The h Bar

4:22 AM

Hello all, is anyone familiar with the conserved quantity in GR which has the form $C = g_{ij} dx^i/ds dx^j/ds$? where $C$ is a constant. Does anyone know where I could find an explicit derivative of this?

John Rennie

@Rumplestillskin That's the norm of the four velocity isn't it? In which case the constant $C$ is just $c$.

Rumplestillskin

4:40 AM

Yeah so it normally comes out when looking for radial geodesic equations. But do you know where there is an explicit derivation of that result? I seem to remember it coming up in one of the old school GR books like maybe Ruffini but I can't seem to find it any more @JohnRennie

John Rennie

@Rumplestillskin Isn't that just the definition of the proper time i.e. it follows directly from $ds^2 = g_{ij} dx^i dx^j$

Rumplestillskin

@JohnRennie Yes you are right. Hmmm I will try find the reference because I may be mixing things up!

@JohnRennie I found it!! Do you have access to the book Gravitation and spacetime by Ohanian and Ruffini??

John Rennie

@Rumplestillskin Let me look ..

@Rumplestillskin No

Rumplestillskin

4:58 AM

Hmmmm I might even write an official question about it as I am a bit lost now that I have found it! @JohnRennie

Slereah

5:36 AM

The norm of 4-velocity isn't necessarily constant

But it is for geodesic

That follows from the fact that GR has a metric connection

0celo7

What's going on

Slereah

the world

is going on

Rumplestillskin

I've added a question about it as there is a part that has me bugged!

@Slereah Are you aware of any treatment of pp waves that is semi understandable? Like in a text book or an undergrad book? The papers I found were quite dense and made my head hurt!

Slereah

pp-waves are surprisingly fairly rare in basic GR textbooks

But basically the idea behind it is that the spacetime has some null Killing vector

as well as a plane symmetry

Rumplestillskin

Yeah I have several stacks of GR books but I can't seem to find any mention of them.

Slereah

5:50 AM

Stephani has a chapter on them

Most other books treat waves in the linearized theory though

Rumplestillskin

I will give it a look shortly!

Slereah

though if you want a simple treatment, Stephani ain't it

Secret

6:23 AM

Last night dream there's this weird metric that is like an alcuberrie bubble with a pair of wormholes inside, all comoving to some destination to the right

where the black thing is the ship

Rumplestillskin

6:38 AM

@Slereah I am familiar with the book. It is not for the faint of heart

Slereah

6:58 AM

"We use various results concerning isometry groups of Riemannian and pseudo-Riemannian manifolds to prove that there are spaces on which differential structure can act as a source of gravitational force (Brans conjecture)."

Secret

7:10 AM

actually, I am not sure if the bubble can remain stable once a wormhole metric is introduced in the flat spacetime region inside the bubble

I also need to check whether there are translating wormhole solutions

Secret

7:38 AM

[Is bored]

Construct a word salad algebra with the following properties: There exists a dedekind sunset, its homorphic inverse is given by the pi cateogory of topos such that it is a cofinite and cofinal functor, with initial segment which satisfy the model of a word salad logic. Now, inject the set of all epidermal reals into the sun. This should result in a corruption of the underlying formal language, such that an abstract nonsense is produced. Now take the uncountable orbits of $🌀^🌀(🌀)$

Secret

8:06 AM

in Mathematics, 1 min ago, by Secret

Perhaps I should have ask: Given a series of events which there are many arrangements to give an apparent pattern, how do we knew which arrangement is (are) the true pattern(s)

Causality is (insert suitable word)

Secret

1:47 PM

Time Travel in Fiction Rundown

►

The time travel that I want to use in my story is a unified model of all of these

and the newest resolution of the grandfather paradox as discussed some time ago in the factory floor will allow a way to wrote the 5th type of time travel

ACuriousMind

2:06 PM

Gnnnh. I never expected to find myself arguing against someone pushing gauge theory as an explanation for something, but here I am :/

heather

@ACuriousMind what?

oh, btw, could you hammer this:

-2

Q: Is quantum mechanics the universal driver of intelligence

I'll elaborate and forgive my layman's terms -- I'm aware that unconsciousness is omnipresent, (I'm talking for myself) and my mind has these habits since childhood of emerging in corners of the universe to sight, like this representation of an illustration at the onset of evolution. This binary...

ACuriousMind

@heather I usually am the guy who answers questions with "actually, here's how gauge theory makes the issue much more clear" but lately a small set of users post similar answers that simply don't make any sense if one actually understands gauge theory. So I find myself leaving very critical comments on posts that superficially look to the uninitiated much like what I tend to write :P

0celo7

@ACuriousMind wot

@ACuriousMind what?

ACuriousMind

I don't see what's so unclear in what I wrote. If you really care to find out what specifically I'm talking about, it's not difficult to do so :P

heather

anyone want to take a look at this question and vote/close vote as you will?

vzn

2:27 PM

Professor Stephen Hawking's PhD viewed two million times / bbc news

↑ rare "viral" scientific paper instance! + dramatic support/ enthusiasm for open science etc... o_O

0celo7

@vzn somehow I doubt those 800,000 people understood it

It's probably all in HE

0celo7

3:01 PM

@ACuriousMind how?

vzn

@0celo7 lol not arguing but exactly how many papers have you read that you understand :P

0celo7

@vzn dozens

What kind of question is that?

vzn

btw in a not-total-nonsequitur, that reminds me, was musing, re this... (1) which of the following has the most fluid dynamics connections? and (2) why is Tenev-Horstemeyer omitted? :) :P

yesterday, by John Rennie

@Slereah: I've just stumbled across this while searching for something else. I imagine you'll already know about it but I mention it just in case it's of interest.

@0celo7 its a question related to (maybe even "mirroring") your own question-implied-doubt

0celo7

3:21 PM

@vzn You think there are 800,000 people out there who can understand his thesis?

They're probably just pop sci people. The people who understand that stuff already know it from HE, etc.

heather

sorry, what is HE

vzn

@heather Hawking-Ellis

heather

oh, ok.

vzn

@0celo7 "understanding" can be a slippery concept cant it? have you heard of this history of the book "a brief history of time"? maybe it would help you with some context... (public/ popsci) interest in Hawking is high lately incl wrt this movie "theory of everything" 2014 imdb.com/title/tt2980516

ACuriousMind

3:38 PM

"Understanding" is not slippery. It has several levels, it's not binary, but it usually isn't particularly difficult to pin down how confident one is in having understood something or how much one understands of it. It may be difficult for some people to admit they don't understand what they pretend to, though.

3

vzn

Blind men and an elephant

The parable of the blind men and an elephant originated in ancient Indian subcontinent, from where it has widely diffused. It is a story of a group of blind men, who have never come across an elephant before, learn and conceptualize what the elephant is like by touching it. Each blind man feels a different part of the elephant body, but only one part, such as the side or the tusk. They then describe the elephant based on their partial experience and their descriptions are in complete disagreement on what an elephant is. In some versions they come to suspect that the other person is dishonest and...

John Rennie

4:08 PM

@ACuriousMind Amen

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