sphere increases with time, some photons that were initially in a superluminally receding region later find themselves in a subluminally receding region. They can therefore approach us and eventually reach us. The objects that emitted the photons however, have moved to larger distances and so are still receding superluminally. Thus we can observe objects that are receding faster than the speed of light (see Section 3.3 for more detail).

It's like assuming all manifolds are embeded submanifolds of $\mathbb{R}^n$ to prove everything and not proving things intrinsically

not very bourbaki to prove something using fucking pictures either

If you understood the picture you'd think otherwise ;)

10:37 PM

I understand the picture just fine

Where does picture fit into ZF?

Proving Euler's formula isn't that hard

@SirCumference FYI: you can't rearrange infinite series willy-nilly

Because you are talking about a bunch of algebraic ratios man, $a/b < c/d < e/f$, those functions represent ratios from this perspective

@SirCumference You have to prove that you can in this case

good luck!

Screw this

I'm still looking for an answer to my original question

10:40 PM

@SirCumference I'm not sure what kind of answer you're looking for. That the Hubble parameter is decreasing is an observational fact, so the Hubble sphere is expanding

All right, that's my answer

Thanks

$\frac{y}{r=1} < \frac{s}{r=1} < \frac{y}{x < 1}$

@bolbteppa for the love of god

@SirCumference Distance is a tricky thing in GR, the meaning of the "proper distance", "comoving distance" and others are not trivial and I admit, I don't understand them well. What I understand, seem to be correct. ACM understands them well, maybe he explains, until that I read your paper :-)

Do you love Jesus Christ?

10:41 PM

Why exactly we're living in a universe where the Hubble parameter (or the sphere) behaves like it does is currently almost certainly unknown ;)

@0celo7 Do you?

@ACuriousMind The most aggravating part of the Universe is how little we know about it

@ACuriousMind Anthropic principle. Sorry for the insult. :-)

@SirCumference The amazing part is how much we do understand

@ACuriousMind That is true, never thought of it optimistically :)

Two sides to every coin ;)

10:43 PM

acm is not a human, he can't use the anthropic principle

@0celo7 If this kind of thinking is tough, get ready for related rates in calculus 1

Jesus

@bolbteppa I'm second year, that's far away

@0celo7 You'll be the first to go when we the machines finally take over.

What?

You're a ~~orc~~ troll

Time for a new thing, isn't it?

10:46 PM

So, uh, I guess that heated debate is over

I'd really really love to see you work out $\lim_{h \rightarrow 0} \frac{\sin(x + h) - \sin(x)}{h}$ using the series definition of $\sin(x)$ tbh, you know that if if $\sin(x) = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \dots$ then $\frac{\sin(x)}{x} = 1 - \frac{x^2}{3!} + \frac{x^4}{5!} - \dots$ so that $\lim_{x \rightarrow 0} \sin(x) = \lim_{x \rightarrow 0} (1 - \frac{x^2}{3!} + \frac{x^4}{5!} - \dots) = 1$, the rest is the interesting part now while before this was the hard part

Nvm

@bolbteppa it can be done

Why exactly that series links to the ratio of the side of a triangle to the hypoteneuse is a bit of a mystery to me

same

10:52 PM

I know it's the Taylor series of that function, but that's fine because I've defined that function using ratios, from your perspective of starting from that series, the best I can do is use complex numbers and Euler's formula to at least link it to a circle, but the ratios is a mystery

@Sir It seems to me clear: "The objects that emitted the photons however, have moved to larger distances and so are still receding superluminally. Thus we can observe objects that are receding faster than the speed of light"

@bolbteppa $\lim_{h \rightarrow 0} \frac{\sin(x + h) - \sin(x - h)}{2h}$ makes the things much easier

You still need to use $\lim_{h \rightarrow 0} \frac{\sin(h)}{h} = 1$ right?

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