The h Bar

Slereah

19:00

I wish there was a big book of just weird spacetime things that was like

Detailed

Visser's pretty good but it skims a lot

It's a pretty short book for the topic it covers

0celo7

yeah that too

it couldn't be done in 700 pages

Slereah

In Euclidian Gravity, Hawking starts a paper with like

0celo7

dude maybe like two new volumes

Slereah

"No theory of quantum gravity could possibly exist without some topology change"

and I'm like

"Slow down Hawking!"

Careful with the hubris!

0celo7

I could print that paper for $1.14 in the Baker center.

Slereah

19:03

Does Straumann also have like

Numerical relativity

And experimental results

0celo7

Although I have to print >500 pages for Herr Prof. Dr. Lang.

@Slereah Yeah, he talks about LIGO and gravity probe.

Nothing fancy.

Slereah

"Once you have a naked singularity, physics starts breaking down in very big ways. Quantum mechanics and general relativity give absurd answers, and they're not even the same absurd answers. "

heheheh

0celo7

@Slereah A very short intro and then references Hawking-Ellis for the analytical results and Shapiro and another book for calculations.

Slereah

Referencing HE is the GR book's secret move

It's what you do when you can't write "the reader can show"

0celo7

Indeed.

Slereah

19:10

Does Carroll reference it all that much?

0celo7

I don't think Carroll talks about spacetime topology enough to do that.

Wald Ch. 8, 9 and 10 pretty much make it a meme.

Slereah

hard to do causality without HE

I don't want to belittle Einstein or the evidence, but it was a poorly understood topic before the 60's

0celo7

Have you read Weinberg G&C?

Slereah

I only have his QFT book

I'm not quite sure when was the first paper that really referenced causality violations

The first spacetime with one was van Stockum in 36, but he didn't notice them

And I don't think Godel's paper mentions them either

Could be Tipler

There's a nifty book that's like

Hawking and a bunch of dudes

Talking about various spacetimes things

From the 70's I think

there's even a neat simple example of a spacetime with CTCs without any causality violation

"General relativity.. an Einstein centenary survey "

that's the one

Centenary is a bit exagerated since it's from 79

Unless they mean when he was born

But no Einstein baby pictures

there's a shitload of big names in that book

0celo7

19:27

@Slereah Well HE is '73.

@Slereah Is that the one you bought that's just a collection of papers?

Slereah

No

That was Euclidian Gravity

A lot of books are collections of papers

"Magic without magic" is another one

cheaper to publish than editing a book!

0celo7

Does Poplawski require anything special?

Could I read it?

Slereah

Mostly knowing some GR

Should be fine

0celo7

He doesn't do like

Slereah

Nah

0celo7

19:29

STIEFEL WHITNEY CLASS

Slereah

He's not the TAKE A PARACOMPACT MANIFOLD type

0celo7

or

ok

although I'm pretty comfortable with paracompact manifolds

oh fuck I have a package waiting...not even in the same state!

Slereah

but what if it's not paracompact, huh???

0celo7

dumb question

Slereah

I wonder if you can have a non-paracompact spacetime

Not sure

0celo7

19:30

what kinds of manifolds are not paracompact

Slereah

The long line

Long line (topology)

In topology, the long line (or Alexandroff line) is a topological space somewhat similar to the real line, but in a certain way "longer". It behaves locally just like the real line, but has different large-scale properties (e.g., it is neither Lindelöf nor separable). Therefore it serves as one of the basic counterexamples of topology. Intuitively, the usual real-number line consists of a countable number of line segments [0, 1) laid end-to-end, whereas the long line is constructed from an uncountable number of such segments. == DefinitionEdit == The closed long ray L is defined as the cartesian...

Paracompactness guarantees the existence of a metric, but I'm not sure non-paracompactness forbids it

"The long line or ray cannot be equipped with a Riemannian metric that induces its topology."

Hm, I guess not

But wait

The metric in GR doesn't induce the topology

Can you have one

0celo7

@Slereah I knew that

@Slereah indeed.

@Slereah huh?

Slereah

Well I guess the question is

Can you have a tensor bundle over a non-paracompact manifold

Such that you can define a metric tensor

0celo7

yeah

Slereah

I have seen a lot of weird spacetimes but I don't think I ever saw a non-paracompact one

Maybe HE will give us clues!

0celo7

19:34

idk, nowhere near my books

I have a debate in 45 minutes

Slereah

Call your opponent a communist

That is how it goes in America

"Together with the existence of a Lorentz metric, the Hausdorff condition implies that M is paracompact"

But wait, the Taub-NUT metric can be non-Hausdorff

Aaaah

NeuroFuzzy

Sanity check: "the geodesic equation" can refer to sorta different ODEs, right? One (which is just the covariant derivative of your tangent vector in the direction of your tangent vector) does depend on the parameterization of your geodesic, one (which is derived from parameterization independent length/variations) does not depend on the parameterization.

0celo7

@Slereah the metric is not Hausdorff either way

you've falling into the GR trap

a space is not its metric

Slereah

Well yes, but "a lorentz metric" here means a section of the tensor bundle

Not the topological metric

@NeuroFuzzy They are the same equation!

0celo7

I'm saying "X metric is not Hausdorff" does not make sense, does it

unless you have the metric topology?

Slereah

19:40

He's not saying that

0celo7

but you said that

Slereah

He's saying that there's a Lorentz metric, and the manifold is Hausdorff

0celo7

I know what he's saying

forget it

NeuroFuzzy

@Slereah ehm well my book is saying that the geodesic equation depends on the parameterization and I could have sworn that's false.

0celo7

but we're pretty sure spacetime is Hausdorff, right

NeuroFuzzy

19:42

By doing it through variational principles

0celo7

although, isn't Taub-NUT the one that has like non Hausdorff properties that can make sense

IDK anymore

Slereah

Probably

0celo7

@NeuroFuzzy it does

Slereah

Non-Hausdorff spacetimes are weird

0celo7

you get an extra term if you don't use an affine parameter

Slereah

19:42

Curves converge in more than one point

0celo7

cf. e.g. Carroll

@NeuroFuzzy the same equation can look different with different parameters

Slereah

Remember that $U^\mu = \frac{dX^\mu(\lambda)}{d\lambda}$

0celo7

::remembers::

@NeuroFuzzy I can give you pages in Carroll if you have access

well I can give pages later

Slereah

So $U^\mu \partial_\mu U^\nu = \frac{dx^\mu}{d\lambda} \frac{dx^\nu}{dx^\mu} = \dot{x}$

Or whatevs

0celo7

what are you babbling about

Slereah

19:49

Who knows

It's been a long day

0celo7

@Slereah that's wrong btw

that's $\ddot x$ in SR

you're a GR fraud

Slereah

Oh yeah

0celo7

almost as bad as @ACuriousMind

Slereah

Forgot to lambda the other U

nvm

"Finally, in absence of paracompactness you cannot construct smooth partitions of the unity and defining a notion of integral is difficult."

Oh no

0celo7

21:29

@Slereah I knew that!

obe

Hi.

Physics Meta

21:43

0

Q: Are capital letters in titles annoying or innocuous?

I ask this having already read a question about minor edits. I've seen several edits in which the only change was replacing capital letters in a title with lower-case letters. This seems, to me, to not improve the post enough to accept as a worthy edit. Is there enough consensus about not havin...

discussion

0celo7

@obe busy

Slereah

YOU KNOW NOTHING

obe

@0celo7 I didn't even say anything.

0celo7

@obe so?

still busy

obe

:L

0celo7

21:53

Torricelli's equation

In physics, Torricelli's equation is an equation created by Evangelista Torricelli to find the final velocity of an object moving with a constant acceleration without having a known time interval. The equation itself is: where is the object's final velocity is the object's initial velocity is the object's acceleration is the object's change in position == Derivation == Begin with the equation for velocity: Square both sides to get: The term appears in the equation for displacement, and can be isolated: Substituting this back into our original equation yields: == See also == Equation of...

huh

obe

Does that really require to be named after someone?

0celo7

I guess

I've never seen it named

dmckee

22:15

@obe The trick is noticing when it was so named. Mechanics was just starting to come together.

Not that I've ever seen it attributed that way in a textbook either.

My students call it "the one without the time", which is the heuristic I gave them for spotting cases when it might be useful.

2

Slereah

Created by Evangelion Torricelli

DanielSank

22:36

Uh, guys, this question and answer are totally bogus, right?

I forget, does special relativity say that I can go a lightyear along a path such that my proper time is, say, 1 hour?

Mike Edenfield

clearly the answer depends on which manufacturer's warp drive you're using.

2

DanielSank

@MikeEdenfield For serious though.

Mike Edenfield

I'm by no means a SR expert but I think that answer is asking for a ton of speculation on things that may not even really exist and doesn't give enough details to pin down a good answer.

DanielSank

@MikeEdenfield I agree that the question is pretty lame.

Mike Edenfield

if it were asking for details about some specific theory of how a possible 'warp drive' might work, maybe, but it kinda assumes everyone knows what a 'warp drive' is supposed to be.

DanielSank

22:44

I am wondering though about Timaeus's claim that you can travel many light years in a few hours. I forget whether or not it works like that.

@MikeEdenfield Yeah, the question isn't so good.

Mike Edenfield

His claim seems to be assuming that FTL travel is indeed possible via some kind of space-bending warp drive.

in that case, sure, the whole point of such a device is to allow us to travel a light year in significantly less than a year :)

DanielSank

@MikeEdenfield He says you can do it without any special energies, etc.

If I accelerate to near speed of light, travel, and then decelerate, certainly something weird happens to my proper time relative to yours.

I just don't recall how to think about this.

Mike Edenfield

I believe he's talking about specific kinda of theroized warp-like devices.

DanielSank

@MikeEdenfield I mean Timeaus's answer here.

Mike Edenfield

Yeah, that's what I mean. The concept behind those proposed devices is usually that you don't accelerate all, you take a "bubble" of spacetime around you and it moves.

so from a GR perspective, you're stationary.

DanielSank

22:47

@MikeEdenfield Oh.

Then the answer is misleading.

Mike Edenfield

Again, not an expert, but thats's my understanding on how they propose to allow FTL travel without violating basic physics.

DanielSank

> Note that you can start at a star that is 10,000 light years away and accelerate at a finite acceleration and experience only 24 hours of your own time and arrive at earth. No exotic energy or warp drives required.

^ No warp drives required.

Mike Edenfield

oh, ok. I also misread his answer.

DanielSank

I'm asking if that's true.

Mike Edenfield

then nm much of what I said :)

DanielSank

22:48

Dang it, I wish I could remember how to think about this.

Mike Edenfield

sounds sketchy to me.

I know distances contract in the direction of travel when you move at relativistic speeds but that seems like a lot.

DanielSank

@MikeEdenfield The other thing that happens is that if I accelerate a lot, say by speeding out into the universe away from you, and then come back, when I get back I will have aged less than you.

Mike Edenfield

but yes, in that case, the acceleration and deceleration would have complicated effects that I am utterly unable to explain :)

DanielSank

^ Twin "paradox"

@MikeEdenfield I think there's a really simple way to compute the differences in our proper times. It's some integral of my trajectory relative to yours. I just don't recall it.

Basically you integrate the instantaneous gamma factor or some such thing.

I just don't think it's right that I can go a light year but experience less than a year in my own frame.

That sounds really bogus.

Where are those theorists who overrun this site when you need them ;)

Mike Edenfield

yeah when I said I was not an expert I meant "I never got past 2-variable calculus in college"

DanielSank

22:52

@MikeEdenfield hah, ok.

Mike Edenfield

I have only recently begun trying to get back into educating myself on math & physics.

unfortunately, the opportunities for inexpensive self-study get very thin at the graduate level :)

DanielSank

@MikeEdenfield Yes. Learning without colleagues is really hard.

What are you trying to learn?

Mike Edenfield

quantum field theory, hopefully :)

but I realized after reading Dr. Susskind's book on classical mechanics that even my integral calc skills are rusty, so I've been working my way through the MIT Open CourseWare undergrad stuff on math & physics

calc, linear algebra, DEs, etc.

I figure I have nothing else interesting to do for the next 5-10 years :P

DanielSank

@MikeEdenfield Sounds like fun.

Mike Edenfield

gives me something to do at work while pretending to listen to customers on sales calls.

I mean.. that's why they make sales people, isn't it?

DanielSank

22:59

@MikeEdenfield I see.

bolbteppa

23:12

@MikeEdenfield Susskind modeled his course on this set of books en.wikipedia.org/wiki/Course_of_Theoretical_Physics and the math for these is all given in the 5 books by this guy en.wikipedia.org/wiki/%C3%89douard_Goursat (first 3 free on archive.org, last 2 most relevant), though if the first math book is too hard this archive.org/details/DifferentialAndIntegralCalculus_109 and then this archive.org/details/coursepuremath00hardrich wil give you a base,

I found Susskind all over the place and had many false starts because of it tbh, if you find that happening too much then use Susskind to complement those books, otherwise Susskind is enough, ignore the man behind the curtain ;)

skill patrol

23:48

Beware @0celo7 if you install iOS 9.0 you have to back it up which took me about 2 hours :-/

0celo7

@skillpatrol I see

debate tournament going over

it should be over

we're not even at the last round

it should have ended half an hour ago

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