The h Bar - 2019-06-13 (page 1 of 2)

« first day (3143 days earlier) ← previous day next day → last day (1789 days later) »

1:37 AM

@Semiclassical ok so I am dealing with a two dimensional universe and singlet entanglement state

@Semiclassical is not the same as non random? But 50-50 along X axis is random. Isn't it? Ok I just have 3 rules,

1. Unknown electron is in mixed state, assuming no one secretly measured it before in a particular axis that I'm would measure later.

2. Once measured in an axis the son is trained and there is cosine square relation when measured at an angle theta. The outcome of this is retained.

3. The reverse of cosine rule is same for entangled electrons in singlet state in a 2 dimensional setup.

4. On measurement the particles lose entanglement, and no useful information can be sent using entanglement.

@EmilioPisanty is what I have enumerated reasonably correct

Oh sorry for the typos, its not the son is trained, is spin is retained, in 2.

3 hours later…

4:24 AM

@VARUN.NRAO what I meant was: If two electrons are not in an entangled state, it is not the case that all outcomes are determined. For instance, suppose you entangle two electrons in the singlet state and measure the spin along the z-axis of the first particle, getting spin up. Then the state of the two electrons is no longer entangled...

If I now measure the spin of the second electron along the z-axis, then I know for sure that I’ll get the opposite result as the first one (so spin down). So for that measurement there’s no randomness ie its outcome is determined.

By contrast, if I were to have measured along the x-axis of the second particle instead, then it’s 50-50 for getting up/down

So while some measurement outcomes are determined for an unentangled state, not all of them will be.

This shouldn’t really surprise, though. An unentangled state is still a quantum state, after all, and so we shouldn’t be surprised to see randomness show up for it as well

It does tell you, though, that getting an intuition for entanglement is a tricky business. You have randomness for unentangled states just as well as for entangled ones.

@VARUN.NRAO you only need this disclaimer when talking about measuring a single electron, to be clear. When talking about a Bell test for two electrons, the initial state is the singlet state—full stop.

(And the singlet state is entangled but not mixed. That’s how the terminology works.)

5:05 AM

@Semiclassical ohhh ok, I got it. Thanks a lot

Abhas Kumar Sinha

5:16 AM

@JohnRennie Sir, How did Einstein Related Gravity with Pseudoforce?

That's very confusing

@AbhasKumarSinha suppose you and I are driving cars and we are travelling at the same speed in directions that are exactly parallel with each other. Then we'll just drive forever the same distance apart. Yes?

Abhas Kumar Sinha

Yes

Okay, then

user image

Abhas Kumar Sinha

So, where's Gravity?

Not on Earth!

On Earth if we start driving north exactly parallel at the equator we will meet at the north pole.

So the distance between us decreases with time as we drive. It looks as if there is some force pulling us together.

OK so far?

Abhas Kumar Sinha

5:22 AM

@JohnRennie how I can be parallel and drive north at the same time on a curve?

The equator is a straight line - it's a great circle which is the equivalent of a straight line on a sphere.

And if we both drive north than both our trajectories make an angle of 90° with the equator (as shown on my diagram).

And if two lines both make an angle of 90° with a third straight line then the two lines are parallel. That's Euclid's 5th postulate.

Abhas Kumar Sinha

Okay, you mean being perpendicular to Equator and being On equator is parallel at that point on the closed sphere

Yes.

So our trajectories start parallel but then converge, as if there was some force pulling us together.

Abhas Kumar Sinha

@JohnRennie Euclid's postulate is only for Plane Surfaces, if I recall correctly

Locally the surface of a sphere looks like a plane. That's why people used to think the Earth was flat. So Euclid's postulate applies locally.

Abhas Kumar Sinha

5:27 AM

@JohnRennie yes,but that's an insane observation, I never noticed that before even I knew it.... Great. What's next?

There's must be a force converging us to a point on a spherical surface

@AbhasKumarSinha Obviously there isn't really a force pulling us together. Our paths converge because we're driving on a curved surface not a flat surface. Yes?

Abhas Kumar Sinha

@JohnRennie agree

@AbhasKumarSinha What GR says is that spacetime is curved, and the reason our paths converge when we travel through spacetime isn't because there is a force between us - it's because spacetime is curved.

Now you might argue that two stationary objects attract each other even when they aren't initially moving, so if they aren't moving how does my analogy of travelling on the Earth apply?

That's because two stationary objects are travelling through spacetime because they are travelling through time, at one second per second.

Abhas Kumar Sinha

@JohnRennie but how space-time is curved?

@AbhasKumarSinha I'm not sure what you're asking. Are you asking what curvature means for spacetime?

Abhas Kumar Sinha

5:36 AM

@JohnRennie what is the meaning of Curvature in Space-time and Why that curve happens?

11

A: What is the universe 'expanding' into?

The balloon analogy is useful in some respects, but it is misleading in one important respect. In the balloon analogy the curavture of the balloon surface is extrinsic while in GR the curvature of the universe is intrinsic. Extrinsic curvature is easy to understand. The surface of a balloon, or ...

5

A: Universe being flat and why we can't see or access the space "behind" our universe plane?

When you're talking about curvature it's important to distinguish between intrinsic and extrinsic curvature. I struggled to find a good summary of the difference: page 6 of this PDF discusses it, or Google for similar articles. A very common analogy for spacetime curvature is the rubber sheet, a...

Abhas Kumar Sinha

@JohnRennie How do you define space-time?

Spacetime is a four dimensional manifold:

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, each point of an n-dimensional manifold has a neighbourhood that is homeomorphic to the Euclidean space of dimension n. In this more precise terminology, a manifold is referred to as an n-manifold. One-dimensional manifolds include lines and circles, but not figure eights (because they have crossing points that are not locally homeomorphic to Euclidean 1-space). Two-dimensional manifolds are also called surfaces. Examples include the plane, the sphere, and the torus, which...

Abhas Kumar Sinha

What gravity has to do with it?

A manifold is basically just something that has dimensions. So a 4D manifold is a collection of points described by four coordinates e.g. $(t, x, y, z)$.

Abhas Kumar Sinha

5:41 AM

Oh oka

Y, I got that

When you travel in spacetime this just means you traced out a path consisting of a sequence of the spacetime points $(t, x, y, z)$.

:50662001 What GR says is that the curvature of spacetime is related to the mass present in that spacetime.

Abhas Kumar Sinha

@JohnRennie how?

What do you mean how?

It just is.

Abhas Kumar Sinha

@JohnRennie So that's a assumption that Curvature is related to mass present in space time. Anything in space-time can be denoted as $(x,y,z,t)$ which I don't see here any dependence of mass

They seem quite unrelated

The specific way in which mass density determines curvature is given via the Einstein field equations.

Abhas Kumar Sinha

5:47 AM

@Semiclassical What are those equations

?

@AbhasKumarSinha Consider regular 3D cartesian coordinates $(x,y,z)$ then consider a vector $(dx, dy, dz)$, where $dx$ is a small displacement in the $x$ direction, $dy$ in the $y$ direction and $dz$ in the $z$ direction.

Abhas Kumar Sinha

@JohnRennie okay

They’re stated here: en.m.wikipedia.org/wiki/Einstein_field_equations

The length of the vector, $ds$, is given by $ds^2 = dx^2 + dy^2 + dz^2$ i.e. just Pythagoras' theorem. Yes?

Abhas Kumar Sinha

@JohnRennie okay

Then

5:49 AM

But the specific form isn’t terribly informative without extensive knowledge of Diff geometry

Now, for spacetime we have to include time, $dt$, as well. It turns out that $dt^2$ goes into the equation with a minus sign:

$$ ds^2 = -c^2dt^2 + dx^2 + dy^2 + dz^2 $$

Abhas Kumar Sinha

Okay,

Now

We also multiply $dt$ by a velocity to convert it to units of distance i.e. $cdt$ is a distance. We do this because you can't add time to distance. You can only add things that have the same dimensions.

Abhas Kumar Sinha

@JohnRennie i understand that part

@AbhasKumarSinha that equation describes flat spacetime. In fact it is so important it has a name. It's called the Minkowski metric.

Abhas Kumar Sinha

5:52 AM

@JohnRennie okay

It is the equivalent of Pythagoras' theorem in flat spacetime.

Abhas Kumar Sinha

@JohnRennie yes

What happens in curved spacetime is that the equation for $ds^2$ changes.

I wrote a long answer explaining this somewhere. Give me a moment to look for it ...

Abhas Kumar Sinha

@JohnRennie how?

Okay, take your time

91

A: What is the connection between special and general relativity?

Suppose we start by considering Galilean transformations, that is transformations between observers moving at different speeds where the speeds are well below the speed of light. Different observers will disagree about the speeds of objects, but there are some things they will agree on. Specifica...

Abhas Kumar Sinha

5:56 AM

@JohnRennie I need some time to digest information

@AbhasKumarSinha GR is typically a year long course, so it does take time to get your head round this :-)

Abhas Kumar Sinha

@JohnRennie but still, those equation don't have mass in them :"(

How Einstein Added mass to the equations?

How mass changes curve? Why other conservative Forces don't?

The curvature is described by an object called a tensor. Understanding what this means is complicated. For now you will just have to accept that tensors exist.

Abhas Kumar Sinha

@JohnRennie i know a bit of tensor analysis

OK. Well one measure of the curvature is a tensor called the Einstein tensor.

Einstein tensor

In differential geometry, the Einstein tensor (named after Albert Einstein; also known as the trace-reversed Ricci tensor) is used to express the curvature of a pseudo-Riemannian manifold. In general relativity, it occurs in the Einstein field equations for gravitation that describe spacetime curvature in a manner consistent with energy and momentum conservation. == Definition == The Einstein tensor G {\displaystyle \mathbf {G} } is a tensor of order 2 defined over pseudo-Riemannian manifolds. In index-free notation it is defined as...

Abhas Kumar Sinha

6:05 AM

Okay

And the matter is described by another tensor caled the stress-energy tensor.

Stress–energy tensor

The stress–energy tensor, sometimes stress–energy–momentum tensor or energy–momentum tensor, is a tensor quantity in physics that describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics. It is an attribute of matter, radiation, and non-gravitational force fields. The stress–energy tensor is the source of the gravitational field in the Einstein field equations of general relativity, just as mass density is the source of such a field in Newtonian gravity. == Definition == The stress–energy tensor involves the use of superscript...

Abhas Kumar Sinha

@JohnRennie well that wiki answered my question... Thanks :)

And what Einstein's equation says is that the Einstein tensor $G$ is related to the stress-energy tensor $T$ by:

$$ \mathbf G = \frac{4 \pi G}{c^4} \mathbf T $$

Abhas Kumar Sinha

Oh okay.... :-D

Oops, I used $G$ twice. The G on the right hand side is Newton's gravitational constant.

Abhas Kumar Sinha

6:09 AM

@JohnRennie know that

Landau-Lifshitz Paeudotensor...

The Landau-Lifshitz pseudotensor is a different object.

Abhas Kumar Sinha

Well, Einstein was veeeey cleaver, I think. He did used his observations skills in such a way that everyone can, but no one thinks that way.

@JohnRennie that can be reduced to zero by choosing a suitable coordinate system

@AbhasKumarSinha you're getting into deep water now :-)

Abhas Kumar Sinha

@JohnRennie indeed!

0

Q: Output intensity in the Mach-Zehnder interferometer

Given a Mach-Zehnder interferomet setup with arm lengths $l_1$ and $l_2$. The (complex) electric field at input and output are given by $\tilde{E}_{in}$ and $\tilde{E}_{out}$, respectively. And the corresponding intensities are $I_{in}$ and $I_{out}$. How to prove the relation $I_{out} = \frac{1}...

6:34 AM

How is chaos theory related to quantum chaos?

Constantine Black

7:04 AM

@akhilkrishnan I am not sure under what context exactly you pose your question but here is a note: since the Schrodinger equation is linear you cannot simply state that the quantum analog of a classical chaotic system is also chaotic, you cannot simply deduce such a fact.
But what you could understand is that what you are really trying to do is check how the phase space is behaving in the non-classical regime, which is not the same of course with the classical regime. The question is how to understand phase space trajectories in the quantum case.

@akhilkrishnan If you are interested in this topic and on the related eigenstate thermalization hypothesis, have a look at this review: arxiv.org/abs/1509.06411 .

7:30 AM

Hello @JohnRennie

so in quantum state does techniques like lyapunov exponents fails?

@Abcd hi :-)

@JohnRennie Could you suggest some laptop for college ...? Budget is like 60-70k INR

@Abcd it's hard to buy a bad laptop these days and 70k INR is a lot of money. You'd get a good laptop for that. Where would you buy it from? Amazon?

Constantine Black

A Lyapunov exponent may give you a strong hint that the motion is chaotic, but does not prove it.

7:41 AM

@JohnRennie Yup Amazon or I will go to shop in the city if it's directly available there.

Let me have a quick look on amazon.in so I can get an idea of what laptops are available.

then what can prove it@ quantum level?

@Abcd I had a quick look at this page

And in that price range there are loads of good laptops.

Morning

@Abcd I would look for one with an SSD drive because that makes a big difference to the speed. Otherwise just choose one the size and weight you like.

7:46 AM

@JohnRennie which is better lenovo or hp or dell

@JohnRennie What is SSD drive, how to see if it's there

@Abcd they are all excellent brands. I personally like Dell but that's really only because I've always worked with Dell and I know the brand well. Lenovo and HP are just as good.

@Abcd Let me see if I can find an example ...

ok

@Abcd take this laptop as an example

@JohnRennie someone told me to get dell inspiron 7000 series

user image

@Abcd you see where I've outlined in red. That shows the laptop has an SSD. The term SSD stands for solid state disk and that type of disk is very, very fast. The disk speed makes a big difference to the laptop speed and I would always go for a laptop with an SSD.

7:52 AM

@JohnRennie oh

@Abcd the Inspiron 7000 series are good laptops, but like I say all laptops in this price range are going to be good.

The laptop I found above is an Inspiron 5000 series. I think they are smaller and lighter than the 7000 series. Do you want a small light one or one with a bigger screen?

@JohnRennie What do you say about this one:

amazon.in/Apple-MacBook-Air-13-3-inch-MQD32HN/dp/B073Q5R6VR/…

@JohnRennie bigger screen but light as well

MacBooks are excellent laptops, but note that they use the Apple operating system not Windows. That means you can run Windows apps. This isn't necessarily a problem because you may not need to run Windows apps.

@Abcd that's the same screen size as the Inspiron I gave as an example. Both have 13 inch screens.

What model is your current laptop? We can use that as a starting point.

@JohnRennie it's very old (5-6 years)... I dont know about it...How to see model?

Usually the model number is written on the bottom of the laptop. What make is it? Samsung? Lenovo? HP?

7:58 AM

@JohnRennie Samsung

NP300E5C

@JohnRennie samsung.com/us/support/owners/product/np300e5c

OK, so that's a 15.6 inch screen and it's quite heavy at 5.07 lb

Do you want a new laptop with the same size screen? Or smaller? Or bigger?

@JohnRennie same size but lighter

@Abcd Ok, so that MacBook wouldn't be ideal because it has a smaller screen.

@JohnRennie how much small in cms?

The screen size is the distance measures along the diagonal e.g. from bottom left to top right.

8:06 AM

oh weird...I thought it's along the rectangle length ...

An A4 sheet of paper is about 14" diagonal. Do you use A4 sizes in India or the US paper sizes?

@JohnRennie Yes we use A4 size

OK so hold a piece of A4 paper over your screen and you'll see the screen is a bit bigger than the paper. In fact it's about 2.5 cm bigger measured along the diagonal.

@JohnRennie Are you considering the microphone as a part of screen

By the screen I mean just the bit that lights up.

8:10 AM

@JohnRennie It's like 3cm bigger sideways (breadth) but smaller in length than the A4 sheet

@Abcd ah yes, OK, the screen aspect ratio is different to A4 i.e. it's a different shape - wider and shorter than A4.

yup

Your screen is 1366 x 768 so the aspect ratio is 1.78

1366 what?

So the width w is about 1.78 times the height h. So $(1.78h)^2 + h^2 = 15.6$

So the height is about 7.6 inches ?

And the width about 13.6 inches?

8:18 AM

1 sec let me convert to cm and check.

@JohnRennie yes

Sorry, for some reason laptop screen sizes are always given in inches. I think it's because the market is dominated by the USA and they don't use metric.

@JohnRennie yes

@Abcd OK. So for a 13 inch screen we have $(1.78h)^2 + h^2 = 13$ giving a height of 6.4 inches and a width of 11.3 inches

16.2 cm by 28.8 cm

@JohnRennie Is that good? I havent tried any more screens so I dont have any idea if that much size is also good or not

@Abcd it isn't really a case of good or bad. Smaller screens make the whole laptop smaller and lighter so it's nicer to carry around. But it also means everything on the screen is smaller. If your eyesight is good then this is probably fine. Lots of people use 13 inch screens and like them.

Bigger screens make the whole laptop bigger and heavier, but with a bigger screen you can either make the text bigger, so it's easier to read, or keep the text the same size and fit more of it on the screen.

@Abcd ideally go to a computer shop and have a look at some laptops so you can see what the different screen sizes look lie.

8:26 AM

@JohnRennie Yes I willl go.

@JohnRennie Just 2 more choices:

This: lenovo.com/in/en/laptops/thinkpad/thinkpad-l-series/…

And this: store.hp.com/in-en/default/…

Please tell how are these.

They are both very nice laptops. The Lenovo has a 14" screen so it's smaller than your current laptop but bigger than the 13" screen on that MacBook we were looking at.

I can't see the screen size for the HP.

Note that the prices of those laptops depend on options like what disk size, what CPU, how much memory, etc.

@JohnRennie Ya I am facing trouble there, Like in hp there are 3 options: 54,49 and 95...Which would be good for me?

The ₹58,799 price of the lenovo is just the starting price.

What I'd suggest is have a look in the shop and decide what screen size and weight you like best. Then come back here and we can talk about which models are best.

@ConstantineBlack so is there any method that confirms chaos @ quantum level?/

@JohnRennie 14 inches, asked them.

8:36 AM

@Abcd OK. The only problem is that you really need to see a 14" screen in real life so you can judge if you like the size.

@JohnRennie Saw this: youtube.com/watch?v=TuFje8_W_fw

I dont like 14 inch... 15.6 is the best.

@Abcd that's a nice way of comparing the sizes.

@JohnRennie yes...

Bigger screens are more like a desktop computer and they are nicer to work one. But a bigger screen means a bigger and heavier laptop and that makes it more hassle to carry around.

Just take a one character wide screen

and scroll a lot

8:41 AM

I actually use a laptop with a 17 inch screen, but i wouldn't recommend that as the really big laptops are ridiculously heavy.

@JohnRennie Yeah, I asked someone and he said there's not much ofcarrying the laptop around in college so weight is not a problem for me

@Abcd but ₹70k is a lot of money. I really recommend going to a shop and looking at some laptops. Then when you've decided what you really like buy it on Amazon where it will be cheaper.

@JohnRennie Ok, thanks!

@Abcd just remember the SSD! :-)

That's the single most important thing!

yep!

9:05 AM

@JohnRennie If you get votes on physics.stackexchange.com/a/121785/123208 it may be because it's been linked here: astronomy.stackexchange.com/a/32269/16685

@PM2Ring ah :-)

@bolbteppa Is there a ressource for the real stress energy tensor of the Polyakov action

wrt $g$ and not $h$

Guessing there might be in topological defect study

@PM2Ring to be honest now that JD appears to have got the message I feel less urgency to post on the Astronomy SE.

Vachaspati does have the NG action of a domain wall

looks a bit weird tho

9:20 AM

@JohnRennie That's fair enough. ;)

user image

the hell is this

Constantine Black

@akhilkrishnan Hey, you should search this out; it is a valid question that- if you are interested in such thinks- can get you a long way. What would it mean to give to you a straight answer of yes or no? I think it's more important to check out reviews or papers such as the one I linked and then use this site for clarifications on certain problems.
Just a final note: it seems that to check quantum chaos you need more info and insight(physical and mathematical) and this makes sense because as I wrote before, you cannot just take the phase space as in classical mechanics. Have fun :)

I guess the most obvious way to do it is $$S[X] = \int d\tau d^nx \delta(x - X(\tau)) \sqrt{g_{\mu\nu}(x)\dot{X}^\mu(\tau)\dot{X}^\nu(\tau)}$$

But that feels like a bit too much integration

I guess I have to recast $\tau$ as a function of $x^0$ or something

I guess mb I can use

DIFFEOMORPHISM INVARIANCE

Just $\tau \to f(\tau)$ with $f = (X^0)^{-1}$

So that I may just integrate over that

Abhas Kumar Sinha

9:41 AM

@JohnRennie you know a gaming Laptop under 80-90k INR with Solid State Disks and having 3-4 USB Ports? (Just Avoid Apple, I find Intel Processors and Windows/Linux OS more interesting than MAC)

Which one you use?

OpenGL 4+ and Vulcan is fine for me

@Slereah what language is that?

@AbhasKumarSinha I don't know that much about the current laptops. They change so fast I can't keep up.

I don't play games so my computers aren't optimised for gaming.

@AbhasKumarSinha it is called mathematics

@AbhasKumarSinha Have you made any progress on the sphere in a cone problem?

Abhas Kumar Sinha

@JohnRennie I'm much into 3D art and 3D rendering, blender, POV Ray and those, so I thought instead of keeping different computers, a single one would work better

@PM2Ring not much, I'm on a holiday, plans for China and Nepal Is there, I'll be resting for few days here... :)

@Slereah thank god you told me, I haven't noticed that....

@AbhasKumarSinha Ok.

9:49 AM

@AbhasKumarSinha a desktop computer will always be better for heavy graphics work. I work mostly on a desktop PC and I use a laptop only when I have to work away from home.

You can drop a mofo i7 into a desktop PC without worrying that it will overheat or draw so much power it overloads the power supply.

@AbhasKumarSinha I don't know what else to tell you!

Abhas Kumar Sinha

@PM2Ring I came up with a very cool formula to find that number of Spheres of unit size that can be stored in given cone...

It's the Nambu-Goto action

if u wish to know what it is

Abhas Kumar Sinha

@JohnRennie that's true, but After an year, I'll have to shift to collage hostel away from home and parents, a PC can be a huge problem here

@Slereah is that related to physics or mathematics?

@PM2Ring Another cool formula to find exact number of sum of primes under a given number from 1 to n

@AbhasKumarSinha See en.wikipedia.org/wiki/Action_(physics)

Abhas Kumar Sinha

9:54 AM

@PM2Ring action $$S = \int L(q, \dot q, t) dt $$ isn't it?

@AbhasKumarSinha Ok, that can be useful. I found a pretty efficient algorithm online for the sum of primes a year or so ago. I've mostly used it for testing programs that generate primes.

@AbhasKumarSinha Yes, action is the time integral of the Lagrangian.

Abhas Kumar Sinha

@PM2Ring here's it, but it's a bit cumbersome, quora.com/…

@Slereah the $h$ stress-energy tensor is the real stress-energy tensor?

@bolbteppa I mean in the worldsheet sure

But not in the target space

submanifold sort of stress energy tensors are all distributions

Abhas Kumar Sinha

@bolbteppa Sir, as in case of circular motion of a object around another one in presence of some force, the Work Done is zero? Isn't it? So, let their be a motion in the form of Spiral such that the object moving in such a path gets at the centre at infinity, so in such case, what should be the work done? Is it infinity, constant or zero?

10:05 AM

Well GSW do a section on strings in curved space-time in ch. 3 and don't talk about the EM tensor of $g_{\mu \nu}$ but do reduce the Polyakov action to a non-linear sigma model if that is useful but I haven't seen anything on this really

Abhas Kumar Sinha

@PM2Ring I wrote that a very long ago in a very undocumented manner, Now, I don't even understand myself what the heck I had written there...

@AbhasKumarSinha I'll have a closer look at it later, but I think the algorithm I found online is more efficient. I can't check right now because I'm on my phone.

@AbhasKumarSinha if the force is tangent to the direction of motion as you have in circular motion then it's zero (dot products), if you have radial motion the work will be non-zero, don't see how you can just guess the answer beyond this

But that summing technique you're using is called inclusion-exclusion. The Möbius mu function is really handy for that. en.wikipedia.org/wiki/M%C3%B6bius_function

e.g. for a 1/r potential you can't even spiral into the center iirc

@Slereah basically if you take $g_{\mu \nu} \neq \eta_{\mu \nu}$ you have an interacting theory and most of the free string theory stuff is gone already, so apart from what GSW do on the beta function I think you're going into new stuff

10:15 AM

@bolbteppa not that new

It's used for cosmic string stress energy tensor

Not all strings are quantum business

Topological defects in the thin'limit

Basically looking for the $g_{\mu \nu}$ EM tensor is like taking the EH action $S \approx - \int m ds - e \int A dx - \frac{1}{16 \pi} \int \sqrt{-g} R d^4 x$ and computing the EFE, the variation of the square root term $ds = \sqrt{-g_{\mu \nu} x^{\mu} x^{\nu}}$ will only contribute to the EM tensor on the right of the EFE's it's basically just like studying EM fields in curved spacetime in a sense the real weirdness is in the $h^{\alpha \beta}$ right?

10:30 AM

Turns out the octionion Lie stuff is more complicated:

"The problem is that the bioctonions, quateroctonions and and octooctonions are not division algebras, so it is a nontrivial matter to define projective planes over them!"

Are bioctonions healthier

Octonions are unhealthy from all that ufc octagoning

10:45 AM

@AbhasKumarSinha I’d be very surprised if the work done was infinite. Considering things really do spiral into the centre

@John Rennie what does baby mandelbrot indicates, does it means homoclinic bifurcation?

@akhilkrishnan I'm afraid I've never heard of a baby mandelbrot

11:00 AM

This Asteroid Has a 1-in-7,000 Chance of Hitting Earth This Fall (~ same chance as getting five 1's in a row in 5 rolls of a dice)

Baby Mandelbrot sets: math.stackexchange.com/questions/51726/… Also known as mini-Mandelbrots. Or Mandelbrats. ;)

@PM2Ring well what does these mini mandelbrots confirm in dynamical systems? ,does they have any role in dynamical systems?

@akhilkrishnan Sorry, I don't know, apart from what the accepted answer says in the linked question. That is, the dynamics in the neighborhood of a mini Mandelbrot are approximately a scaled version of the dynamics of the whole Mandelbrot.

The babies which are centred on the real axis have minimal distortion, compared to those far from the axis. But even those babies must differ from the main "mother" set, since the babies have an "umbilical cord" connecting them to the mother.

11:34 AM

mathpix.com

4

This looks really good

Someone please remind me to make a community ad for it if I haven't posted it in a couple of weeks

2

11:48 AM

OMG! @RyanUnger he ruptured his Achilles' tendon

da raptors definitely have them on the ropes tonight

@JohnRennie ams.org/notices/201208/rtx120801056p.pdf

check out fig. 2

@Slereah :-)

Mithrandir24601

@EmilioPisanty assuming you're still planning on coming to Bristol in August and want to give a talk, would you rather give it in the theoretical physics group or the maths one? (People from both groups sometimes go to both)

apparently the SET of a Nambu Goto cosmic string is given by cambridge.org/mw/academic/subjects/physics/…

let's investigate

@skullpatrol I know

@Mithrandir24601 judging by his work I'd say physicists

@Slereah "Now in paperback, this book is the first comprehensive and coherent introduction to the role of cosmic strings and other topological defects in the universe."

implying this is a good thing

12:05 PM

I have a book on topological defects but it's focused on domain walls

So I just buy this book and a book on monopoles

And I'm all set for every dimension

I meant the paperback part

true

I do like a book I can whack someone with

MTW is pretty good for that

the book does have the SET but no derivation

"Cosmic wiggly string in black hole spacetime"

What is a wiggly string

Does it have a wiggly action

From what I can see of topological defect SET, the proper action does seem to be $$\iint d^p\sigma d^nx \delta^{(n)}(x^\alpha - X^\alpha(\sigma)) \sqrt{\det\left[g_{\mu\nu}(x) \partial_a X^\mu(\sigma) \partial_b X^\nu(\sigma) \right]}$$

Bit of a mouthful

and of course that is a Very Bad SET

Colombeau shenanigans

So that the Lagrangian density is just $$\mathcal{L} = \int d^p\sigma \delta^{(n)}(x^\alpha - X^\alpha(\sigma)) \sqrt{\det\left[g_{\mu\nu}(x) \partial_a X^\mu(\sigma) \partial_b X^\nu(\sigma) \right]}$$

Mithrandir24601

12:30 PM

@RyanUnger that would've been my guess and definitely the case if Mark Dennis' group still existed, although the maths department also have good talks that are relevant to people who aren't just mathematicians, so it's maybe best not assuming anything

12:43 PM

@Slereah why is there a delta function

why can't you just do the integral over x and remove it

problem solved

@RyanUnger Gotta do the variation wrt $g$

As u may recall point particles do have such a delta in their SET

I forgot nonsense like that

point particles are not physical

Well no, but they are mathematical certainly

also ur not a physicist

poor vantage point for deciding physicality!

idk I don't trust anything physicists do with delta functions

I tried finding a Fancy differential geometry version of that but alas it was not to be

But that's probably fine

12:50 PM

not very confident there

Feel free to devise the Proper Action of $p$-branes for GR if you feel like it

it's probably in those deligne books

Is it

I tend to find that string theorists don't seem to care that much about fancy math

it's all coordinates

let's see

Also as @bolbteppa mentionned, string theorists don't rly care about the SET in the target space

Since the metric of the target space isn't dynamic

and gravity is done via strings

I don't think any realistic source in GR uses the NG action

Even topological defects aren't actually $p$-dimensional

just do proper math man

Looking up Deligne

user image

12:58 PM

no I mean like

start working on the penrose inequality or something

shrug

As that one dude said

I am not good enough at math to do math

And not good enough at physics to do experimental physics

I am stuck in the limbo of theoretical physics

« first day (3143 days earlier) ← previous day next day → last day (1789 days later) »

Transcript for

Jun '1913

The h Bar

General chat for Physics SE (physics.stackexchange.com). For M...

join this room
about this room

00:00

06:00

12:00

18:00

all times are UTC

site design / logo © 2024 Stack Exchange Inc; legal

mobile