The h Bar

Debanjan Biswas

07:01

Hello sir!

I have a question.

John Rennie

Hi :-)
What do you want to ask?

Debanjan Biswas

Is Newton's third law of motion universal because conservation of momentum is universal?

John Rennie

Yes

Debanjan Biswas

Thank you sir very much for help!

John Rennie

OK :-)

Debanjan Biswas

07:11

Sir does Newton's third law work in quantum and relative physics?

John Rennie

Yes, because momentum is conserved in quantum mechanics and special relativity.

2

In general relativity things are a little more complicated, but basically conservation of momentum still applies.

Debanjan Biswas

Again thank you sir!

Manas Dogra

$3\times 3=6+3^*$---How does this represent the fact that there cant be a two quark hadron---I know the reason due to confinement and the meaning of LHS of that equation(bound state of two quarks(fundamental reps of SU(3) ), and also can do the math why it is 6 and 3 dim irrep on RHS...but not why this decomposition represents the fact that there cant be a two quark hadron?

ACuriousMind

07:50

@ManasDogra Confinement means that all states we actually see are color-neutral. What does color-neutral mean in terms of SU(3) reps?

Sir Cumference

@DebanjanBiswas Newton's third law doesn't really hold in relativity. "Classical Mechanics" by John Taylor gives a good intuition:

Manas Dogra

08:10

@ACuriousMind 1. But then what? There is no 1 on RHS that's why?

But even in 3*3*3 there is a 10 which is the baryon decuplet. In that way can't the 6 on RHS give rise to a bunch of colorless states?

ACuriousMind

@ManasDogra I don't know what you mean - the decuplet has nothing to do with any "10" color representation

there's a 1 in $3\otimes 3\otimes 3$ because the $3^\ast$ from the $3\otimes 3 = 6 \oplus 3^\ast$ tensors with the third $3$ into a $1\oplus 8$

and that 1 is the colorless 3-quark state

the decuplet is a "10" flavor representation of the approximate SU(3) flavor symmetry between up, down and strange, not a 10 color representation

Feynman_00

Is this a standard procedure solving equations with Fourier transform?

ACuriousMind

08:25

What does "standard" mean there?

there isn't a book of approved standard equation solving procedures, exactly :P

Slereah

@ACuriousMind Have you never seen an engineering math book

Feynman_00

Slereah, you kill me every time :P

ACuriousMind

@Slereah no

I live in blissful ignorance

Slereah

They love to have big books of standards for math

dlmf.nist.gov

State approved equations

ACuriousMind

like..."solve this equation according to ISO 652421"?

Feynman_00

08:31

@ACuriousMind I mean if it's common to choose a delta function there. Up to this day I didn't know how to solve in that situation

ACuriousMind

@Feynman_00 I don't really understand why that matters. If it solves the equation, it solves the equation - why is it relevant how many other people solve it that way?

Feynman_00

Because if it this has a name I can search more about it :P

Slereah

You basically have three standards for Fourier transforms

Debanjan Biswas

@SirCumference I don't know what are you telling about. Shouldn't Newton's third law hold in any way?

Slereah

Depending on which side you put your 2 pi factor

left, right, split down the middle

Feynman_00

08:37

Anyhow, thanks to that I'm now able to solve heat equation transforming time too

ACuriousMind

@DebanjanBiswas There is an ambiguity about what "Newton's third law" means in a general context. If you mean "forces are opposite and equal", then it's false e.g. in the presence of EM fields. If you mean "momentum is conserved", then its generally true but you have to assign momentum to fields. See physics.stackexchange.com/q/114466/50583 and its linked questions for plenty of discussion around the validity of Newton's law.

That's why you get John saying it's true (momentum is conserved) and SirCumference saying it's false (forces are not necessarily opposite and equal in EM/relativity)

John Rennie

@DebanjanBiswas At speeds close to the speed of light things get a little complicated because the momentum is no longer given by p = mv. Instead we get p = mv/√(1 - v²/c²)

Slereah

sometimes I wonder if it is such a good idea to drill various laws into people's heads and then tell them that actually no, they're not true :p

ACuriousMind

I approve of teaching people early that laws are made to be broken :P

Manas Dogra

@ACuriousMind Oh..sorry I confused the flavor and color representations

Thanks

Sir Cumference

08:40

Drilling into people's heads things that are true for 99% of everyday life seems reasonable :P

Feynman_00

@Slereah It develops a physical mindset imo

Slereah

sometimes

sometimes it just makes people wonder about relativistic mass for 30 years

Sir Cumference

If there's one thing I kinda wish most people were taught about Newton's laws, it's that the first is really just a special case of the second

Feynman_00

Lol

Sir Cumference

Namely F=ma with F=0 implies a=0

It somehow never occurred to me until I read Taylor in sophomore year

Slereah

08:45

Newton's laws were written in a different context

Feynman_00

@SirCumference the first actually provides a framework for the second

Slereah

When he says that objects at rest are in rectilinear motion, he means "And not standing still as in Aristotle's physics"

Sir Cumference

well, I'm not too familiar with aristotle's physics

Slereah

We probably should be dropping Newton and Euclid's lists of theorems really

Sir Cumference

I did find it worthwhile when my textbook mentioned it tho. Would be useful to note in intro physics classes

Slereah

08:47

There are better versions of them now

Feynman_00

Imagine a Aristotle PSE

Slereah

That's what people did in ancient greece

Go to the Agora, ask Aristotle some questions

Feynman_00

I expected Philosophy SE in place of Greece

Sir Cumference

I wonder if there's a good way to teach an intro physics class without making it feel like everything falls out of the sky

Like give a good motivation for the definition of force and whatnot

ACuriousMind

@SirCumference see physics.stackexchange.com/a/70188/50583

Sir Cumference

08:50

I doubt there'd be enough time for that tho

Slereah

just push the student

he'll get it

ACuriousMind

joshphysics' answer is excellent and imo everything you really need to know to understand how Newton's laws work in a modern framework

Slereah

you just have to remember that basically no physics concept is intuitive

people have argued for centuries about what a line was

Sir Cumference

@ACuriousMind Interesting, I'll give it a read later tonight

Slereah

So it's a bit of a tall order for a kid to be expected to pick it up in an afternoon

Feynman_00

08:51

I wanted to repost that link but I was overwhelmed with laziness

Slereah

Basically this

Sir Cumference

@Slereah It depends how you view it I guess. There's an intuition for most of math, and if you accept the applications of math to physics, you get an intuition for the physics

Usually the trouble is that second step tho

ACuriousMind

@Slereah eh, people in the past were clearly just stupid

May 3, 2021 at 16:28, by ACuriousMind

imo, "intuition" is just a word for "I have seen this so often I don't need to think about it anymore" like 90% of the time

Slereah

@ACuriousMind Babies born now are as smart as babies born in the past though

Sir Cumference

@ACuriousMind That's very different from my definition :P

I'd say something's intuitive when it feels natural and obvious

Slereah

08:55

Can't expect them to come up with it any more than cavemen

Sir Cumference

Knowing how to apply e.g. the fundamental theorem of calculus without thinking is different than having an intuition of it imo

Slereah

I don't think anybody has an actual intuition for the FTC

Sir Cumference

The sum of all changes in a function equals the net change :P

That always holds. And it still holds when you take limits and end up with derivatives/integrals

Slereah

I'm not even sure we do for the pythagorean theorem

convergence of the sum of 1/2^n otoh

Big square become little square

very easy on my caveman brain

Sir Cumference

@Slereah well are we considering the pythagorean theorem to just be the 2-norm

Slereah

08:58

Just as Pythagoras himself did

Sir Cumference

I'd seen a good intuition for why the 2-norm is usually the most preferable one

imo most definitions in math are meant to formalize an intuitive concept. e.g. rings formalize the concept of multiplication, inner products formalize the notion of angles, etc.

Slereah

Angles didn't exist in Japanese mathematics until the arrival of the Dutch

It's not as intuitive as you'd think

Sir Cumference

I mean inner product spaces are still motivated by the notion of angle, no?

namely giving a precise definition for them

Feynman_00

Japanese Physics before then: $\omega=\dot{}$

Sir Cumference

I'm not saying angles are an obvious thing to come up with, but just that math begins with taking a rough idea and giving a formal definition for them

Slereah

09:02

They just used lengths for everything IIRC

Sir Cumference

in fact the decision on which axioms to accept in math is a matter of what you intuitively want to accept as true

all right i oughta stop philosophizing and get back to grading

Slereah

09:14

If you want to do intuitive physics like geometry you can always check the constructive relativity stuff :

Metric tensor is just a lil circle

And the curvature of space is the deformation of that circle into conics

Doing all of physics as defined by the objects themselves instead of abstractions into arrays of numbers is what people have done historically a lot, really

But once we found out about analytical geometry we just sort of never wanted to go back again

It is either very powerful or we are very dumb

Sir Cumference

There's more to intuition than just seeing things visually tho

generally being able to break down an abstract concept into something familiar shows up throughout math

Slereah

The circle basically does 1) set a length 2) tell you that things are the same in every direction

if you deform the circle, you are changing those things

That is the connection between Euclid's geometry and modern Cartan geometry

ACuriousMind

@SirCumference if multiplication is so intuitive, why do we need to teach kids multiplication tables? :P

Slereah

Just teach kids about dagger compact categories

ACuriousMind

multiplication is only "intuitive" to you because you've known how to do it for so long you've forgotten that it was once alien to you

Sir Cumference

09:26

I was thinking along the lines of how we define things in math

i.e. whether we interpret something as a useful notion to define

ACuriousMind

that something is useful doesn't mean its intuitive

Sir Cumference

If it formalizes an intuitive concept, I'd say it's useful

but yes, the converse doesn't necessarily hold

Slereah

Stiefel Whitney classes are very useful I am told and yet I will never understand what they are

Sir Cumference

I do feel like it tends to hold for most of my experiences with math though

Debanjan Biswas

Are there any research going on Newton's third law now? And also on conservation of momentum?

Sir Cumference

09:28

@ACuriousMind The exact values for multiplication aren't based on intuition, but knowing when to apply multiplication is often based on intuition

Slereah

I mean by modern standards we don't look at Newton's third law for that, but there are research into conservation of momentum yes

Feynman_00

I know what I'm about to say will sound stupid but I still find stunning that basic arithmetical operations succeed in describing phenomena. No special reason, but if a kid asked me "why does it work like that?" I would get a ticket to Mars

Sir Cumference

stuff like repeated addition or more general applications. that's what we typically try to instill in elementary school

Slereah

A somewhat recent topic in momentum conservation was

Abraham–Minkowski controversy

The Abraham–Minkowski controversy is a physics debate concerning electromagnetic momentum within dielectric media. Two equations were first suggested by Hermann Minkowski (1908) and Max Abraham (1909) for this momentum. They predict different values, from which the name of the controversy derives. Experimental support has been claimed for both.David J. Griffiths argues that, in the presence of matter, only the total stress–energy tensor carries unambiguous physical significance, and how one apportions it between an "electromagnetic" part and a "matter" part depends on context and convenience.Several...

It is connected to the EM Drive that you may have heard of recently

ACuriousMind

@Feynman_00 ah, the unreasonable effectiveness of mathematics

@Slereah that's one of these problems where many people agree that it is solved but not so many agree on the solution :P

Slereah

09:31

the best kind of problem

Debanjan Biswas

Do we know why conservation of momentum true? Or what is underlying physics behind it?

Sir Cumference

there's probably an intuition tying it to translational symmetry

but it's like 5:30am and i gotta sleep

Slereah

I mean there is no fundamental reason why it is true

It could be false and that wouldn't change mathematics, just physics

ACuriousMind

@DebanjanBiswas generally Noether's theorem, for a "simple" exposition without Lagrangian mechanics see physics.stackexchange.com/a/439249/50583

as long as your system is symmetric under translations, you'll have conserved momentum

Slereah

you can look at examples where that symmetry is broken and see what happens, too

like if you are Aristotle, once again

and you think that all heavy objects move towards the center of the universe

Sir Cumference

09:34

@DebanjanBiswas basically what symmetry means is that if you translate the entire system to a new location, it won't affect how the system evolves

Slereah

That is a preferred point

If you have an object initially at rest, it will drop towards the center of the universe

gaining momentum

That is an example of a theory that doesn't conserve momentum and isn't translation invariant

Sir Cumference

@ACuriousMind I do gotta say that on the topic of intuition, I find a lot of people who say it's critical to math and a lot of people who say it's irrelevant

My entire experience with math had been the former, along with other mathematicians I've talked to, so I can't really see it from the latter perspective

Or rather, I don't see it as something beyond rote memorization. But that might just be me

ACuriousMind

@SirCumference I think the problem is that it's not really clear what "intuition" is

Sir Cumference

Lots of resources like 3Blue1Brown and betterexplained.com are based around the importance of intuition

@ACuriousMind Yeah, I guess it's how you want to define it

For me I just have a gut feeling when everything seems crystal clear and beautifully makes sense

Debanjan Biswas

Isn't there more fundamental thing with more physical arguments better than Noether's theorem?

Sir Cumference

09:38

I don't really know a better word for it other than "intuition" tho

Slereah

why worry so much about what you cannot define :p

Sir Cumference

well it's an emotion I guess

it's the sole reason I like math. and the reason I think math is so great

there's this adrenaline rush when you spend many hours on a statement and suddenly get a realization on how to view it much more simply

ACuriousMind

@SirCumference Sounds to me that you just like understanding stuff :P

Sir Cumference

i guess so lol

ACuriousMind

that's what I mean when I say "intuition" is mostly code for getting used to things - everything becomes "simple" once you understand it

but people tend to conceive of understanding as binary - either you understand something or you don't - and often want to jump over that gradual process of acquiring understanding

Sir Cumference

09:46

that's true. I guess I wasn't sure how you defined "understanding" earlier

ACuriousMind

"intuition" is what - in retrospect - is imagined to allow you to skip/shorten that dreadful period where you neither understand something nor not understand it

Slereah

also trying to use intuition can backfire

because metaphores only work so far

sometimes you have an unintuitive counter example

PM 2Ring

I guess there's some built-in intuitive stuff. But a lot of what's intuitive is built on a foundation that's grown through exposure and practice.

Sir Cumference

@Slereah well, the challenge is making an ever more precise intuition ;)

which gets harder and harder, but also more rewarding

I think this is a good article on intuition vs rigor: betterexplained.com/articles/…

Slereah

Best advice I can give is that typically for any physics thing you will have many different descriptions available

just go through them until you find one that clicks

Sir Cumference

09:49

I do think I've had less luck with making physics intuitive compared to math. There's no real logic basis for how our universe happens to work

Slereah

well yes

PM 2Ring

It's like improvising in music. When it happens, it just flows. But you can't get to the state of being able to freely improvise without listening to a lot of music, and learning the fundamentals of how to play or sing. And then practising. A lot.

Sir Cumference

Like I found a really satisfying intuition for a general wave uncertainty principle, but if I try to apply that to physics, I kind of have to just "accept" that momentum and position are related in a wavelike manner

Slereah

the universe works the way it does, but it could work differently

Sir Cumference

hence I don't really have a satisfying explanation for the heisenberg uncertainty principle

Slereah

09:51

that's why you have to observe first

Sir Cumference

@Slereah Yeah. I do feel like math is more about logic whereas physics is more about observing

Slereah

if there was no other alternative physics would be easy

Sir Cumference

that's not to say everything in math has a fundamental basis, but most of my experience with it is about logical connections

ACuriousMind

@SirCumference Physics is about looking at reality and devising a model of it; not about somehow "deriving" reality out of nowhere

Sir Cumference

@ACuriousMind unfortunately, yes

ACuriousMind

09:52

even though the latter idea somehow got stuck in a lot of theorist heads :P

Sir Cumference

which is still cool in its own right with how much it reveals. but it does always leave some dissatisfaction with "why"

ACuriousMind

what answer could there possibly be as to "why"?

PM 2Ring

In Kepler's & Newton's times, they didn't really talk about mathematics. They talked about geometry. Even number theory was thought of in geometric terms. Algebra was just a bunch of dubious bookkeeping tricks that could be used to solve geometry problems.

It was dubious because it wasn't intuitively obvious like geometry. ;)

Sir Cumference

@ACuriousMind well, I guess it's a matter of how satisfied you end up feeling with an explanation :P

just an emotion

Slereah

I mean people used algebra but it was more for accounting

PM 2Ring

09:54

Even though Euclid's axioms have various large philosophical holes in them.

ACuriousMind

@SirCumference I find the disappointment goes away once I force myself to realize the question isn't meaningful :P

Sir Cumference

well my options are either turning to some religion/philosophy or just accepting it's a moot effort

first isn't really that appealing to me but I've been struggling to do the latter

ACuriousMind

the first step is realizing that "cause and effect" are social constructs, not physical truths

at least that's my pithy summary of Norton's Causation as Folk Science which I always recommend to people thinking that causation is a fundamental aspect of physics

Sir Cumference

that's an interesting perspective

PM 2Ring

@Slereah Fair point, although that's (mostly) just addition & subtraction. And the theoretical basis for arithmetic was still Euclid's Elements.

Sir Cumference

09:57

though i gotta wonder where the fine line between social constructs and physical truths is

welp it's 6am and I still am only halfway done with grading, I probably should call it here

Slereah

Hm

Sir Cumference

Night y'all

Slereah

Prequantum bundle has the hbar as a term of the curvature

and the symplectic structure does relate position to momentum, ergo relates to mass

and I guess the quantization part is the Weil integrability condition

Maybe the scale has nothing to do with the bundle, just the integrability condition

Slereah

10:14

Is polarization related to mass?

Slereah

10:24

Probably need to read up on symplectic geometry really

That's the problem of GR, mass is basically meaningless as far as geometry goes

Damn equivalence principle

Slereah