Anybody know software to plot 3D plane waves?

hm, I haven't really used Octave before, I'll take a look, thanks

I wonder... if locality can be a special case of nonlocality fulfilling certain constraints

iopscience.iop.org/article/10.1088/1742-6596/701/1/012001/pdf

this paper does not really said much though

This is like the antithesis to Secret's previous video, but if you need a laugh:

Anyone know how to combine these metrics by multiplying them together? $ds_1^2 \otimes ds_2^2= \bigg (\frac{dxdy}{xy}\bigg)\bigg( \frac{dxdy}{y-xy} \bigg)$?

What do you mean multiplying them together? I'm not sure what you're trying to do

I'm trying to combine metrics. I know that you can add two metrics and get another metric

but I want to try multiplying

...why?

I think this combination of two or more metrics it's called the "product metric"

the product metric is the natural metric you get on $M\times N$ for two pseudo-Riemannian manifolds $(M,g_M)$, $(N,g_N)$

it does not involve multiplication :P

and your $\mathrm{d}s_1\otimes\mathrm{d}s_2$ doesn't make any sense either, since the result of tensoring two metrices together would be a (4,0)-tensor, not another metric

oh then I guess I misunderstood what I was reading :P

anyhow all I know is that the two metrics on the RHS are metrics for pseudo-Riemannian manifolds

I see now that $g=g_1 \oplus g_2$

on $M \times N$

$g(X_1+X_2,Y_1+Y_2)=g_1(X_1,Y_1)+g_2(X_2,Y_2)$

$X_i$ and $Y_i$ are elements of the tangent space of $M_i$

sure ($\oplus$ is the notion for the direct sum, which is a product, after all)

(and yes, the people who thought it was a good idea to call something that's both a product and a coproduct a "sum" were definitely confused :P)

lol

so I definitely have $g_1$ and $g_2$ given. Not sure what to do next

say for simplicity $M \times M$, where $M$ is Minkowski in 1+1 dimensions. Then I have $g_1=\frac{dxdy}{xy}$

and $g_2=\frac{dudv}{u-vu}$

well, you should call the coordinates on the second $M$ differently, say $u$ and $v$

okay

then you have coordinates $(x,y,u,v)$ for $M\times M$ and the metric is $g_1\oplus g_2 = (xy)^{-1}\mathrm{d}x\mathrm{d}y + (u-vu)^{-1}\mathrm{d}u\mathrm{d}v$

oh okay

and this would be 4 dimensional?

yup

What does ::this font:: connote?

Sorry, I'm way too young to know the nuances of text speak

::chuckles::

I'm used to using it for descriptions of what the writer is doing

i.e. it's for talking about yourself in the third person

ohhh

Why do I get the feeling you picked this up in an internet cafe or something

or you want to normal order your sentence

:D

Double normal ordering, in case you forgot to do some

@NiharKarve I think it hails from message boards/forums having things like ::smile:: as the code to insert an emoji (way back when not everyone was using a phone with a dedicated keyboard for these things :P) and then people started using it as code for emoting in general

@ACuriousMind :o how old are emojis?

I don't mean the emojis that are now part of Unicode (but that also already started in 2009, apparently), I just mean faces/symbols like that that the bulletin software then rendered as pictures

Ah, that makes sense

I think you can punch out a smiley with ALT+NUM8

Or some single digit numpad key

yeah, that's because they're Unicode now

ALT+NUM is often the combination to directly enter a Unicode code point

Obviously :) is infinitely better

it is!

Why do lots of physicists grads go on to do finance?

the finance markets are essentially statistical systems :P

what types of questions could one ask about the above $M \times M$?

so if you've done a bunch of statistical physics, it's a pretty natural choice of work

touché :P

I feel like I should go through the exercise of verifying that it's indeed a metric

although I more expected this one to be cited at me for that very simplistic explanation :P

hehe

Stuff like "The Big Short" has scared me into believing working there errs on the unethical side

well...I, for one, won't do anything to disabuse you of that notion

can anyone give me a hint on how to derive the EFE from it?

@geocalc33 derive the EFE from what?

the four manifold you helped me define with the product metric

because it's a spacetime right?

Sure. But the EFE don't follow from "having a spacetime"

yeah I have to introduce mass

(also it's not really a spacetime because it has signature (2,2))

how do you figure?

because you added two metrics of signature (1,1)

oh

I thought if I did the product metric of Minkowksi 1,1 with itself it would be a spacetime, my bad :

is there a way to make the signature 3,1? I think 2,2 would be a very weird thing

it says: 2,2 is "ultra hyperbolic" and "unpredictable

Yes, the IVP is ill posed

Did you get that from the square thingy?

yeah, on the wiki article titled spacetime

@FadedGiant Kinda random, but I don't think I've ever heard that many engineers go into the stock market. Is that a thing? I always thought the nice thing about engineering was that the math was basically reliable up to some certain accuracy, and as long as you had some idea where that was you could deal with it consistently. I never got the impression the stock market played nice enough for that same mindset.

@JMac and PDEs are used quite a bit in engineering, right? (which I would have thought is a big factor)

@NiharKarve Yeah they definitely can be, but the good thing is that when you're solving them, if you do it properly the answer is very likely to be "close enough" for whatever system you're looking at. At least for me, the systems we dealt with behaved pretty reliably on the scales we were concerned with. I just would never expect the stock market to behave like heat transfer or stresses or something. Since it's kinda based on people, I wouldn't expect it to be about the same every time.

@Secret thx for sharing! :) think this stuff is deep & a path to the future but agreed, this paper sketchy... there is lots of much better stuff lying around but scattered/ in bits and pieces. EmQm is now a years-long, sizeable contingent/ movement/ research program worldwide, alas almost nobody around here is into it... but that seems the case with lots of other cutting edge stuff too... :(

@van forgive me for asking, I'm just curious to know - how did you get into quantum foundations? I can see you primarily do CS

re stock market: there is an entire field called "financial engineering" and there is a lot of engineering-type work being done in it. its typically more called quant work. one of the basics of the field is that the celebrated black-scholes equation is an analog of heat transfer... much more deep connections between physics + finance leading to field of econophysics but its relatively new 21st cetury stuff...

@NiharKarve hi you are forgiven :) it is a long story, but some of it comes down to a book found as a teenager: cosmic code by heinz pagel. iirc given to me by family as gift. it is a paperback somewhat in the spirit of hawkings brief history of time. ps its vzn

Ugh, naff autocorrect

@vzn I see :)

@NiharKarve your profile says cutting edge ML + robotics etc, music to my ears :)

@vzn "financial engineering" isn't engineering in any traditional sense, which is what I was thinking of. You don't get accredited by an engineering board for studying "Financial engineering". It's really a field in finance, and still deals with things I would consider much less reliable than the traditional use of engineering.

Like, my uncle has an engineering degree, and an MBA, and now does work in investments and stuff. I would trust him with investments because of his MBA, not because of his engineering degree.

it is engineering in a nontraditional sense. it is a new field. it has similarities to electronics + physics & other engineering fields. there is accreditation but not by typical engr boards/ societies. it is a young field and the 2008 crash is a case study of its immaturity.

it is close to software engr.

@vzn The issue is that unlike those fields of engineering, finance doesn't necessarily follow a stable enough set of rules to be considered engineering in any of those senses. You might model it like thermodynamics or something, but that doesn't mean it actually follows laws that are stable like thermodynamics on the engineering scale.

If people in finance could just make more money as reliably as a software engineer designs a program or a team of mechanical engineers design a car, it seems like it would be impossible not to get rich off that field. In theory anyone could implement it the same way and get the same results, and you can't just make resources out of nowhere.

What's the opposite of a normal force called?

Sorry, nevermind.