The h Bar

Anonymous

5:00 PM

He also has a few lectures on Measure theory and Lie algebra...if you're interested in that kind of stuff

enumaris

I feel sleepy

Anonymous

(haven't watched those yet)

Sir Cumference

@ACuriousMind Huh, I guess I misunderstood it. Then we have a good definition of math, i.e. defining the axioms as true and deriving true statements from them, right?

enumaris

What's the definition of math?

ACuriousMind

@SirCumference I think you'll find that except for logicians and other foundationalists, mathematicians rarely view math in those terms

Anonymous

5:01 PM

Anyhow, as Balarka says, probably you're better off learning multivariable calculus first

heather

@Danu I would enjoy learning about these topics, but I would also like to learn about h-principles before I grow into a mathematical recluse.

Anonymous

and build on linear algebra

Anonymous

Then you could take basic analysis....not a good idea to jump onto advanced topics directly without background

Danu

@heather I think there's not really a point to that. h-principles is a pretty advanced thing.

Sir Cumference

@heather Learn linear algebra before multivariable

ACuriousMind

5:02 PM

I mean, the algebraist that introduces group theory may pay lip service to the axioms by mumbling something about e.g. the axiom of choice, but the practice of the subject rarely involves the actual axioms

Danu

(for example, I'm not too confident I could quickly learn how to use them, and I'm a math phd student)

heather

@Danu i suppose, yeah. it just seems interesting.

Balarka Sen

I think one could write a Mathcamp course notes on h-principles for high schoolers tbh.

bolbteppa

@Semiclassical "While de Broglie presented a first order development of the quantum trajectories (integrated from the velocity), Bohm himself did a second order (integrated from the acceleration) emphasizing the role of the quantum potential. The differences between both approaches appear when one considers initial ensembles of trajectories which are not in quantum equilibrium. Except for this issue, which will not be addressed in this book, both approaches are identical"

arxiv.org/pdf/1206.1084.pdf P7/8

Balarka Sen

But there just isn't one

heather

5:03 PM

and @Balarka's explanation made sense so far, so I wanted to keep going.

bolbteppa

How big a deal is that

Semiclassical

Well, as it says, it depends on your take on quantum equilibrium

if you assume that's true, then there's no practical distinction at all

Balarka Sen

@heather There really is no "intro to" h principles. They are a relatively recent and deep and hard branch of mathematics and the texts are usually unreadable. I am filtering through the perspective I have gathered on it over the course of months of reading those.

bolbteppa

@BalarkaSen can you use the h-principle to solve the hypergeometric equation or equations like that?

Semiclassical

@bolbteppa why would you want to

Balarka Sen

5:04 PM

You can't use the h-principle on everything lol

enumaris

Does the Banach-Tarski paradox disprove the axiom of choice

Semiclassical

there's a reason why we love series solutions, lol

heather

@BalarkaSen well yeah. i'm not saying it was a reasonable wish =)

Balarka Sen

There isn't anything wrong about the wish either!

bolbteppa

I gave up and am just trying to relate everything to hypergeometric equations now :(

Balarka Sen

5:05 PM

It's cool math

ACuriousMind

@enumaris No. Btw dropping the axiom of choice also produces some weird effects. Lemme search the transcript....

Danu

@bolbteppa You should work on electro-magnetic duality in N=2 supersymmetric gauge theories

Semiclassical

@bolbteppa Painleve 4 lyfe

Danu

there's hypergeometric series EVERYWHERE

Semiclassical

@Danu I think that's mostly because periods of riemann surfaces show up everywhere in there

bolbteppa

5:06 PM

Once I write up the notes on this, going to go over Lame equations and Painleve (again ffs)

This stuff is insane

Semiclassical

and periods of riemann surfaces generically satisfy picard-fuchs equations, which are hypergeometric (or appropriate generalizations thereof)

Danu

Yeah, probably

Semiclassical

in particular you don't get equations with irregular singular points

enumaris

how can you make 2 copies of a ball from 1 ball tho that's just weird yo

Semiclassical

hence the usual series solutions have a hope of working, with the only possible issue being log terms

Balarka Sen

5:07 PM

@heather If you want to read some cool topology without having to go down the rabbithole, try Colin Adam's "Knot Book".

bolbteppa

I can't imagine what you'd do with equations which don't have at most 3 regular singular points :p

Balarka Sen

I haven't gone through it thoroughly, but I have heard very good things about it.

ACuriousMind

@enumaris E.g. without choice, the dual space of a vector space can be the zero vector space! An infinite-dimensional vector space without any non-trivial linear functions on it is also just weird.

heather

okay. well thank you =)

Semiclassical

eh. i've dealt with equations that had more than three :)

Balarka Sen

5:08 PM

If you read it I'll probably too.

Semiclassical

though tbh I very much relied on mathematica being able to solve them, at least in terms of generalized hypergeometric functions

bolbteppa

Riemann's differential equation

In mathematics, Riemann's differential equation, named after Bernhard Riemann, is a generalization of the hypergeometric differential equation, allowing the regular singular points (RSPs) to occur anywhere on the Riemann sphere, rather than merely at 0, 1, and ∞ {\displaystyle \infty } . The equation is also known as the Papperitz equation. The hypergeometric differential equation is a second-order linear differential equation which has three regular singular points, 0, 1 and ∞ {\displaystyle \infty } . That equation...

This is like Hypergeometric's father

ACuriousMind

@enumaris The essence of why the B-T paradox works is that the "cutting" maps do not respect the notion of "measure" or "volume", and hence you shouldn't expect them to preserve volume to begin with

Emilio Pisanty

@DanielSank I think the matrix is a bit of a red herring brought about by the representation

Semiclassical

yeah

Emilio Pisanty

5:09 PM

I think you're just seeing the fact that $a$ is an eigenfunction (in the classical case!) of the operator $\{H, \cdot \}$.

enumaris

hmmm

heather

@BalarkaSen i might give it a go then.

enumaris

how catastrophic would it be if we had to get rid of the AC?

heather

i'm looking it up and it seems interesting.

ACuriousMind

@EmilioPisanty I see we agree ;)

Secret

5:13 PM

losing the axiom of choice will also make analysis very unwieldy, such as losing baire category theorem

bolbteppa

15

Q: Hahn-Banach without Choice

The standard proof of the Hahn-Banach theorem makes use of Zorn's lemma. I hear that, however, Hahn-Banach is strictly weaker than Choice. A quick search leads to many sources stating that Hahn-Banach can be proven using the ultrafilter theorem, but I cannot seem to find an actual proof. So... ...

I think you would lose things like HB

Secret

It's really a small cost to pay to have nonmeasurable sets due to axiom of choice, then to deal with a whole wilderness of non well orderable sets without the axiom of choice

(I am fine with either btw)
But it is quite a big deal to lose baire category theorem

(and trust me, I am pretty sure nature can never really demonstrate the existence of a nonmeasurable set)

bolbteppa

Is a set smaller than the plank length measurable or non-measurable? runs

Secret

It will probably be buried in the noise for that measurement to be meaningful, I think

Semiclassical

@bolbteppa Mu

Secret

5:18 PM

so it probably will not have physical significance

heather

okay, wow, this knot book is cool

Balarka Sen

It is seriously cool

enumaris

hmmmm

tough questions

crap, my script is now a throwing an error where it didn't used to throw this error...

those errors are hard to fix -.-

time dependent errors lol

Anonymous

@enumaris Heh...had one like that around two weeks back. The same program when executed the first time gives the correct output but when run the second time doesn't give any output at all (on the third or fourth run it again works!). Later realized that it was a POSIX incompatibility on Windows :P

Balarka Sen

@heather This book actually has a lot more than I anticipated. If you read it that'll be fantastic.

heather

5:25 PM

@Blue i just have a normal bug, in the sense that it is not time-dependent but i still have no idea what's going on =)

@BalarkaSen okay. it's very readable/interesting, so i think i'll read through it all =)

enumaris

I think my query is too long

I want to pull 10k different things, so I have a "WHERE ID IN (?,?...,?)" kind of statement...

where there's 10k different ?'s

probably SQL is throwing an error saying that's too many

hmmmmm

any SQL experts in here? :P

Anonymous

@enumaris Are you afraid of asking on SO? :P

Anonymous

(I am)

enumaris

well I don't want to ask a vague question

bolbteppa

Quantum non-equilibrium

Quantum non-equilibrium is a concept within stochastic formulations of the De Broglie–Bohm theory of quantum physics. == Overview == In the Copenhagen interpretation, that is, the most widely used interpretation of quantum mechanics, the Born rule ρ ( x , t ) = | ψ ( x , t ) | 2 {\displaystyle \rho (\mathbf {x...

enumaris

5:30 PM

generally when I post to SO it's like a very concrete 1-step answer kind of question

bolbteppa

Is that what they mean about equilibrium in the quote above

Semiclassical

yeah

Anonymous

@enumaris Same here. I used to get a question ban almost everytime there :P

enumaris

Is that the De Broglie-Bohm equivalent of the Quantum Kinetic Equations?

heather

@Blue i don't go over there very often; it's always rather frustrating.

(except when just googling; i mean to ask a question.)

Semiclassical

5:31 PM

the "predicted properties" in that section is worht looking at

Anonymous

@heather They seem to be waiting to pounce on you and downvote you $24\times 7$ ;)

Semiclassical

as far as reasons I find the notion of quantum non-eq to be distateful :P

Anonymous

And sometimes even non-duplicate questions get closed as duplicates (of a vaguely related question)

bolbteppa

'thereby violating the assumption that signals cannot travel faster than the speed of light'???

Semiclassical

yea...

bolbteppa

5:32 PM

If he's doing non-relativistic QM that's not a problem right

Anonymous

I have some serious appreciation for those who manage to get 10k+ rep there on SO

Semiclassical

well, I think it'd let you do nonlocal signaling instead of just nonlocal correlation

standard QM (and as such equilibrium BM) lets you do the latter but not the former

danielunderwood

@enumaris Surely there's another field that you can use the WHERE on if it's that many? The only other thing I could think of would be to select them all and filter in your code or run 10k selects with the individual ids

heather

@Blue basically, yeah. it's weird. a really simple, sometimes bad answer with just code pasted in gets 10 upvotes, but a good question gets 10 downvotes with "trivial" or "read the docs" in the comments.

enumaris

There are alternatives

but I worry that the alternatives will miss stuff

Novalium Company

5:35 PM

Al + O2 = Al2O3 Why does Al stay without an index and why is the index of the oxygen 3? I mean, I know this is pretty basic but has been bugging me for a while. Why isn't it Al2 + O3 = Al2O3?

enumaris

I can filter on a date for example, do something like date>something, but then I might miss a few rows

Semiclassical

I'm not totally clear on this stuff tho

enumaris

the way I have things set up right now looks at one table and matches another table and pulls the indices of one table that doesn't appear in the other, and then I select all those indices out...which is why there's 10k+ of them

pulling by index

individual index

so it's basically "WHERE INDEX IN (INDEX1,INDEX2,...,INDEX10000...)"

danielunderwood

Can't you just do the select in that query if it pulls the indices?

enumaris

hmmm

lol duh

I guess that would be the way to go

Anonymous

5:38 PM

@heather True, yeah. And the "rude comment" thing seems real when you go there. Any simple "Did you even read the documentation?" comment will get 10+ upvotes, even when it is extremely hard to dig up the required detail from the documentation as a beginner. I guess that prevents the homework vampires though. Anyhow, the chat rooms on SO are somewhat more helpful.

Anonymous

Especially the Python chat has some helpful folks hanging around

bolbteppa

enumaris

I think my brain didn't go that route cus I'm only pulling stuff from one of the joined tables

bolbteppa

How does that relate to normal QM density matrices

enumaris

so it seems a bit weird mmmhm

Semiclassical

5:39 PM

No idea. But the $\rho$ in there isn't a density matrix, it's just the probability density as a function of position

enumaris

@danielunderwood thanks :D

Semiclassical

I'm sure there's stuff in the literature on this, but I steer clear of that so I can't help

heather

@Blue yeah, i had a bad experience in there a couple times, so i haven't been over there for a while.

but in general that chat is more helpful than most of SO, yeah.

bolbteppa

publish.uwo.ca/~wmyrvold/Bohm.pdf

ACuriousMind

@enumaris It's not an unusual pattern to join two tables and then only read fields from one of them (or even only shared fields).

bolbteppa

5:41 PM

That has some comments by Einstein, Pauli, Heisenberg on Bohm

Semiclassical

yeah

including Einstein's remark to the effect of it being too cheap

enumaris

@ACuriousMind yeah, but it's just the way my brain logics

Constantine Black

@Danu :) I just meant what little I have came in contact with(and it's mostly algebra and basic geometry), but yes you are correct, I don't think I have a lot of knowledge. If I manage to get to the program I'm currenlty studying for, topology won't be the first think to learn. As for LMU, I also have it in mind.
So, thanks for your opinion.

bolbteppa

Cool

danielunderwood

Or joining 10 tables if the db schema wasn't set up for use lol

enumaris

5:43 PM

well I'm no SQL wiz

Semiclassical

@danielunderwood on that note, a title I saw randomly the other day (but didn't follow up on)

enumaris

This is actually my first time using a LEFT JOINlol

Semiclassical

arxiv.org/abs/1208.6416

un-derped

Emilio Pisanty

@Semiclassical there's a hat stack exchange?

Semiclassical

yeah, but it's only open during the holidays

Emilio Pisanty

5:44 PM

I knew it

Also: thanks SE for the very nice Stack Overflow nalgene bottle

Semiclassical

hahaha

the title of what i linked, for those who didn't look: "Relational Databases and Bell's Theorem"

I mean what

enumaris

are they building Relational Databases using entanglement now?

Emilio Pisanty

@enumaris are you sure you want a left join?

enumaris

like if your row changes in one database, it should change accordingly in another FTL? :P

@EmilioPisanty pretty sure, I am finding all entries in one table that doesn't have a corresponding set of entries in another table after all.

Emilio Pisanty

I mean, I reckon some 50% of all left joins out in the wild could just as happily be straightup joins

@enumaris I.... don't think that's what left join does?

Semiclassical

5:47 PM

huh, the stuff they do in the middle of the paper (past the horrible category stuff) actually looks like the kind of argument I've been doing lately

Emilio Pisanty

you might be able to manipulate it into that

enumaris

Left join, afaik, takes all the entries of the left table and all matching entries

danielunderwood

@Semiclassical Well that's something I never thought I'd see. I think relational databases have pretty strong mathematical background that's related to set theory, but I don't know the technical details

Emilio Pisanty

@enumaris yes

enumaris

it fills the right table's columns with NULLs where there isn't a match

Emilio Pisanty

5:48 PM

when the latter exist

@enumaris yes

enumaris

so I do a left join and find where all the NULLs are to find rows in the left table that didn't match

then I pull the left table's contents

danielunderwood

@EmilioPisanty Shouldn't all left joins (or right or inner) be happy as normal joins? The left/right/inner just return less and have better performance I thought?

Emilio Pisanty

@danielunderwood I've never fully understood

Semiclassical

"In database language, this says exactly that there is no ‘universal relation’ on the whole set of attributes which yields each of the ‘observable relations’ by projection"

enumaris

by "normal join" do you mean outer join?

cus by "normal join", I'm thinking of an inner join lol

Emilio Pisanty

5:50 PM

but as I understand it, on that $A \setminus B$ diagram, you'd be just as happy using join instead of left join

@enumaris no, just join

enumaris

since that's the kind of join you get if you type something like "Select a.x,b.y from a,b where a.x=b.y"

what's "just join"?

Emilio Pisanty

like the one here

data.stackexchange.com/physics/query/778206/…

danielunderwood

I'm actually not sure what join is. I thought it was normally the same as an outer, but I wouldn't bet on it

Emilio Pisanty

SELECT
  questions.Id AS [Post Link],
  cast(questions.CreationDate As Date) AS 'date',
  initialQs.Id AS [Post Link]
FROM Posts questions
JOIN Posts initialQs

no surname needed

enumaris

isn't that an inner join

Semiclassical

5:51 PM

"In particular, we shall see that the question of whether an “empirical model”, of the kind which can be obtained by making observations of measurements performed on a physical system, admits a classical physical explanation in terms of a local hidden variable model, is mathematically equivalent to the question of whether a database instance admits a universal relation"

enumaris

there's only 4 possible joins right

danielunderwood

Woah I didn't know there was an SE data explorer

Emilio Pisanty

@enumaris ¯\ _(ツ)_/¯

enumaris

inner, left, right, outer

logically those are the only 4 possibilities

Emilio Pisanty

@enumaris so what's the one in my code sample?

enumaris

5:52 PM

so a "normal join" has to be one of those lol

Semiclassical

is the phrase "universal relation" one which sounds familiar to your database experience?

I have an inkling of what it measn

enumaris

I think your code sample is an inner join...but that only returns rows where both tables have a matching entry

Emilio Pisanty

@Semiclassical not mine

Semiclassical

"Here we take a universal relation for the instance by definition to be a relation defined on the whole set of attributes from which each of the relations in the instance can be recovered by projection. This notion, and various related ideas, played an important role in early developments in relational database theory [refs]"

Emilio Pisanty

@Semiclassical ugh

I was thinking tensor products but that's a universal property, innit

Semiclassical

5:54 PM

lol

enumaris

839

A: Difference between JOIN and INNER JOIN

They are functionally equivalent, but INNER JOIN can be a bit clearer to read, especially if the query has other join types (i.e. LEFT or RIGHT or CROSS) included in it.

Semiclassical

Universal relation assumption

The universal relation assumption in relational databases states, that one can place all data attributes into a (possibly very wide) table, which may then be decomposed into smaller tables as needed. However, the assumption that a single large table can capture real database designs is often plagued with a number of difficulties. The "nested universal relation" model has attempted to address some of the problems and offer improvements. == References == == External links == Who won the Universal Relation wars? by Alberto Mendelzon...

enumaris

They are functionally equivalent, but INNER JOIN can be a bit clearer to read, especially if the query has other join types (i.e. LEFT or RIGHT or CROSS) included in it.

I guess I forgot the Cross join...but in what scenario would u use that...

Emilio Pisanty

@Semiclassical lolz

enumaris

anyways, yeah it seems a "normal join" or just saying "join" is an inner join

in my scenario I can't use an inner join because I need entries from one table that doesn't exist in another

Semiclassical

5:55 PM

loll, that external link

Emilio Pisanty

@enumaris fair enough

@Semiclassical lolz

I don't know why that wasn't obvious to me from the title

Semiclassical

haha

enumaris

crap, I can't comment in a json file -.-

Semiclassical

I sorta get what they're saying, insofar as it's a question about counterfactuality: whether every possible measurement has a well-defined value even if it's not actually measured

Emilio Pisanty

@enumaris sure you can

it might impede a machine from reading it, I dunno

but you sure can

just take a crayon and write on your screen

enumaris

5:58 PM

5695

Q: Can comments be used in JSON?

Can I use comments inside a JSON file? If so, how?

json comments

Emilio Pisanty

I'm sure work won't mind

enumaris

lol

Emilio Pisanty

maybe a felt marker is better

enumaris

I appended a date to it to tell me when the file got appended

Semiclassical

It jives with the semi-slogan I've had lately: That bell's theorem is all about whether you can impute $\pm$ values to counterfactual measurements in a way that preserves the correlations.

enumaris

6:00 PM

but it don't work

ACuriousMind

@enumaris that sounds like a classic XY problem - why do you feel the need to comment a file that's usually only read by machines?

enumaris

the file is human readable

and I read it sometimes

I guess I can find another format

but that would result in me modifying my code to accept this other format lol

danielunderwood

Just add an "appendedDate" property to the object? Or grab the timestamp of the file

Or write a custom JSON parser that will allow you to comment :D

ACuriousMind

Well, it's human-readable (that's much easier to "debug", after all!), but it isn't intended to be read by humans

enumaris

I have multiple appends happening on multiple days

I'd like to know what data was appended on what date

I mean, I know there are ways I can solve this

but

just not as simple as I thought

ACuriousMind

6:02 PM

If you want to preserve some information, just include it as an actual field and ignore it when parsing the file

enumaris

by writing a line lol

danielunderwood

[{"date": timestamp, "data": {...}}, ...]?

Semiclassical

(With the basic conclusion being: It's always possible to impute values to counterfactuals in such a way as to preserve the correlations, but it's not always possible to do so by only using $\pm 1$ values)

nitsua60

36

Q: We'd like your feedback on our new Code of Conduct!

tl;dr: We've put together a code of conduct (CoC) that is a bit more comprehensive than our existing be nice policy because we feel that our current policy isn't meeting our needs. Some background, our reasons for doing this and a link to the draft can be found below. We'd like your feedb...

discussion featured behavior be-nice-policy code-of-conduct

Semiclassical

(blah blah blah blah)

nitsua60

6:03 PM

SE's looking at a new Code of Conduct, and would like your feedback ^^

2

enumaris

yeah all solutions require me to modify more than one line :P

nitsua60

(Anyone mind starring the second of those messages? If one stars the first it'll just show up on the board as the url, which probably won't entice anyone to look.) (Thanks!)

danielunderwood

Or instead of appending, you could create new files with the timestamp as filename

ACuriousMind

@Semiclassical Uh...isn't "imputing values to counterfactual measurements" just another name for "realism"?

Semiclassical

yep

the point is more the local vs. nonlocal bit

enumaris

6:05 PM

@danielunderwood yeah...but then I'd end up with too many files eventually

Semiclassical

I can ramble on about what I have in mind but I'm not sure that's wise :P

enumaris

it's not essential that I know the date the data was appended on

I'll just leave it lol

oh wait

shoot, the json saves one giant dict...if I append now I'll have multiple dicts...hmmm

ok I think the way I have it set up won't work lol

welp, got some more work to do...no biggie

there's other failings that I found as well

good thing I saved multiple backups of the master file this time so I don't have to rerun 20 hours of analysis :P

Novalium Company

Guys, I know there are some elements like hydrogen, oxygen, bromide... that can't exist alone so we write them with index 2. For example Al + O2 -> Al2O3 (this is unbalanced tho) and here we see that oxygen is written with index 2 because it hardly can exist alone. My question is, why chloride (Cl) (which is one of the elements that hardly exist alone) is alone in Na + Cl -> NaCl?

enumaris

You also have H2O

where O is now alone

Novalium Company

H2 + O2 --> H2O (unbalanced) is the reaction?

Where O is not alone.

enumaris

6:15 PM

the answer is elements that "don't like to be alone" are those that bond with other atoms. In the case of Oxygen, it can bond with itself to form O2 or bond with Hydrogen to form H2O.

Semiclassical

HO^- + H^+ ->H20 is the more typical one

enumaris

Are you asking about how salt is actually created? I don't know the reaction generally used to "create" salt.

danielunderwood

The index is dependent on the reaction, not the element. Na + Cl -> NaCl is with ions if it is. But I think $2\rm{NaOH} + \rm{Cl}_2 \to 2\rm{NaCl} + \rm{O}_2 + \rm{H}_2$ would be more typical

enumaris

the general answer is "there is no hard and fast rule about what to "write and index 2 on" for chemicals and chemical reactions

^mismatch quotes error

I'll let you guys feel the awkwardness by not editing my post

Just like (if I leave a random parenthesis around

ACuriousMind

@enumaris (okay

Novalium Company

6:18 PM

So Na + Cl -> NaCl is actually not the typical reaction?

enumaris

@ACuriousMind ahahahaha I beat u to it

ACuriousMind

dammit))

(closed yours and mine ;) )

enumaris

lol

ACuriousMind

@NovaliumCompany No, pure natrium and pure chlorine are rather rare :P

enumaris

why the hell is this count query taking 7 minutes...

Semiclassical

6:19 PM

@bolbteppa btw, the discussions about Pauli and Heisenberg's viewpoints re: Bohm's work (pages 11-13) are pertinent to what we've been discussing

ACuriousMind

@enumaris Generally a sign either your database has died or your WHERE/JOIN conditions are poorly chosen

enumaris

oh shoot it's cus my Python script wasn't done writing the table yet LOL

danielunderwood

@NovaliumCompany Note that the one I listed may not be the typical one either, that just happens to be the one I know of

enumaris

I think I made the two requests kill each other

bolbteppa

Cool, it's interesting they say in his QM book he was claiming you couldn't get hidden variables then changed his mind

Novalium Company

6:21 PM

Ok, actually, why some atoms like to bond with themselves? Like O2, H2...?

and others don't?

enumaris

It has to do with their valence electrons

Semiclassical

yeah

if memory serves he came upon it while doing stuff with semiclassical analysis? lemme find a source for that

wikipedia glosses it as such:

"His first book, Quantum Theory, published in 1951, was well received by Einstein, among others. But Bohm became dissatisfied with the orthodox interpretation of quantum theory he wrote about in that book. Starting from the realization that the WKB approximation of quantum mechanics leads to deterministic equations and convinced that a mere approximation could not turn a probabilistic theory into a deterministic theory, he doubted the inevitability of the conventional approach to quantum mechanics"

for a more direct source, see the bottom of this page (remarks by bohm himself): books.google.com/…

danielunderwood

It might be useless for chemistry uses, but because it's energetically favorable. I think in the case of covalent bonding, the atoms want to have a full valence layer and share orbitals for some electrons (but I'm not 100% sure on that)

enumaris

The question is better suited for a chemistry answer than a physics one

danielunderwood

On that note, is the system of two hydrogen atoms solvable by hand?

enumaris

6:26 PM

from a physical perspective it's like "cus the equations theoretically say so even though I've never solved these particular equations cus that would be too annoying"

Semiclassical

I think the main difference between the first- and second-order formulations of pilot wave theory is what exactly one is trying to recover

Novalium Company

H2 + CO2 --> H2CO3 (unbalanced). Why can't we write it: H2 + C + O2 --> ...?

enumaris

@danielunderwood highly doubt it, it'd be a 4 body problem

danielunderwood

I had that feeling. Would be a neat exercise if you could though

enumaris

@NovaliumCompany the things on the left show what you started with

Semiclassical

6:28 PM

in the second-order, one is trying to recover classical mechanics. one does that by rewriting the schrodinger equation into a form that looks like the hamilton-jacobi equation plus an extra term

enumaris

if you write it H2+CO2 it means you started with a hydrogen molecule and a carbon dioxide molecule

ACuriousMind

@danielunderwood If by "by hand", you mean "has it got an analytical solution", then likely no, because this is already not the case for the ionized hydrogen molecule with one body less, cf. physics.stackexchange.com/q/266216/50583

enumaris

if you write H2+C+O2 it means you started with a hydrogen molecule, a carbon atom, and a oxygen molecule

Semiclassical

which if nothing else gives a nice way to recover the classical limit: if this term is small enough to be neglected, then you're done

enumaris

@NovaliumCompany you can write whatever you want, but what you write changes the meaning

Novalium Company

6:29 PM

H2 + C + O2 isn't possible? Why?

ACuriousMind

@NovaliumCompany Nobody said it is not possible.

Semiclassical

it's possible, it's just different

Novalium Company

Isn't it the same? H2 + C + O2 --> H2CO3?

bolbteppa

Seems like Bohm always has at least an interesting starting point for everything

Novalium Company

When C + O2 --> CO2

enumaris

6:30 PM

it's not saying the same thing

read my comments above

Semiclassical

(returning to my spiel) that doesn't mean what you've got is equivalent to classical mech prior to making that approximation. it can't, because all you've done is rewrite the schrodinger equation

Novalium Company

@enumaris I read it. H2 + C + O2 would give H2CO3 woudn't it? (unbalanced)

Semiclassical

it's just making it clearer where the difference between quantum and classical mechanics lies

enumaris

Not sure if that's the chemical reaction that would generally occur

but my comments only tell you about the left hand side and why the 2 expressions differ

danielunderwood

I don't know about the reaction, but I'd imagine it's not favorable. If you put in energy, you'll get some amount of H2CO3. I think most of the chemical reactions you'll see are ones that can happen spontaneous. For a bit of a different perspective, you could look into nuclear reaction branching ratios

ACuriousMind

6:32 PM

@NovaliumCompany Yes it would (to a very small extent, most of the stuff on the l.h.s just wouldn't react at all). But it is a different reaction than $\text{H}_2 + \text{CO}_2 \to \text{H}_2\text{CO}_3$.

Semiclassical

by contrast, I take the first-order approach to be directed toward the simpler question of getting trajectories out of the Schrodinger equation

Novalium Company

I know it's different, but would give the same thing?

Semiclassical

not worrying at all about recovering classical mechanics, but just trying to get some notion of trajectory

danielunderwood

If the reaction occurred. I imagine that combination would be happier just staying as carbon, oxygen, and hydrogen

ACuriousMind

@NovaliumCompany Yes, but with a different rate of reaction (likely an infinitesimally small one, I don't think you would observe significant formation of carbonic acid just when putting hydrogen and oxygen in the vicinity of carbon)

Semiclassical

6:34 PM

that both the first- and second-order formulations are equivalent (subject to quantum equilibrium) reflects the fact that both of them (at least in this presentation) are extracted from the Schrodinger equation

Novalium Company

@ACuriousMind Why not?

ACuriousMind

@NovaliumCompany Because the rate of reaction depends on how "reactive" the components are and how energetically favourable the reaction is.

It's complicated and you'll have to ask a physical chemist if you really want the gritty details

Novalium Company

Ok thanks :)

Semiclassical

I'm not conversant on how the two formulations differ once you break equilibrium, tho

ACuriousMind

And carbon on its own is pretty stable, cf. diamonds, pencils

danielunderwood

6:41 PM

@NovaliumCompany if you're asking that question, you may want to look into branching ratios. I think nuclear/particle physics makes it a bit more clear that there are more possible reactions that what I've seen in chemistry. Unfortunately, I can't really find any information on branching ratios that isn't technical

Griffiths' particle physics has a decent introduction I think, but probably a little out of the way if you're interested in chemistry.

Speaking of which, what do you guys that hate Griffiths think of that book? Is there a more up to date book that people use?

danielunderwood

7:02 PM

Actually you may get some explanations if you look up stellar nucleosynthesis. Most explanations probably won't explicitly mention branching ratios, but they'll give you an idea that multiple pathways are possible

Balarka Sen

7:20 PM

@Sid England vs Columbia is basically American football.

Emilio Pisanty

7:35 PM

-1

Q: Weber Electrodynamics

Last year, just for the fun of it, I decided to verify (not derive) Maxwell's 4 differential equations using the scalar and vector potential function definitions of the fields. I performed the spatial derivatives on the left of each equation to see if I got the right hand side of each equation. ...

electromagnetism

I'm out of closevotes =|

anyone round here care to take a look?

@ACuriousMind, say?

ACuriousMind

reading

and closed, pretty clearly non-mainstream

Emilio Pisanty

thanks for taking the time =)

also, I imagine OP and answerer are the same person?

and that they're misrepresenting their relationship to the resource they quote, too

ACuriousMind

@EmilioPisanty I can't really comment on accounts being related; it's better if you put such speculations in a flag.

danielunderwood

I've heard people try to dispute qm and relativity, but I have to say em is a new one

ACuriousMind

@danielunderwood We get non-mainstream physics users on almost every topic once in a while :P

danielunderwood

7:50 PM

Silly me thinking of em as untouchable

I almost feel like we could have a Dinner for Schmucks type of situation here, but that would probably just be too much to handle

Shing

can this question really be answered by newton mechanics?

54

A: Why don't we feel the subtle speed change of Earth's elliptical orbit?

John Rennie's answer is right from the viewpoint of General Relativity -- but since the question is tagged with Newtonian mechanics, it deserves a Newtonian answer too. In the Newtonian framework, I think the best answer to "why don't we experience this force" is that we can't feel forces that a...

does newton physics explain how free fall frame = inertial frame (due to the Sun in the question)? I think this is a key to this question

bolbteppa

'Weber electrodynamics is mathematically consistent. Maxwell's electrodynamics is not. '...???

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