@0celo7 Hm, if you just had asked me "what does averaging over the direction of $p$ mean", I'd have said "integrate over the sphere with radius $p$, then divide by volume of that sphere". That LHS looks as if it is meant to be that, I'd assume a typo.
@ACuriousMind Ok, that's as I thought. He argues rotational invariance restricts the integral to have the form $\delta^{ij}$, and then the proportionality constant may be determined.
Why does rotational invariance restrict it like that?
You have to write $\vec p = \lvert p \rvert \times (\text{spherical unit vector})$ and integrate $p^i p^j$ of that, which will have the $\theta,\phi$-dependence of the spherical unit vector.
The FLRW metric is an exact solution. Our universe is not actually the FLRW metric (since, for one, the matter content cannot be approximated by a homogeneous/isotropic fluid)
@0celo7 : Caught me. Yeah, I starred your first sentence about Zee. However, if you are serious about your second sentence, I foresee a lot of disappointment coming your way...
@Hippalectryon pastebin.com/rX790JSt there's the solution if you care. In Python this time. I didn't bother with many of the details, but anyway, there you go. Why don't you just solve the full eqns?
Also, I think there might've been a typo in the equations (the integral end point), so I changed it. You can change it back, obviously, if you so feel.
@alarge sigh go ahead & continue to paper-cut it to death with fineprint etc... hey have long heard far worse slings & arrows in here & elsewhere... :|
...but maybe some of the researchers cited have been published in nature & various other highly esteemed/ prestigious journals :)
@vzn What's with the reaction? You wrote Nature in all caps, italics, boldface and an exclamation point at the end. I just pointed out that this is not a scientific contribution to Nature. I did not say that this would make the contents any less newsworthy or valid.
@vzn Well, most likely not peer-reviewed though. The most typical case is that the editors ask someone (whom they often know) to write an opinion piece about a certain topic.
Not that it really matters if it were refereed or not.
@alarge its likely to be "peer reviewed" by editors who are generally expert/ highly qualified. but ofc agreed this is not (quite) same as scientific peer review.
I've never heard of an invited review paper being rejected (surely there must be cases, though), and those go through proper peer review. I think it is even less likely that an invited piece of news would.
@alarge "peer review" has both formal & informal meanings. the editors will sometimes suggest/ ask for revisions or quality concerns quite like referees. its not clear if the paper was "invited".
Yes, and Nature for example employs editorial rejections where papers that are not deemed worthy by the editor are not even sent forward. It's still not the same thing as peer review.
Given that almost all pieces of news are invited (as pointed out on Nature's website), it most probably was.
its not explained how "invitations" work. typical magazines also have stories initiated/ "pitched" by authors. as for "peers", editors are roughly "peers" of writers. but not exactly scientific peers in the other technical sense of "peer reviews". ofc both the editors & writers have strong scientific credentials to write & edit in their chosen areas.
Well I suspect invitations in Nature work like in any other journal: The editors ask someone they know, someone who has contributed to their journal, or someone who has written a lot on the subject.
Thx... I have an extremely long threaded question on GR and a recent answer to Timeaus requires another long reply... should I add to what already exists or start a "new question" (with all the attendant hassle of cross referencing and quoting)?
@Hippalectryon It worked for me as well, that's why I didn't notice it, but the return type is still off, so I'm not sure if it is actually doing the right thing or if you're just a bit lucky.
@Hippalectryon I checked now and fsolve only seems to care about the first element of the array. So the algorithm is a bit wrong (I guess you should be using an optimizer instead of trying to find the root)
@alarge Hmm it's becoming really late here so I have to go, I'll probably try to modify it tomorrow. Since I'm kind of new to the method I'd be glad if you can modify the code so that it determines R (the simplified version, not the full one with additional terms), but if you don't have time or don't want to it's fine, thanks for your help so far anyway :-)
Zee stresses the following point many times, but in case you skim: You can change summed indices at will. For instance, $V^i g_i=V^j g_j=V^k g_k$ as long as $i,j,k$ are all taken to run over the same set of values.
@Icosahedron The author will tell you at the beginning of the book if the summation convention is used. If it is used, he will tell you when it is not used before or next to the relevant equation.
It shows me that you're not ready for Hawking & Ellis, and I hope you see that too. But it's not dumb, I think many people are uncomfortable with indices.
HE doesn't introduce the summation convention, they just use it.
@Icosahedron Sachs & Wu GR for Mathematicians requires a "comfortability with geometry and topology fit for a second year mathematics graduate student" or something of the sort.
