/phg/ - Physics General

Learning the basic math to understand the models I am interested in. I want to understand particle pairs, local and global broken symmetry, and spooky motion.

This is an Ashkenazi Jew board you fucking low IQ plebeian

A, then it's not too bad. I don't agree that undergrads don't have the skills to learn basic GR, but it's not expected from you to become very knowledgable about the field.

you have to go back to where you came

Entanglement stuff. My linear algebra sucks though so it's hard.

electromagnetism, I've had some problems with the math because of my calculus, but I'm finally getting it

Trying to come up with something for undergrad research

No idea where to start. Im only an undergrad so I dont understand half the shit I read on arxiv or elsewhere

i really wanted to do something statistical in condensed matter but i just have no idea. the professors here are obviously very intelligent and nice but are busy and dont have much time to talk

What are you currently learning?

Don't do undergrad research, please trust me on this. Just do your best to firmly grasp everything you're being taught and have patience.

>unified field theory
>E/M charge field
>reevaluation of relativity and quantum mechanics
>how 20th century physics since the Copenhagen interpretation is autistic screeching hiding behind fake math

milesmathis.com/

Jesus christ, the autism. He's also wrong, the extra terms comes from non uniform motion and you get them with a proler derivation if he used vectors as he should.

Been running some simulations to produce crystals and send some laser induced shocks through them.

1 semester of research is required although most undergrads do 3 semesters or 1 and an internship depending what they want to do

What are your views about the relation between math and physics? I understand they are not the same thing in many ways, but recentky I've seen a thrend of physicista that feel "pride" for no being "rigorous". I have no problem with skipping tedious proofs, but I do have problema when the objects don't make sense.

Plasma discharge tube that accesses zeropoint radiation. In other terms, free energy.

Newtonian Mechanics and Basic Electromagnetism . Solving IE Irodov problems.

Don't listen to that undergrad, do your undergrad research. It's good to expose yourself to things you don't understand to help prepare yourself and build breadth and intuition otherwise you will become bottlenecked too soon. If you feel like you're overwhelmed, it'll pass and it's good to get used to that feeling now while you're young. You will only go further away from the known and into the unknown and clinging to the "known" knowledge will prevent you from really branching out.

It's not that bad to only have 1 semester of thermo, but 1 of mechanics is weird. What level was it?

My undergrad had 3.5-4 semesters of it.
1. 1/2 - 2/3 of the first semester intro series are introductory mechanics using 6 ideas that shaped physics book,
2. sophomore 2 semester Intermediate mechanics using Morin (actually difficult)
3. Junior or Senior Theoretical mechanics which includes mostly lagrangians and chaos using Taylor (not hard)

Does anyone know a good place to start self teaching physics. I'm currently looking at the stuff offered on MIT open courseware, as well as Feynman's introductory course notes. Wondering if there was anything else out there that is worthwhile.

classical em, everything starting from the basics

I spent more than 1 hour trying to understand how to sum

[math]x_{1}=A_{1}\sin(\omega t+\phi_{1})[/math]
and
[math]x_{2}=A_{2}\sin(\omega t+\phi_{2})[/math]

and get something in the form of

[math]x=A\sin(\omega t+\phi)[/math]

again. I couldn't.

I'm struggling my way through the part of QFT that leads into the Feynman rules.

Doesn't help that the textbook is brutally honest about just straight up ignoring infinities sometimes, which I'm too much of a mathematician to just accept.

Currently reading university physics (freedman) and juggling lectures of Feynman and Walter lewis to prepare myself for going back to college this summer. Idk shits really interesting but its too late for me I'm 24 w/ shit high school GPA. Sucks when you have to pay your own way through college, I'll probably have to settle with some shit business degree

>/mg/ is making fun of us again

Hehe.

Can you define 'makes sense' rigorously though?

If you want to do any serious research you need to know some quantum mechanics and if you're really serious some quantum field theory as well. You can shoot for these types of projects or just go with standard undergrad stuff like data collection and lab work. Since research seems required for you though I'd shoot higher since it'll put you apart from your peers.
I recommend studying some quantum mechanics(or qft if you already know it) on your own. Then when you've learned a reasonable amount you should go to professors working in fields that interest you about research projects. Make sure you mention your current knowledge and what you're studying, it gives a good impression. I personally went around asking professors when I was done with Griffiths and halfway through Shankar. A particle theorist took me on and guided me into learning therest of quantum, some qft, then the relevant gauge theory and literature. By "guided" all I mean is that he recommended books and what to emphasize and skip in them, I did all the learning myself.
Now some recommendations on where to learn this stuff. Classical mechanics from chapters 1,2,8 of Goldstein are all you really need. Special relativity from the first 4 chapters of Schutz's general relativity book are important when you get to qft, and you'll need tensors at some point anyways. For quantum mechanics Shankar, Cohen-Tannoudji, and Sakurai are worth looking at. Griffiths might be helpful for the really basic stuff. For qft you really need to look at everything. Peskin and Schroeder is the standard, but I found Lahiri/Pal and Tong's notes very helpful when first starting. Mandl/Shaw is old but it might help things click and Srednicki is a bit more advanced. Try to at least know special relativity and quantum before asking professors as they are the bare minimum for most research. Don't be afraid to talk and tell them what you're interested in, helping out undergrads in research is part of a professor's job.

>physics not science

What textbook you using?

I'm going through Mark Srednicki's book, it seems to have good examples.

I hate the idea of just learning the Feynman rules without knowing how to derive them, but everyone who I talk to and knows this stuff thinks going through the detail like I am is a waste of time.

I just want to rigorously understand everything, gosh.

Tensors, curvilinear coordinates, virtual displacements. If you are already using abstrtact concepts, you can't just live with a shit interpretation.

True. Sometimes my professors think I'm dense if I keep asking them to make it make sense. They'll only respect my question if I prove I can do the calculations correctly, which is apparently the bar for saying you 'understand it'.

For example, when I ask 'what the hell is SU(2) and a spinor and why does this work?' I just get told,

"What you never heard of pauli matrices or quaternions? SU(2) is just a simply connected double cover of SO(3) and you have to go around 4pi to get back where you started."

Or more mathy people will say:

"Some Clifford algebra on some so-and-so space"

And I'll only have learned trivia and lingo within those fields without really knowing what the hell a spinor on SU(2) is.

If anyone does have a good intuition for this btw, let me know. I don't even have a specific question, it's just objects like these (and pretty much 90% of QM and QFT) where the more I think about it, the less goddamn sense it makes.

Learn manifolds bro. It all makea sense after that.

Thanks. I've been dabbling in some topology or more mathy physics texts recently, but I still think I'm at the point where it just seems like definitions and hasn't completely 'clicked'.

The only thing I've really appreciated so far is exterior product and integration of boundaries. That was pretty cool.

arxiv.org/abs/1604.06527
>This produces a general formula for the group of Symmetry Protected Topological (SPT) phases in terms of Thom's bordism spectra; the only input is the dimension and symmetry group.
>is it bad that my uni specializes in something
No.
>particle pairs
Formation of for instance Cooper pairs is a physical fact, not a mathematical one. Though there are mathematical ways of classifying if a particle pairing can give you an exactly solvable system or not.
Tinkham has a good introduction to BSC superconductivity via Cooper/Peierls pairs.
>local and global broken symmetry
Vector bundles. Specifically principal complex/Hermitian [math]G[/math]-bundles. Gauge transformations arises naturally in this setting as fibre-preserving endomorphisms of the universal bundle.
>spooky motion
There's no such thing.
>No idea where to start.
It should be your advisor's job to tell you that.
Miles Mathis is a famous crank my dude.
>I understand they are not the same thing in many way
They are, and they should be treated as such. Theorists that do not value and maintain at least some level of rigor are nothing more than experimentalists.
Use Weinberg for QFT and supplement with Streater-Wightman.
Also renormalization by the cancellation of counterterms is a physical procedure, not a mathematical one. You being a mathematician or not has nothing to do with it, because there is no mathematical justification for why we do it, just why and how it works.

you absolute bumblefuck
It's literally sine addition formulas, it should take 5 minutes to identify what you need to do

>>>/mg/ you fucking weeb autist.

math is part of physics though

>local and global broken symmetry
I'd also recommend Forster's hydrodynamic fluctuations, broken symmetry, and correlation functions, we used it in the second part of the graduate stat mech course and it was pretty nice.
I'm working on developing some solvable models in qm that form good approximations to more widely studied models and then doing some corrections to see if these methods yield better results than other numerical methods. Not really that exciting but given that I'm not knowledgeable enough to do the type of research that I actually want to do, it acts as a good project to get my name on a paper and as something to do until I can build my knowledge/skill set.

google.com.mx/url?sa=t&source=web&rct=j&url=https://people.math.ethz.ch/~salamon/PREPRINTS/diffgeo.pdf&ved=2ahUKEwjPguPss-LZAhUFXa0KHclcAhwQFjABegQICRAB&usg=AOvVaw1KPRGdpYVoXQzIrsrfgcnX

I think it's not that easy because you have different amplitudes for each 'x'.

>math
Fuck that unphysical garbage!!!

You should study a little bit of representation theory. You want to represent some symmetry group, so you need a space in which to act. In some case you need a spinor space, which has to follow certain rules.

Try to make a parallelism with vectors in linear algebra: you just know that a vector is an element of a vector space, which in itself is just a bunch of rules.

If you want to have a classical analogue of a spinor, look at the belt trick. Penrose book "Road to Reality" explains it in some detail.

All it comes down to is representations of the Lorentz group, 3 rotations and 3 boosts that preserve the interval s^2=t^2-r^2. Fields are defined on spacetime. Knowing how spacetime transforms, we want to know how fields defined on it can transform. A scalar field is such that f(x)=f'(x'), clearly if x'=Lx, then f'(x)=f(L^-1x). A vector field is such that f'_u(x')=L^v_u f_v(x). A representation of a group is assigning a matrix to each element M(L) such that successive Lorentz transformations also have a matrix M(L'L)=M(L')M(L), there is an identity M(no transform)=Identity, and there is an inverse M(L^-1)=M(L)^-1. The scalar field is an example of something that transforms under a trivial representation M(L)=I for every L. The vector field transforms under the representation M(L)=(L), just Lorentz transform matrices. The question is, are there any other representations of the Lorentz group? As it turns out there is a non-trivial representation which is SU(2) and we call objects that transform under it spinors. Spinors in 3 dimensions should be familiar, they are just the spin of a spin 1/2 particle. The significance of the Pauli matrices is that i times them form a basis for the Lie algebra of SU(2), the tangent space at the identity of the Lie group SU(2) itself, and finite SU(2) elements can be obtained by exponentiation. I recommend reading the chapter in Peskin and Schroeder's qft for this whole procedure. The idea behind obtaining it is to generalize quantum angular momentum into 4 dimensions, then find it's commutation relations, then anything satisfying these commutators serves as a good representation. The actual mathematical way of doing this procedure in general is where complicated math like Clifford algebras come up which in a sense generalizes all of this to non physics situations.

Are by chance enrolled at the Technical university of Denmark?

I've read tons of stuff on representation theory and symmetry groups. There are a lot of totally intuitive examples and applications I understand, it's mostly just spinors and SU(N) symmetry groups I still find weird.

The closest intuitive explanation I've heard is that it's the 'square root' of a geometry, whatever that's supposed to mean.

I've also tried exploring taking Laplace spherical harmonics and putting in half-integer values, but then the raising and lowering operator trick that you do doesn't truncate, so there is something more going on.

Does anyone here know good courses on theoretical classical mechanics? I wanna prepare my first semester of theoretical physics.

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>They are
Sounds like something a physishit with an inferiority complex would say.

Right, taking SO(1,3) into a SU(2)xSU(2) representation is mathematically straightforward, but it's the interpreting the results that makes me scratch my head.

If we have SO(1,3) with three generators of rotations (J) and three generators of boosts (K), the algebra is (maybe off by minus signs).

[math][J_i, J_j]=\epsilon_{ijk}J_k[/math]

[math][K_i, K_j]=-\epsilon_{ijk}J_k[/math]

[math][J_i, K_j]=\epsilon_{ijk}K_k[/math]

Then you introduce some operator, [math]S_i=\frac{1}{2}(J_i+iK_i)[/math] and it (along with it's conjugate) satisfy:

[math][S_i,S_j]=\epsilon_{ijk}S_k[/math]

And it's conjugate forms a disjoint group. So it's SU(2)xSU(2), great. But what the hell is this operator?!?

We take a state, and we are taking the superposition of a rotation and an IMAGINARY boost along the axis of rotation. What is that?! I'd like to hear an explanation for this, because at this point to me it seems like we're firmly in math-land, far away from attempting physical interpretation.

[math] S_i=\frac{1}{2}(J_i+iK_i) [/math]

[math] [S_i,S_j]=\epsilon_{ijk}S_k [/math]

By square root of geometry we mean that want write a "square root" of the d'Alembert operator in the Klein-Gordon equation. A Lorentz invariant quantity such that it multiplied by itself gives the d'Alembert, which is determined by the geometry of the system. You can postulate that these will be combinations of derivatives with gamma "objects" which turn out to be matrices. Assuming this square root of geometry thing about what the gamma matrices do you can get the standard definition as the clifford algebra with the anticommutator. First assume that the gammas work through the derivative, i.e. they work on internal space unrelated to spacetime components, then write the product of gammas as 1/2(commutator + anticommutator). Now contracting the two derivatives with the commutator gives 0 which leaves 1/2{gamma^u, gamma^v}D_u D_v which we want to be the box D^u D_u which is satisfied if the anticommutator is 2g. This viewpoint is much more helpful than the standard one you see. Essentially the idea is that given a vector you can represent it as a matrix with useful properties. I recommend Elie Cartan's book on spinors in which he takes this viewpoint. Here's a page about it being done in 3 dimensions sjsu.edu/faculty/watkins/spinor.htm

I meant square root in a more general sense. In the context of taking the square root of Klein Gordan equation alone it seems like an ad-hoc trick that just happens to work, but I assume there is a lot deeper geometry going on.

My (somewhat) understanding is that in much the same way you need complex numbers when taking roots of reals in one dimension, you need more "complex numbers" for representing all the "complex axes" of higher dimensions, which are encoded in the Clifford algebras. Is this essentially correct?

>sjsu.edu/faculty/watkins/spinor.htm

Woah, this is cool, how have I never seen this?

How important is chemistry for physics. I am getting by so far by, but every now and again i run into a term that i don't know. Just assume i don't know anything about chemistry.

Depends, what are you doing? What kind of terms?

Concrete TQFT and some deep string theory.

You are much better off than you are the other way around.

>t. direct phd in quantum dynamics with bsc in chemistry

I don't even know how my research group is in the Chemistry Department at my school.

Just curious, what are some examples of chemistry terms you run into in TQFT and string theory?

Organic concrete cobordism, locally-alkaline manifold, and so on.
With string theory there is usually some deeper stuff going on in the background which I can't quite grasp yet, but that's mainly due to my low knowledge of chemistry.

i'm studying computer architecture, reading the code book by petzold.

This doesn't belong in this thread faggot

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I'm a brainlet only getting my MS since I bombed my qual, but i'm working on developing a CNT-AAO scaffold for assisted nerve growth in severed spinal column. I plan on trying to go back for my PhD in maybe bio/neurological physics or trying to get back into CMT

There are novel monoidal Turaev polymerization reactions involving ribbon catenanes.

Suit yourself.

susskind lecture on youtube

Hey guys!

Just letting you know that this is the Science & Math board, please take this thread to >>>toy as it does not belong here.

Warmest regards,
/mg/

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why are you so salty about physics

>susskind lectures on youtube
youtube.com/watch?v=pyX8kQ-JzHI&list=PL6i60qoDQhQGaGbbg-4aSwXJvxOqO6o5e

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...

Reminder that Calculus was invented by a Physicist: Isaac Newton.

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Reminder that Archimedes was doing integrals two millennia before either Newton or Leibniz.

Reminder that Archimedes was a physicist, engineer, inventor, astronomer and mathematician at same time.
And not a pure mathematician.
>en.wikipedia.org/wiki/Archimedes

Are you the same anime poster who was upset about being dumped by a physicist?

He already has a new girlfriend :c

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Well physicists are the best mathematicians anyway, because they're all but pure.

thats rough

>And not a pure mathematician.
There is no other kind. So in other words he wasn't a mathematician?

Archimedes, just as John von Neumann was a Applied mathematician.

John von Neumann applied math to economics, computer science and physics.

Archimedes applied math to physics, engineering and astronomy.

>What is that?! I'd like to hear an explanation for this
>using incorrect intuition to understand something yields "spooky" results
Wow who would've thunk??
Integrals are pretty deep stuff as can be seen in the recent proof of the Cobordism Theorem. They can be used everywhere instead of Grothendieck-Deligne-May spectra to obtain a greater level of physical intuitions in our highly rigorous proofs, this is a meta-theorem.
>Well physicists are the best mathematicians anyway
Literally this.... The cobordism hypothesis can be (and has been) proved (by Mathematical Physicists), so where are the proofs of this homotopy "hypothesis"? Answer: there are none, because cobordism hypothesis is the cornerstone of something concrete (i.e. TQFT, string theory) while this homotopy hypothesis is the cornerstone of absolute algebraic wank.
And while we're at it, I would like to add that those mathematicians that dislike the supposed "lack of rigor" in physics should also reject statements proven assuming generalized RH/CH.

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>Applied mathematician
No such thing.
>John von Neumann applied math to economics, computer science and physics.
So what you're saying is that he was an economist, computer scientist and physicist? That's pretty cool.

Yes, an engineer invented a branch of engineering. Your point being?

en.wikipedia.org/wiki/Leonhard_Euler
Leonhard Euler
>was a Swiss mathematician, physicist, astronomer, logician and engineer
> He is also known for his work in mechanics, fluid dynamics, optics, astronomy, and music theory.
>Euler was one of the most eminent mathematicians of the 18th century and is held to be one of the greatest in history.
>He is also widely considered to be the most prolific mathematician of all time.

t. Greatest mathematician is also a Physicist and a Engineer.
Explain this.

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>mathematicians of the 18th century
Mathematics didn't even exist in the 18th century yet. This is false information.
>Greatest mathematician
How does someone become the "greatest mathematician" without being a mathematician?

>Mathematics didn't even exist in the 18th century yet

David Hilbert
>the most influential and universal mathematicians of the 19th and early 20th centuries
>did the mathematical formulation of quantum mechanics
>worked alongside Einstein
en.wikipedia.org/wiki/Einstein–Hilbert_action

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David Hilbert
the greatest mathematician of 19th and early 20th centuries.
Did work in Theoretical Physics.

Explain that Pure math-fag.

>Euler, Von Newman, Bernoulli, Lagrange, Laplace, Gauss, John Von Neumann applied math to Physics
Engineers applying math to physics is common practice.
Mathematicians can also do other less important stuff on the side. What is your point?

what does pure-math nerds can even do in life except high school teacher??

poor guys, just let them screech

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>Von Newman
It's John Von Neumann, or Neumann János

Wait, was there someone named Von Newman? Google doesn't bring up anything on that name.

only few of us know his name

Euler, Bernoulli, Lagrange, Laplace, Gauss, John Von Neumann applied math to Physics

Even David Hilbert applied his math to Physics
>the most influential and universal mathematicians of the 19th and early 20th centuries
> Nearly simultaneously David Hilbert published "The Foundations of Physics", an axiomatic derivation of the field equations (see Einstein–Hilbert action).
>Additionally, Hilbert's work anticipated and assisted several advances in the mathematical formulation of quantum mechanics.

en.wikipedia.org/wiki/David_Hilbert#Physics

Redact: my point stands

>Euler, Bernoulli, Lagrange, Laplace, Gauss, John Von Neumann applied math to Physics
Engineers applying math to physics is common practice.