The h Bar

Bml

00:28

@naturallyInconsistent Hi. On Math SE I posted a question closely related to Physics (Thermodynamics) and concerning the problem we discussed yesterday. If you are interested, here is the link:

0

Q: How to solve (or verify) the following inequality?

The following question is directly related to this one and involves the resolution (or verification) of an inequality. Again, the first part of my question is dedicated to the creation of the (necessarily physical) context, the second part to the transition to mathematical language, since my goal...

123

04:31

Hello Everyone...

Ryder is not Rude.

05:05

Hi

Ryder is not Rude.

06:17

Can ChatGPT o1-preview Solve PhD-level Physics Textbook Problems? (Part 2)

►

Ryder is not Rude.

06:28

Does that^ sound like a possible chatroom bot for this room :P

PSQs preferred.

Ryder Rude

07:53

Cosita Divina

►

hi

John Rennie

08:36

Is there a frame in which the magnetic dipole of e.g. an electron looks like an electric field?

I was about to answer a question about magnetic fields on the main site by saying that all magnetic fields are just electric fields viewed from a different inertial frame, but then it occurred to me this might not be true for the magnetic field of an elementary particle.

For example if I rotate around an electron at some suitable frequency would its magnetic dipole look like an electric field to me?

naturallyInconsistent

@JohnRennie This cannot be true; Lorentz boosts preserve $\vec E\cdot\vec B$ and more importantly $\vec E^2-\vec B^2$

PM 2Ring

08:51

@RyderRude Some more Latin music from Australian women. Here's singer Katie Noonan & German-born guitarist Karin Schaupp. First, the Jobim classic, Wave.

Wave

►

A sad one, Manhã de Carnaval

Manhã de Carnaval

►

@JohnRennie Related:

6

Q: Can an electric field be converted into a magnetic field and how? If not, then why?

My teacher says that a rest charge creates an electric field and a moving charge creates both electric and magnetic fields. But, the cause of a magnetic field is velocity, so, is there something which changes an electric field into a magnetic field? Question: Can an electric field be converted in...

electromagnetism special-relativity magnetic-fields electric-fields inertial-frames

Ryder Rude

09:32

@PM2Ring thanks. Love these

PM 2Ring

Katie is a treasure. She sings a wide variety of genres. Check out her Beatles covers.

Ryder Rude

thanks. I will look it up

Across the Universe

►

she has changed the pace. It is a great voice

imbAF

In this thread, they give this:
https://physics.stackexchange.com/questions/808871/orthogonality-of-lorentz-transformation/808882#808882

$(\Lambda^{-1})^{\alpha}_{\ \ \sigma}=\Lambda_{\sigma}^{\ \ \alpha}$

Would it be a problem if I would write:

$(\Lambda^{-1})^{\alpha}_{\ \ \sigma}=\Lambda_{\ \ \sigma}^{\alpha}$

What I am trying to find out is whether the placement of which indix comes first has a meaning or not.
I know that there's a meaning regarding which index is up and which is down. But what about which is before and which is after?

ACuriousMind

@JohnRennie Regardless of whether you mean an inertial frame or a more general frame (because the frame you mention rotating at a certain frequency would not be inertial), the answer is no: $E\cdot B$ is not only a Lorentz invariant, but it is equal to the scalar $F^{\mu\nu}({\star}F)_{\mu\nu}$, so it is an invariant in all frames. So when $E\cdot B \neq 0$, there cannot be any frame in which $B=0$.

John Rennie

And E.B ≠ 0 for an electron ...

ACuriousMind

09:43

@imbAF The specific meaning of the convention depends on your source, but it is usually fixed which of the two indices refers to the row and which to the column of a matrix. Obviously for non-symmetric matrices these are not interchangable.

imbAF

@ACuriousMind In most cases the lower index represents the the row and the upper the column

But that is not what I am asking

ACuriousMind

no

imbAF

no?

ACuriousMind

the row/column is the position of the index (first or second), not the upper/lower distinction

I understood your question perfectly well, you just didn't understand my answer :P

imbAF

Ah soo

So then

ACuriousMind

09:46

You may, for instance, see someone expressing $A = A^T$ in indices as ${A^i}_j = {A_j}^i$

imbAF

Give me one sec please. This definitely complicates things

@ACuriousMind I was about to ask this

Then what if

$A = A^T$ in indices as ${A^i}_j = {A^j}_i$

Does this makes sense?

NO, right?

ACuriousMind

no

imbAF

In no circumstance, what I just wrote, takes place

?

ACuriousMind

it's a violation of the first of the two golden rules of index notations: 1. Free indices must have the same upper/lower position on both sides of an equation 2. No index may occur more than twice, once upper and once lower

whenever you write something that violates one of these two rules, it's wrong

imbAF

Where did you get this rule from? Is there like a book/file I can look online, with the rules

ACuriousMind

09:50

it's just how index notation works :P

imbAF

We were given NO rules in four vector algebra in my lecture

Free indices ???

ACuriousMind

"free index" is just an index that's not summed over

it's standard terminology, see e.g. Wiki

imbAF

so free and contracted? Is this the jargon used to highlight the difference between the types ?

Vincent Thacker

@imbAF The terms are "free" and "dummy" indices

ACuriousMind

however, calling these the "golden rules" is more of my personal preference :P Probably upwards of 90% of errors in index notation could be caught by the students making them if they just carefully checked each of their equations for whether or not they obey them

imbAF

09:53

I don't understand the 2nd rule. No index may occur more than twice, in which scenario

Ryder Rude

We can also express $A=A^T$ as $A^{\mu} _{\nu} v_{\mu} w^{\nu} = A^{\mu}_{\nu} w_{\mu} v^{\nu}, \forall w, v$

ACuriousMind

@imbAF in all scenarios

imbAF

Can you give me an example of it

ACuriousMind

if you have something like $A^\mu B_{\mu\mu}$ (3 $\mu$s), that's an error

imbAF

@ACuriousMind Ah this is what you mean

Cuz I was like, where else can an index appear if not up or down

I was trying yesterday to derive an expression that relates the transpose of a transformation with it's inverse

But because I would write
$A = A^T$ in indices as ${A^i}_j = {A^j}_i$

Ryder Rude

09:55

Or in the abstract A(v,w)=A(w,v)

imbAF

And had this as my starting point

and I would end up in an expression where there were no contracted/dummy indices

Vincent Thacker

@imbAF The correct way is $(A^T)^i_j = A^j_i$

The $T$ is needed

imbAF

@VincentThacker No, ACM said that is incorrect

This is the right expression:

$A = A^T$ in indices as ${A^i}_j = {A_j}^i$

Vincent Thacker

@imbAF Oh, if you're equating it back to $A$, then yes of course

imbAF

@VincentThacker or because you keep the T, then you are correct ?

Ok, then one follow up question

ACuriousMind

09:59

yeah that index placement is questionable, it's ${(A^T)^i}_j = {A_j}^i$ for consistency

(mathematically the different upper/lower order of the indices on the $T$ represents that if $A : V\to W$, then $A^T : W^\ast \to V^\ast$)

imbAF

Then, when we write down the matrix, is there a difference between:
${A^i}_j$ and ${A_i}^j$

Vincent Thacker

@imbAF Yes

imbAF

In both cases i should represent row, or so I decide

and j the column

So what is the difference then?

ACuriousMind

@imbAF of course there's a "difference", because the rules of index notation don't allow you to write a $=$ inbetween those two, do they?

imbAF

Yes, I know there must be a difference, but what is it

considering that
In both cases i should represent row, or so I decide
and j the column

Vincent Thacker

10:01

@imbAF Conventionally, the first index is the row and the second index is the column

imbAF

Yeah, that is true in both situations,

Vincent Thacker

But the choice of row/column indices, which dictate how it is written out on paper and how matrix multiplication "appears" on paper, is secondary

imbAF

But that still doesn't answer my question, about what is different between the two. I take it so, I make the convention that the first index is the row and the 2nd the column

ACuriousMind

@imbAF I don't understand the question - the difference is the index position. Once of these expressions has the first index of the A as a lower index, while the other has the first index upper

naturallyInconsistent

It should be noted way earlier that if you want to discuss the symmetry or skew-symmetry of matrices, the two indices involved should both be upper or both be lower. You don't discuss the symmetry of matrices when one index is upper and the other is lower

imbAF

10:04

And how does that affect the matrix representation

Vincent Thacker

@imbAF What are you considering $A$ as? Does the index placement carry any tensorial information?

If it does then they are not the same

imbAF

if I have to give an example, a lorentz boost

Vincent Thacker

@imbAF Then the boost matrix isn't a tensor itself

ACuriousMind

@imbAF Well, maybe you need to take a step back and ask what "the matrix representation" really is: For a 2-tensor (a "matrix" in a more naive world), there are four possible index positions: $A_{ij}$, $A^{ij}$, ${A_i}^j$, ${A^i}_j$. Each of these are, if you just stubbornly start from a set of numbers $A_{ij}$ and apply the rules of raising and lowering indices, different sets of numbers in general

naturallyInconsistent

@imbAF The Lorentz boost matrix is neither symmetric nor skew-symmetric

ACuriousMind

10:06

so clearly, not all four sets of numbers can describe "the same matrix", even though they are equivalent representations of the same tensor

imbAF

Hmmmm... I am confused

I think I need to be more precise in what I say

ACuriousMind

which of these four sets is your "matrix" depends on your concrete use case, but for Lorentz transformations we usually have then acting on vectors $v^i$, so that the equation $w = \Lambda v$ is $w^i = {\Lambda^i}_j v^j$ in indices, so the index placement "first upper, second lower" is "the matrix" in this case

imbAF

ACM wrote:
$A = A^T$ in indices as ${A^i}_j = {A_j}^i$. This example highlights that whichever index comes first represents the row, while whichever second the column. So ${A^i}_j$ writen as a matrix, is just the matrix of $A$. ${A_j}^i$ it can also be written in a matrix format, and it is the transverse of $A$. In this example the positioning has meaning and a consequence for the matrix representation.

Now, I am trying to do the same for ${A^i}_j$ and ${A_i}^j$.
Assuming that ${A^i}_j$ is the matrix of $A$. Then what would ${A_i}^j$ be?

Vincent Thacker

@imbAF $g_{ik}g^{jl} A^k_{\; l}$

imbAF

Ah ok

just the result of some matrix multiplication. Which depends on what you are calculating

ACuriousMind

10:17

To be honest, once we get to index notation with different positions, I find trying to think about "matrices" superfluous and often more confusing than helpful

imbAF

But how is it less complicated to not think of the structure that you are considering

ACuriousMind

just manipulate the index expressions; the important thing is that in the end you can do that in your sleep, not that you can somehow translate everything back into "matrices" - as soon as you get objects with three indices, all that goes out the window anyway

imbAF

Because the rules are the result of how i.e a vector and a matrix multiply together

ACuriousMind

@imbAF As someone who loves abstract algebra, I would argue the matrix is not the "structure" anyway - the structures under consideration here are abstractly (multi-)linear maps, and for bilinear maps, matrices and index notations are equivalent ways of talking about them, but the index notation generalizes to higher tensors, while the "matrix" thinking does not

imbAF

multi(-)linear maps? bilinear maps?

ACuriousMind

10:21

If you look at how mathematicians do abstract linear algebra, they don't start from the matrices - they start from the linear maps, and then after having proved stuff about bases etc. they mention "oh, by the way, you can now use a basis to get a bunch of numbers that represent this linear map in a particular basis, and you can arrange those numbers into a matrix"

Vincent Thacker

@imbAF The tensorial information contained in the indices is not in general fully displayed by writing it as a matrix

imbAF

I see

Than I need to do abstract algebra on top of linear one

ACuriousMind

@imbAF If you have no idea what I'm talking about, you would have to take a linear algebra course that introduces tensors the mathematicians' way, sorry :P

imbAF

Linear Algebra Done Right is what I will start with

ACuriousMind

I'm just saying this to make clear that "the matrix" is not as fundamental as you think, and you lose nothing by ceasing to think about matrices and just work with indices

imbAF

10:23

I mean I know linear algebra, but to what extend not sure

@ACuriousMind Ok, then I want to consider the following case and not think of vectors/matrices

Let's say we have the following: $x'^{\mu}=\Lambda^{\mu}_{\ \ \nu}x^{\nu}$ And this is the correct way of writing. It represents the multiplication of a matrix and a vector

I will forget what it means

and just write

$x'^{\mu}=\Lambda^{\delta}_{\ \ \phi}x^{\omega}$

Why is this wrong, and which rules I am breaking / not following ?

Vincent Thacker

@imbAF The free indices don't match

imbAF

Rule 1, in what ACM said, that would be

?

And, do I need linear or abstract algebra to understand this:
" they start from the linear maps, and then after having proved stuff about bases etc. they mention "oh, by the way, you can now use a basis to get a bunch of numbers that represent this linear map in a particular basis, and you can arrange those numbers into a matrix" ?

Vincent Thacker

@imbAF This should be in linear algebra

imbAF

Ok. So not think of vectors and matrices, but just follow the 2 rules

Because as you said @VincentThacker The tensorial information contained in the indices is not in general fully displayed by writing it as a matrix

ACuriousMind

@imbAF I mean, it might not be absolutely necessary, but yes, I would expect a physics student to understand at least enough linear algebra to understand the relationship between abstract linear maps, bases and matrices. This should be in every linear algebra course.

imbAF

10:33

I might know that, buy I am not sure what linear map is

Or how it translates from german to english

ACuriousMind

It's literal translation - in German it's lineare Abbildung

imbAF

Or I would say you have a definitionsbereich X and than an abbildung

Ok then yeah I know xD

Vincent Thacker

@imbAF Yes

I would consider the index notation as a generalization of the matrix notation

The usual way of multiplying matrices - taking the dot product of the rows of the first with the columns of the second - is a special case and is only one way of visualizing it

imbAF

what would be another case?

If I am not misunderstanding your statement "The tensorial information contained in the indices is not in general fully displayed by writing it as a matrix", what you are saying is that with index notation one can represent abstract entities (for lack of better words) other than vectors and matrices, i.e tensors $A^{\mu\nu}$ etc etc

or is that not the case?

ACuriousMind

well, there are two aspects here: Index notation as such, and the notion of upper and lower indices

imbAF

10:40

What do you mean?

ACuriousMind

if you want to make contact with "normal" linear algebra, then when we have upper and lower indices, we are talking about a vector space $V$ and its dual $V^\ast$. The vectors from $V$ are written with upper indices, the vectors from $V^\ast$ with lower indices.

A linear map $V\to V$ is equivalently an element of $V\otimes V^\ast$, and so it is written with one upper and one lower index, and this then straightforwardly extends to all tensors/multilinear maps, but if you don't know the definition of tensors in terms of multilinear maps you can't see that (yet)

Vincent Thacker

@imbAF Don't want to confuse you further but if you did representation theory there's a good chance you would've had to compute matrix multiplications with "matrices" of more than 2 indices

imbAF

Would it be incorrect to ask if the vector with upper index is written as $a=(a_1,a_2,a_3)^T$ and the lower one as $$a=(a_1,a_2,a_3)$ ?

Vincent Thacker

@imbAF This is a convention and not a necessity

ACuriousMind

@imbAF no, that's right, that's the usual convention in terms of row/column vectors and matrices

imbAF

10:44

@VincentThacker Haven't done that. And it has been the bane of my existence for like most of my bachelors time. I want to do it, but I have so many things that I also need to do, and I can't find the time

Vincent Thacker

Again, it goes back to what I've said earlier - how it is written out on paper is secondary

imbAF

Ok, I need to get rid of, how it is written on paper

Vincent Thacker

You can choose to write both however you wish as long as you keep track of the contractions correctly

imbAF

But I guess, that has to do with a fundamental understanding of what is going on. And only by reading linear algebra/abstract and representation theory

Slereah

@ACuriousMind Idyllic view

imbAF

10:46

I could achieve such an understanding, that will allow me to not "materialize" what we write

@VincentThacker I see

Slereah

Those things tend to not be taught or only taught at the beginning, when the students have no idea what's going on

ACuriousMind

Personally, I never really understood how physicists expect anyone to understand the index stuff without the abstract mathematical view, but many seem to be doing just fine :P

imbAF

But then when I ask someone how can do these

hey what are we doing mathematically, could materialize it

they say, I am not sure, I am following the rules

Ok....

ACuriousMind

@Slereah I know this is apparently unusual, but I had to take an abstract linear algebra course in the first semester that did all this before the physicists started with the indices...

Slereah

Physicists love indices

and mathematicians, really, up until quite recently

People loved analytic geometry so much that we just used it for everything for 500 years

imbAF

10:49

@ACuriousMind That's why I wanted to do my masters for mathematical physics, but can't :(

Vincent Thacker

What led me to the correct mathematical view was the absolute confusion of physicists' attempts to explain "contravariant" and "covariant" indices

Which were the terminologies I initially saw when I was learning it the first time

imbAF

@VincentThacker you mean like a 3D matrix, (as to how is written in paper)

ACuriousMind

@VincentThacker yeah, I could rant about that all day :P

Slereah

obviously something being covariant or contravariant means the vector will be horizontal or vertical

the most important distinction in physics

Vincent Thacker

@imbAF Yeah and higher ones as well

Slereah

10:55

It is weird to see very serious physicists talk about something being a row vector or a column vector like it's a meaningful distinction and not just a notation

imbAF

I do have one question about "contravariant" and "covariant" indices.
Do the concepts of covariance and contravariance in math have any correlation with how we use them in physics in special relativity. What I mean is the following:
covariant components are perpendicular projections while contravariant ones are parallel projections in each axis. But this is when one considers for example a non cartesia plane and finds out the projection of a vector in such a plane

In physics you have covariant and contravariant vectors. And the difference is that the covariant four vector for example has negative spatial components

Slereah

They're the components of vectors and dual vectors, and those are defined by their respective transformation laws

imbAF

Is this how the projection in math is translated in physics ?

ACuriousMind

@Slereah I mean...in their mind, it is a meaningful distinction! They just haven't organized their understanding of the topic in the same way as us math lovers, but in most cases, their way works, too, as much as I dislike it

Slereah

Well it works on a computational level

but it is a bit weird

ACuriousMind

11:00

@imbAF I never understood what "covariant" and "contravariant" meant except as synonyms for "has an upper index" or "has a lower index" and it's not been a problem, don't think too hard about this at this stage :P

imbAF

Yes. But I thought at some point, what is the mathematical meaning of them

And it turns out, it's how projections of a vector are calculated

But sure I will stop at the physics part

ACuriousMind

mathematicians don't really use those words in this geometric context

it's just a historical naming

imbAF

So they don't use them at all?

Or, just out of curiosity, in what context they do use them ?

ACuriousMind

I'm sure you can find some that do, but I've never seen this terminology in any prominent place in any differential geometry text

imbAF

I feel like if I have the time to study linear,abstract algebra and representation theory, all the fragmented stuff I understand

Slereah

11:04

it's the name

co-variant : vary with the base

contra-variant : vary the opposite of the base

ACuriousMind

they'll mention it when discussing coordinate bases for cotangent vectors: Then the components of tangent vectors transform covariantly (meaning the same as the coordinates) and the components of cotangent vectors transform contravariantly (meaning with the inverse of the transformation of the coordinates)

imbAF

Will become clearer. But I don't have the time. Idk why the program is so useless that let's you wonder about stuff after giving a half-assed explanation

Slereah

the Jacobian of your coordinate transformation will be the same/the inverse of that of the base

imbAF

what is the base?

ACuriousMind

since physicists are obsessed with talking about everything in coordinate bases, they have grabbed onto the terminology as important

Slereah

11:05

You know, the basis vectors

imbAF

Yeah the basis vectors of some vector space

ACuriousMind

I don't think it is useful at this point to try to teach you differential geometry in chat :P

imbAF

Yeah that is another thing

Hold on a sec

If all I did in my bachelor was "Hoehe Mathematik", trivial crap really. Is that supposed to be enough to understand all these mathematical concepts

I don't understand how that makes sense

Slereah

I'm afraid if you want to get a good vibe of physics and math you have to read on your own too

imbAF

So, linear algebra, abstract algebra, differential geometry and representation theory. Throw in lie algebra for the fun of it xD

@Slereah I fully agree. It's just that 24h are not enough

ACuriousMind

11:09

I mean, one thing I keep saying in this chat is that it is possible to not understand something and still keep working with it

you do not need to understand all the details and mathematical subtleties in order to manipulate equations according to the rules

you can just accept the rules and learn later where they come from or what's really going on

modern physics and mathematics is so vast you simply cannot go down every rabbit hole as soon as you encounter it

imbAF

@ACuriousMind This here is 1000000% true

Whenever I question something, I end up realizing that I need to read additional 30 books to understand it

And when this keeps happening over and over again, you realize how little you know

Slereah

Do I have to get the Image

Ryder is not Rude.

Chose your rabbits wisely.

imbAF

And that is demoralizing to a great extent

ACuriousMind

the physics courses are mainly trying to get to you a point to have some overview over the breadth of modern physics, this necessarily sacrifices any depth and mathematical sophistication a "proper" treatment of the topic would have - but a proper treatment would not fit into the one semester and the course has to get somewhere

imbAF

11:12

Just by asking about the indices, I was reminding that I need to read linear algebra, abstract algebra, differential geometry and representation theory

Slereah

Ryder Rude

Also, the indices in index notation need not refer to natural numbers

there is the abstract index notation

in which they refer to vectors

Slereah

another good use of classesb is that you learn a bit of the physics that sucks

imbAF

@ACuriousMind And I feel that. I feel that I know just some stuff from wiki. I feel that I don't have a fundamental understanding of stuff.

Slereah

I probably wouldn't learn thermo or electronics on my own bc it sucks ass, but it is useful to know

imbAF

11:14

@Slereah Preeeeach!

ACuriousMind

"But when do I really understand how everything works?" - "That's the fun part, you never do!"

Ryder Rude

@imbAF are u doing relativity now

Slereah

@ACuriousMind Can't all be Goethe

imbAF

I am not sure, I might take a year off just to study the math part. That would solve all my problems

or hope so xD

So then someone who is good/competent in String theory, I am taking it as an example because of how many other things you need to know, how does that person learn all those stuff during his university ?

Is that possible ?

ACuriousMind

@imbAF first of all, most string theorists do not actually know all the formal math

Slereah

11:19

@ACuriousMind most?

Who's the guy that does

Is it Urs

imbAF

I am pretty convinced that majoring and studying math is the best way to understand physics

Ryder Rude

on youtube, everyone says string theorists are the smartest

ACuriousMind

@Slereah I'm just hedging my bets :P

Ryder Rude

@imbAF in math courses, they wouldn't teach u physicist math mostly

or it depends on the course

imbAF

Why would you need that? When physics math is just dirty

derivations

Ryder Rude

11:22

maybe a mathematical physics course would be good

Ryder is not Rude.

Study what you enjoy.

ACuriousMind

@imbAF I took a lot of pure math classes in parallel to the physics classes and honestly I think that's the best way (if your schedule allows for that kind of workload): You see the abstract math, but not what it's good for, and then you can see the physicists doing stuff and go "oh, that's what I saw in math class but applied to the real world"

imbAF

I would do mathematical physics, but not offered unfortunately

@ACuriousMind My schedule unfortunately does not allow it. But I did come to the realization that you need math and then everything else follows

I also realized that I need to do my masters in mathematical physics, if

fundamental understanding is what I am after

But not offered where I am

Ryder Rude

@ACuriousMind but the pure math classes have to be selected wisely. E.g. i read that if u pick up a functional analysis math book, it doesn't discuss topics relevant to rigorous qm

ACuriousMind

but the mathematical explanations of what was going on in the physics math usually arrived delayed, so this did not free me of having to develop a tolerance and understanding of the non-rigorous ways physicists usually work

Ryder Rude

11:24

so u would instead have to pick up math classes that teach physics math

ACuriousMind

@RyderRude this depends very much on the functional analysis book: One part of functional analysis is operator theory very much relevant to QM, another is talking about function spaces and differential equations and Sobolev embeddings which is very much not :P

imbAF

@ACuriousMind Ok but the thing is, the people who are able to do these kind of things, are people like Dirac, who just find a way even though they don't have a clear mathematical way of doing what they want (his equation). But the average person ain't dirac

Ryder Rude

yes. It is much better to just pick up QM focused functional analysis books if ur goal is QM

imbAF

And the average person uses logic to go from A to B not imagination or intuition

You are born with those things I guess

ACuriousMind

@imbAF but getting through a QM course does not require you to be Dirac and invent QM on your own, it just requires that you take the ideas presented to you and apply them to very specific and simple topics that have (ideally) been pedagogically selected to not require the in-depth understanding you're lacking

imbAF

11:27

Ok and after i am done with the uni

I don't have the fundamental understanding that I want

ACuriousMind

that's very much doable compared to "being Dirac", I think, even though I'm not saying it's easy

well after university you need to figure out what you're doing with your life, that's unavoidable :P

imbAF

@ACuriousMind That's what I am finding about the University. It's just a trial of what physics is. No true fundamental understanding of what is going on. And I agree with Sleerah, that you need to additionally study stuff. But the pace at which you need to learn new things it's so rapid, that you practically are left behind and you got to learn more and more

Slereah

also you need the rote learning really

Ryder is not Rude.

^

Ryder Rude

It is not a trial, i would say. It is just focused on applications instead of foundations. Plently of full time physicist dont understand foundations

Slereah

11:31

Knowing the fundamental meaning of the Physics isn't gonna help you diagonalize matrices

2

imbAF

@ACuriousMind Well research. But that's not possible if you haven't read like 40 math/physics books in like 5 years on top of finishing studies xD

Ryder Rude

E.g. a QM uni course would not discuss the measurement problem or Bell inequalities

And a QFT uni course would teach u to calculate amplitudes

It's just application focused

Slereah

Physics is a lot of mindless calculation you gotta do

imbAF

@Slereah that's math

Ryder Rude

Plenty of professional physicists do their job without knowing foundations

Slereah

11:33

Yeah well that's also a lot of physics :p

Ryder is not Rude.

Shut up and calculate

imbAF

But again, if you know math, you can, after thinking hard, give a physical intepretation of whatever you are doing

I mean Penrose is a mathematician, not a physicist primarily

Ryder Rude

Yes, but on the flip side, theoretical physicists do too much idealisation. They have no clue how experiments work

especially measurement devices

ACuriousMind

@imbAF it is, I know plenty of people who do research without having the kind of deep mathematical foundations we're talking about here

Ryder Rude

so it is not like u understand physics "better" using deep math. U don't understand practical measurements that way

Amit

11:35

Perhaps undergraduate physics education needs a basic philosophy of science course? Nothing too fancy, but a few basic ideas to give the student the right perspective on the role of math in physics. I personally used to get hung up way too often on trying to perfect my understanding of a certain mathematical topic, only to ultimately find out that this rabbit hole contributed next to nothing to my physical understanding, and this time could be better spent focusing on the physics.

Ryder Rude

with deep math, u only get an understanding of an idealised Platonic sandbox

imbAF

@RyderRude And then you can adjust it to reality. I don't think that is hard to do

ACuriousMind

the overwhelming majority of physics research is not "do this in a mathematically rigorous way", not even in theoretical physics, it's "get to some interesting statement in whatever way you can", where "interesting" is relative to your subfield :P

if the way you took passes as acceptable among your peers, it's good enough, never mind the rigor

Ryder Rude

@imbAF it is hard. making measurement devices and collecting real world data is a different skill

ACuriousMind

@RyderRude Do you know a lot of theoretical physicists? How are you comfortable making such a sweepingly generalized statement?

Ryder is not Rude.

11:38

Use your time wisely.

imbAF

@ACuriousMind which course you attended in math?

Ryder Rude

@ACuriousMind sorry. I meant they generally know very less about measurements compared to experimental physicsts

ACuriousMind

@Amit Yes, but for that physicists would need to get over their performative disdain of philosophy in general :P

Ryder Rude

@Amit I'm not sure how much philosophy of science would benefit

imbAF

If you have attained the most idealized and generalized expression about something, I see it as impossible not to be able, via boundary conditions and approximations, not reach down to a specific real life scenario

ACuriousMind

11:40

Jan 13 at 19:29, by ACuriousMind

@Mr.Feynman uh, sure: real analysis, differential geometry, complex analysis, algebraic topology; linear algebra, abstract algebra (mostly ring theory), algebraic geometry, sheaf cohomology (which was about deriving Verdier duality); functional analysis, Lie group theory, representations of the Poincaré group (which more generally developed Mackey's and Harish-Chandra's theory of representations)

imbAF

@ACuriousMind Ok thanks

Ryder is not Rude.

Getting that idealization is going to take a lot of your time and energy.

ACuriousMind

note: not all of these are equally helpful for physics :P

imbAF

@ACuriousMind I wouldn't think otherwise.

Ryder Rude

@Amit philosophy of physics could help in understanding what physics describes and doesn't describe tho

imbAF

11:42

@RyderisnotRude. But the benefit is that after attaining that, you can derivate any specific scenario easily

Ryder is not Rude.

Yes.

Slereah

@ACuriousMind Reminds me of that anecdote where a mathematician met some huge big wig of QM like Heisenberg or whoever else, and the mathematician argues that math was useful in the development of QM because it taught us the difference between symmetric and self-adjoint operators, and the QM guy responded "so what's the difference?"

Amit

@ACuriousMind Performative indeed! Feynman was such an outspoken critic of "philozophers" (to use his favorite pronunciation) but then himself gave the Messenger lectures which in my mind are exactly the kind of philosophy of science that a beginning student needs. It's really performative because I see again and again that the most famous physicists did not dislike philosophy of science per se, they just disliked when non-Physicists had what to say about the topic :)

Ryder Rude

e.g. many physicits would conflate a physics model with the universe itself. This has created a lot of confusion especially in understanding consciousness

philosophy of science would help with that

thats for theoretical physics. For experimental physics, epistemology would be useful

ACuriousMind

@imbAF I'm afraid that's where you're right in a very idealized way, but wrong in all the ways that matter: A frequent complaint about more mathematical physics texts is that the connection to "real" physics is tenuous - for instance why do we spend hundred of pages proving stuff about the existence of solutions to differential equations, for instance, if the physicist just solves the specific equation they're interested in in two pages and it's trivial to check it's a good solution?

2

Ryder Rude

11:46

@Amit yes. I saw one of his lectures had a philosophy section. He did do philosophy ofc, but just dislikes professional philosophers

Apparently, this disdain was a thing for physicists of Feynman's generation

ACuriousMind

and that's not even getting into the problem that often, physics is just chugging through a bunch of complex computations instead of making some high-minded derivation - it was a running gag in my analysis classes that the mathematicians could do all the abstract proofs, but when it came to actually computing an integral, the physicists were typically much faster and more comfortable with the task because computing stuff is what you do all day in physics courses

Ryder Rude

in Einstein's generation, physicists got along with philsoopjers

there is a philosopher who trash talked physicists of Feynman's generation because of this

i read his quote. He was talking about the good old days of the previous physicists

Slereah

@ACuriousMind I had a pretty miserable time when I did my year of pure math but boy I was the only one who could actually do an integral

Amit

@RyderRude Which doesn't really make sense, even by his own standards. Just because a person has a PhD in Physics, doesn't mean he didn't master bongo drumming, and by the same token, a PhD in philosophy doesn't mean you didn't build a particle accelerator in your garage ;)

Ryder Rude

@Amit it is easy to be annoyed at philosophers tbf. They use confusing sentences instead of simple and clear

but only some philosophers, not all

ACuriousMind

11:50

@Slereah yes, exactly! the mathematicians eventually catch up if they continue to do stuff where they have to compute integrals or whatever, but the fact is that a lot of what you need in physics has to be trained by exercise, not just abstractly understood

Ryder Rude

@Amit also, philosophers in those days misinterpreted theory of relativity a lot, which annoyed Feynman

Slereah

same for proofs really

ACuriousMind

my abstract understanding of linear algebra did not make me any better at doing index notation computations, doing a lot of index notation computations made me better at those computations

Slereah

Most proofs are just the same tools over and over

It's pretty rare you have to break out some obscure theorem

ACuriousMind

yes, math has similar but different trained skills

Slereah

11:52

Just gotta use the Cauchy inequality over and over

That's why I liked Geroch's big list of GR proof tricks

> The role of key theorems has been assumed instead by 'methods of proof', for indeed there are a limited number of these, which do occur over and over. In fact, the following eight methods of proof will suffice for most results in this subject :
'Introduce a timelike vector field (and, usually, then consider its integral curves)', 'Carry information about closed curves and compare with what one had at the beginning', 'Connect timelike or null curves together, and smooth the corners, to obtain new curves', 'Find a sequence of points with some property and ask for an accumulation point', 'C…

Amit

@RyderRude Of course, and Philosophy of science as a separate academic field is a rather modern development anyway. It only became an important part of Philosophy as a whole in the middle of the previous century more or less. It's hard to really blame Feynman for having a very different view of Philosophy in the era he grew up in.

Ryder Rude

@Amit oh. But also, Feynman was a bad philosopher according to Sean Carroll

or rather, he was bad at philosophy

Tbh i don't think Carroll is that good either. But he values philosophy at least

Amit

Perhaps, Idk the context that Carroll refers to

Ryder Rude

it was in a podcast

i assure u...he said Feynman and a lot of physicists are bad at philosophy

Ryder is not Rude.

He's too much of a show-off for my tastes.

imbAF

11:55

@ACuriousMind because knowing the proofs, it means that you know in which scenarios you can use it. And you might encounter a scenario which is confusing to you and that you cannot solve with what you know. But if you start from the ideal/generalied expression and you try to reach to your real life case, along the way, you might find out that, Hey this is a new case, so new conditions etc must be considered

And you end up adding a new particular scenario in the pool of different/ particular cases

@ACuriousMind I fully agree with this, I need to just write more in index notation

Slereah

Feynman's pretty hard to listen to I find tbh

He has the thick New York accent

He is walking over here

Ryder is not Rude.

The Bronx accent is the worst of the New York accents imho.

Slereah

Sopranos - Linguistic compilation

►

Transcript for