The h Bar

Jack

00:11

Can someone help at physics.stackexchange.com/questions/244084/… it's about current mesh equations (circuits)... should be an easy question...

ACuriousMind

@Jack No. Please have a look at our homework policy, such questions are off-topic here.

Kyle Kanos

@ACuriousMind Well that sucks :\

ACuriousMind

Hey, @KyleKanos :)

Kyle Kanos

Hi

ACuriousMind

How have you been?

Kyle Kanos

00:24

Pretty good

You?

ACuriousMind

All is well

Kyle Kanos

Are you Germans ready for a President Trump?

ACuriousMind

We have our own political issues going on, I think most are not too focused on that currently

Kyle Kanos

Oh yeah, ZeroHedge said something about Merkel getting spanked in the elections

ACuriousMind

Well, the recent elections were not federal electrion, so although many like to interpret them as some sort of judgement of the current government, it's not really clear how much this was really about Merkel's politics

The rapid rise of a new authoritarian and in parts nationalist party is generating heated debates nonetheless

Kyle Kanos

00:34

So is the pinned message from DavidZ indicative to the devolution of chat since my inability to regularly attend (not indicating that me leaving made a difference, just that I never noticed chat was bad or something whilst here)

ACuriousMind

It's kinda gotten worse, yes :P

Kyle Kanos

I bet 1 USD that I'd have made it worse :\

ACuriousMind

Not sure about that, but I'll refrain from assigning blame, anyway

Kyle Kanos

Well following the paper trail, it seems to stem from arguments with Duffy and we all know how much I enjoyed him.

And why are the queues so dang full all the time!?

ACuriousMind

@KyleKanos Now that's a good question

The...signal to noise ratio is steadily getting worse, imo

0celo7

00:41

@DeNiSkA a little

Kyle Kanos

Obviously there's some people stopping reviewing (or at least are reviewing so sparsely that i don't even notice)

0celo7

@ACuriousMind A lot of new people have joined

@Slereah I figured out who the Gerard is

It's not ol' 't

Kyle Kanos

Gerard Butler?

0celo7

What?

ACuriousMind

@KyleKanos Is that so? I couldn't point to any specific user I see less frequently in the reviews

0celo7

00:43

I bought a used book that has an inscription from one of the authors to his (now dead) colleague. Apparently his estate is selling his library.

Kyle Kanos

@ACuriousMind Some people just hit skip instead of trying to actually vote

There's >20 questions in the queue & they only vote on 3

0celo7

::feels bad because never votes::

Kyle Kanos

And then there's the guys who insist on voting to leave open everything

0celo7

holy fuck 50 questions in the queue

Kyle Kanos

@0celo7 Vote dammit!

0celo7

00:45

@KyleKanos sorry

ACuriousMind

@KyleKanos Yeah, but that was always the case, wasn't it?

Kyle Kanos

ACuriousMind

I really feel we get more low quality content lately :/

Kyle Kanos

@ACuriousMind Possibly.

0celo7

@ACuriousMind I wanted to do a Q&A on something...

I've now forgotten what it was

ACuriousMind

00:46

Abstract indices.

0celo7

Oh, proving that the light cone is a null hypersurface. Is that on-topic?

@ACuriousMind Lol

I really should do that, but it was already massive

and I didn't even get to indices

I basically need to post the first chapter of a differential topology text :D

1 min ago, by 0celo7

Oh, proving that the light cone is a null hypersurface. Is that on-topic?

Kyle Kanos

Names I'm seeing frequently: ACM, me, ChrisWhite, JohnRennie, Gert, user36790, BillN, CuriousOne & rob. And one of those guys is voting to leave just about everything open

ACuriousMind

@0celo7 I'd say so, as it seems that's usually not explicitly done anywhere, right?

Kyle Kanos

9 users out of about 200 users with sufficient rep to vote :/

And you wonder why Duffy keeps saying "It's the same people voting to close questions?" Because no one else is stepping up

0celo7

@ACuriousMind At least that I can find, but we know how (terrible) my googling skills are

amazon.com/Lorentzian-Geometry-Edition-Chapman-Mathematics/dp/…

Found that on the first page of my copy.

I take it "Paul" is the second author and "Gerard" is the first guy in the "acknowledgements" section.

ACuriousMind

00:51

@KyleKanos Hm, you're right. Danu only does it infrequently, Jim vanished some months ago, Martin also seems to vote almost never now...it could really just be that we were barely operating at the necessary amount of reviewers and are now below it

Kyle Kanos

I definitely think we're below threshold

0celo7

::votes::

ACuriousMind

@KyleKanos Yeah, but I tended to think that it's because we get more stuff to vote on, now I'm not so sure anymore

0celo7

Wow, no one cares about the thing in my book

Kyle Kanos

There's a lot of good <3k'ers doing good jobs because there are some low-quality questions hitting the queues with no votes on them.

@0celo7 More pressing matters

ACuriousMind

00:54

@0celo7 I'm kind of shocked one would sell a book with such a personal notice in it

0celo7

@ACuriousMind "Gerard" died in 2013.

ACuriousMind

Still, his heirs apparently didn't care about it...or never knew it was signed, I guess

0celo7

The book is otherwise in perfect condition.

It had some sticky stuff on the cover, but that came off with some cleaning solution.

ACuriousMind

tmi

0celo7

@ACuriousMind Sticky stuff has never been too much for you before

Kyle Kanos

01:00

You guys are a little creepy at times

0celo7

Just a little, right?

Kyle Kanos

Yes

0celo7

Ok, that's fine.

Ok, I have voted.

user54412

One day, I want to find whatever place in the world uses Latin characters but is entirely oblivious as to how punctuation works, where spaces around commas are determined by a coin flip at each occurrence, and where one is not only allowed but encouraged to insert newlines in the middle of sentences so as to maximally break the flow of the writing. This place must exist, since it sources so many of our posts.

6

0celo7

It's called American High School.

@Slereah lel, this book says "see Hawking and Ellis"

It's not possible to write a GR book without referencing HE

ACuriousMind

01:04

Mar 24 '15 at 13:55, by Jimnosperm

I can not understand how people are so terrible at punctuation.why do so many people not put a space after a period or a comma ? they have spaces between other words.and then,those same people sometimes put a space before and after a question mark or some other punctuation mark .it's so arbitrary.but seriously , where does this come from ?It's not like there is ever any time where a period that ends a sentence doesn't follow with a space.why are they so lazy ?

@ChrisWhite ^still my favourite post about that phenomenon

Kyle Kanos

@0celo7 Come back in 24 hours to vote 20 times again

So what happened to Jim?

user54412

@KyleKanos for Trump?

0celo7

Froze, probably.

Trump gets me excited in a special way.

ACuriousMind

@KyleKanos He...just disappeared :(

0celo7

@Slereah I think I need Penrose's book too

ACuriousMind

01:06

Or, rather, just never came here again

user54412

6 mins ago, by ACuriousMind

tmi

Kyle Kanos

@ChrisWhite For him too.

0celo7

I have a book fetish, halp

ACuriousMind

@0celo7 Don't get it on your book again.

Kyle Kanos

@ACuriousMind Hmm. I'm going to have to find him

0celo7

01:06

@ACuriousMind Sticky like from a sticker, you perv.

Kyle Kanos

We did a round of interviews back in January. You would not believe the shoddy resumes people turned in :/

0celo7

@ACuriousMind Have you heard of a "topological hypersurface" before?

ACuriousMind

no

0celo7

@Slereah Ok, once I have O'Neil, Penrose and Choquet-Bruhat, I will have all of the GR books.

Kyle Kanos

@0celo7 One is enough

0celo7

01:09

No, it really isn't.

Kyle Kanos

Okay, 2 is enough

ACuriousMind

@0celo7 Nerd.

0celo7

@ACuriousMind Define nerd.

@KyleKanos Maybe. I think you could go a long way with HE and Straumann.

Kyle Kanos

@0celo7 I'm pretty sure Franklin's all I need.

0celo7

Can you prove that the null cone is a null hypersurface using theorems in Franklin?

Kyle Kanos

01:11

Probably not because it's stupid

0celo7

...what is wrong with you

ACuriousMind

@0celo7 The beauty of that word is that it defies definition ;)

Kyle Kanos

@0celo7 Probably nothing, why?

0celo7

@ACuriousMind Do you know what a Lipschitz continuous manifold looks like, heuristically?

ACuriousMind

@0celo7 I don't even know what a "Lipschitz continuous manifold" is formally, why are you asking me these weird questions?

Kyle Kanos

01:12

0celo7

@KyleKanos You don't appreciate the finer points of differential topology?

Kyle Kanos

Is coming in November

@0celo7 I guess not

0celo7

@ACuriousMind A manifold where the transitions functions are Lipschitz continuous, probably!

user54412

That's even weaker than a C^1 manifold

0celo7

yes.

but stronger than $C^0$

user54412

01:14

seems like the sort of weird thing Slereah would like

Kyle Kanos

I was about to ask who Slereah was, then i remembered

0celo7

the weirdo

Kyle Kanos

And @0celo7 ruined the spacing of my message :/

0celo7

what

Kyle Kanos

What what?

ACuriousMind

01:17

At least he didn't say "Huh?" :P

Kyle Kanos

And now no one's even trying to figure out what the message was :(

0celo7

@KyleKanos Not falling for it

Kyle Kanos

@0celo7 Well then

ACuriousMind

I'll bite

0celo7

ACM likes to play rough like that

ACuriousMind

01:20

What thing related to the number 5 is coming in November?

Kyle Kanos

Well what do I have four of?

ACuriousMind

Oooooh

0celo7

Cars?

ACuriousMind

Congratulations, I guess

Kyle Kanos

@0celo7 I hate you

@ACuriousMind Thank you!

0celo7

01:22

TVs?

Kyle Kanos

@0celo7 Stop being so superficial

0celo7

@KyleKanos wtf a car is much better than a kid

Kyle Kanos

@0celo7 No

ACuriousMind

@0celo7 Xou're such a romantic

user54412

So is "#5" the name? :p

0celo7

01:23

@ACuriousMind So I've been told

Kyle Kanos

@ChrisWhite For now

0celo7

@KyleKanos Dunno, got a car today, I'm much happier than if it were a kid :P

Kyle Kanos

@0celo7 Because you're like 18

user54412

Girl? Her friends can call her Chanel?

0celo7

Wow

Kyle Kanos

01:24

Well it's too early to find out yet, but we tend to wait until birth to find out genders

@ChrisWhite Took me a minute :(

ACuriousMind

And here I thought number 5 was a robot

0celo7

why am I reading HE?

I flipped to this random page and started reading

Kyle Kanos

@0celo7 Because you're bored?

0celo7

@KyleKanos No, I was going to prove something

Kyle Kanos

Oh yeah, null hypersurfaces or something

0celo7

01:27

ah, yes, danke

First I need to find some pathological spacetime where the null cone is not $C^1$

Kyle Kanos

Do you have Alzheimers?

0celo7

Yes.

Kyle Kanos

Okay, that explains the lack of remembering what you're doing

I spent 2 hours in a meeting about how to fill out a document that has instructions on how to fill it out

ACuriousMind

Sounds like a worthwhile use of your time

Kyle Kanos

Yep. And no coffee. Or water

ACuriousMind

01:30

You had to suck the ink from the pens for nourishment?

0celo7

@ACuriousMind What notation do you use for Lipschitz continuity

Kyle Kanos

@ACuriousMind No. I had to listen

ACuriousMind

@0celo7 I don't use any notation for it

0celo7

@ACuriousMind huh

@ACuriousMind Ah. A Lipschitz manifold is a manifold with a pointy part.

Makes sense, the point of the null cone is pointy.

Hmm, isn't that a conifold? Or something?

Kyle Kanos

There's not enough Fortran users on CodeReview

ACuriousMind

01:35

Is there anyone except you?

Kyle Kanos

There's one other guy who answers questions, but there's like 8 people who've asked questions

user54412

... in the world? ;)

Kyle Kanos

There's Steve Lionel

And Arjen Markus

So there's at least 2. I've kinda been forced to move off Fortran & use C++

ACuriousMind

So...you can name all the Fortran users by name? Not a good sign, I'd say :D

2

Kyle Kanos

@ACuriousMind There's some on SO that I'm aware of too: High Performance Mark, MSB, Alexander Vogt

0celo7

01:45

@ChrisWhite is the correct term for the set of future directed null geodesics from a point the null cone or light cone

Kyle Kanos

190

A: Reputation cut down by 100

I'm the one responsible for your loss of reputation. I originally came across this now deleted question to which you responded with a useless, snarky answer: $9999 will be the minimum cost. You could ask Mr.Google if you want more details. I flagged your answer as "rude", which it was. If y...

> Unfortunately, "rude" flags from moderators carry an instant 100 point reputation loss, which I felt was justified in this case.

Wow

Did not know that

Apparently happens with 6 spam votes.

ACuriousMind

@KyleKanos What, that spam and offensive flags carry that penalty, or that mods can cast those on their own?

user54412

@0celo7 I read "null" and "light" interchangeably

Kyle Kanos

@ACuriousMind Both. Wasn't aware

I don't spam, so I'm not really aware of the penalty

And the spammers I do see tend to have 1 rep anyway

0celo7

@ChrisWhite according to Wald, the light cone is the set of timelike and null vectors in $T_pM$ and the null cone is its exponential map

ACuriousMind

01:48

@ChrisWhite You would say something like "The first beams of sunnull hit my face"?!

Kyle Kanos

@ACuriousMind You don't?

0celo7

Stupid question: why do we call the exponential map the exponential map

Kyle Kanos

Because that's its name?

0celo7

@KyleKanos The one from Riemannian geometry

not the one $\exp z=\mathrm{e}^z$.

Kyle Kanos

@0celo7 I'm (vaguely) aware

0celo7

01:50

Does it have to do with Lie groups?

ACuriousMind

@0celo7 Because it fulfills $f' = f$.

Kyle Kanos

Let $v ∈ T_pM$ be a tangent vector to the manifold at $p$. Then there is a unique geodesic $γ_v$ satisfying $γ_v(0) = p$ with initial tangent vector $γ′_v(0) = v$. The corresponding exponential map is defined by $\exp_p(v) = γ_v(1)$.

So there's an exponential in its definition

Or something

0celo7

huh?

Kyle Kanos

That's a copy-pasta of Wikipedia

0celo7

@ACuriousMind um, what are you differentiating wrt. there

Kyle Kanos

01:51

Because I'm not quite as lazy as you

0celo7

@KyleKanos I know what the definition is, you ass

ACuriousMind

@KyleKanos No, that's the definition of $\exp$, which is defined by the $\gamma_v$ on the r.h.s.$

Kyle Kanos

@ACuriousMind There is an exponential there, that's all I cared about

0celo7

sigh...

Kyle Kanos

@0celo7 So you'd be aware of the exponential in the name?

Which is what I said

We call the exponential map the exponential map because that's its name.

user54412

01:53

@ACuriousMind do you prefer incandescent nullbulbs or null-emitting diodes?

ACuriousMind

@ChrisWhite I like the nullbulbs :)

@0celo7 Levi-Civita connection

0celo7

@ACuriousMind uhhh

now I'm very confused

ACuriousMind

Then everything is normal, I guess ;)

0celo7

oh come on

Kyle Kanos

The only useful variables to differentiate with respect to are price, volatility, interest rate and time

0celo7

01:58

@ACuriousMind ...

7

Q: Riemannian geometry: ...Why is it called 'Exponential' map?

The exponential map $exp_{p}:T_{p}M \to M$ given a suitable $v \in T_{p}M$, returns $p$, displaced along the geodesic uniquely determined by $(p,v) \in TM$ for unit "time". So, what does the above have to do with the familiar concept/s of exponentiation? Why does this map carry this name?

this is confusing to me as well

Kyle Kanos

Me too because it's a bad link

Looks like it's mapping reals to a circle.

0celo7

what does that have to do with $f'=f$

I don't know what ACM was talking about

Kyle Kanos

Well isn't the derivative of the exponential also the exponential?

0celo7

yes

it doesn't make sense to take the derivative of the exponential map and have it equal the exponential map

Kyle Kanos

IDK.

And I'm going to bed now

Goodnight all

0celo7

02:02

bye

Kyle Kanos

@0celo7 Don't forget:

0celo7

Meh.

@ACuriousMind Ok apparently if you use a bi-invariant Riemannian metric on a matrix Lie group, then the Riemannian exponential agrees with the matrix exponential

but I want to understand your comment

ACuriousMind

Yes, the exponential of Lie groups is the Matrix exponential. That's because the exponential map is always defined as the solution to $f' = f$ (if you understand that suitably), and in every case where the usual power series makes sense, it solves that equation.

0celo7

Ok so you were talking about Lie groups?

ACuriousMind

No, the "idea" of $f'=f$ is always there, the Riemannian geometers did not choose that name at random.

0celo7

02:09

where the heck is $f'=f$ in Riemannian geometry

@ACuriousMind I'm not trying to be obtuse, I don't see it

ACuriousMind

I am trying to be obtuse, though. Think about it.

0celo7

@ACuriousMind is $'$ supposed to be the differential

0celo7

02:33

@ACuriousMind can you at least tell me what the $'$ is supposed to be, I can figure out the rest

I've looked in about 5 books now, none of them talk about it

@ACuriousMind Ok even Milnor says it's just because of Lie groups

So no one sees what you're talking about :/

ACuriousMind

You know, this would be a nice question for History of Science and Mathematics: How did the exponential map of Riemannian geometry get its name?

With that, good night.

0celo7

03:39

0

Q: How did the exponential map of Riemannian geometry get its name?

I've read in several books, including Milnor's Morse Theory and Petersen's Riemannian Geometry that the exponential map in Riemannian geometry is named so because it agrees with the exponential map in Lie theory, at least for a certain choice of metric on the Lie group. Is this the real reason ...

mathematics differential-geometry riemannian-geometry

Secret

04:26

-2

Q: How Do Low Kenitic Energy and High Kinetic Energy Atoms Attraction differ?

Will atoms of 2 difrent energy levels electron and/or Kinetic attract more than 2 Atoms at he same energy level? Do 2 high energy level atoms attract more than 2 low energy atoms?

electromagnetism gravity energy kinematics subatomic

I cannot give an exact answer to this question because (unless it is hydrogen molecule) anything else goes into chemistry territory as we deal with electronic wave functions (in its simplification, molecular orbitals)

Secret

04:47

https://www.sciencedaily.com/releases/2016/03/160314111131.htm

Seems these guy got the idea from LIGO..?

John Rennie

06:16

@ACuriousMind The reason I like the Physics SE is (possibly misguided) notion I can do some good - help people enjoy physics as much as I do. But right now it isn't a fun place to be. On the one hand we have John Duffield and Jokela Turbine doing their best to stamp their own idiosyncratic views on the site ...

... and on the other we have an endless stream of one rep users who are only interested in getting someone else to do their work for them. I still dutifully go through the review queues, but now it's all close, close, delete, delete - not fun at all.

So when I see a question from someone who I think is genuinely interested, if a bit hapless, and I can see a way to turn it into something interesting and informative then I'm going to grab it with both hands.

And I don't apologise for that.

@Secret yes it's chemistry really, and specifically excimer chemistry. but then I started out as a chemist and I've always found this a fascinating area.

Danu

10:16

@KyleKanos I think CuriousOne should see this :P

@ACuriousMind I just don't have energy to seriously engage the VTC queue these days.

...but I'll take a crack at it now

Danu

10:36

Why are there so many old questions (2013 and earlier) in the queue?

ACuriousMind

@JohnRennie I don't begrudge you that. And I'm not saying you shouldn't have answered that. But the question just doesn't make sense to me, neither syntactical nor semantic. You seem to have somehow divined what the asker was after - when you do that, could you edit the question so it becomes intellegible to the rest of us?

Danu

Indeed, @JohnRennie I think you could be more active in editing questions---and don't be afraid of changing them too much.

Physics Meta

11:03

0

Q: Resource recomendation - very specfic topic?

Let us say that I want source of information that gives worked examples for a very specific topic (let us call it X). I have access to a (pretty good) library and have searched both this and the world wide web endlessly for some examples - to no avail. Clearly what I am after can not be found by ...

discussion

John Rennie

@Danu I'm generally reluctant to modify a question beyond correcting typos because it would annoy me intensely if someone did that to one of my questions. However I frequently regard my answer as a sort of exegesis, so the combination of the question and my answer makes sense.

Secret

11:21

http://www.math.washington.edu/~grunbaum/Starshapedpolyhedron.pdf

Interesting shape

List of unsolved problems in physics

Some of the major unsolved problems in physics are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result. The others are experimental, meaning that there is a difficulty in creating an experiment to test a proposed theory or investigate a phenomenon in greater detail. == Unsolved problems by subfield == The following is a list of unsolved problems grouped into broad area of physics. === General Physics/Quantum Physics === Entropy (arrow of time) Why did the universe have such low entropy in the past, resulting in th...

"Locality
Are there non-local phenomena in quantum physics? If they exist, are non-local phenomena limited to the entanglement revealed in the violations of the Bell inequalities, or can information and conserved quantities also move in a non-local way? Under what circumstances are non-local phenomena observed? What does the existence or absence of non-local phenomena imply about the fundamental structure of spacetime? How does this relate to quantum entanglement? How does this elucidate the proper interpretation of the fundamental nature of quantum physics?"

ACuriousMind

@Secret That's not an "unsolved problem" so much as a problem of language. For every precise definition of "non-local" that question can easily be answered by examining the formalism of quantum mechanics. All the confusion about "locality" is because people play word games with it instead of defining what exactly they mean.

Secret

I see.
One reason I like quantum mechanics is because it helps me to grasp this concept

for example, nonlocality can be observed in entanglement and also in your example mentioned around a few weeks ago when a wavefunction collapses

PS I should have use > to made that into a block quote so as not to be confused with asking a question ,lol

List of unsolved problems in philosophy

This is a list of some of the major unsolved problems in philosophy. Clearly, unsolved philosophical problems exist in the lay sense (e.g. "What is the meaning of life?", "Where did we come from?", "What is reality?", etc.). However, professional philosophers generally accord serious philosophical problems specific names or questions, which indicate a particular method of attack or line of reasoning. As a result, broad and untenable topics become manageable. It would therefore be beyond the scope of this article to categorize "life" (and similar vague categories) as an unsolved philosophical problem...

> What is art

List of unsolved problems in economics

This is a list of some of the major unsolved problems, puzzles, or questions in neoclassical economics. Some of these are theoretical in origin and some of them concern the inability of orthodox economic theory to explain an empirical observation. == Behavioral economics == Revealed preference: Does Revealed Preference theory truly reveal consumer preference when the consumer is able to afford all of the available options? For example, if a consumer is confronted with three goods and they can afford to purchase all three (A, B, and C) and they choose to first purchase A, then C, and then B - does...

> Why the economic regression cycle became more frequent

List of unsolved problems in linguistics

This article discusses currently unsolved problems in linguistics. Some of the issues below are commonly recognized as unsolved problems; i.e. it is generally agreed that no solution is known. Others may be described as controversies; i.e. although there is no common agreement about the answer, there are established schools of thought that believe they have a correct answer. == Concepts == Is there a universal definition of word? Is there a universal definition of sentence? Are there any universal grammatical categories? Can the elements contained in words (morphemes) and the elements contained...

> What makes a word, a word

List of unsolved problems in information theory

This article lists some unsolved problems in information theory which are separated into source coding and channel coding. There are also related unsolved problems in philosophy. == Channel coding == Capacity of a network: The capacity of a general wireless network is not known. There are some specific cases for which the capacity is known, such as the AWGN channel and fading channel. Capacity of the broadcast channel: The capacity of the broadcast channel, or the case in which a single transmitter is sending information to many receivers is unknown in general, though it is known for seve...

Suprisingly few compared to others

Originally, I was almost planning to ask MSE the question "Is there exist a physical phenomeonon which is impossible to be comprehend because all possible routes to analyse it by inference, deduction, logic etc. lead to the halting problem, thus undecidable", and then this question was then kinda of answered when I saw the hightlighted example

Should I have found this out a bit later, people will be seeing the following in MSE (using my extremely limited capability in writing mathematical formalisms...)

> Define a physical phenomenon to be an element $x \in R$ where R is the set of all realisable physical phenomenon such that

$\{\forall x \in R : \text{x satisfy all known equations of physics}\}$

Define the set of all human knowledge as $H$

Define interpretation as the map $I : R \rightarrow H$

Question: Is there exists $x \in R$ such that

$$I(x)\equiv \halting problem$$

and thus the value is undecidable?

END QUOTE

correction: "all known" should be "at least one"

ACuriousMind

11:56

@Secret Once again, you're not really making sense. When you write down mathematical objects, their definitions have to mean something. What the hell is the "set of human knowledge"? What does "$x$ satisfy all known equations of physics" mean? What is the "set of all realisable physical phenomenon"?

Secret

I am not sure about the others (they are themselves incredibly vague concepts), but for "satisfy at least one known equation of physics", one can rigourously defined it as when you making a substitution of this object x (I am not sure what type of math object is this, except that it has to be a subset or something) into these equations (be it EFE, or navier stokes, or schrodinger equation, then you satisfy the equation

in the sense similar to how you can verify something is a solution of an equation

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