The h Bar

Slereah

8:00 AM

I have only seen a reference to Dirac's GR book once

It was in one of Those papers

On how to build wormholes FOR REAL

Because Dirac's book is one of the rare GR book to have the Bertotti-Robinson spacetime in it

which makes sense, I suppose

It's not a very relevant spacetime from a cosmological point of view, but it's a very physics spacetime to study

Ryan Thorngren

what's that spacetime like?

Slereah

It's the spacetime generated by a homogeneous electric field

Ryan Thorngren

oh man

sounds kind of like Godel's onion

but worse

Slereah

it's not a terribly complicated spacetime

but it's of limited interest

at least globally

Ryan Thorngren

okay I guess it would be like Godel's onion if it has a uniform E field and also was slowly spinning about an axis

anything with an infinite amount of energy is gonna be weird somehow

Slereah

8:05 AM

Well, the FRW spacetime has infinite energy :p

and you're living in it

Ryan Thorngren

infinite action, not energy right?

or what, what's T in the FRW universe? it's not zero?

John Rennie

The stress-energy tensor is certainly not zero in the FLRW geometry.

There are energy density terms and pressure terms.

Ryan Thorngren

well. that is a lot of energy then

ChoMedit

When you learn about the mathematics for physics, what are your strategies? How to attack them?

Secret

Step 1: Don't try to interpret every step of the workings with physical meaning e.g. $\langle \psi_a | \psi_b\rangle$ don't really have a physical meaning

Step 2: Think about how the equations are being simplified as you take account of physical constraints such as e.g. the size of the system, e.g. upper limit and lower limit of e.g. pressure etc.

Ryan Thorngren

8:16 AM

^what do you have against transition amplitudes

also ChoMedit that wasn't a very specific question

bolbteppa

Doing global GR is the result of not growing out of said phase :p

Ryan Thorngren

lately I need to read about modular forms and it's very difficult to read the number theory literature, but this might not be what you're asking about

ChoMedit

My question is for general areas of physics. I think there may be a consistent way to study the required mathematics.

bolbteppa

I want to watch these videos on modular forms in string theory, skimming the first one he does things really nicely

Laces 2015: (Mock) Modular forms and Applications to Strings ( J.A. Harvey Lecture I)

►

Slereah

@JohnRennie Well, Minkowski space is a FRW spacetime :p

Ryan Thorngren

8:19 AM

oh cool thanks

I've been watching Don Zagier's series

they're more mathematical, but he talks about some jones polynomial things

Slereah

@bolbteppa Global GR is great

Ryan Thorngren

Don Zagier Lecture: Day 1

►

what do you mean by global GR

John Rennie

@Slereah also a Schwarzschild spacetime, a Kerr spacetime, etc, etc

Slereah

@JohnRennie really most spacetimes have Minkowski space as a limit

Global GR is looking at the global properties of a spacetime

Rather than just the local properties encoded by the stress energy tensor

Ryan Thorngren

so you can look at topology, the conformal boundary, what else?

bolbteppa

8:21 AM

first lecture he derives poisson summation and sets up a theta function and some more stuff, are those Zagier lectures insane

Ryan Thorngren

yeah he's nuts but he makes it work somehow

Slereah

@RyanThorngren Causal structure, singularity analysis, Cauchy problem

Ryan Thorngren

only thing I don't like is he's very dismissive to his audience

Secret

Actually, what mathematical object is responsible for the topology of the spacetime in the context of GR?

Slereah

that kind of stuff

@Secret The topology is

same as with every manifold

it's the atlas

Although if your spacetime is well behaved enough, this is equivalent to the Alexandrov topology

in which case you can say the metric is

Ryan Thorngren

8:23 AM

I'd ask what mathematical object encodes the causal structure!

Slereah

@RyanThorngren also the metric!

There aren't that many mathematical objects in GR at its core

Ryan Thorngren

that's not what I mean

Secret

right, so for well behaved spacetimes, the stress energy tensor (which by Einstein Field Equations, is linked to the metric tensor) will have some control on the global topology of the spacetime?

Ryan Thorngren

of course the manifold with metric contains all the data

but if I ask you, "what's the causal structure of this spacetime?" how will you answer me?

Slereah

There's a few equivalent statements for it

The most common one is that the causal structure is a partial order on the spacetime

$a \ll b$ if there's a future-directed timelike curve from $a$ to $b$

etc

Ryan Thorngren

8:26 AM

yeah that's good, though a very large piece of data

Slereah

you can do it as the set of light cones for every points, too

or as the topology defined by causal diamonds

The causal structure has basically the property of being the same under conformal transformation

or should I say Weyl transformation

Ryan Thorngren

yeah

so there should be some conformal invariant way to specify it

Slereah

you can even define spacetimes without manifolds or metrics

Ryan Thorngren

I heard of something like this for 2d spacetimes

Slereah

simply from the causal structure

Ryan Thorngren

8:29 AM

where there are many simply-connected flat Lorentz surfaces

Slereah

It's the approach used in causal sets for quantum gravity

ChoMedit

Is there any considerable reason that why the temporal dimension is 1?

Ryan Thorngren

not unless you wear two watches

Slereah

@ChoMedit well, observational evidence, for a start

Also matter isn't terribly stable with two time dimensions

ChoMedit

That is very clear. By the way, I'm interested in your last sentence. Stability of the matter. What does it mean?

Or.. is there some reference for it?

Slereah

8:32 AM

When you're working with multiple time dimensions, you have to solve differential equations with multiple times

Those are very badly behaved

Either there's no solutions, multiple solutions, or unstable solutions

2

Secret

determinism breaks down, if I recall?

Slereah

that too

Also there's a lot of weird side effects

Like the photon isn't stable in 2 time dimensions

Ryan Thorngren

hey slereah take a look at this abstract tell me if it makes sense to you arxiv.org/abs/1601.06304 I thought it was an interesting take, but I wonder how a GR person would feel about it

Slereah

@RyanThorngren Makes sense if he only considers conformal field theory, I suppose

if you want to know more about causal structures you can try this : arxiv.org/abs/gr-qc/0501069

a pretty good paper on the topic

Ryan Thorngren

cool thanks, I'll have a look

I think what he does is okay for effective field theory but you do need to understand the RG flow, which of course flows between CFTs

Slereah

8:36 AM

The basic idea behind causal structures is that the set of causal structure is $$\text{Coset}(M) = \text{Lor}(M) / \text{Weyl}$$

With Lor the set of Lorentzian metrics

Ryan Thorngren

yeah

Slereah

You can just define it as the equivalence relation of all weyl related metrics, although that's not the most satisfying definition

Also I think it doesn't work that well for spacetimes that are really badly behaved, IIRC?

Like I seem to recall that causal structures are only conformally related if you assume at least distinguishing spacetimes

Ryan Thorngren

hm I don't see what could go wrong

you mean in the sense of the partial ordering

?

Slereah

I'm not quite sure what goes wrong, but the theorem proving that causal structures are identical for Weyl related spacetimes requires distinguishing spacetimes

i'm not aware of any counterexample for bad spacetimes, though

Ryan Thorngren

distinguishing seems like a reasonable assumption

otherwise you have points sitting on top of eachother or somethign

Slereah

8:41 AM

I beware of "reasonableness" requirements :p

that's how you end up thinking all spacetimes are inextendible globally hyperbolic

Ryan Thorngren

haha well I think other spacetimes are above my pay grade, and are for the algebraic geometers or whoever to tangle with

basically I don't know how quantum mechanics can make sense without global hyperbolicity

Slereah

it doesn't make a lot of sense :p

Usually it loses unitarity

Although then again

Even in globally hyperbolic spacetimes, it does

Ever tried to solve an electron orbitting a black hole?

Ryan Thorngren

using what, string theory? good luck :P

Slereah

No, just QFT in curved spacetime

The Hamiltonian isn't hermitian :p

It corresponds to the electron getting lost in the black hole

Ryan Thorngren

yeah

that's not surprising

and probably not a good description of what actually happens

Slereah

8:47 AM

true

Although when spacetime isn't globally hyperbolic, that's exactly what happens

You can just have particles popping out for no reasons

Ryan Thorngren

haha

that's why they created the naked singularity in half life

to see what would happen

and all the aliens came out

Slereah

this is what happens

Ryan Thorngren

lol

Slereah

"The worry is illustrated in Fig. 3.1 where all sorts of nasty things - TV sets showing Nixon's "Checkers speech", green slime, Japanese horror movie monsters, etc. - emerge helter-skelter from the singularity."

Ryan Thorngren

lost sock, the ultimate embodiment of negative entropy

Secret

8:50 AM

hmm that's an interesting point, did anyone tried to calculate the entropy of a naked singularity?

Slereah

what entropy

Secret

I don't know, does a naked (ring shaped) singularity has enough structure to talk about microstates of sorts?

Ryan Thorngren

I think the density matrix looks like $\sum_{anything and everything} |psi>_universe \otimes |anything and everything>$

so you're interested in log of the number of all things

which you should apply zeta fn renormalization and probably the answer is lost sock/2pi^2

Secret

I only know we can talk about something called soft modes on event horizon, but since naked singuarities lack event horizons, the information has to be encoded on it, I guess...?

Ryan Thorngren

I missed some bra's in there but hopefully you get the joke :P

Slereah

8:54 AM

Also don't write raw text in tex :p

$|\text{Anything and everything}\rangle$

or $|\mathbf{Anything and everything} \rangle$

$|\mathfrak{Anything and everything} \rangle$

Ryan Thorngren

haha it doesn't compile for me anyway

Slereah

what kind of tincan mathjax are you running

Ryan Thorngren

but if you really want to make a strong point nothing beats a paragraph of \mathbb

Secret

4

Q: Entropy of a naked singularity

According to the wikipedia article http://en.wikipedia.org/wiki/Naked_singularity: "Some research has suggested that if loop quantum gravity is correct, then naked singularities could exist in nature, implying that the cosmic censorship hypothesis does not hold. Numerical calculations and some ot...

Ok found something, so basically, since we cannot predict beforehand what is sprewed from the naked singularity, we have no way to count its microstates

Ryan Thorngren

honestly an empty tin of mathjax it seems

I've smoked all my mathjax

Slereah

8:57 AM

Well there are some hints

A naked singularity may still have a mass

But of course nothing forbids that mass from running negative, if we're willing to have naked singularities, anything might go

Ryan Thorngren

can we make a naked singularity in AdS?

Slereah

Well you can remove a point from AdS :p

But otherwise, it is geodesically complete

Ryan Thorngren

that's hardly an essential singularity

I mean in asymptotically AdS

Slereah

Probably?

Ryan Thorngren

like you can make a black hole and look at the CFT dual state, which is mixed

Slereah

8:59 AM

Although proving it sounds like a nightmare

Ryan Thorngren

there's some nice picture about the Ryu-Takayanagi screens not dipping into the event horizon

Slereah

Like I suppose you could do the equivalent of the Kerr solution in AdS

and look at the extremal solutions

Ryan Thorngren

yeah

Slereah

AdS is fucked up enough as it is, no need for singularities

it's already not globally hyperbolic

Ryan Thorngren

isn't it just a box

Slereah

9:00 AM

Hell, in some definitions, AdS is nakedly singular

it's just that the naked singularity is the boundary at infinity

Ryan Thorngren

hm

well that's nice to imagine

Slereah

But that's for the harshest definitions of naked singularities

Ryan Thorngren

turning the CFT cylinder into a twice punctured sphere

Slereah

when a spacetime is nakedly singular if it's not globally hyperbolic

Ryan Thorngren

I have to decide what operators to put at the punctures

Secret

9:02 AM

Something probably random: Suppose we have a region of spacetime where random objects get sprewed out, I wonder if an observer can locally determine whether it is a region where determinism fails, or just one end of a CTC (thus what seemed to be a fountain of arbitrary objects is actually coming from another location in spacetime?)

Because if I recall correctly, both CTC and nondeterministic regions of spacetime violates unitarity, which caused me to wonder if there are ways to distinguish between them without the full information of the global structure of the spacetime

Slereah

@RyanThorngren isn't a cylinder already a twice punctured sphere

Ryan Thorngren

just another way to look at things

Slereah

smbc-comics.com/comic/inaccuracy

Ryan Thorngren

I'm disturbed now you say ads is not globally hyperbolic because I've definitely heard people talking about cauchy slices for it

lol

I bet doing acid with NdGT would be great

Slereah

AdS admits a foliation by spacelike hypersurfaces

But those are not Cauchy surfaces

You have timelike curves that go off to infinity at arbitrary $t$ and never go further

and vice versa, you have timelike curve coming from infinity that didn't exist before

Ryan Thorngren

9:12 AM

yeah that makes sense

but all the trajectories of massive particles stay bounded right

Slereah

You can probably salvage it by requiring nothing to come from infinity I suppose

yeah massive particles are alright

Ryan Thorngren

I mean the theory is gapped from the perspective of the CFT

Slereah

well, as long as you don't have any Rindler particles :p

Ryan Thorngren

okay you're right I'm talking about some specific theory there, type IIB string or something

I can see how it could go wrong otherwise

Slereah

yeah fortunately AdS isn't that bad

I think it's fine if you just specify some boundary conditions at infinity

which is reasonable

Ryan Thorngren

9:15 AM

that's what I was trying to say with the punctures

but it wasn't very insightful

people like ads a lot where I hang around

Slereah

you know me, I love spacetime

Ryan Thorngren

lol

Slereah

Except the Beem spacetime

Secret

and he investigates some of the most pathological of the spacetimes

Slereah

and the Geroch spacetime

fuck those

Secret

9:17 AM

actually, thinking about another scenario:

Ryan Thorngren

$e^{i\pi} = -1$ test

fail

Secret

Giving a branching spacetime, then physics will become nondeterministic at the branching point, I think I need to figure how the causal structure there differs from a local event in a CTC

Ryan Thorngren

success!

how can spacetime branch

Slereah

Non-Hausdorff manifolds

Ryan Thorngren

oh god why

haha

Slereah

9:19 AM

It's a very mildly investigated theory

it's not pretty

link.springer.com/article/10.1007/BF01646486

cf here for instance

aip.scitation.org/doi/abs/10.1063/1.1665474BF01646486

Secret

the aip link rotted

Slereah

RIP

Secret

Error: The Requested Article is unavaiable

I think one question that might be potentially interesting for curation purpose (or whatever) is the classification of nonunitary spacetimes

Slereah

what the hell is a non-unitary spacetime supposed to be

Secret

so far we have branching points, CTCs and naked singularities

(I am not sure if there is a formal term, its just something that pops up) Basically a region of spacetime where unitarity fails

Slereah

9:23 AM

unitarity of what

Secret

so one cannot e.g. talk about the time evolution of a quantum field in such region?

Probability wise, it will not be conserved in such regions

That is, the probability of any physical process happening will fail to be conserved in such regions

such as near CTCs and naked singularities, particles will suddenly pop out or disappear to nowhere

(I really need to dig the correct terminology for what I have in mind of the intuitive notion of "a local region in the spacetime manifold where the observer is situated in" to express this properly)

Slereah

"Let $(M,g)$ be a Malament-Hogarth spacetime containing a timelike half-curve $\gamma_1$ and another timelike curve $\gamma_2$ from point $q$ to point $p$ such that $\int_{\gamma_1} d\tau = \infty$, $\int_{\gamma_2} d\tau < \infty$ and $\gamma_1 \subset I^-(p)$. Suppose that the family of null geodesics from $\gamma_1$ to $\gamma_2$ forms a two-dimensional integral submanifold in which the order of emission from $\gamma_1$ matches the order of reception at $\gamma_2$.
If the photon frequency $\omega_1$ as measured by the sender $\gamma_1$ is constant, then the time-integrated photon frequen…

Malament-Hogarth spacetimes are a meme!

Secret

9:38 AM

Gah, it is impossible to draw these spacetimes

This is a big incomprehensible mess

GR f*** up the notion of "distance between A and B" so much that I cannot triangulate where the concepts are located in a diagram

and that is why I found quantum mechanics slightly more intuitive, because I can at least draw a space of parameters to guide my calculations

> If the photon frequency ω1 as measured by the sender γ1 is constant, then the time-integrated photon frequency ∫p2ω2dτ as measured by the receiver γ2 diverges as p2 approaches p."

Ok then, so that means anyone who tried to read the solution of the halting problem will be fried by intense gamma rays instead

Slereah

yes

"Suppose that $p \in M$ is a Malament-Hogarth point of the spacetime $(M, g)$ (that is, there is a future-directed timelike half-curve $\gamma_1 \subset M$ such that $\int_{\gamma_1} d\tau = \infty$ and $\gamma_1 \subset I^-(p)$). Choose any connected spacelike hypersurface $\Sigma \subset M$ such that $\gamma_1 \subset I^+(\Sigma)$. Then $p$ is on or beyond $H^+(\Sigma)$."

"There is nothing in the known laws of physics to prevent a false signal from emerging from the singularity and conveying the misinformation to $\gamma_2$"

Secret

Never seen $H$ before

Slereah

Cauchy horizon

Secret

I see

I wonder if hypercomputation is doomed to fail for all spacetimes, as in whether there is a no-go theorem for hypercomputation...

Slereah

it looks unlikely

Tanuj

10:03 AM

Guys how many divisions are there in a Kelvin Temperature scale?

Slereah

It's a standard unit, so you just use the SI divisions

ie kilo, mega, giga, etc

Tanuj

I mean to get relation between Celsius and Fahrenheit scales, you do something like $\dfrac{T_{f}-32}{180}=\dfrac{T_{c}-0}{100}$

Slereah

The division of Kelvins is the same as the celcius, only the origin point differs

Tanuj

I was wondering how to do this to get a relation between Kelvin and Celsius scales

Slereah

So $T_k = T_c + 273.15$

Tanuj

10:08 AM

What's the lowest temp of Kelvin scale?

Slereah

The lowest temperature is $0K$

Tanuj

273.15 right?

Slereah

It is equivalent to $-273.15 ^\circ C$, yes

Tanuj

So 0 K is the origin for Kelvin scale?

Slereah

Yes.

The division of kelvins is that there is $273.15$ kelvins between absolute zero and the triple point of water

Tanuj

10:12 AM

Okay so in the formula I wrote above, when I wrote 32 for the Fahrenheit scale, do I write it as the origin temperature of the scale?

Slereah

I already gave you the formula above

Tanuj

@Slereah I know the formula! I was asking what's that 32 in the above formula I wrote, you see I'm trying to understand stuff

Secret

> On the Fahrenheit scale, the freezing point of water is 32 degrees Fahrenheit (°F) and the boiling point is 212 °F (at standard atmospheric pressure). This puts the boiling and freezing points of water exactly 180 degrees apart.[6] Therefore, a degree on the Fahrenheit scale is 1⁄180 of the interval between the freezing point and the boiling point.

> According to a story in Germany, Fahrenheit actually chose the lowest air temperature measured in his hometown Danzig in winter 1708/09 as 0 °F, and only later had the need to be able to make this value reproducible using brine.[10] This is

> one explanation given why 0 °F is −17.78 °C, but the ammonium chloride cooling temperature actually is −3 °C, whereas that of NaCl is −21.1 °C; the other explanation is that he did not have a good enough brine solution to obtain the eutectic equilibrium exactly (i.e. he might have had a mixture of salts, or it had not fully dissolved). In any case, the definition of the Fahrenheit scale has changed since.

This is SO ARBITRARY for a 0 F definition

so, 180 is due to farenheit has 180 divisions and the freezing point of water is shifted up by 32

Slereah

10:49 AM

"A modification of this example also serves to challenge the first dogma of observation. Create a past-truncated Minkowski spacetime by deleting all those spacetime points $r$ such that $t(r) \leq 2000 \text{B.C.}$"

What was so awful about that time that we have to delete it

"The past-truncated Minkowski model of Fig. 5.3 is, of course, very artificial (at least for those who do not subscribe to the creationist line of Protestant fundamentalism)."

bolbteppa

11:12 AM

If $S = - m\int ds - e \int A_{\mu} dx^{\mu}$ is the action for a particle in an EM field, how does it change if you allow magnetic particles with charge, e.g. what happens to the Bianchi identity

Slereah

Which Bianchi identity?

bolbteppa

Yikes, you have to modify the EM field tensor apparently

Magnetic monopole

A magnetic monopole is a hypothetical elementary particle in particle physics that is an isolated magnet with only one magnetic pole (a north pole without a south pole or vice versa). A magnetic monopole would have a net "magnetic charge". Classical theories of electromagnetism, represented by Maxwell's equations, disallow magnetic monopoles. Modern interest in the concept stems from particle theories, notably the grand unified and superstring theories, which predict their existence. Magnetism in bar magnets and electromagnets does not arise from magnetic monopoles, but from electric charges (i...

$dF = \frac{1}{3}(dF + dF + dF) = 0$

Slereah

oh yeah

Basically the electric and magnetic fields become "symmetric" if you add a magnetic charge

bolbteppa

'the Cabibbo–Ferrari relation'

'N. Cabibbo and E.Ferrari [2] have shown that if one introduce a second four-potential it is possible to eliminate the Dirac string.' I remember some waffle about Dirac strings

'The quantization of the theory remains a challenging open problem. The same can be said of its non-abelian extension'

Slereah

11:28 AM

"In the philosophical jargon, we have a paradigm case of Hempelian deductive-nomological explanation"

the horror

Secret

what does that even mean?

Slereah

Who knows

Secret

This is what I read: (incomprehensible) deductive (incomprehensible) explanation

Secret

11:45 AM

[continue on the british saying stuff]

29. Perfect with the following tone C#----F#, is the same as the british meaning

also 37 is really weird, how is that a punishment, you are wasting time on something that does not deserve a figurative "thank you" in any piece or form

because the truth is, the irresponsible won't even take note of that passive aggressive anyway

That's the problem of dealing with irresponsibles. Unlike trolls, you cannot make them regret their actions with the silence treatment

Slereah

12:55 PM

"Perhaps we have missed something. Suppose that Kurt tries over and over again to kill his grandfather. Of course, each time Kurt fails—sometimes because his desire to pull the trigger evaporates before the opportune moment, sometimes because although his murderous desire remains unabated his hand cramps before he can pull the trigger, sometimes because although he pulls the trigger the gun misfires, sometimes because although the gun fires the bullet is deflected, etc. "

Why does Gödel hate his grandfather so much

John Duffield

I'm confident that there are no magnetic monopoles. The electron has an electromagnetic field, not an electric field. IMHO it's missing the trick of electromagnetic unification to say it has electric charge and then say some other particle might have magnetic charge.

Slereah

shoo shoo @JohnDuffield

John Duffield

I'm confident there are no wormholes either. IMHO if you've ever read David Finkelstein's 1958 paper you'll appreciate there are significant issues with it. And of course with the 1935 Einstein-Rosen paper.

Slereah

Jesus that's a poorly OCR'd paper

John Duffield

I'm fond of quoting Einstein, but I don't quote from the Einstein-Rosen paper.

Slereah

1:12 PM

journals.aps.org/pr/abstract/10.1103/PhysRev.110.965

there's the original paper

ChoMedit

Could we make a magnetic monopole? Not in a fundamental particle sense.

Slereah

Yes, there are objects similar to magnetic monopoles in condensed matter physics

They occur in superconductors, from what I can remember

John Duffield

You could make a very long solenoid.

One end of it is a magnetic monopole.

ChoMedit

@JohnDuffield Could we call that magnetic monopole? It has its own pair even though it is very far away...

Slereah

This paper doesn't really say anything new on wormholes, at least with modern eyes

John Duffield

1:18 PM

@ChoMedit : it isn't really a magnetic monopole.

@Slereah : when it comes to wormholes, I think this Einstein quote is worth noting: "it is easy to show that both light rays and material particles take an infinitely long time (measured in "coordinate time") in order to reach the point".

Slereah

Well for the Einstein-Rosen bridge, obviously

Since they are joined at their event horizon

Physics Meta

0

Q: Can this Q be reopened for answering?

What could happen if we collide two subatomic particles with an energy of 39TeV? Or could we ever reach 40TeV? Closed as too broad, but - see comments - there is scope for a good answer. I'd have written more (times, energies), but comments aren't the right place for it.

support

John Duffield

If it takes an infinitely long time to reach the event horizon, it takes forever to cross the bridge, so you can never ever cross it. So it isn't a bridge.

Slereah

Well yes

John Duffield

Besides Einstein and Rosen and Finkelstein were talking about particles, and particles aren't wormholes in any shape or form.

Slereah

1:22 PM

Nobody is pretending that the Einstein-Rosen bridge is traversible.

I am aware.

You seem to be under the impression that those are mysterious issues that physicists aren't aware of

Those are all pretty well known facts of general relativity.

John Duffield

@Slereah : some people are suggesting that wormholes are traversable, when that goes against the grain of what Einstein said.

Slereah

He seems to be back on word salads

Let's discreetely withdraw

John Duffield

I accidentally hit ENTER above. I've since corrected it.

Slereah

Nobody is suggesting that the Einstein-Rosen solution is traversible.

and almost nobody is even suggesting that traversible wormholes are physical.

John Duffield

But some people are suggesting other wormholes are.

Slereah

1:26 PM

Yes, which doesn't go against what Einstein said, as far as I'm aware.

His argument was fairly focused on the Schwarzschild metric

John Duffield

See what Kip Thorne advocates. He's one of the authors of MTW.

Slereah

I'm well aware of Thorne's work, yes

John Duffield

IMHO the Schwarzschild metric is crucial. IMHO Oppenheimer and Snyder got it right with their 1939 paper on continued gravitational attraction. It ties in with what Einstein said. What Thorne says doesn't.

Gotta go. Sorry.

Slereah

Same old Duffield

bolbteppa

Instead of equations and derivations, names of authors and old essays are used to derive results :p

Slereah

1:36 PM

Worst part being that these are fine little old papers

This isn't even a case of old papers being wrong

just unrelated to the matter

Not that I particularly believe wormholes are physical either, but whatever incoherent argument is trying to come through JD probably isn't the reason why

Nobody even really thought about traversable wormholes until the 70's or so, so it's pretty unlikely that papers from the 30's will say much on the issue

Balarka Sen

@bolbteppa lmao

I'm going to use and abuse that statement

Slereah

Also really Oppenheimer-Snyder isn't a great paper to make a point about physically realistic models since it's not at all physically realistic :p

Dust collapse models are easy to deal with but they're not v. good

bolbteppa

It probably is actually using the kind of thinking you'd use in math and physics, just in that fatally flawed 'argument from authority' language instead of the language of math

Slereah

They tend to produce naked singularities

bolbteppa

Poor guy, I tried to encourage him to study math once at least :(

Slereah

1:44 PM

A bold attempt

bolbteppa

Maybe Newton's Principia is wordy enough but with the jist of calculus and physics, a good start to ween off the quoting famous authors as a compromise :p

Slereah

Newton's principia is really not a great place to learn math

It's from the era when using Euclid's geometry for almost everything was still the trend

It's not very readable by modern standards

Balarka Sen

marxists.org/archive/marx/works/download/…

bolbteppa

Yeah it's terrible, but I remember buying the huge blue one before any other book thinking it was the davinci code of math and well...

Balarka Sen

This is the right place to learn calculus

bolbteppa

1:46 PM

Isn't there some Marx calculus theorem haha

Slereah

It's a nice book to have for historical reasons

but I wouldn't recommend calculus from Newton or algebra from Diophantes

bolbteppa

I think he was part of the whole rigor/infinitesimal arguments before Weierstrass

Balarka Sen

Marx? Well, no, he wasn't aware of Weierstrass's work

But he got a good bit far himself

He was mostly learning mathematics in his last few years

Slereah

I really don't know why the tumblr people are so in love with Marx, really

Since he was a white straight bourgeois man

You'd think he would be the worst thing

bolbteppa

My sense is it's sycophants trying to say 'oh he did great things in THE calculus', but I have no idea tbh

Mathematical manuscripts of Karl Marx

The Mathematical manuscripts of Karl Marx consist mostly of Karl Marx's attempts to understand the foundations of infinitesimal calculus, from around 1873–1883. A Russian edition edited by Sofya Yanovskaya was eventually published in 1968, and an English translation was published in 1983 (Marx 1983). According to Hubert C. Kennedy, Marx "[...] seems to have been unaware of the advances being made by continental mathematicians in the foundations of differential calculus, including the work of Cauchy." In the same text, Kennedy says "While Marx's analysis of the derivative and differential had no...

Balarka Sen

1:49 PM

Ah Cauchy not Weierstrass my bad

He didn't do any breakthroughs

He was just attempting to understand calculus more rigorously

Slereah

aren't we all

Balarka Sen

the differential was an elusive concept then

Slereah

I wonder what was the big problem that made people realize that infinitesimals didn't work

Balarka Sen

You quickly run into trouble if you think about $dy/dx$ as a "fraction of infinitisimals"

I think $d^2y/dx^2$ doesn't play well at all with the chain rule

bolbteppa

Hmm I know people say that stuff, but I think Euler's old calculus book was using differentials the way we do more or less, and DeMorgan and all these guys, and Leibniz was using them in some form, it seems like (comparatively) really complicated fourier series things or uniform convergence etc really kicked these guys into rigor, but I could be wrong

Balarka Sen

1:57 PM

$$\frac{d^2y}{dx^2} \neq \frac{d^2 y}{du^2} \left ( \frac{du}{dx} \right)^2$$

bolbteppa

They used higher order ones more relaxedly back then too

ia800201.us.archive.org/BookReader/BookReaderImages.php?zip=/6/…