The h Bar

12:01 AM

@ACuriousMind does an interaction term always mean fields are converting into each other? Or are there different ways they "interact"? In other words, what exactly does "interact" mean?

ACuriousMind

12:35 AM

@StanShunpike Quantum fields don't "convert into each other". What an interaction term does is make the amplitude for processes non-zero where not the same number and type of particles going in as come out. Visually, it's "interaction" because now Feynman diagrams are allowed with vertices, while in a free theory, all graphs are just a bunch of non-intersecting lines.

Sir Cumference

12:47 AM

Am I the only one who thinks Universe should be capitalized?

Or, well, capitalizes it

ACuriousMind

@SirCumference No.

dmckee

Pet peeve: Article title on the lines of "How can [X] tell us about [Y]?" when the author really means "I want to use [X] as a launching point for a discussion about [Y] even though it doesn't really tell us anything at all".

Sir Cumference

K good

HDE 226868

@SirCumference I feel the same way about Solar System.

Sir Cumference

Thank you

Pet peeve of mine

Also when people say "other solar systems" or "other suns"

cough planetary systems cough other stars cough

HDE 226868

12:54 AM

I think there was a question on Astronomy about this.

Result: not quite conclusive.

Sir Cumference

Sadly

matscienceman

could it be "other star systems"? Or is that also technically not correct?

Sir Cumference

@matscienceman Star systems refer to stars orbiting a common center of mass

Planetary systems are the contents surrounding them

matscienceman

Thanks

Is there a general term for both? To incorporate both planetary systems and star systems?

Sir Cumference

Unfortunately, not

And even more confusing: the Solar System includes the Sun and its planetary system

It isn't just the planetary system

Wrap your mind around that

matscienceman

1:05 AM

:)

user54412

@ACuriousMind Haha. So basically capitalizing makes you look like a contemporary of Newton.

dmckee

@0celo7 Nothing really. I started to give a mangled history of the later watering down controversy, but realized that I did not know of what I typed.

I's a fine and drinkable bourbon. Enjoy.

matscienceman

I thought they were already beginning to capitalize the universe - I mean, some guy is "selling" real-estate on the moon.

Sir Cumference

OH!

Danu

1:39 AM

1

Q: Up and Down Voting a Moderator

Do moderators know when you are down or up voting all their answers? Is it anonymity for all?

Sir Cumference

What kind of question is that?

Danu

This got me thinking: What if you consistently, strongly, feel that some user's posts are bad or detrimental to the site so that a large chunk (say, >50%) of the posts "deserve" (according to your arbitrary criteria) a downvote.

Sir Cumference

It'll be seen as suspicious and you're the majority of your votes will be automatically undone

Danu

1. Should acting accordingly be allowed? 2. If yes, then it's kind of funny that, if you go through a bunch of the relevant posts in a row (say 10+) and downvote most of them, your votes will be reversed. 3. Is "working around" the problem (2.) allowed or not?

Sir Cumference

By the system

Danu

1:41 AM

^No need to tell me the basic workings of the site ;)

Sir Cumference

Oh crud, just saw your rep XD

Danu

heyo @MikeMiller

ACuriousMind

14

Q: Downvoting serial answers without serial downvoting

In the past days I've encountered a particular user who has made a "serial answering": he has answered several different (even uncorrelated) question with almost the same answer and the same sketches. The problem is that some things in those answer are misleading, and some others plainly wrong. ...

discussion down-votes

Sir Cumference

Forget what I said

Danu

@SirCumference I'm also a moderator.

Sir Cumference

1:42 AM

Oh...

Mike Miller

@Danu: I hVe the same problem on MSE

Sir Cumference

Well, er, sorrry....

Danu

@ACuriousMind Right, I forgot about that one.

@SirCumference No need to apologize!

@MikeMiller Yeah, I imagine it's way worse over there!!

ACuriousMind

In particular, I guess dmckee answers your question quite directly:

> I'd also like to add that the policy of voting the content and not the user is usually interpreted as implying that you should not single out a single user for down-votes. If you find yourself using the "all actions" tab in another user's profile to hunt down post to dislike you are straying into the dark side.

Danu

@ACuriousMind Hmm... "straying into the dark side" is still fairly ambiguous but yes, that's probably the closest to an answer one can get.

Mike Miller

1:47 AM

In practice I just downvote the questions when they show up which is when I see them

it's not my fault that their questions are always bad.

Danu

hahaha

Let's hope not ;)

dmckee

Mind you, that leaves a common situation without a good suggestion.

Danu

@dmckee Do you think you can come up with a more explicit answer?

dmckee

What if you and the (wholly hypothetical, I'm sure) serial bad poster both spend a lot of time in one (or a few related) tag?

Danu

^lol

nail on the head

dmckee

1:51 AM

@Danu Nah. I think it is an outstanding issue with the Stack Exchange system.

Danu

@dmckee I guess...

Mike Miller

Where's the issue?

Danu

Perhaps one has to make such a small sacrifice to have many other nice things.

@MikeMiller What if you see so many posts by the relevant user(s) that your "downvote as I see them" is actually fast enough to qualify as "serial"?

2

Mike Miller

@Danu: I suppose that's an issue. I don't personally use the site in such a way that this is possible - I rarely ever look at postd older than, say, 3 days ago. Which means I don't downvote someone more times than they post in a day, which unless they're posting a lot of wuesfions can't qualify.

ACuriousMind

@Danu Well, unfortunately, data for how often that situation actually occurs is inaccessible to us. We just don't know the algorithm for detecting serial voting.

Danu

1:58 AM

Like I said, I suppose it's a sacrifice for the greater good.

Mike Miller

I'm still not sure what the sacrifice is. The risk of having your downvotes invalidated?

I would probBly also be a serial close voter, I think.

Danu

@MikeMiller The impossibility of resolving this small issue.

user54412

@Danu So what if I go through a tag and vote (up and down) on essentially every question and answer?

user54412

I've done this before (while retagging the astronomy imports), and I've considered doing it again.

user54412

I'm sure that will result in me consistently upvoting some users and consistently downvoting others.

dmckee

2:37 AM

@ChrisWhite Part of the answer is that if you are reading all those posts it will (on average) spread the votes you apply to any one user out in time.

Of course we don't know the details, but rumor has it that intervals play as big a part as raw numbers, and I would conjecture that votes given to other users may also factor in somehow.

Slereah

3:26 AM

Hello

"In the past days I've encountered a particular user who has made a "serial answering": he has answered several different (even uncorrelated) question with almost the same answer and the same sketches. The problem is that some things in those answer are misleading, and some others plainly wrong. "

I wonder who that could be!

0celo7

@Slereah did you play AC Brotherhood

Slereah

which one was that

0celo7

right after 2

Slereah

Oh, Assassin Creed 2 and a half : Faffing About

Yes

Sir Cumference

Howdy

0celo7

3:42 AM

UBISOFT

Slereah

Ah yes

Falling through the floor

The oldest bug in 3D gaming

It's been 20 years since that bug has existed and nobody has any solution to fix it

It still happens

0celo7

Landed in some water

Final quest is fucked

Sigh

Slereah

I think it's due to rounding errors

that's what you get for using floats

0celo7

4:00 AM

SHOTS FIRED

0celo7

4:36 AM

And the award for most confusing ending in any video game ever goes to...

Slereah

5:54 AM

@0celo7 : Not even close

0celo7

6:23 AM

@Slereah o

what's the most confusing then

Slereah

Hm

Antichamber is pretty confusing all throughout, I'd say

0celo7

weird god/alien thing telepathically forcing you to stab your friend is p. strange

Slereah

but then again it's an artsy game

0celo7

mainstream

Slereah

What about Mario 2

0celo7

6:24 AM

I'm sure some crazy indy person could make a shit ending

Slereah

IT WAS ALL A DREAAAM

0celo7

It Was All A Dream- Biggie Smalls

►

Slereah

Oh

Sanitarium was hella confusing

Oh, and what about the ending of Half Life

0celo7

haven't completed that one

Slereah

You kill the big boss, and then the accountant comes around to talk your ear off about the cosmos

0celo7

6:26 AM

DUDE

LITERALLY PLAYING

STOP IT

Slereah

Well mb play it faster???

It's been out for like 20 years

I might as well spoil the Lion King

(MUFASA DIES)

0celo7

I just got a machine that can run it dude

Slereah

what did you have before, a ZX Spectrum?

0celo7

@Slereah you piece of

@Slereah Mid 2009 MacBook Pro

Slereah

Oh right, the macs

Why would you buy a mac

Mac has no games

0celo7

6:28 AM

Half Life is on Mac

All Valve games are

in any case, I'm going to bed now

the next Assassin's Creed crashed

don't want to bother with that now

Ezio got OLD

it's only been 4 years since the last one

Slereah

Too much assassinatin'

0celo7

he does kill a LOT of people

Stan Shunpike

I am confused about this Lagrangian $\mathcal{L} = \mathcal{L}_{\mathrm{field}} + \mathcal{L}_{\mathrm{int}} = - \frac{1}{4 \mu_0} F^{\alpha \beta} F_{\alpha \beta} - A_{\alpha} J^{\alpha}$

I don't understand what the Lagrangian is telling me.

What exactly about the field does it help me understand?

Slereah

Well same as all lagrangians

Using the usual methods you can find the field dynamics and the conserved quantities

Just from inspecting though you can tell the first term is a kinetic term while the second one is a source term

(or interaction term, depending on your perspective)

Generally you can tell a few things by just looking at a lagrangian

Stan Shunpike

6:47 AM

@Slereah what does kinetic mean? When I think kinetic, I think of a particle moving. What does a classical field do with its kinetic energy?

Slereah

it corresponds to the energy associated with the free propagation of the field

Stan Shunpike

Are we talking about light?

As in light propagating?

Slereah

more generally than that

That's the lagrangian of electromagnetic fields, though, so it is light propagation here, yes

Stan Shunpike

So by "source" does that mean where the field interacts with itself?

Physics Meta

0

Q: Answer your own question - worked examples

The question: Trajectory of projectile launched from planet's surface raises an interesting issue. The SE system allows for Answer your own question posts as a sort of mini-blog way of posting interesting information. I think this is a good thing and I've used it several times myself. However h...

discussion

Slereah

7:00 AM

No

The source of the EM field is a current

Stan Shunpike

@Slereah what kind of current?

Slereah

you know, an electric current

Charged particles

Stan Shunpike

But I thought we were talking about light...

Slereah

You can generate light with oscillating currents, yes

Stan Shunpike

7:17 AM

Ok that explains a lot. So the source term generates the field then? In this case, the field being electromagnetic radiation? Is that true for all sources/interactions?

Slereah

You can have source-free EM radiation

Those are the fields that obey the vacuum Maxwell equation

$\Box A_\mu = 0$

Stan Shunpike

7:29 AM

@Slereah cool! That was very helpful. Thanks a lot!

Sir Cumference

8:26 AM

@HDE226868 Oh my god, I just realized. You're the star in Cygnus X-1.

Mind = blown

*near

Tell me I'm the first to realize it?

Secret

8:54 AM

@ACuriousMind
I am not sure...
The question was inspired from my electromagnetism lesson 1 back in my 2nd year, where the professor was revising very briefly about vector calculus.

He begins with a question by simply writing a tuple (4 6 7) and ask us whether this is a vector

He then explains that (4 6 7) is not necessary a vector, because e.g. (4 6 7) can represent 4 apples, 6 oranges and 7 bananas in a barrel, and this will obviously not change when you rotate your view. He then explains that to be a vector it has to obey a transformation rule

Secret

Perhaps, another way to phrase the question is, if we wrote an n-tuple, must it always represent a rank 1 tensor (vector or linear functional)?

Bass

10:22 AM

@Secret an n-tuple is something else than a n-vector. You can write what you want in an n-tuple, but for the n-tuple to be a vector or tensor, it must transform accordingly. Nobody prevents you from writing $(p_x,\mathcal L, g_{xx})$ in a tuple, but this 3-tuple is neither a vector nor a tuple of scalars.

Huy

10:36 AM

@Bass: if I can put a vector space structure on 3-tuples of that kind, why shouldn't I be allowed to call it a vector?

Stan Shunpike

@0celo7 how does one prove maxwells equations are consistent with SR?

Bass

@Huy how does it transform when you rotate in that new vector space structure?

Huy

@Bass: I don't care but why should that be important for something to be called a vector space?

@StanShunpike: check out the covariant version of Maxwell which is obviously invariant under Lorentz

Stan Shunpike

@Huy smarrrrt ;)

@0celo7 @Huy yeah, but I know that version is Lorentz invariant. Griffiths however says in his book that Maxwell's equations in vector calc form will allow us to predict the motions of stuff in a way that's invariant, although what one considers a magnetic field in one frame may be an electric field in another. I wanted to prove that the vector calculus Maxwell's equations have these properties Griffith is describing

Bass

11:05 AM

@Huy this is a matter of definitions. You're talking about the algebraist's definition of a vector. Of course, anything that can be added and scaled is an algebraist's vector. There are other definitions, as you are surely aware of. If I ask you, what is an axial vector, what would you answer?

Physics Meta

0

Q: Editing Rejections and Penalty Time

How many times can your edits on another persons question be rejected before it's disabled? How long is the penalty?

discussion support editing

Huy

@Bass: that I've never heard of that before, unfortunately

Bass

11:54 AM

@Huy the physicists define an axial vector (or pseudovector) as a "thing" that transforms as a vector under rotations, but reverses it's sign under a reflection (for example the angular velocity or magnetic field vectors). AFAIK mathematically they are defined as $1$-forms (vectors) or $(n-1)$-forms (pseudovectors), because in metric spaces there are canonical isomorphisms between $T_pM$, $T^*_pM\simeq\Lambda^1M$ and $\Lambda^{n-1}M$.

(please correct me if that doesn't make sense)

David Z

Sounds about right, but I'm no expert

Secret

I understand that you are allowed to put any mathematical object or arbitrary symbols as elements of a tuple. But I am wondering whether in the literature there are examples of these n-tuples that represents meaningful quantities because as far I have looked, they either describe tensors (vectors and one forms) or pseudotensors (e.g. The axial vector that is mentioned)

If someone wrote an n tuple wuthout any further description, is it the only infomation we can learn from it is that the elements of the n tuple form an ordered set?

Bass

@Secret Strictly speaking yes, but notation almost always needs context. If someone writes $p_x$, this could be the momentum's $x$ component, or the probability that the event $x$ occurs, or something else. However, in a physics book about classical or quantum mechanics, it most likely denotes the $x$ component of the momentum. Similarly, if you see an $n$-tuple in a physics book, chances are high that it's meant as a vector

Huy

@Bass who on Earth writes $p_x$ for the probability that an event $x$ occurs?

Secret

12:10 PM

I see

Bass

@Huy not me :P I was just searching for a simple example that shows that you cannot expect mathematical notation to tell you everything. You almost always need context. If you have a better example, appreciated :)

Huy

of course you always need context but that $p_x$ as prob. of event $x$ was a bit unusual. :P

I think "test function" would be a good example since I often find myself confused what space of functions I'm looking at now

Secret

P.S. For statisticians, they wrote probability as P(event x)

Huy

and the funny thing about it is that some people even write $S(R^n)$ what normally would be the Schwartz space, but what they mean is just compactly supported smooth functions

Bass

I think I have seen $P(X)$ and $P_X$ for the probability of event $X$. Not sure where tho

David Z

12:21 PM

Pretty sure I've seen both those as well.

I think in some cases I've seen $p(X)$ and maybe even $p_X$, but that would be quite rare.

Secret

12:45 PM

(Double check my understanding of the term "Geometric meaning" as used in physics) Given an arbitrary set S (or more generally a mathematical object M). We say that M has a geometric meaning if under some kind of transformation, the new components of M is a relation of the old components of M i.e. $$M'=r(M)$$ For example the christoffel symbols in the levi citva connection obeys $$\Gamma^{\alpha '}_{\beta ' \gamma '}=\frac{\partial}{\partial}-\frac{\partial}{\partial}\frac{\partial}{\partial}$‌$?

PS it is hell to type partials on a phone!

Bass

@Secret I'm not sure if "geometric meaning" is something that is defined strictly. The one definition that makes sense for me is in the sense of "intrinsic geometric meaning". Things that appear in one coordinates set but not in another are no intrinsically geometric objects, they are artifacts of the set of coordinates.

The Christoffels are such an example. For cartesian coordinates, they vanish, but not for polar coordinates, so they are no intrinsic property of Euclidean space. Examples of intrinsic geometric objects are the scalar curvature, the metric tensor, the Ricci, Riemann, Einstein, Weyl tensors etc

Secret

1:18 PM

Having been reminded by Acuriousmind, Slereah and others on how we cannot always visualise things. I then tried to understand the physics via the equations.

But then in the context of geometric meaning, I then get a bit confused because as you mentioned, it does not seemed to have a strict definition

Because knowing that I cannot visualise everything in physics, I want to better understand the criteria for a mathematical formulation to have a geometric meaning but the examples I have seen so far are either tensors or exterior algebra related entities

e.g. $$\mathbf{T}=T^{a'b'c'd'}_{e'f'g'h'}e^{e'}\otimes \cdots \otimes e_{h'}=T^{abcd}_{efgh}e^{e}\otimes \cdots \otimes e_{h}$$

Bass

I don't understand what you're looking for. What is your exact definition of "geometric meaning"?

Secret

Another example are metrics such as the squared interval in special relativity $$ds^2=-dt^2+\sum_idx_i^2$$ general relativity texts often say these are geometric entities

Therefore I am wondering what does these thing have in common with tensors and exterior algebra objects that make them have a geometric meaning (that is they can exist as coordinate free objects)?

Or in other words, if we work with these objects by just manipulate them purely algebraically (e.g. expanding them, grouping them etc.) what is the 'thing' that pops out that told us the object we are dealing with is a geometric object and hence has a geometric meaning?

that is, how do we know a mathematical object or formulation M used in a model has a geometric meaning if all that is available are expression that came out after doing some algebra on/with M?

Slereah

1:33 PM

In math geometry is basically the notion of a topological space associated with a metric function

David Z

Hey, maybe I can recruit the chat's help with something. I'm trying to expand my answer to this question:

4

Q: Hanging chain in a planet's gravitational field

The curve for a chain hanging between two poles in a uniform gravitational field is known as the catenary. Is there known an expression for the curve of a hanging chain on a planet of mass $M$ which has a gravitational field of $M/r^2$ ? Let the rope have length $L$, uniform mass-density $\rho$...

newtonian-gravity lagrangian-formalism statics variational-principle

to include a solution to the differential equation

$$(r'' r - r'^2)(r_\ell + r) = r(r'^2 + r^2)$$

where $r$ is a function of an angle $\phi$ and $r_\ell$ is a parameter that can be adjusted to fit initial conditions

From Mathematica, I get a solution with two constants of integration

$$r = \frac{4r_\ell^2K^4}{i\sqrt{K^2}(-4 + 4K^2 + r_\ell^2K^2)\cos\varphi + 4r_\ell K^2(1 - K^2) \pm \sqrt{K^2}(4 - 4K^2 + r_\ell^2K^2)\sin\varphi}$$

where $\varphi = K(\phi - \phi_0)$, and $K$ and $\phi_0$ are the constants of integration. I think either can be an arbitrary complex number, as far as the math is concerned, anyway. But it's a lot easier for them to be real, so I restricted myself to looking at the case where both are real numbers.

In that case the solution reduces to

$$r = \frac{2K}{\sqrt{1 - K^2} \pm \sin[K(\phi - \phi_0)]}$$

The problem: this is supposed to represent the shape of a chain in a gravitational field, where we have two boundary conditions, namely the radii of the endpoints $r(0)$ and $r(\Delta)$, as well as the total length of the chain $L$. The solution has to be fit to those three conditions. How is it possible to do so with only two parameters?

Is this a sign that I do have to consider complex values of $K$ and $\phi_0$ that happen to produce real $r$?

Another problem: the solution isn't dimensionally consistent ;-) because of terms like $4 - 4 K^2 + r_\ell K^2$. I'm not quite sure what to make of that...

I can work around it by formulating the equation in terms of a "reduced $r$", namely $r/r_\ell$, but it still seems strange that Mathematica would produce a dimensionally inconsistent solution in the first place.

Secret

3:00 PM

Shouldn't the equation be $$(r'' r - r'^2)(GM\lambda + lr) = lr(r'^2 + r^2)$$

Thus if you divide both sides by l then you obtain $$(r'' r - r'^2)(\frac{GM\lambda}{l} + r) = r(r'^2 + r^2)$$

Thus you get $$r_\ell=\frac{GM\lambda}{l}$$

Since $l$ arise from the constraint that the rope has to be of length L, won't $r_\ell$ be the parameter that has to satisfy this, thus leaving only the two boundary conditions $r(0)$ and $r(\Delta)$ to be fit by K and $\phi_0$?

0celo7

@StanShunpike I was just wondering about that the other day

I don't know

mb ask a question on the main site

Danu

4:21 PM

0

Q: quantum physics

Find the dependence of the energy levels of the system parameter s (formula and schedule) for the Hamiltonian $H(s)=(1-s) H_0+sH_f$ $$ H_0=1/2- 1/2σ_z+0.1\cdot σ_x$$ $$H_f=1/2 +1/2σ_z$$

quantum-mechanics homework-and-exercises hamiltonian

@DanielSank

"quantum physics"

@DavidZ +1 for coming back to it (almost 5 years later!) ;D

David Z

@Secret hm, well... $l$ is an arbitrary constant times the length of the rope, but I don't think it's actually set by the length of the rope. But anyway: you're basically saying we have three free parameters, $r_\ell$, $K$, and $\phi_0$, and three conditions which determine them, $r(0)$, $r(\Delta)$, and the length of the rope $L$. But there's also the condition that $r$ has to be real for all $\phi$.

@Danu I was prompted by a comment on reddit. Someone suggested that this problem has never been solved.

I don't know if that's true, of course

Danu

@DavidZ Hmm..

Can you ping me about this sometime soon?

I might be interesting in looking at it

but will be having a goodbye party in an hour or so

(leaving Amsterdam again..)

David Z

@Danu sure, I suppose so

Mike Miller

Oh, because of that bounty I can't downvote.

Danu

@MikeMiller Hmm?

Mike Miller

4:34 PM

@Danu: I bountied my instanton question, so don't have enough rep to downvote bad Phys.SE questions.

David Z

@MikeMiller ah. Well if you post a few good answers to things, that should resolve itself shortly.

Mike Miller

I'll have to wait until I see some questions that really should be migrated :)

David Z

lol, fair enough

Although there are always questions coming in that only need basic physics to answer. That being said, it is sometimes hard to tell when they are destined to be closed as homework-like, if you're not quite familiar with the genre.

Danu

@MikeMiller Oh... You bountied it again?

Mike Miller

No, just the first time

which removed my association bonus

Danu

4:41 PM

Oh, right.

Mike Miller

@DavidZ: More to the point I don't want to encourage such questions too much, just like you don't

David Z

Yeah, I get that

Bass

6:12 PM

@Secret The Lorentz metric is a (0,2) tensor on a manifold. I don't think there is an answer that satisfies you. The mathematician's understanding of "geometric meaning" is that it is an intrinsic property of the space and not some artifact of our way to look at the space (eg coordinates).

There are many connections from geometry to algebra. Imagine a table surface. If you use some length measure to draw a 2D grid and label the left-bottom corner as the "origin", you get a correspondence between the algebraic object $\mathbb R^2$ and your table surface. This makes it possible to calculate things algebraically that would be difficult in pure geometry.

We do not "know" that the maths have geometric meaning. We give the math a geometric meaning by setting up a correspondence like coordinates.

3