The h Bar

naturallyInconsistent

01:12

@Mr.Feynman as long as it aint the ... toys ... drawers... you're fine

qwerty

01:46

@naturallyInconsistent I'm sure all is forgiven/ expected when you're a cat

zzzzz I'm so tired

naturallyInconsistent

@qwerty that's why in the kitty abode it is just all over the place miehehehe

@qwerty fluffy duvet attack

qwerty

I didn't know cats wore clothes :p I assumed this was like the meme... "on the internet, no one knows you're a --dog-- cat"

@naturallyInconsistent I wish I was in bed lol T_T

naturallyInconsistent

02:11

fluffy duvet attack can be done almost anywhere

123

06:01

Hello Everyone...

Ryder Rude

07:17

hi

123

Hi @RyderRude

I would like clear few concepts.

Ryder Rude

07:50

@123 hi

@123 just ask. if anyone knows, they will answer

5

123

Sure

Does any object and location in the universe can be considered as frame of reference? like surface of Earth, human, bus, train, airplane, or an empty space .

we embed coordinate system to the frame of reference.

I have learned frame of reference is physical idea. and coordinate system is mathematical concept

Mr. Feynman

@ACuriousMind Incidentally, I'm not sure that I ever mentioned it or that I should write a supplementary answer there, but I eventually found a not-so-deep reason as to why indices behave like that (even if your point still stands of course)

Slereah

A frame of reference is typically represented by 4 objects

one object as the origin, and three objects to define directions

If you're in a bus that will be for instance be your seat and the 3 orthogonal walls :p

Then you can define positions in terms of lines passing through those objects

Mr. Feynman

The reason I'm talking about is related to Clifford algebras. The Dirac matrices exhibit the same "weird" index behaviour. In reality, you should consider them as acting on the tangent space. Oh, ok. I've found the message

Feb 15 at 20:29, by Sir Crackpot

A more proper way would be that the map $\gamma:\mathbb{R}^{1,3}\rightarrow\mathfrak{gl}(4,\mathbb{C})$ is invariant, but $X$ is not, so when we make a Lorentz transformation, $\gamma(X)\mapsto\gamma(\Lambda X)$

123

08:25

@Slereah Hello , Thanks.

naturallyInconsistent

@Mr.Feynman The "weird" is actually not weird at all. Earlier, I mentioned the answer: of the 4 indices on the Lie algebra generators, two of them are proper Lorentz tensor indices stating which component of the matrix is being referred to, and these tensor indices must be one-up-one-down in order for the matrix exponential to work correctly. The other two indices, however, are labels, and there is no contraction with the metric, there is no rhyme or reason or mathematical consistency relation

that they should be having.

That's why ACM's answer also complained that they can be both on top, or both below, or what have you, as long as you have a completely consistent way to deal with them.

Ryder Rude

09:03

The Fly is a really bad movie which has good ratings

it has a mysterious first half but then there's no plot

imbAF

@naturallyInconsistent I have one question I want to ask about notations in four vector algebra. I yesterday was discussing with ACM and Mr.Feynman about a particular issue that I was having

imbAF

09:16

I thought about how to solve exercise d) in a logical manner. In a way that I can argue what I did and I thought of doing the following

Since 1d) it essentially says that I need to use eq. (4). I though to look at eq (4) component-by-component and then observe that certain components of L^{mu nu} are related to the Ki in eq(6) and other components of L^{mu nu} are related to the L_i.

But what i don't know is whether I also need to change the indices $\mu\nu$ at $L^{\mu\nu}$ to so actual value to show what I want e,g $\mu=0$ $\nu$

naturallyInconsistent

09:33

@imbAF this is almost close to a question I might be able to help, but as it currently stands, I'm not sure what you are asking

imbAF

10:09

What do you mean?

naturallyInconsistent

What are you even asking?

imbAF

Whether in order to rewrite angular momenta and boosts via the generators, I need to explicitly give concrete values to mu and nu in eq 4. Or not

Because I can consider an arbitrary generator, which would translate to keeping $\mu\nu$ arbitrary and considering an element of the generator

naturallyInconsistent

Concrete values of i in L_i are mapped to specific mu nu values in Equation (4)

imbAF

So then, I need to argue that i.e $L^{\mu\nu}$ where \mu=0 and \nu arbitrary is a boost

naturallyInconsistent

Yes, something like that.

imbAF

11:01

Is it correct to say that:
The rotation generators J_i are related to the spatial components $L^{ij}$ of the Lorentz generators::
$J_i=\frac{1}{2}\epsilon_{ijk}L^{jk}$

123

Inertial frame of reference

In classical physics and special relativity, an inertial frame of reference (also called inertial space, or Galilean reference frame) is a stationary or uniformly moving frame of reference. Observed relative to such a frame, objects exhibit inertia, i.e., remain at rest until acted upon by external forces, and the laws of nature can be observed without the need for acceleration correction. All frames of reference with zero acceleration are in a state of constant rectilinear motion (straight-line motion) with respect to one another. In such a frame, an object with zero net force acting on it, is...

Pls read the first sentence. They said inertial frame of reference is a stationary or uniformly moving frame of reference. My question is that "stationary" or "uniformly moving" with respect to what?

Because if frame of reference is inertial. We can never say whether it is stationary or uniformly moving.

qwerty

> All frames of reference with zero acceleration are in a state of constant rectilinear motion (straight-line motion) with respect to one another.

all you had to do was read the next paragraph.

123

11:16

I was confused why they said stationary word. Is there any explanation to use word stationary

qwerty

why?

naturallyInconsistent

@imbAF IIRC, yes. You can also invert this equation for the other side.

imbAF

but J_i is not the rotation operator right

cuz the rotation operation is the lorentz transformation of that particular rotation right?

naturallyInconsistent

@123 You are yet again stuck at the most ridiculous places. Stationary is a special case of "uniformly moving", and it is simply necessary to write like this because English itself required that people say things like this. The language assumes that $v=0$ is different from $v\neq0$ even though we now know that it is not so.

imbAF

@naturallyInconsistent the rotation transformation in 4D = angular momentum ?

naturallyInconsistent

11:21

@imbAF ah, yes, if you have non-zero spin, then the rotation operator will have spin parts too. However, at the location where you are doing these expansions, you are only dealing with scalar, i.e. spin-zero, fields.

imbAF

I am not considering spin or anything

123

Sorry NI my bad.... Thanks to clear me. 😊

imbAF

I mean it's crazy that 3 days in and I have no clue wtf the exercise wants

But can you tell me how LT are related to angular momenta and both how are related to generators

so you have : 1. Generators , 2. Angular momenta/boost operators, 3. LT

can you give me an overview or picture how things are connected

naturallyInconsistent

@imbAF The infinitesimal 3D rotation operator, i.e. Lie algebra generator, ends up being the same thing as angular momentum operator. In 4D you also have boosts, which is a hyperbolic rotation, but it no longer has the symmetry properties like rotations do.

imbAF

And if I am asked to write the momentum operators, via the generators of $SO^+(1,3)$

using $(L^{\mu\nu})^\rho_{\ \ \sigma}=i(g^{\mu\rho}g^\nu_{\ \ \sigma}-g^{\nu\rho}g^\mu_{\ \ \sigma})$

Is it asking for me to give the LT corresponding to angular momenta operators and boosts?

Or their generators

naturallyInconsistent

11:27

If you are asked to write the momentum operators, then because of the equality, it has to be the generators, not the LT group elements

Anyway, the closest thing I can give you as the reason why these things have to be linked, is Noether's theorem.

imbAF

and why not the LT eleemnts?

aren't the momentum operators and boost operators the elements?\

naturallyInconsistent

I dont know how much clearer you expect things to be. ACM also tried to explain to you. They cannot be the same thing because only the Lie algebra generators form a vector space. You keep wanting to confuse these things with group elements, which do not form a vector space at all. Things don't work if you continue to insist on wrong stuff.

I'm off work and time to go play,

bye~~

imbAF

Thanks

Mr. Feynman

11:50

@naturallyInconsistent If you're talking about the indices $\rho,\sigma$ in $(L^{\mu\nu})^{\rho}{}_\sigma$, I'm talking about $\mu\nu$.

qwerty

12:04

@naturallyInconsistent don't drink and derive

naturallyInconsistent

12:29

@Mr.Feynman I'm saying $\mu\nu$ are labels

Mr. Feynman

@naturallyInconsistent Yes, just very unfortunate ones :P

That kind of label that works kind of fine with some formal manipulations

naturallyInconsistent

if you think about it, there is no fortunate way to do it

Mr. Feynman

Probably there is some way to work index free. Never bothered to figure it out ngl

NOTE Book

Hi

Can someone help me understand when can we apply conservation of mechanical energy? I know it is true when work done by non conservative forces is zero but I don't understand how external forces affect this

Mr. Feynman

12:55

@NOTEBook External forces (in general) make work, i.e. provide/subtract energy

Ryder Rude

13:27

@ACuriousMind should we call the representations on $V \otimes V$ and $V\otimes V^*$ as contravariant or covariant representations?

Relativisticcucumber

if i have a 'simple square' lattice i.e. simple cubic but in 2d with a 3 pt basis and each atom has one valence, my professor has said that, in this case, one band is full and one is half full, so we have a metal. i do not understand this deduction. how does one get to "x bands are full" from the number of valence electrons of the atoms in the lattice?

NOTE Book

13:50

@Mr.Feynman Does it means we are only allowed to use conservation of mechanical energy when internal conservation forces are there?

Ryder Rude

when we have an operator $A$ acting on a vector space. then the adjoint of Av is $v^* A^*$. This means the inner product indices correspondence between operators $A$ and $A^*$ on the vector space and its dual

but also, without any reference to an inner product, we can talk about another correspondence between operators on $V$ and operators on $V^*$. and operator $A$ on $V$ corresponds to $(A^{-1})^T$ on $V^*$

what is the relationship between the above two ideas about correspondence between operators on vector space and operators on dual

Ryder Rude

14:33

ok so the relationship between these two ideas is simply that when $A^* = A^{-1}$, inner product is preserved.

the second idea is a weakened version of this idea. when we don't have an inner product, we want to talk about preservance of $f(v)$, $f\in V^*, v\in V$. This induces the map $A\to (A^{-1})^T$ from $V$ to $V^*$

i mean from operators on V to operators on V*

and when we do have an inner product, we want to talk about the preservance of <a,b>. This leads to the condition A^*=A^-1

Slereah

15:04

> The atomistic philosophy does not possess the Notion of ideality; it does not grasp the one as an ideal being, that is, as containing within itself the two moments of being-for-self and being-for-it, but only as a simple, dry, real being-for-self.

Claudio

15:33

what do I do when the mathjax extension stops working?

I reloaded everything already

I restarted the whole laptop and nothing, bruh moment

Slereah

15:55

Buy a new laptop?

Claudio

I might be cooked this time hahah

Time to buy that rtx 4090 finally

Akhilesh G

16:32

Hello guys, this is a chemistry doubt is I was thinking this would somewhere be linked with physics aswell. I couldn't find any chemistry group.

1 u = 1.67377 x 10^-24 grams (1/12th carbon weight of carbon)

Atomic Mass of Sulphur = 32 u

Atomic Weight of Sulphur = 32 * 1.67377 x 10^-24 grams = 53.56064 * 10^-24 grams

Why does google say it is 32g? And moreover 1 mole of Sulphur should also 53.5g? Isn't it?

Please clarify my doubt.

NOTE Book

@AkhileshG You have to multiply with Avogadro number as well

53.56064 * 10^-24 grams * 6.022*10^23 will give you the mass of 1mole of S atoms

Akhilesh G

But multipling with Avagadro number will give me wieight of n (6.022*10^23) sulphur atoms. I just want weight of one sulphur atom in grams

NOTE Book

Weight of 1S is 1u right?

Akhilesh G

Atomic mass of S = 32 u

NOTE Book

Since 1u = 1.67* 10^-24g mass of 32u= 32*1.673*10^-24g

Sorry that was a mistake you are right 1S=32u

So weight of 1S atoms is 53.56*10^-24g

Akhilesh G

16:41

@NOTEBook Yes, and that will 53.56064 * 10^-24 grams

Oh wait

NOTE Book

This is the weight of 1 S atom

Akhilesh G

It all makes sense now

You multiply this with Avagardro number and you get the weight of 1mole of Sulphur

NOTE Book

Yes

Akhilesh G

Which turns out to be 32 g

Oh nice!

Thank you!

NOTE Book

Welcome :D

naturallyInconsistent

17:59

@Relativisticcucumber each atom's valence states hybridise to give Bloch waves of different types. Started with 3 valence states, so there must be some way to squirrel away 3 electrons, i.e. 3 states, which we can label as lowest energy, middle energy, and highest energy. You now have 3 electrons to fill them, so the lowest energy states will be double-filled by spin-up-down electrons, leaving one electron to fill the middle energy state. This fills the middle energy state half-way, so metal.

Sir Cumference

18:16

Wonder what ever happened to Emilio

Haven't seen him here in a while

More Anonymous

18:59

Has anyone seen this inequality for Von Neumann entropy?

$S(\rho_U) \leq log(\text{dim}_C \text{span}U) $

I saw it here:

https://assumptionsofphysics.org/presentations/20240724-IPMU24NonAdditiveMeasures.pdf

ACuriousMind

@SirCumference since he's made an edit on the site yesterday, I don't think anything's "happened to him" :P

More Anonymous

19:34

@Mr.Feynman Sounds like a Feynman story to me :p

user430580

19:52

What's a quark? The noise made by a well bred duck. Ba-dum-tss.

Sir Cumference

@ACuriousMind Sometimes I forget there's more to this site than the chat lol

2

Mr. Feynman

20:16

@SirCumference What? Do we have a site now?

@MoreAnonymous I should write a book about myself and weird things that happened to me. a 2-page book

Mr. Feynman

21:03

Somehow interacting/free vacua returned to my life

Relativisticcucumber

@naturallyInconsistent hmmm this seems to highlight a general confusion i cannot resolve, which is this whole notion of "filling bands". i dont understand how to tell how many slots are available. im trying to formalize this into a more specific q but am currently coming up blank

when i understand band structure, it will be the happiest day of my life

Relativisticcucumber

21:27

another thing that is similar that has confused me immensely is that my professor said the number of allowed values of the crystal momentum in the first brillouin zone is "as many sites as there are in the lattice" ?? i am perplexed. I thought all values of k are allowed since energy dispersions are effectively continuous in k so i thought it should be all values of k in that zone are fair game ??

im not even sure if what im saying is making sense. im losing my mind over this.

@ACuriousMind long live emilio

imbAF

21:43

In reciprocal space what is the meaning of this quantity: $\vec k_{\nu}=\sum_{\alpha=1}^3 \frac{\vec b_\alpha}{N_\alpha}\nu_\alpha$, where $N_\alpha$ are the nr of lattice points in direction $\alpha$

?

Obliv

This question probably doesn't make sense but do you think irrational numbers aren't "real" in the sense that we can't ever measure with infinite precision so how could we ever measure an irrational number

yeah ignore that, it's not a very thought out question

Ryder Rude

22:31

i think irrational numbers may or may not be real, but we can never know for sure

some people believe that universe is ontologically made of math. this could involve irrational numbers being real

Relativisticcucumber

based on this logic i get that k can be $\frac{-\pi}{d} < k < \frac{\pi}{d}$

imbAF

For one dimension right?

Relativisticcucumber

yeah that will suffice

imbAF

The easiest way to understand that is consider a 1D lattice

And you consider a wavelength equal to L

then you decrease it in value until $\lambda=2a$ where a is the spacing between two adjacent lattice points

That means that every lattice point/atom will oscillate in the opposite direction compared to its adjacent atom

the total nr of wavelengths, values

amasses to the nr. of lattice points in the dimension

very nicely illustrated here

Phonon

A phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, specifically in solids and some liquids. A type of quasiparticle in physics, a phonon is an excited state in the quantum mechanical quantization of the modes of vibrations for elastic structures of interacting particles. Phonons can be thought of as quantized sound waves, similar to photons as quantized light waves. The study of phonons is an important part of condensed matter physics. They play a major role in many of the physical properties of condensed matter systems, such as thermal...

qwerty

@Obliv this guy thinks stuff like that en.m.wikipedia.org/wiki/…

definitely fringe opinion

Ryder Rude

22:50

what do u think about many worlds interpretation and its compatibility with born rule