@Slereah The real statement is that we do not need to have the same types of introductions. There will, however, always be a need for introductions that treat things better. Even if it is just a niche, it would scratch an itch.

@Amit You literally cannot have found a worse example for your point. Classical mechanics is the one field of study whereby every century we find something completely new---we are STILL finding new things about Lagrangians and Hamiltonians!

@SillyGoose And now for professors and book authors to write them down pedagogically...

@SillyGoose s/calculus/measure theory/

@SillyGoose It is totally not clear, but if it exists, it is often the case that the integral version is nicer to show properties with.

Thinking about it, considering the moduli space at the Minkowski metric is gonna be the wordt place to do so since that's where the topology is the worst

That's where all the isometries converge

I dislike it when people start to go ballistic. As rational as the physics community portrays itself quite often I run into these a particular kind of people who disincentivize conversation.

Rant over

@MoreAnonymous re your question about temperature: I suspect this is one of those silly issues to do with terminology.

It's like saying numbers are countable but the number line isn't.

@JohnRennie perhaps but as you point out silly and not a reason to be rude

@MoreAnonymous There is never a reason to be rude. Sadly it happens.

I wasn't commenting on the rudeness or otherwise of the comments to your question. I was just trying to answer it. I commented here as I don't think what I've said counts as a full answer.

I didn't mean you are being silly! :-)

If people are being rude flag for their comment for the mods to look at.

None of the comments look particularly rude to me. Flatterman is back on his hobby horse but that's just him.

@JohnRennie agreed

@JohnRennie thanks

@JohnRennie if you remember this question. I solved it for the special relativistic case as well. Interestingly the answer does not reduce to the naive one in classical mechanics

Could you cross check the answer?

@naturallyInconsistent Okay, I am probably indeed ignorant of such developments.. but would you say these discoveries actually enable us to carry out calculations better for classical physical phenomena? What I wanted to emphasize there is the "ideal codification" part.. and btw I realize this is a bit tricky too, because this formalism is also now extended to apply to QM

It can be tough to judge me being a theory bloke but I can tell you that some of the worst math I've seen has been in papers for dynamical systems, including robotics

People do really weird math in classical mechanics since they have to simulate very complicated systems

@Amit The most common result of a calculation (especially integration) is zero; any mathematical scheme that makes it obvious that some calculation will end up to be zero and thus can be omitted from actually performing a calculation, is an important advance. Note that conservation laws are versions of these: the deviation from momentum conservation is always going to be zero, etc.

And then you have schemes that actually improve the computation of tiny perturbations.

When you have to model objects which can change shape, change mass, break, etc, you have to use really complicated formalisms

if you want to avoid having to just do very heavy numerical calculations

@naturallyInconsistent Okay, I understand the idea but just wasn't aware any progress is still done there :) Thanks 👍🏻

In the case of symplectic computations, it turns out that if you want to naïvely numerically integrate things, then you really ought to know that you should avoid Hamiltonians like the plague. The whole point of having Routhians in Goldstein, is precisely because, while Hamiltonian analysis makes it much easier to extract the conserved quantities and thus eliminate entire computations, the leftover degrees of freedom will be BADLY numerically unstable if you use naïve integrators

And so you are supposed to convert to Lagrangians for those specific degrees of freedom, called Routhians

Sounds cool, like the name of an arthurian legend

The progress in the last half century made this problem go away---you are supposed to use symplectic integrators that are shown to work well with Hamiltonians, and then you do not have to care so much.

So these manifolds actually turn out to be useful?! Amazing ;)

But, as you might suspect, the teaching of stuff move incredibly slowly, and so dangerous non-symplectic integrators are still being taught.

Doran and Lasenby even just blithely claim that everybody should only try to integrate Hamiltonian mechanics, and made no mention that this advice could easily have landed people in tears!

Physics students are used to hear "so what you did up till now was the bad formalism.. here is how it really should be done" it's good for the ego, humbling, .. :D

@Amit I am actually not sure that the symplectic manifolds mathematical machinery is useful to that. They certainly are all worded that way, but the work does not necessarily need the mathematical machinery in order to work, or even be discovered.

@Amit More like anger inducing

Maybe I could modify my observation then. When the problems with a physical theory become mainly calculational rather than theoretical, it implies it is about to be superseded theoretically. WDYT? :)

I am probably just being a historicist, which I don't really like

I don't know if that is a useful observation, or even a true observation

Fair enough, I'll make no more historicistic comments :)

It is more fun to study the cases when the seriously established theories start having a lot of inconsistencies and experimental refutations, because that is when paradigm shifts are incoming.

Hi

@Slereah i have studied philosophy

on wikipedia :P

I think i was premature in declaring the modern world as peaceful times becuz the period since world war 2 is only 80 years old. So this era is probably a fluke going by the reputation of human history

it's a disgraceful fluke... 'cause we just did a lot of smaller wars in this time since WW2, we hardly even took a break, lol

WW2 only made people afraid of nukes, not of war in general

Yes, everyone had been constantly invading everywhere until only 80 years ago. So 80 doesnt mean shit. Invading and mass murdering era is not gone. Global tensions r rising up again right now

I think our kids' or grandkids' generations wont b so lucky

We worry about employment and stuff. They wud worry about staying alive. Becuz the next war wud kill a lot, even going by % population, becuz of nukes

@RyderRude What do you mean "constantly invading everywhere"?

Again, the past is not a place inhabited by murderous barbarians (at least, not any more than the present is :P)

I beg you to learn some actual history

@ACuriousMind yes, maybe people in most countries were still living peaceful lives. But i expect the% of population in danger to be higher in the past

@RyderRude Based on what evidence?

And they often killed entire cities after winning

Even if correct, there are other dangers apart from war

Yes, the diseases were worse in the past

I know some people who try to claim this (prime example being Pinker's The Better Angels Of Our Nature), and I know some scholars who disagree with this analysis

@ACuriousMind there r many cases of emperors mudering entire countries after winning

what both of these sides have over you is that they cite actual evidence and not some completely ahistorical idea of what "emperors" were like

@RyderRude "many cases"? Name 5.

Genghis khan is one

Alexander did do mass murders of civillians, didnt he?

He most certainly did not

Nor did most people

@RyderRude Did he?

Again, cite some evidence

@RyderRude Talking about percentages, when looking back at history there's another percentage-like bias to avoid: history is by definition a lot longer than just the immediate past, so you really should be quantifying the frequency of wars rather than the amount. Phrases like "our bloody human history" are true but that's because history is so long

Mass murder was not a smart idea in ancient times since you conquered territories to get their riches

and this was not an era where it was particularly practical to recolonize a land like that

They used to be rage fueled, not rational

I'll take any evidence at all over this deeply warped picture of the past you seem to have

Lemme google

lawl

@RyderRude Again that term, "rage-fueled". Where did you "learn" that "fact"?

Natives were mass murdered. (no citation needed)

@user85795 exactly!

Thank u @user85795 :)

The massacre of natives was in the modern era and also not quite massive as you'd think

they were also not particularly rage fueled

Well i only claimed the last 80 years to be relatively peaceful, so the native american genocide does count in the past

they were just to steal the local land

But that's not war if they can't fight back 🫣 lol, j.k.

The Brits mass murdered in India.

@user85795 Most "slaughters of natives" I know of are in the context of colonialism and are very different from (though no less horrible) "emperors" killing their enemies after winning.

@ACuriousMind but it does mean that the past was worse

Wasn't the Holocaust mass murder.

It certainly was

also a modern phenomenon, though

@RyderRude Colonialism is a rather modern invention

@user85795 thank u :) British Empire mass murdered in Ireland too

Mass murdering an entire population was just not too practical to do before the modern era?

Also this was before nationalism where people might have such motivations to do this

@ACuriousMind but i only claimed the last 80 years to be relatively peaceful. So any mass murder before that supports my claim

@Slereah But the bible seems to encourage this at some parts, so I'm not sure it wasn't done... just took longer

@RyderRude You've been making claims about Ancient Greece or whatever, talking about "rage-fueled emperors" and Alexander the Great

@Amit The bible is mostly tall tales

There were no actual such gigantic massacres of canaanites

Now saying "we haven't had a holocaust lately so it's more peaceful now than in the past" is a completely different claim from what you've been implying before that.

@ACuriousMind that may be wrong. I will have to research. But i have read anecdotes from historians about that too. Several historians say that Alexander wasnt much betr than Genghis

Not to mention we still have concentration camps right now

No I'm not talking about it as historically accurate, I'm taking it only as evidence that the idea of such mass murder / ethnic cleansing of different types was already present

Yes indeed.

But even if it's wrong, @user85795 has given great examples about why the past was awful comapred to the last 80 years @ACuriousMind

I mean the natives are still badly treated right now

including up to murder

@RyderRude Are you sure you're not saying that only because you happen to be on the non-awful side of things? :)

en.m.wikipedia.org/wiki/Great_Famine_(Ireland)

and still getting thrown out of their lands

Pls see this. One million deaths

There are still famines right now caused by colonial powers that force farmers to farm non-food crops

@RyderRude Are you aware of the Pax Mongolica? I imagine the people living right after Genghis' conquests were also saying "oh, how peaceful our times are compared to what came before!", arbitrarily drawing a line between the "past" and the "present", where the "present" conveniently starts right after the last great massacre of the Mongol horde's invasion

That's what you're doing: You're drawing a completely arbitrary line in the sand to declare "the present" as better than "the past"

not to mention I'm not really that optimistic about the future in just a few years

the fact is that periods of conflict and periods of relative peace have always alternated with each other since the dawn of civilization

It's the old statistical trick to look at some stochastic graph and find the one scale at which it goes the way you want

@ACuriousMind u r right. It seems like i am engaging in a fallacy. I will have to think about it

Because we have a hard time to comprehend the hard reality that the only peace we ever had on this earth is the peace between two wars

Btw here is the stuff about Alexander being a mass murderer : serious-science.org/….

He wasnt much better than Genghis

@ACuriousMind but u still have a good point. I will have to come up with a better criterion of "average peace"

Tbf i did just mention that i was premature in declaring the modern era as peaceful

And that the next world war wud kill a gr8 percentage of today's population

I guess my new hypothesis is that countries dont tend to be expansionist anymore becuz we arent an agriculture and land based society anymore. So i hypothesize that the past used to have more frequent invasions and mass murders becuz of expansionist mindset of empires @ACuriousMind

Today, we still have some expansionist countries

But most countries dont worry about land

@RyderRude You still haven't established that any of this was more frequent in the past

Also modern times have the threat of nuclear war if the war between the wrong countries occur

Yes, Genghis Khan and Alexander the Great were exceptional conquerors who killed a lot of people. There wasn't one of them every 10 years or whatever it is you're thinking

It makes the landscape of modern war a bit different

Information is the next "war."

Is it weird that this conversation made this song play in my inner ears? lol

@Slereah this is y i think modern peace is a huge fluke. We r heading toward an era much worse than even Genghis Khan's mass murders

Becuz nukes wud kill like 50% of everyone

For a person living in the heart of the Roman Empire, there were hundreds of years where their homeland was not invaded, plundered or whatever. Much like the wars of the US and that of many European nations today, Roman wars did mostly not occur on Roman soil

It occured even less afterward since it was pretty hard to raise huge armies outside of that

While the Greek poleis warred with one another, the sack of one of the greater cities was rare. Athens went 400 years (from ~480 BC to ~80 BC) without a major invasion

and here you are, @RyderRude, somehow convinced that the not-even-a-century since the last world war is somehow an unprecedented era of peace. Do you understand why I want evidence?

Welll.... i shall yield now on that one. I agree modern peace is a huge fluke

They never had the internet back then :P

And even more temporary compared to some pieces of peaces of the past

The modern peace isnt much remarkable, yes

@Amit classic

✅

:)

I thought technology brought peace becuz countries stopped worrying about expanding land when information became the new land

But US has invaded for oil

And Russia has invaded for some idiotic reason

@RyderRude Do you understand what the cold war was? Like, why it was called "cold" and why it more or less stifled any actual expansion from either side?

Not defending US. Dont get me wrong

Both are idiotic and wrong

@ACuriousMind i dont know much about cold war, yes

I will have to read about it

A cold war is a war without heat :P

Am i wrong in thinking that an inter-galactic colonisation wud bring lots of human peace

Only genetic engineering imo

Becuz when u have entire universe to go to and be safe, why go to war

I think we go to war becuz we r cramped on earth

But ideological wars r not solved by an intergalactic expansion

As shown in Star Wars prequels

They had a one government democracy for the entire galaxy

@Amit i also think AI can bring lots of human peace if they are friendly AI

From where I'm standing, technology indeed brought "peace". But not information technology and cultural understanding or whatever. It was the fear of the atom bomb and the doctrine of mutually-assured destruction. You seem to have no concept of how universally present the threat of nuclear war was in the public consciousness during the cold war.

I am familiar with mutually assured destruction. It is partly responsible for this fluke of peace

@RyderRude So you don't even really know about the most significant geopolitical concept for the immediate post-WWII period and yet you proclaim to know what changed the nature of war with such confidence.

But i dont thik Mutually assured destruction is an advantage in the long term

MSD is a double-edged sword

@RyderRude I'm not saying any of this is "good"

And the other edge is much worse

you're once again jumping to judgements without first making sure you've got all the facts

@ACuriousMind it brings some good by bringing this fluke of peace

Becuz it makes countries afraid to attack each other

But i think MAD is not worth having in the long run

Becuz having MAD around also means having the capability to destroy the world. And there will someday be some crazy leader who wont be afraid of MAD

Some people do argue that MAD is a good thing lol

I always think about people who watch "Dr. Strangelove" today and enjoying it... how often they don't understand the level of chill (in addition to hilarity) this movie must have induced due to when it was released

Only becuz it has been responsible for the peace in the last 80 years

@Amit i still havent seen it. I will see it now

You're lucky, you're gonna have a lot of fun I think :)

I love old movies. I've never seen a Kubrick movie

Except The Shining

I thought The Shining was bad tho lol

Oh, it's a totally different style

Yes, it's not for everyone. Very weird movie

I thought it wasnt scary

The house was chilling tho

I didn't watch many Kubrick films, but Dr. Strangelove is a classic, also very well known, though probably not as much as 2001

I turnes off 2001 becuz the first 20 minutes only had chimpanzees :P

With regards to horror films, I have a general dislike for them so The Shining is one I'm not gonna try anyway :)

But i love satire movies

lol

With Dr. Strangelove, it's really nearly solely the genius comic ability of Peter Sellers that makes this movie so hilarious

I loved almost all of the "Pink Panther" movies

That star Sellers... (the new ones aren't nearly the same)

Ive not seen them but the cartoon had great physics

Ahah, that I can't recall

There was this one time Pink panther got sucked into a vacuum

And then the vacuum sucked itself

They vanished into a singularity

I mean a vacuum cleaner, sorry

Yeah, somehow I guessed that's what you mean :)

It's the one. Near the end

But you should really watch Dr. Strangelove and imagine what it would be like to see it in 1964... omg

I will watch it next

This vacuum cleaner scene made me think for long whether it was actually possible :P

In principle, I mean

You started early?! :) I don't remember such thoughts intruding on my cartoon fun as a kid, lol

This one scene was just mindblowing to me :)

But i also had some very shitty physics concepts back then

Soo shit even for child standards

I thought things passed through water....

I guess im still an idiot lol :P

They don't pass through water??

Idk :P

JC apparently knew they didn't

I also imagined air as things passing thru it

As if air was a spooky substance

@Amit whats JC

It depends on what you mean by pass through I suppose

Jesus Christ

That's how he did that trick

Oh. I was behind by 2000 years of physics

lol

He taught us about surface tension yeah

and probably he did it after a very long fast to be light enough

which all fits nicely together, fasting is holy

Lol

also, maybe it's called "fast" 'cause it lets you go "fast" on water??

hi -- i have a question about the effective potential in the radial equation. it seems that if you have any orbital angular momentum, then there is an angular momentum barrier, which i guess results in a decreased chance of finding a particle in the innermost radius. i get where this result comes from mathematically, but conceptually i dont see why it should be the case that something with orbital angular momentum cant be found at a low radius somewhat regardless of the form of V(r)

There this is stuff called idk... it is a lot of particles that almost pass thru everything

I forgot their name

They dont interact much

neutrinos?

Yes!

@RyderRude wow, first time I saw this now. I can now see why it can be somewhat disturbing to a kid's perception of reality lol -- that end

Socially challenged particles

lol

@Amit lol. Glad to know im not the only one :P

or just snobbish

Cartoons used to be such innocent fun, no complications, just moving pictures with fun, clever and thought provoking events for kids to enjoy

And very little if any talking

Perhaps even Socrates would have approved

@Amit yes.. These days they dont make cartoons like that. They had very creative physics

Like gravity used to turn on after u look down

I think they make the characters talk too early in today's cartoons. Talking can stifle the development of imagination I think, because the network of language is much more restricted than the visual one

Yes, the looney tunes were mostly silent

They had just had music playing all the time

@Amit another completely ahistorical claim; for instance political and satirical cartoons have a tradition that goes back to the beginnings of the artform. Just because you watched a bunch of "innocent fun" cartoons as a kid (and as a side note you may be surprised to discover they aren't all that "innocent" if you watched some of them today!) doesn't mean that's what "cartoons" in general were

Good music very often, too

@Amit this is a great analysis!

consider, for example, 1942's Der Fuehrer's Face

@ACuriousMind I'm not sure what you mean -- you mean they weren't necessarily aimed at kids?

@Amit Yes.

Oh, I understand that. What I meant to convey was, the cartoons that kids used to watch

but that's not what you said!

Agreed, I stand corrected

it's not that "cartoons" as an artform changed, it's that you and the kind of media you consume changed

@ACuriousMind wtf lol

@ACuriousMind I was trying to claim, however lamely I may have phrased it, that the kind of cartoons / animated pictures kids watch today is different than it used to be

oh hey, Wikipedia gave us a button to toggle full-width display again!

my understanding is, he defines the S_z spin up and down as eigenvictors in hilbert space

Which span the space. with eigenvalues h\2 plus or minus

@Mad Why would it be anything other than the operator for spin in the z-direction?

Sakurai is one of the reasonable people who doesn't put silly little hats on every operator :P

Thanks for confirming

I find it difficuilt to read into his mind. I generally do not find the book well formulated, i am stuck with it nevertheless since its canon to my professor

Wow. This book starts with spin?

I guess it wants to take it easy using finite dimensional Hilbert spaces maybe

however. there is something to be mentioned.

This is the representation given if the defined mapping hermetian.

@RyderRude imo the first chapter is mostly notation using spin as examples -- spin isnt really treated until later on -- mostly in ch 3 i think

@Relativisticcucumber yes. I was also thinking it was just to introduce QM using a finite dimensional hilbert space

I see no physical reason why one would assume this.

Otherthan forcing eigenvalues to be real.

Interesting that wikipedia draws the line at 1945... @RyderRude

Infact, he is forcing by defining it like this, the operator to have such eigenvalues and eigenvectors. Is thi sbased on the empirical conclusion of Stern gerlach?

@user858770 thanks for this. I think maybe this is either becuz MAD has reduced the frequency of mass murders, or becuz they count post-World war 2 world as modern becuz of the UN

@Mad But eigenvalues of observables have to be real

when you measure a physical quantity, you get a real number

that's the whole point of declaring that observables are self-adjoint operators

@user858770 after going through the list, it seems like post WW2 mass murders are even more frequent

@RyderRude also there are so many links at the bottom

Nevermind

I don't think The Encyclopedia Britannica devoted this much space to human suffering.

Crazy that post WW2 massacres are more frequent. I guess massacres dont correlate well with invasions

Becuz massacres are mostly domestic

Other countries dont need to get involved. Minorities often get massacred

MAD only prevents invasions

lol

Sorry, can't help but notice @Mad vs. MAD thing happening here

I noticed that too lol

I think i shud hypothesize better. It was very dumb to think that less invasions mean more peace

Becuz massacres are mostly against domestic minorities. No correlation with invasions

@ACuriousMind Kronecker weeps

Trying to figure out if I should use $d$, $T$ or $*$ for the differential map

all have pros and cons

since they all are a bit overloaded as symbols

the push forward?

yes

I like the $*$ because it reminds you of where the index in the related vector goes

I mean, you can pretend that the star is contracted with the index. Is that a horrible way to think about it? lol, anyway it's just a memorization device

The $\ast$ is a limb: $f_\ast$ is the pushforward - the $f$ is kicking something forward with its leg. $f^\ast$ is the pullback - the $f$ is pulling something backward with its arm

$\phi^{🤜}$

lol, nice

Is phySE past its peak popularity or is it growing

I see many top users have retired from the site

But they r a minority. Most top users remain

My way to go is the following: $df$ is the differential and $f_*$ the pushforward

I mean, they are the same thing but depending on the context I make a distinction

When I only care about the map between tangent spaces locally approximating the function $f$, I call it $df$

When I'm concerned with getting a vector field on $N$ from a vector field on $M$ given a diffeomorphism $f:M\to N$, I call it pushforward $f_*$

A generic differentiable function cannot be used to pushforward fields

@Slereah Whoah, you can raise emoji indices

the wonders of unicode

$R^{🤌}{}_{🤌}$

Italian Ricci scalar

Seems like many users left during covid

joshphysics and seleneroutley left in 2020/2021

I liked their stuff. Maybe they hav left temporarily

$\varepsilon_{🍕🍝🍦}$ -- the Levi-Civita symbol (.. that it's time for dinner)?

lol, didn't know emojis and mathjax could be friends

not the case for all implementations of mathjax

but it does work here

Hello everyone, someone please tell that why the pairing of nucleons reduces energy in the shell model? Or why does pairing reduce energy in general.

does anyone know any place, any resource, where I can find kind of a list of all the topics in all the graduate level physics subjects like QM, ED, Nuclear Particle, Atomic Mol. etc. I want to know what I have covered and what not for my interview. @Amit @Mr.Feynman anyone.

@ShikharChamoli Is Google broken? :D

@ShikharChamoli Please don't ping users randomly.