The h Bar

peterh

01:24

@Real I agree. If we would be around 10 times more, it had probably a significant chance

@Real The main problem with the current system, that it creates continous conflicts and sick directives (f.e. closing and later deleting interesting exercises), while it is not really attractive for research level members.

David Z

@Real We've tried that before. It was a rather spectacular failure.

@Ulthran What @DanielSank said, and also, learn math. Being very comfortable with calculus is a huge advantage. If you do go into physics as a career, then later on you will have the chance to specialize somewhere on the spectrum between theoretical and experimental physics. For theory, you need to know math very well, and for experiment, you need to be good with tinkering.

2physics

01:40

I have a question about the papers on arxive.org website, I wanna now if they publish any paper? Are their published papers peer reviewed? and if people can refer to its papers?

anybody can help?

0celo7

@2physics are you the guy with the grandpa

2physics

@0celo7 what do you mean?

@0celo7 I don't know.. maybe I'm the grandpa :D does it make difference?

0celo7

perhaps.

did you make a post about your grandpa

2physics

no

why did you ask?

0celo7

01:58

clearly someone was asking about their grandfather

2physics

@0celo7 okay, it was not me.

@0celo7 both of my grandpas have passed away.

@0celo7 can I ask a question related to the nuclear physics here?

0celo7

yes

We do not guarantee you will get an answer

or that if you do, it is correct

2physics

alright, I haven't searched it yet btw.

when the electron is in its wave form, what makes it bounded(didn't find a better word! lol) to the nucleus?

if you want to explain it to a high school guy, how'd you do that?

0celo7

02:19

Dunno, I'm not a physicist

2physics

@0celo7 thanks.

DanielSank

02:33

@DavidZ FWIW being good at math makes experiment a lot easier too.

0celo7

@2physics np

@ACuriousMind I took a 3x3 determinant correctly oh I'm so happy

Ulthran

@Ocelo7 Now try a 5x5

0celo7

@Ulthran I'm not in high school, so no.

Ulthran

@Ocelo7 :P Is that so useless it can only be done in high school?

0celo7

yes

currently doing quantum mechanics homework

Ulthran

02:44

Currently on my 15th hour of stoichiometry... So... Much... Fun...

0celo7

to be fair I use stoichiometry a lot at work

Ulthran

What do you do?

0celo7

undergrad research

Ulthran

Chemistry?

0celo7

solid state physics

Ulthran

02:46

Ah

I would imagine it's a bit more fun when you're doing it as a means to an end rather than just doing questions 1-99a-z though

0celo7

it's not fun

and it's one calculation

then you make the thing

Secret

I just figure out possibly the simplest proof that division by zero will collapse any algebraic structure it is present in:

Suppose we have a set with elements a,e and closed under @. Given two axioms 1) a finite sequence of e@e@e=a and 2) e is an identity under @. Then by closure a@a=e or a@a=a

However note that by axiom 1, a@a=e@...@e@a. Then by repeatly using axiom 2 we get a@a=a. Thus if a is not at least a neutral element of a we have a contradiction. Moreover by using axiom 1 twice a@a=e@...@e@...@e. Using axiom 2, we get a@a=e

Therefore a@a=e=a. Thus the set has only one element e QED

Shing

03:09

I am almost driven crazy, it took me so long, but I still can't figure it out how to install numpy into my python

Secret

What is numpy?

0celo7

something that rhymes with lumpy

Shing

03:49

@Secret a package in Python to do linear algebra/scientific computation

Noah P

06:45

chat.stackexchange.com/transcript/message/31873112#31873112 Aww @JohnRennie

alarge

07:16

@2physics arXiv is a preprint website, so most things there have either been submitted or already published in a peer reviewed journal. You can cite papers off of arXiv, but typically you'd cite the version that got published (but in some fields the review process may take too long).

@Shing If you're on Windows, the easiest way forward is to probably use Anaconda or some other Python distribution. On other platforms the problem doesn't really exist.

@BernardMeurer How about checking out the courses on Coursera, edX or Khan Academy, and if you're not into watching videos, see what books they recommend.

John Rennie

@NoahP :-)

@SirCumference: you don't need calculus to analyse linear motion in special relativity. However you do need calculus to understand accelerated motion. Even if you are only interested in linear motion, understanding the (very simple) differential geometry that describes SR will make a huge difference to your understanding of SR.

But unless you're 0celo7 and doing screwy calculations for fun, only a basic understanding of calculus is needed to understand SR well.

John Rennie

08:02

@NoahP BTW I passed the info about Crest on to my brother, and it's something the school already does. He mentioned there's a similar scheme his school does called Headstart - I don't know if you've ever come across that one.

Noah P

08:21

@JohnRennie I've heard of them, but I don't think our school offers them

@JohnRennie @DavidZ Do we call this homework?

0

Q: How to prove my mathematical induction that a pendulum follows SHM?

Could someone please tell me how I can prove that a pendulum is following SHM. I know the differential equation and the angle I used is 20 degrees. It is also fine if the proof or conjecture is by lagrangian mechanics. Thanks.

mathematical-physics

John Rennie

I'd close as insufficient prior research, though I've given the OP a chance to respond.

Noah P

Okay

@JohnRennie When a magnet attracts a metallic ball, would I be correct in saying that the energy is drawn from the magnetic field and transferred to KE of the ball?

John Rennie

It's not as simple as that.

If you consider an isolated system there is an energy stored in the magnetic field. For example if the isolated magnet was an electromagnet you would need to put electrical power in to create the magnetic field.

However when you have two objects the total energy is a property of the system and can't easily be pinned down to any single object.

Noah P

But would the introduction of a steel ball then reduce the magnetic potential of the magnet and increase its own?

And then the MPE of the steel ball is transferred to KE as they are attracted?

John Rennie

08:36

Not necessarily. I don't see any reason why the presence of the unmagnetised ball should have any large effect on the magnetic field.

Noah P

So when it is attracted to the magnet, where on earth is that energy coming from?

There must be some sort of negligible effect?

John Rennie

Potential energy doesn't have an absolute value. It looks as if we must be getting energy from nowhere as the ball falls in, but that's only because the absolute value of the potential energy isn't defined.

Noah P

Okay

John Rennie

The way to look at this is to consider a cycle involving letting the ball fall in, then taking it back out to it's original position.

Noah P

That makes alot more sense

0

Q: Does a magnet create energy?

I know what i am asking is not possible , but the scenario what i am pondering over I cannot explain. So let's assume their is a huge magnet subtending from the top of the burj khalifa (Tallest building, Dubai). The magnet is so powerful it can pull objects from the ground below. I keep a series ...

electromagnetism

See the first comment; completely non-sensical IMO

John Rennie

08:43

If you find you can get a net amount of energy out there's obviously a problem because you'd have non-conservation of energy.

But as long as the net energy change balances out to zero there's nothing to worry about.

Noah P

@JohnRennie You call that a problem? I call it a miracle, and a solution

John Rennie

If it's any consolation I remember getting very puzzled about exactly this point as an undergraduate. It seemed to me that there must be negative energies involved, which i found most disturbing.

Noah P

::shudders::

Secret

0

Q: Prove, give counterexample or show trivial conclusion of the existence of mathematical objects with empty sentences?

Recall in classical logic a sentence $\phi$ is a boolean valued statement that may be true or false (To narrow down the scope, we restrict ourselves such that the empty string has its usual properties being an identity element wrt concatenation). Then $\phi(M)$ is a statement about some mathemati...

proof-writing formal-languages

My experience told me that I have to be careful not to let any of my questions closed. Because my questions are generally too weird that once closed the chance for them to reopen is close to zero no matter the edits

Put it in another way, once the question is closed, people will have an excuse to no bother about it anymore because there is too much weirdness to resolve in order to make the question meaningful

I am kinda glad this phenomenon is less common in my experience in PSE because physics have restrict the number of possibilities of me asking weird things

Another phenomenon is that generally, even if an edit is done to the question to clarify concerns raised in the comments, most people generally don't retract their close votes. Therefore, my philosophy is that you must get the question right before it attract the first close vote as once that happens, you are done and it will be closed

Noah P

09:03

@Secret Completely agree with that

See the comments of this question:physics.stackexchange.com/questions/269040/…

Secret

To me, most of the time, if a quesion is closed it is the same as the community saying the following:

"This question is not interesting, and we don't fucking care whether you will elaborate that to us because we don't bother to understand"

Noah P

I think that's a little harsh @Secret

Secret

well, maybe that's only for a few cases where the comments are not being read by the users. I have seen couple of examples where there are no response when the OPs ask for clarification in the comments and try to fix their questions

for PSE, this phenomenon is more common in the homework like questions

The good news is that at least for PSE, based on the latest correlation data DavidZ collected, close votes are not strongly correlated to interest, thus when we finally fix that homework like closing reason, there is a way to improve the situation

David Z

09:58

@NoahP eh, I wouldn't, but I would consider it unclear

@Secret I might have goofed up that analysis a bit - I fixed some issues with it and the interest correlation came back, though not as strong as before. Anyway, I'm currently working on a meta post with details.

Secret

ok

Emilio Pisanty

11:16

@JohnRennie Can I ask what this was?

Emilio Pisanty

11:29

It looks relatively close to the money to me, though there's still some way to go in firming it up.

John Rennie

11:46

@EmilioPisanty We were having yet another ~~argument~~ constructive discussion about the homework policy and Daniel challenged me to provide a definitive description of the current policy. That was my attempt. I left it deleted so that only the high rep users would see it.

But Daniel doesn't agree with that policy, ACuriousMind seems ambivalent and DavidZ says it's pointless anyway as the idea is to eliminate the term homework from the policy.

As of right now I have absolutely no idea what any changes are intended to achieve. That answer is the way I think things should work, but I seem to be in a minority of one.

Emilio Pisanty

12:04

@JohnRennie That's a grand state of affairs.

John Duffield

@NoahP : it isn't. You do work when you pull the magnet and the ball apart. In similar vein you do work when you lift the ball. It's all fairly straightforward stuff, see my answer. The books always balance.

2physics

@alarge thanks. so, since some of the submitted papers may be rejected by the referees of peer reviewed journals , therefore we can't cite the papers on arXive I mean we better not to use them as references. right?

Noah P

12:18

@JohnDuffield Answer looks good, but what if I had two steel balls at a distance, and then I instantaneously magnetised one? Then theres no work done in moving them apart (I see they your answer addresses this, but the comment I replied to did not)

John Rennie

@EmilioPisanty Tell me about it :-(

alarge

12:41

@2physics Sure you can use them as references. Peer review is no guarantee of correctness either. If the paper did get rejected, it'll probably be resubmitted to some other journals until it goes through.

2physics

@alarge yeah, you're right.. thank you for your answer & help.

ACuriousMind

@peterh This is the exact definition of a link-only answer. Why would you click "Looks OK"?

It's fine as a comment, but it is not an answer unless it summarizes the actual answer to the question in at least one sentence.

2physics

@alarge and a more general question, what is the criterion for a paper/research to be used as a reference for future works? something that most researchers, referees and journals accept.

ACuriousMind

@2physics Uh...a reference is a reference. You put it in because it is relevant to what you wrote, or you even cited it. How would anyone be able to "reject" that?

0celo7

@ACuriousMind wait did you just recommend closing an Urs post!??

Noah P

12:52

0

Q: How can the universe expand if there is gravitation?

We live in an expanding universe - so I'm told. But how can that be possible? Everything imaginable is attracted by a bigger thing. So, why can't gravitation stop the expansion of the universe? I know the "Big Bang" theory, but is it possible that the expansion of the universe is caused by the at...

cosmology universe space-expansion big-bang

@JohnRennie surprised that you touched that with a barge pole

ACuriousMind

@0celo7 We don't close answers, but yes. No exceptions to the rules.

0celo7

@ACuriousMind you know what I meant.

2physics

@ACuriousMind I mean at least it should've been reviewed by some other researchers , isn't it?

ACuriousMind

@2physics Surely it will look better if you have a peer-reviewed reference.

If you can only find viXra papers to support your claims, you'll have a hard time :P

0celo7

viXra is legitimate @ACuriousMind

ACuriousMind

12:55

But I don't think there are hard rules against citing e.g. a preprint before it is actually reviewed/published

Though it may depend on the journal you yourself want to publish in

2physics

@ACuriousMind I don't know how to explain my question, I want to know if arxive papers are trustworthy to be used as references? because I've seen some papers/researched published in there which have been falsified/rejected by other researches/papers/reasonings which have been published there on arxive too!

researches*

ACuriousMind

arXiv is...pretty trustworthy, although you can certainly find some nonsense on there. I think if you cite something, you should be competent enough in the field to judge whether it is trustworthy or not yourself. If for some specific paper you're not sure, ask someone you trust who is.

2physics

@ACuriousMind ok thanks. you know, you read sth there and think yea it's a good idea and then after a while you find out oops somebody has questioned the idea and has rejected it with some acceptable reasons which you didn't care before.

0celo7

@ACuriousMind how do you take your eggs? Steak?

What cut of beef is your favorite

ACuriousMind

@2physics Well, that's the way science goes, no? That some proposals may have been wrong or shown to be irrelevant doesn't make them "untrustworthy"

Finding out if someone later pointed out issues with something you find interesting is just due diligence in research

But you can also have that with published peer-reviewed articles

Peer-review is no guarantee for correctness, especially not for papers that are inherently speculative

@0celo7 Yes, I take my eggs as steak ;)

@0celo7 A large cut

John Duffield

13:09

@NoahP : imagine the ball you magnetize is so much bigger than the other ball that you can't see it moving. Focus on the other ball, the little ball. It now moves faster towards the big ball. More of its mass energy is converted into kinetic energy. After it hits, this kinetic energy is dissipated, and the little ball is left with more of a mass deficit.

Noah P

@JohnDuffield Sure, I get that, but I felt his comment didnt mean that

0celo7

@ACuriousMind cmon

@ACuriousMind do you not know what I mean?

John Duffield

@NoahP : OK noted. No probs.

ACuriousMind

@0celo7 I do

0celo7

Filet, sirloin, prime rib, etc

ACuriousMind

13:10

I just like messing with you :P

0celo7

I hadn't noticed

ACuriousMind

@0celo7 I'm not sure I unequivocally prefer one over the other

0celo7

Flank steak?

Porterhouse, New York strip?

ACuriousMind

@0celo7 I'm also not really familiar with all the English names for the parts

For instance, if I eat steak, it's rather often labeled as "rumpsteak" here, but it appears an American might call that sirloin

John Rennie

Actually I think it's a fair question, and it touches on an important principle in GR. A solution to Einstein's equation isn't some space that then evolves backwards or forwards in time, the solution is a **spacetime**. That is, it is a 4D function of spacetime that exists for all values of $t$ as well as $x$, $y$ and $z$. This is why you'll hear people (like me!) saying time doesn't *flow* in GR.

So when we solve the equations to get the FLRW metric we end up with an object that is expanding infinitely fast at $t=0$ i.e. $\dot{a}/a \rightarrow \infty$ as $t \rightarrow 0$. So asking why t…

0celo7

13:18

@ACuriousMind I know what a rump steak is

Noah P

@JohnRennie I mean that I'm surprised you're not still traumatised

0celo7

I don't know what a New York strip is in German

Jim

@NoahP I agree with John, it was an easy question with a simple answer. And we've seen much more traumatising questions

John Rennie

@NoahP Like I said, I think it's actually a perceptive question.

Noah P

@Jim I've provided some myself, hence the comment

@JohnRennie Yes - did you see my suggested edit? It was rejected, but I still think it would be helpful

Jim

13:21

@NoahP Are you the reason I have PTSD now?

Noah P

@Jim I had some particularly irritating questions on dark energy and the friedmann equation, so possibly

ACuriousMind

@0celo7 No, Wikipedia indicates that what's called a rumpsteak here is actually a different part of the cow than what's called a rumpsteak in America

Jim

@NoahP no, if you know enough to reference the friedmann equations, it won't be trauumatising

2physics

@ACuriousMind True, but it seems some referees think that just published works are trustworthy. one has asked me why didn't you mentioned this and that in your references! ..you know somebody doesn't care about "correctness" they just care about what may others think about them if they accept this paper/idea for publishing. I don't understand how sb can comment on judge sth that doesn't know enough about it.

Noah P

@Jim If you ask @JohnRennie about it, you'll get what I mean

Jim

13:23

official questions or chat questions?

ACuriousMind

@2physics I'm not sure I follow you.

Did they say your references were bad or did they just suggest including more things in your references?

Those are two totally different things

Noah P

@Jim Both

ACuriousMind

I'm also not sure how you jumped to the conclusion that someone here "only cares about what others may think"

Noah P

It was a set of problems I was completing

2physics

@ACuriousMind both, and quite irrelevant questions

ACuriousMind

13:26

Getting all judgemental because someone said something you don't agree with is usually not a constructive course of action.

@2physics Have a look on Academia, there are a few questions over there about referees asking to include irrelevant references, iirc

2physics

@ACuriousMind not here, I'm talking about people who accept to judge papers

Jim

@NoahP I read the official ones. They were good mostly. Traumatising questions are like "If nothing can escape a black hole, how can the Big Bang exist? Doesn't that mean scientists must be wrong?"

Secret

@ACuriousMind I knew if I had a structure $K=(S,\cdot)$ where $S$ is a set and $\cdot$ is a binary operation which obeys closure, then $K$ is a magma. But what if I have a structure $R=(S,@,*)$ where $*$ and $@$ are binary operators does the algebraic structure of $R$ has a term to refer to it?

Noah P

@Jim The way they expanded in chat and the time they took was traumatic

ACuriousMind

@2physics ...I meant "here" as "in this situation", I know you aren't talking about people in this chat. Sorry, that might have been badly phrased.

Jim

13:27

@NoahP Also yes

peterh

@ACuriousMind Because - although it is link-only - it seemed very HQ, and what it only needs that somebody copies the essential part of 8.3 into the answer. Anyways, the link rotting problem has only a quite small chance in the case of the Arxiv. We can say, I decided in the spirit of the rules and not in their literal sense.

0celo7

@ACuriousMind I thought you said it was a sirloin

ACuriousMind

@Secret I don't think there's a unique name for that. I remember someone joking it should be called a "rg", since some call rings without identity "rngs", and this would be a ring without identity and negatives.

Secret

ok

Noah P

It amuses me that the accepted answer is different to the answer that John Duffield awarded his bounty to on this question: physics.stackexchange.com/questions/251385/…

ACuriousMind

13:30

@0celo7 After reading a bit, I'm now just baffled how much disagreement there seems to be over the partitioning of a cow.

0celo7

@ACuriousMind If a question wants me to "describe the topology" induced by a basis, can I draw a picture?

ACuriousMind

@0celo7 Uh...probably?

0celo7

how do I actually answer the question

2physics

@ACuriousMind you know when journal staff ask you to judge a paper, if you don't know enough about the issue , you shouldn't accept to do that. but sb doesn't care and comment on everything . that's what I mean.

ACuriousMind

I mean, there's no unique way to answer that question, if you think your best description is a picture, then draw one

0celo7

13:31

I could not give an $\epsilon$-$\delta$ proof of what subspace topologies you get on a line embedded in $\Bbb R^2$ with various topologies

I actually do not know how to do it

2physics

@ACuriousMind ok thanks

ACuriousMind

@2physics Yeah, I'm saying you shouldn't directly jump to conclusions like "this reviewer doesn't know enough about the issue" just because they said something you disagree with.

You can think it, but it's not constructive to directly tell that to everyone

0celo7

@ACuriousMind lol

yuggib

@ACuriousMind because they assume the axiom of choice

0celo7

Oh my god

there's a choice maniac in my analysis course

he's asked like three times if what we're doing assumes AoC

yuggib

13:34

the Banach-Tarski paradox on cow partitioning

0celo7

the prof clearly does not give a shit

ACuriousMind

@peterh Most link-only answers only need someone to copy over the essential parts. The whole point of marking them as link-only answers and recommending deletion is to get someone to do it!

2physics

@ACuriousMind sure. It was just a complaining. :D

0celo7

Yeah, riddle me that mathematicians

how come I can't get infinite steak if AoC is true

@ACuriousMind QM homework wants me to assign "physical meaning" to

ACuriousMind

uh

0celo7

13:38

I'm pretty sure this is a spin-1 matrix, but we have not covered that.

ACuriousMind

Yeah, it looks like the matrix representation of a spin operator for spin 1

0celo7

Don't know about that $1/\sqrt 2$

We haven't talked about spin other than 1/2 thus far

ACuriousMind

@yuggib If accepting the axiom of choice gives us the ability to make two cows' worth of beef out of one, then I think you just gave the ultimate argument for accepting the axiom of choice :D

yuggib

@0celo7 just double steak

0celo7

@ACuriousMind e.g. Witten would be unconvinced

ACuriousMind

13:40

@0celo7 That's just a normalization factor

0celo7

@ACuriousMind clearly

yuggib

@ACuriousMind exactly

0celo7

but still, am I just supposed to dream up spin 1 operator?

ACuriousMind

@0celo7 Why not, you seem to dream up differential geometry with no problem? :D

0celo7

@ACuriousMind speaking of that, I do not understand the proof I was searching for in my dream when I read it yesterday evening. I had another nightmare about it

ACuriousMind

13:41

@0celo7 I'm sure we can try to apply Banach-Tarski to tofu

0celo7

I have to fit geodesic balls into small places

ACuriousMind

@0celo7 Why do you call these "nightmares", actually? Haven't you got any actual nightmares?

0celo7

These are my nightmares

ACuriousMind

I'd take failing at some proof over being chased by a horde of nondescript but terrifying entities every day :P

yuggib

@0celo7 He's just being thorough

0celo7

13:43

@yuggib no, because he's always been wrong

yuggib

anyways if you were wondering, C is necessary also for nonstandard analysis

Jim

In the last 90 days, there were at least 71 questions closed due to insufficient effort. This does not include homework-like questions, questions closed as unclear, or anything else. Only those where someone has specifically closed a question using a custom reason that includes "insufficient effort" in the comment. 71. In 90 days. If this is the case, remind me again why we don't make this a close reason?

yuggib

and you also need CH to make all the nonstandard constructions equivalent

@0celo7 then he's aware of his own weaknesses

0celo7

@yuggib I was not

@yuggib he keeps making comments

They're never helpful

yuggib

:-D

there is always someone like that...luckily they usually do not survive the first couple of years

peterh

13:51

@ACuriousMind Btw, in my opinion, a 7k+ user being obviously a physicist, deserves an above average lenience, especially if there are strong mitigating circumstances, too. I copied the 8.3 into the answer, while I also fixed the latex incompatibilities :-) At least this I can do :-)

@ACuriousMind Now the link-onlyness isn't a problem any more, although it could be maybe better, if the citated text would be self-contained (there are references to external tables, etc) and only the really important part would be there. But it requires only some deletion which is much easier as the copy-paste with the latex conversion. Bye until the end of the CET worktime.

Secret

(Later) I think I have divided by zero. More interestingly, the subalgebra of that algebraic structure are groups under + and x respectively. Yes I have forgone the distributive law. I will tell you guys later after I took my bath

Jim

@Secret Nothing is more interesting than dividing by zero

yuggib

@Jim dividing by zero is not so interesting; dividing by an infinitesimal however...

Jim

14:06

@yuggib but in those cases, you know what happens. When you divide by zero, who knows what happens. It's undefined. Magnets start flying out of windows. Babies start crying sideways. Up is blue. It's interesting

yuggib

14:20

@Jim You don't always know...

what happens when you divide an unbounded number by an infinitesimal?

when you divide by zero you're just doing metaphysics

Secret

Ok guys I am back, to begin I will present the raw result in the form of the Cayley table

As we look at the X Cayley table, it is easy to see it is isomorphic to $\mathbb{Z}/3$

Now since all the elements are here, the structure is closed under + and X

In addition, it is commutative as evident from the symmetry of the Cayley tables

ACuriousMind

@Secret The raw result of what?

Secret

The raw result of the rules of this algebraic structure summarised in the cayley table (excpet it is not distributive)

---
Now, highlighted in blue are the additive and multiplicative identities respectively

Alex

Hi

ACuriousMind

@Secret Why are you telling us this?

I.e. why should be care about that Cayley table?

Secret

14:32

I'd like to consult your guys to see if there are contradictions I overlooked, despite I have systematically run through many cases

because if there isn't then it is an interesting structure because there is nontrivial division by zero

i.e. 0 has a multiplicative inverse here

ACuriousMind

@Secret See, that is something you should have started with instead of saying it only after I asked you.

Alex

@ACuriousMind In QM. For the free particle you stated that: Every eigenfunction of $\hat{P}$ is one of $\hat{H}:= \hat{P}^2$. So would the common eigenbasis be all the eigenvectors of $\hat{P}$?

Secret

ok I will keep in mind to mention the aim when I present something next time

ACuriousMind

@Alex Yes, correct

Secret

Now, if we look at the X Cayley table, it is easy to see that every element has a unique multiplicative inverse, including zero. Likewise, in the + Cayley table every element has a unique additive inverse

ACuriousMind

14:35

@Secret Also, when you say "contradictions", you have so say contradictions to what. You haven't told us what this is suppsed to be. A ring? A semi-ring? Just a structure with two binary operations?

Secret

I have struggle to find a term for it because it is kinda like a semiring except there are no absorbers nor distributive law

ACuriousMind

So what do you expect us to do?

If you can't tell what this should be, then how are we supposed to point out "contradictions"?

Secret

Well, whenever I think I found something interesting, I tend to share to my friends and we discuss together about it as they can often see things I overlooked to ensure it is not an empty happiness. For this case, the contradictions I am looking for are those that plague division by zero systems such as 0=1, a=1, a=0

ACuriousMind

If we call the set with three elements $\mathbf{3}$ for a moment, then all you've done is write down two maps $\mathbf{3}\times\mathbf{3}\to\mathbf{3}$.

You can't tell us what sort of algebraic structure they are supposed to be, but for some reason you call those maps "addition" and "multiplication"

Why do you call them that if there's no distributive law?

Alex

@ACuriousMind Okay thanks. One small query...If we first measure the energy then it would collapse the quantum state into one of the eigenvectors of the common eigenbasis, then measuring the momentum would give the same state (since it is common...). But what if we measure the energy and collapses into a member of the eigenbasis of the hamiltonian which is not a member of the common eigenbasis then would measuring momentum change the state into one which is a member of the common eigenbasis?

Secret

14:39

Wait, so + and X are only defined if there are distributive law, otherwise they are only some generic multiplication operator?

ACuriousMind

@Alex Yes, also correct :)

@Secret Well, there's no hard an fast rule, but in the absence of a distributive law, I'm wondering why you call them "addition" and "multiplication"?

What do they have to do with actual addition and actual multiplication

Alex

@ACuriousMind Unexpected, I have never been right twice in a row on chat...

ACuriousMind

@Secret It seems to me you find this interesting merely because you attach the words "addition" and "multiplication" to those operations, and never stopped to think about why you do that.

Secret

Hmm... you are right, it seems I can only call those identity elements under the respective operations respectively because the way they are written out, the + and X does not really "interact" with each other due to the lack of distributive law

So I am guessing, one cannot really call some identity elements "multiplicative identity" or "additive identity" without the distributive law (as that is the only law I knew that make + addition and X multipication, unless I overlooked something)

@ACuriousMind By the way, in the + Cayley table, what kind of group is that. It is one element off from being isomorphic to the Cayley table of $\mathbb{Z}/3$?

ACuriousMind

@Secret It's not a group.

Secret

14:53

but it is closed under +, each element has unique inverses indicated by the identity entries 0 appearing only once per column and row, is associative and the identity elemetn 0, isn't that the 4 criteria needed to be a group?

ACuriousMind

@Secret It's not associative.

If it were, you would have $0+1 = 1+1 \implies (0+1)+a = (1+1)+a\implies 0+(1+a) = 1+(1+a) \implies 0+0 = 1+0 \implies 0=1$.

Secret

Wow that not obvious. How do you managed to see that. I always find associativity hard to check because there are so many cases?

ACuriousMind

@Secret I knew it was not a group because all groups with prime order $p$ must be $\mathbb{Z}/p\mathbb{Z}$

In particular, this one seemed to violate Cayley's theorem, since it would have had $\{0,1\}$ as a subgroup, but 2 does not divide 3.

Secret

No wonder that grid of $\begin{matrix}1 & 0 \\ 0 & 1\end{matrix}$ look familiar...

Secret

15:12

hmm... in that case, I think we have found the necessary condition for division by zero implies trivality: Since without the distributive law two operators cannot be called addition and multiplication respectively. It means for zero to have a multiplicative inverse, zero cannot be an identity.

Also since zero has a multiplicative inverse, it cannot be an absorber. This means there is no element that can be called zero (since it is neither an absorber nor an identity) that will satisfy the criteria for division by zero. Therefore in general, division by zero does not exist in all conceivable algebraic structures

except the trivial field

wait a sec, there's a mistake in my presentation. I will reanalyse later...

Secret

15:30

Ok after correction I basically have two copies of $\mathbb{Z}/3$ one for X one for +. However attempt to include at least one sided distributivity immediately result in the trivial condition e.g. 0+1=1 => 0(0+1)=01 => 00+01=0 => a+0=0 =>a=0, thus collapsing the structure into GF(2)

John Rennie

@Jim we can only have a limited number of close options and we're at the maximum. So if we wanted to make insufficient effort a close option one of the other options would have to go. The path of least resistance is to use it as an unofficial option.

ACuriousMind

@JohnRennie If we want to make the policy chaos perfect we could try to discuss whether we really need an explicit "non-mainstream" close reason :)

David Z

15:48

@Jim Because people don't seem to agree on the definition of insufficient effort, I guess

John Rennie

@ACuriousMind: I have yet another quasi-meaningless question about QFT, but I will ask it of you only if you haven't anything better to do. Shall I go ahead?

(If you say no I will only sulk for a short time)

peterh

@JohnRennie Possibly there are too many claim for new close reasons. The MO has fewer as the current PSE. Maybe their number could be reduced, for example over high school level there are quite few exercises in the net around. But efficiently learning something can be done only if you have exercises, too. It could be a breakthrough point, when the homeworks of the physics students would be converted to an exercise library.

ACuriousMind

@JohnRennie Go ahead

John Rennie

@ACuriousMind Suppose I'm considering the scattering of two particles. We start with them at infinity so they don't interact and we can describe the initial states as $|1\rangle_a$ and $|1\rangle_b$ (I'm not sure what notation indicates the particles are different). OK so far?

ACuriousMind

@JohnRennie Well, we would usually write the initial state as $\lvert p_1,p_2\rangle$, where $p_1,p_2$ are the momenta, but okay

DanielSank

15:59

@EmilioPisanty based on your present set of bounties totaling 1 kRep, I think you should change your handle to "Emilio Moneybags Pisanty".

John Rennie

Once they start interacting we no longer have well defined states like $\lvert p_1,p_2\rangle$, so we give up and use perturbation theory to calulate what happens.

In the calculation are we (in an ill defined way that I haven't thought through) expressing the state of the particles as a sum of different free field $\lvert p_1,p_2\rangle$s?

ACuriousMind

@JohnRennie Not really.

John Rennie

Ah, OK, that's not unexpected but disappointing.

Since it would have provided a nice simple interpretation for virtual particles.

Damn that real world! :-)

ACuriousMind

The actual intermediate state of the process appears nowhere in the calculation, actually, it's fully encoded in the time evolution operator

2physics

what do I have to install to be able to see equations here in chatrooms? I've asked it earlier but I couldn't fix it.

ACuriousMind

16:10

@2physics Look in the upper right corner of the chat room.

2physics

@ACuriousMind search you mean?

John Rennie

Where it says For MathJax see ...

ACuriousMind

@2physics No. Read the room description.

John Rennie

17

A: Any chance of MathJax in chat?

As a workaround while this request is pending, there exist several client-side workarounds that can be used to enable LaTeX rendering in chat, including: ChatJax, a set of bookmarklets by robjohn to enable dynamic MathJax support in chat. Commonly used in the Mathematics chat room. An altern...

You can install some Javascriptlets that will translate the MathJax into equations.

Wrong and proud of being wrong ...

-2

A: How can the universe expand if there is gravitation?

One simple explanation is that the universe is not expanding at all. In the absence of external force, the center of mass of all the physical bodies in universe will stay stationary. So, essentially bodies are moving in such a way that center of mass is stationary while in our limited vision we ...

Given what a great learning resource this site is I'm amazed how resistant people can be to learning anything from it.

Emilio Pisanty

@DanielSank I just have too much of the damn thing around.

John Rennie

16:19

@2physics I used the bookmarks described on this page (with Chrome) and they work very well.

@ACuriousMind: aha, so that's why you disappeared from the chat for a few minutes.

Emilio Pisanty

That said, this does look a bit scary

John Duffield

@Jim : that's an easy one.

DanielSank

@EmilioPisanty Poor you ;)

@peterh I've said this before and I'll say this again: the user should not be taken into account in any way when judging a question.

3

2physics

@JohnRennie yup thankyou. it worked

@ACuriousMind thankyou too

John Rennie

@2physics Cool :-) I tend to use only the on demand translation as it's not that often I need to see the equations. I've actually got pretty good at truning MathJax into a mental image :-)

2physics

16:26

@JohnRennie how do you type formulas so fast? do you use any software or you memorize characters

John Rennie

@2physics there isn't that much to memorise. If you use MathJax a lot you find you remember (most of) it without even trying. I still have to consult a MathJax reference from time to time e.g. if I've trying to write something i have done for a while.

The good old 90:10 rule applies - 90% of the stuff you need to write can be done with 10% of the MathJax syntax. Though in my case the rule is nearer 99% and 1%.

2physics

@JohnRennie wow, that's great job

@JohnRennie you know I used to type equations in some software such as "mathtype" and then it converts it in the way you type it here

don't know anything about mathjax and latex

John Duffield

@JohnRennie : "Given what a great learning resource this site is I'm amazed how resistant people can be to learning anything". I'm afraid your answer is wrong too. Gravity does not make space fall down. Or up. Gravity is not making the expansion faster.

0celo7

16:42

People who smile all the time are so smug

What is up with that

John Rennie

@0celo7 Smug? Or plotting a fiendish revenge?

0celo7

There's a dude in my QM class who smiles all the time

He's smiling right now

It's creepy

It's not even a full smile. More like a smirk

John Rennie

Plotting a fiendish revenge I'd say. Kill him first.

0celo7

In class?

Last time I followed your advice I got a beating

John Rennie

Yes, you want as many witnesses as possible to testify that he was smirking at you in an evil way.

@0celo7 what, over that parallel port card? That's a bit extreme.

0celo7

16:48

No fooling around with funds @JohnRennie

My prof has a nun on call

She has a large ruler

Secret

Once the following is proved, its forever bye bye for all conceivable division by zero discussions

Extreme attitude no. 2: If something does not work, then it will be proved into nonexistent.

For example if a PSE question is nonsesne and I am trigger happy, then the question will be erased from history

Luckily I am not tirgger happy

Likewise if something works, then it will be promoted sky high

There is no middle ground

Because middle grounds are wasting our time

ACuriousMind

@Secret Once again, I have no idea what you're talking about.

2physics

@JohnRennie I want to learn how to use various facilities to answer/ask questions on SE, things like uploading pictures, or quote some parts of question in the answer, using various kinds of typing/fonts, adding hyperlinks, using various colors or how to highlight a line.. I mean all such stuff which can help you to explain your thoughts better. how can I learn it? I mean where to start? is it all about knowing mathjax? or you have to know sth more than that?

Secret

Sorry I got carried away because of fnally finding a way to show in the most general case divison by zero is undefined except for the trival ring

ACuriousMind

Also, theorems need precise statements. Defining "algebraic structure" and "zero element" *inside the proof of a theorem about algebraic structures and zero elements is very bad style.

Secret

16:53

ooops...

John Rennie

@2physics There are various answers explaining how formatting works in the SE. I'll have a dig around and see if I can find a link ...

Secret

EDIT: Fixed by moving the definitions outside

ACuriousMind

Also, you've again posted a screenshot of a website where a link would have sufficed and would have been more convenient since it doesn't become obsolete with edits.

Secret

> since it doesn't become obsolete with edits

Ok I did not aware of that (probably because I seldom edited away screenshots...)

Will keep that in mind

ACuriousMind

@Secret You have misunderstood me: I meant that giving a link to the site where you wrote that would have meant anyone could also see the current version of it

Like, now that you wrote:

2 mins ago, by Secret

EDIT: Fixed by moving the definitions outside

the screenshot doesn't contain up-to-date information anymore, and so is useless

Secret

16:58

I see

Well there's really nothing interesting because it is still a hap hazard work in progress but here is:
http://secretuniverse.wikia.com/wiki/Division_by_zero_theorem

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