The h Bar

« first day (3946 days earlier) ← previous day next day → last day (1279 days later) »

Physics Meta

00:36

Please reopen this question per the discussion we had in the comments. The question has the following unique twists: 1.Discussing the number of mirrors: From a physics standpoint will be the exponential increase in mirrors needed per Kelvin increase. I was about to add this to an answer. People h...

2 hours later…

John T.

02:12

Any meteorologists/enthusiasts can elaborate on storm development and different types? How is rotation factored into the creation of stuff like hurricanes or super cells?

also what causes the absence of storms? like droughts are defined as when water stores deplete but what happens to cause the depletion in the first place?

Is this all related to some fundamental concept?

Euler 2

03:04

@JohnRennie ohk

5 hours later…

Slereah

08:25

@BalarkaSen Synge's book on general relativity

It's an exact formula but only insofar as you know the world function $\Omega$

Which isn't really a trivial quantity

You can approximate $\phi$ in terms of the curvature, though

Since derivatives of $\Omega$ will involve the curvature

Korra

08:43

So my line of thinking is $p^μ=m\frac{dx^μ}{dt}$ implies that $m\frac{dx^μ}{dt}$ is unitless in mass dimensions since p and m has the same dimensions

So this should imply that the dimension of $d^4x$ has mass dimension 0

Am I correct?

Or is it -4

Can no one confirm?

@Slereah ?

John Rennie

09:00

> since p and m has the same dimensions

Huh?

Nihar Karve

well in geometrized units momentum and mass do have the same units

ACuriousMind

@JohnRennie if you use c=1, this is true (velocity has mass dimension 0)

@Korra I don't follow your conclusion - p and m have the same mass dimension, and the mass dimension of m is 1 (why do you think we call it "mass dimension"?)

the mass dimension of the volume form $\mathrm{d}^d x$ is $-d$

Nihar Karve

@ACuriousMind (Korra almost certainly meant to write "$\frac{dx^μ}{dt}$ is unitless..." instead of "$m\frac{dx^μ}{dt}$ is unitless...")

ACuriousMind

perhaps (in that case I don't follow the reasoning that the volume element has mass dimension 0) :P

Slereah

09:23

Sometimes I wonder if people try to make their questions more jargon-heavy if they're asking for weird topics

If you ask something weird about causality in GR are you more likely to go all causal structure jargon to do it to be taken seriously

Slereah

10:09

Reading some cutting edge theoretical physics paper arxiv.org/pdf/1208.1043.pdf

ACuriousMind

11:00

@Slereah at least "Have you ever seen the sun in the sky?" is a question I can confidently answer in the positive :P

Balarka Sen

12:00

@Slereah Oh cool

Synge is a name I recognize from math. I didn't know he was a physicist too

Charlie

12:16

Everyone turns to the dark side eventually

ACuriousMind

according to your profile, that would be chemistry

Slereah

Chemists are much more evil than physicists

Charlie

Actually chemistry is officially "the dark arts", physics is "the dark side" :p

rigour and algebra are synonyms to a chemist

Daniel Underwood

12:50

Junior astronomers hate getting put on board update duty, but someone's gotta make sure that stuff is still up there.

Slereah

V. I. Arnol’d, “Kepler’s Second Law and the Topology of Abelian Integrals (According to Newton),”

Is that what Newton was about

ACuriousMind

@DanielUnderwood stars/planets/galaxies is a weird list

aren't galaxies made of stars and planets?

Vincent Thacker

@ACuriousMind I think it means the planets in the Solar System

ACuriousMind

@Slereah at this point "what Newton was about" is a hermeneutic exercise akin to people trying to interpret holy texts :P

Slereah

Newton is a hard read but still understandable

Daniel Underwood

13:09

yeah I took planets to mean planets in the solar system, but I don't know about stars/galaxies. I suppose you could have stars without galaxies, but I feel like stars are part of the definition of galaxy

Though I doubt the comic was intended for that much thought :P

ACuriousMind

13:23

it's xkcd, you never can tell whether the next comic will be a throw-away joke or an actual platformer with a gigantic world filled with easter eggs!

Korra

13:39

@ACuriousMind yes that's a mistake

Physics Meta

Q: What happens when upvoting the automatic comment indicating duplicate?

When flagging a question as a duplicate, a comment appears under that post: "Does this answer your question?..." I have noticed that sometimes this comment has been upvoted. Also I have noticed that the post has been closed as a duplicate after that comment got 5 upvotes, which led me suspect tha...

discussion support comments duplicates up-votes

Korra

@ACuriousMind so the mass dimension is -4 right?

ACuriousMind

yes

Korra

I referred to some notes and saw that length has mass dimensions-1

@ACuriousMind This should certainly mean that $partial^μ×partial_μ$ has mass dimensions -2, right?

ACuriousMind

@Korra no, the derivative has mass dimension 1

because it's an inverse length, conceptually

Korra

13:59

@ACuriousMind Okay, so $partial^μ×partial_μ$ has mass dimensions 2

Right?

ACuriousMind

@Korra it's not that simple - the index position plays a role since the metric tensor has a dimension, too!

but if we work in the convention where the coordinates $\mathrm{d}x^\mu$ have dimension -1, then the metric tensor is dimensionless, and indeed $\partial^\mu\partial_\mu$ ends up having mass dimension 2

maybe I should have mentioned this at the start - there's different conventions for how to attribute mass dimensions to coordinates/the metric tensor, and that can affect everything else - see the discussion here

Korra

@ACuriousMind I know that $p^μ=partial^μ$

ACuriousMind

14:14

yes, then $\partial^\mu\partial_\mu$ (you have to write \partial to get the actual symbol) has mass dimension 2

Korra

Thanks!

For the mathjax tip too

@ACuriousMind I am asking all these questions since I have quizzes to attempt and don't want to go wrong

You don't mind if I ask more in future, right?

ACuriousMind

you can always ask questions here

2 hours later…

Emilio Pisanty

16:00

@rob can I ask you for a sanity check here?

A: Why can't hydrogen and helium fuse?

Hydrogen and helium can briefly bind together to make lithium-5, but this is an extremely unstable nuclide which falls apart instantly (with a half-life of ${\sim}4\times 10^{-22}\:\rm s$) and which actively requires energy to make (i.e. it is an endothermic process, as opposed to how we normally...