/pg/ - physics general

[Anonymous No.11313811]

Hamiltonian dynamics edition.
I'll be making these threads every couple of months to test the waters.

[Anonymous No.11313880]

>>11313811
Sup. Whatcha wanna talk bout

[Anonymous No.11313930]

>>11313880
physics

[Anonymous No.11313933]

>>11313930
Anything in particular?

[Anonymous No.11313980]

>>11313933
I'd guess he'd want to go for Hamiltonian Dynamics.

But in my opinion, "learning physics" really just is learning the math to learn physics. How would a physics general look like on /sci/. You won't get effortful responses are any topic, simply because there's no names attached

[Anonymous No.11314003]

>>11313980
Not at all. The most interesting parts of physics in my experience always manifest within the actual experiments, reality. No need to discuss pointless theories just for the heck of it.

[Anonymous No.11314238]

>>11313980
This reminds me:
I've picked up Hofer's book on symplectic Capacities and Hamiltonian Dynamics, but I can already recognize most of the material from the summary.
Do I need to fuck around with research papers to learn more about the subject or is there some holy grail I haven't found?
>You won't get effortful responses are any topic, simply because there's no names attached
You mean you don't put effort into random shitposting for the general sake of it?

[Anonymous No.11314257]

I do very applied, experimental physics.

Probably it's mid-PhD crisis but recently I've found myself wishing I did something less applied.

Also my supervisor just quit for reasons unknown which means many things but I don't fully know what.

[Anonymous No.11314984]

what do u think of convergent linear accelerators to break apart leptons?

[Anonymous No.11314998]

>>11314984
We should be focussing on muons, aye

We already know everything about electrons, muons are the future

[Anonymous No.11315144]

>>11314238
Try Guillemin & Sternbergs' Symplectic Techniques in Physics.
>>11314984
What makes you think leptons have internal degrees of freedom? Actually asking.

[Anonymous No.11315187]

>>11314998
high energy physics isn't the future of anything

[Anonymous No.11315365]

Where do I start with Physics?

[Anonymous No.11315375]

>>11315144
It's at least in interesting place to look, with the muon g - 2 and neutrino masses

[Anonymous No.11315389]

Just started self teaching physics, what level of maths should I be revising? I had no idea there would be so much of it

[Anonymous No.11315450]

>>11315389
"If the math exists, some physicist applied it to something." - Sun Tzu.

[Anonymous No.11315629]

>>11315450
How wrong. "If the math exists, it's because a physicists invented it".

[Anonymous No.11316134]

>>11315375
I'm not sure how they can imply hidden degrees of freedom in the muon, anon. As far as I know those things don't require anything beyond the standard model to explain and leptons being [math]irreducible[/math] is kind of an axiom (as far as axioms go in practical QFT).

[Anonymous No.11316149]

Threadly reminder to work with mathematicians.

[Anonymous No.11316153]

>>11316149
threadly reminder that mathematicians never know shit about physics and it is better to ignore them until you can copypaste their results when convenient

[Anonymous No.11316606]

>>11313811
bump because I miss these so much

[El Arcón No.11316619]

>>11315450
no

>>11315629
yes

[Anonymous No.11316623]

>>11315389
>what level of maths should I be revising?
None. Learning pure math is for losers and fags. Stick to physics.

[Anonymous No.11316630]

>>11315629
Based and Diracpilled.

[Anonymous No.11318218]

>>11316606
Cute.
>>11316623
>the undergrad studying subjects in depth
>the postdoc reading the appendix from physics books

[Anonymous No.11319090]

As a mathematician who wants to know shit about physics (thanks poster above) I've been beginning to read landau lifschitz. Will these guys actually justify their calculus of variations or will I need to look elsewhere for the details? I know the first book is great, but what of the others? Is there a good order beyond the sequence by volume number?

[Anonymous No.11319132]

>>11319090
>justify their calculus of variations
They don't. If they do their books would be quadruple their volume.
The mathematical foundation of classical mechanics is symplectic geometry, that of quantum mechanics is von Neumann algebras and that of field theory is jets. There are texts on these topics with a physics slant here and there. Feel free to look up names such as Guillemin, Woodhouse, Von Neumann, Strocchi, Brezis, Sardanashvily, etc.

[Anonymous No.11319223]

How do I learn symplectic geometry as an engineer? There are some 'simple' machines out there that are giving me nightmares.

[Anonymous No.11319294]

>>11319132
>symplectic geometry
>von neumann algebras
these are things i've been learning and will continue to learn this semester, so that's good.

[Anonymous No.11320597]

>>11316153
>copypaste their results
Thank you for subscribing to the Journal of Mathematical Physics, sweetie!

[Anonymous No.11320610]

>>11319223
Either there are some niche fileds that do apply rigorous and abstarct symplectix geometry to engineering and you are going to find articles and maybe books designed for that, or you are talking about hamiltonian/analytical mechanics. For the latter, any applied book of it should work. Or maybe you are talking about dynamical systems?

[Anonymous No.11320628]

>>11319132
>The mathematical foundation of classical mechanicals is sympletic geometry
That's a geometric approach to mechanics which is really useful but not necessarily the only approach nor the foundations. Considering that in classical mechanics you are working almost always on the cotagent bundle, symplectic geometry is an overkill. You can start with lagrangian mechanics and prove almost everything through standard calculus of variations. If you have gelfands book by your hand you can justify most of the procedures used in physics texts. The worst gap I think there is with this approach is the development of the Legendre transform but Spivak covers it decently. This will not satisfy all the questions a mathematician would ask. Mathematicians obviously see this as not the best approach to build the foundations, but I believe that physicists do understand why they teach it in a certain order, as a way to also understand the physics they are modelling so starting with hamiltonian vector fields and symplectic forms will end you without a clue of why these objects appear in physics.
>>11319090
So I suppose you should grab gelfand and Spivak.

[Anonymous No.11320669]

How to deal with dumb as fuck professors who are jealous of you and try their best to interfer in your Academic career??

[Anonymous No.11320681]

>>11320669
First make sure you just aren't a narcissisit faggot or a schizo. If you aren't well then it depends on what they are doing. Also fuck off that's not physics.

[Anonymous No.11320710]

>>11316134
Axiom of what? In the SM they are fundamental, yes, but the SM only describes nature approximately. The muon g-2 anomaly implies BSM if it does not disappear, but not necessarily compositeness of leptons, I agree. However QFT is theory while leptons are phenomonology, it survives very well without ever introducing leptons

[Anonymous No.11321215]

>>11320710
>axioms of what
Streater-Wightman axioms of QFT, specifically the one about quantum fields transforming as irreps under the double cover of [math]SO(1,3)[/math].
My point is that if the theory suffices in explaining the phenomenon can then we don't need any extra fluff (such as internal degrees of freedom of the leptons), especially not those that isn't even necessary to explain said phenomenon.

[Anonymous No.11321235]

are all experimentalists boomers?

[Anonymous No.11321242]

What force keeps 2 particles from breaking the Pauli exclusion principle, even in degenerate matter?

[Anonymous No.11321304]

>>11321242
I don't think it's correct to say this, but I suppose you could relate it to the interaction of spins as Pauli's principle follows from the spin statistics theorem.

[Anonymous No.11321612]

>>11321235
It just seems that way because it takes a lot of training to do modern physics experiments.

[Anonymous No.11322775]

>>11321215
>Streater-Wightman axioms
Weren't those uncapable of describing anything beyond extremely basic scenarios?

[Anonymous No.11323023]

>>11322775
No set of axioms is known to describe the standard model fully

[Anonymous No.11323051]

>>11314003
ilovefuckingscience tier. the math is the most interesting part of physics and quite honestly, physics is just applied math and I love math much more than stupid experiments and 'woo look at the pwetty stars'

[Anonymous No.11323288]

>>11315629
delusional.
t. mathphys

[Anonymous No.11323294]

>>11316153
>never know shit about physics
the reason you can even do physics is because of math and its underlying structure which keeps physics afloat. hell, you wont even have basic arithmetic without math let along path integrals

[Anonymous No.11323428]

>>11316153
>physicists need to resort to meme perturbative calculations and force retarded interpretations because they don't understand the mathematical aspects of their theory
Lmao

[Anonymous No.11323485]

When you get a hold of two magnets and push them you can feel that pushing, turn the other way and they slam together. What is that? the feeling between these two magnets? I mean there is *something* there, isn't there. The sensation is that there is something there. What is it? What is going between these two bits of metal? Why are they doing that or how are they doing it? inb4 I think it is a perfectly reasonable question.

[Anonymous No.11323525]

>>11323485
It's a question more suited to /sqt/ but since this general is always dead, I suppose there is no harm. Moving charges (currents) always generate magnetic fields however, these magnetic fields can interact with other moving charges as well in a way given by the loretnz force law https://en.wikipedia.org/wiki/Lorentz_force.. In magnets what you have is arrangement of molecules in such a way that there are many little currents that go around the surface of the magnet. Forget that the other magnet also has a magnetic field for a while, what the first magnet "sees" is that there are moving charges on that magnet, so the first magnetic field porduced interacts with this set of charges. The second magnet does the same to the first one. To be more precise, the magnetic field can only change the direction of the moving charges, but because of the properties of permanent magnets, there are also other kind of fields thath interact in a way to try and keep the currents as they are. Therefore, the net result is a pull of the whole object. However, you will notice that if you charge some furr or whatever with electrostatic charge, a permanent magnet, no matter how strong, will not pull the object. A permanent magnet is actually pretty weird and so It's difficult to model without some backround knowledge on general EM theory.

[Anonymous No.11323528]

>>11323294
Literally the exact opposite. Physics tends to invent new mathematical concepts to describe what they're doing some 40-200 years before mathematicians can finally formalize that shit.

[Anonymous No.11323539]

>>11323525
I'm pretty sure he saw >>11323449 and found this shitpost somewhere in his folder.

[Anonymous No.11323552]

>>11323528
Physics discover them? Because of the autims of pure mathematics, many people believe thath mathematicians only work on formalizing shit. While from a mathematical point of view how physicists developed the theory of QM was not rigorous, the mathematical ideas that were used came from pure mathematical research. Matrices, operators and abstract vector spaces were concepts no physicists in their right mind knew at the time and know linear algebra is basic even in engineering concepts. You may be right, that the procedures used by dirac have in their essence concepts that were still new in a formal mathematical setting, but he still uses very abstract notions developed by mathematicians. Einstein had to learn riemannian geometry to develop GR. If doing things heuristically is not math, well that's another debate, but no one denies that newton developed calculus just because he wan't rigorous. The case were shit seems to fall appart is with QFT as no one knows how to formalize it, but ffs it still uses really abstract mathematical concepts that physicists didn't develop.

[Anonymous No.11323567]

>>11323539
Close, except I was really curious so I googled and found that video which didn't really answered my question, but this anon explained: >>11323525 but of course I don't really fully understand the explanation except there is something there. Some little currents form the Lorenz force.

[Anonymous No.11323581]

>>11323567
To clarify some concepts, in physics a field is in itself a physical object governed by "field equations". Maybe you heard of the maxwell equations, these equations tell you how the fields behave and evolve through time. What exactly are these fields made up? Classically, they are as fundamental as particles. Light, maybe you heard, is actually a field that is not attached to anything. I.e. it is traveling through space. These fields are what interact with matter and affect them in different ways. The loretnz force is a description of this interaction between a magnetic field and a moving charge. What we also know is that moving charges generate their own magnetic fields.

[Anonymous No.11323767]

>>11323552
dude dont even bother with retarded physicists. folks like these are what give physics a bad name. I am one of the belief that math and physics go hand in hand and this was very much the way of the past, e.g. Lagrange, Hamilton, Laplace, etc. are names well known in both physics and math because the two subjects were so closely related

[Anonymous No.11323799]

>>11323767
To be fair, I know plenty of brilliant physicists who parrot the same bs. I think there's an unhealthy tradition of trying really hard to demarcate what is math and what is physics, and this has generated some sort of grudge in the fields till the point that experts in the fields seem unable to talk in a middle languange. This goes to mathematicians too, as I've seen really good mathematicians almost take offence when they hear about applications and intuitive/heuristic/physical arguments. I've shit you not that some get scared if in a calc test basic kinematics comes even if it requires no knowledge besides the definition of velocity and acceleration. I just don't understand how high level academia can have such narrow minded.

[Anonymous No.11323946]

>>11323581
But we don't even know what a charge is, correct? So we can't really answer lots of fundamental questions since we don't know what those fundamentals are.

[Anonymous No.11323974]

>>11323946
Charge is a property of matter. It's a scalar quantiy that we can measure and therefore define at least in an instrumentalist setting. For the purposes and goals of physics we know what it is exactly. If you want to deny this through pseudo-philosophical u can knoe nothin crap just understand that in order for modern physics to work as a model for reality, yes you have to assume certain things about the nautre of reality. If you don't like that, no problem no one is forcing you to do physics.

[Anonymous No.11324208]

>>11322775
That's not the point; you [math]definitely[/math] want your fields to form reps of [math]\operatorname{Spin}(1,3)[/math], regardless if Streater-Wightman axioms are able to reproduce the full power of QFT. No one said that those are complete, but they (as well as the additional completeness assumption on the Hilbert space) for sure form a lower bound.
>extremely basic scenarios
If you consider a full theory of free fields, which forms the basis of literally every scatter computation, to be "extremely basic", then I really don't know what to tell you.
>Weren't those uncapable of describing anything
No axiomatic approach to general QFT (i.e. not TQFT/CFT) has yet been completely able to capture what QFTists are doing. The closest we have is Haag-Kastler's local operator nets and Strocchi-Swieca/Osterwalder-Schrader's analytic constructions of Wightman/Schwinger functions, and these in some scenarios the regularity requirements are too stringent to produce any useful [math]S[/math]-matrix.
Aside from obvious obstructions like Haag's theorem, we can't find the Poisson structures needed for Kostant-Souriau-Sardanashvily geometric quantization of jets, and Zhang-Baez's AQFT struggles to get even basic classical limits like WKB. One needs to strike the perfect balance between formalism and applicability in order to produce useful axiomatization of QFT.
The gap is much less significant than you think, however, as CFTs (IR fixed points of QFTs) can in fact be fully captured by the mathematical theory of Friedan-Shenkar's gauge system. Not to mention Atiyah-Lurie's axiomatization of TQFTs has produced much progress in both physics and mathematics.

[Anonymous No.11324236]

>>11314257
get a tenure and then switch focus.
about your pi, you'll probably get a new one, look into it and see if you can choose who it will be and start begging your favorite prof in the area to accept it.

[Anonymous No.11324246]

>>11315187
it is the future of high energy physics.

>>11315389
the basics would be calculus (1d, multivariable, differential equations) and linear algebra (some unis teach analytic geometry before it).
you can go quite a long way with just calculus and dif. equations. linear algebra is always helpful but only will be essential in later courses, specially quantum mechanics (for which you need some basic complex calculus)

[Anonymous No.11324259]

What undergrad level textbooks can you guys recommend?

[Anonymous No.11324267]

>>11324259
Weinberg

[Anonymous No.11324273]

>>11324259
a bunch. for the most important disciplines: purcell electromag, reif thermal, cohen-tannoudji quantummec. classicalmec is w/e if you know the math, marion/taylor/other.
dont fall for the feynman meme.

[Anonymous No.11325226]

https://link.springer.com/book/10.1007/978-3-319-51777-3
Has anyone here read this?
Is it good?

[Anonymous No.11325652]

>>11325226
Never mind, I googled his name later.

[Anonymous No.11325684]

>>11316149
i hate mathematicians tbqh

[Anonymous No.11325686]

What's everyone's thoughts on MIP* = RE? Apparently it disproves Connes' embedding conjecture. Since operator algebras are the basis of anything quantum, does this have any implications outside of complexity and computability theory?

[Anonymous No.11325822]

Physics anons - what's the difference between light dose and fluence rate?

[Anonymous No.11326443]

>>11325686
It may probably have some influence on how SRE phases are defined on lattice systems, but I doubt it could touch anything in the continuum limit. The reason I say this is because SRE phases are defined (according to Wen) as equivalence classes under local unitary transforms, which can in turn be represented as finite-depth quantum circuits. See https://arxiv.org/abs/1004.3835

[Anonymous No.11326444]

anyone else have problems with general notation like z=xy, which may assume that x and y cause z, but in fact it can be rearranged in 3 different ways and suddenly y and z can cause y. Usually it is obvious from the context, but I really struggle with this stuff in the EM equations. Everything there seems cyclic to me, and I can't separate causes and effects.

[Anonymous No.11326540]

>>11326444
just read lol.
but yeah, the equal sign isnt the best sometimes

[Anonymous No.11326571]

For gradschool level, what Statistical Mechanics book(s) would you use?

[Anonymous No.11326952]

Is the gravitational field strength also a force?

[Anonymous No.11327744]

What‘s the best way to go about intuitively understanding a lie algebra? I understand that a lie group is a continuous symmetry just fine, and I *kinda* get that an element of said group‘s lie algebra is a symmetry very close to the identity, but it hasn‘t really clicked for me yet, moreso for actual applications of said algebra.

[Anonymous No.11327759]

Unironical question here, If i have 2 pairs of insulating gloves rated at 12kv, and i put one pair inside the other pair of gloves, will less amps leak than if i were to only wear 1 pair?
would it then insulate 24kv?

[Anonymous No.11327782]

>>11327759
>will less amps leak than if i were to only wear 1 pair?
Yes (through your hands/body anyways), it's like putting a resistor in series.
>would it then insulate 24kv?
no, your breakdown voltage will still occur at 12kv.

[Anonymous No.11327783]

I have a few questions regarding Hamiltonian dynamics
1. What is the main reason for the Kac theorem? Why does area conserving maps have a finite mean return time?
2. How can you prove that any map that is derived from a Hamiltonian dynamics is area preserving (and thus the Kac theorem hold)
3. Are there any chaotic non area preserving maps that have an infinite mean return times? Do any of these maps have an accelartors mode with an infinite mean stickiness time?

Thank you

[Anonymous No.11327785]

>>11327744
>and I *kinda* get that an element of said group‘s lie algebra is a symmetry very close to the identity
you are selecting elements near the identity by choosing theta<<1, that is, since the symmetry is continuous, you can choose those that are inf. small.
why that's useful though, is because the lie algebra (lie group near identity) can be interpreted like a cotangent bundle which connects to dif. geometry, which gives you a bunch of insights.
most physics books dont explain this (because it is not super relevant except for developing the jargon and some basic notions) or explain very poorly.
i myself dont know much about it. but you either have to find a more advanced physics-focused book about it or go learn it "properly" by studying from a math group theory book.
i have an enormous list of group theory books, though i admit i have no idea what the best route is

[Anonymous No.11327804]

>>11320610
I just don't know what to do anymore. What I really want is something that tells me if I put this collection of parts together that for some set of values of the parts they'll do what I want. So like if I want to search for something I want, I have to put parts together than optimize the values on the parts and then check if they're what I want and how well they do. Then cause it's search, I figure out what parts to connect together based on how well those optimized things did, but this doesn't work very well, cause the optimization for one set of parts may not actually do what I want even though for some values it's possible. I heard, perhaps quite wrongly from some popsci mag, that symplectic geometry lets you do dynamics topologically? And like doing stuff topologically sounds much better than working with actual values.

My specific problem is figuring out how to enumerate all possible devices which act like mechanical clocks consisting of rigid bodies which may be connected to each other with springs, dampers, kinematic constraints(although this is not really necessary as you can make technically constraints from other rigid bodies). Contact between rigid bodies may be assumed to be frictionless, although it is best to assume that all rigid bodies are subject to some form of damping. I don't know how to formally define what a clock does, although I think a useful definition for a clock is something that rotates as close as possible to a constant rate despite some finite amount of variation in input torque. And of course the rotating output is subject to some form of damping, so a flywheel spinning at some given rate disconnected from the input is not a valid clock.

[Anonymous No.11327881]

>>11327759
if you're fucking around with anything at high voltage that can deliver milliamps of current you really need to be fucking careful. If this is work related, ask for proper training or equipment. If this is something you're diying, you probably shouldn't be touching it in the first place
>>12 kv, 24 kv
when you're at voltages like that, shit gets weird. Air can ionize, things were 'nonconductive' at low voltages actually have low enough resistance that they can be treated like conductors. The added glove will certainly help, but I would not recommend it. Doubling gloving will be less effective than a monolithic glove. In breakdown, that thin layer of air will ionize a heckuva lot easier than plastic. Me, I just use nitrile gloves when working with high voltage, but that's only because the stuff I'm working with has low capacitance and my power supplies can't provide more than a couple microwatts. I don't recommend doing this though as you can still painful shocks if you touch the wrong part and arcing through your body can damage power supplies.
>>11327782
what you really have is capacitors in series, and we all know that when you put capacitors in series, the voltage across each capacitor sums up. So it could work. I would highly recommend against doing this because A. not using rated safety equipment is generally a recipe for disaster, and B. dielectric strength is actually geometry dependent.

[Anonymous No.11327898]

Do physicists write their own DE? It would be awesome to come up with your own since thats the most fascinating part in the DE course: even if it is a rare case of a really simple DE, how the hell did someone think of it. Even something as simple as y'=y. It is a brilliant idea to think of growth in terms of the value of the function itself. But how do you develop this type of intuition. And anything more complicated than that is completely mind boggling. I mean once it is explained to you, it is easy. But how do you come up with 2nd/3rd order DEs on your own, i.e. thinking of a rate of change in terms of a nth-derivative of y AND maybe also x.

[Anonymous No.11327912]

>>11327881
Yes i know, i'm just asking random stupid questions. I have a pair of gloves rated for 20kv. I was thinking about making an arc with a Flyback transformer. Of course, I'm not willing to do it because i don't have any experience with HV and i can kill myself easily.
What safety measures do you suggest? if one were to do it, wouldn't it be safer to use a battery instead of plugging a power supply to the home grid? so you dont have to worry about grounding

[Anonymous No.11328853]

>>11315144
because they have mass & electric charge, thus at least three forces internally, one too small to detect

[Anonymous No.11328882]

>>11313811
So, I want to relearn a lot of physics since I've been out of school for a while, if I wanted to attain a solid, graduate level education in physics, what books would you recommend? So far, people have told me LL, while old, is still the gold standard and is basically everything foundational you'll need.

[Anonymous No.11329056]

>>11328882
landau books are great and have some timeless sections, but they are terse and a bit old overall. i'd use them as complements.
recommendations are as follows:
mechanics: goldstein; quantum mec: sakurai; e&m: jackson; these are standard textbooks in all grad schools.
for statistical mechanics, there's no book considered the de facto textbook. you can use kardar, huang, pathria, le bellac.

if you want to, you can google "quantum mechanics syllabus grad university of X" to find out what books they are using in cambridge or eth zurich or w/e. spoiler: most are using what i recommended

[Anonymous No.11329062]

>>11328882
>>11329056
also, if you google like that, you can often find the notes used in those courses written by the professors and the proposed exercises and problems (some also created by the prof or from other books).

[Anonymous No.11329118]

>>11321242
The Pauli exclusion principle has nothing to do with forces.

[Anonymous No.11329210]

>>11329118
you are mistaken

[Anonymous No.11329268]

>>11329210
Degeneracy pressure is not a force.

[Anonymous No.11329422]

Why does the weight of a body not make it accelerate faster in free fall?

[Anonymous No.11329441]

>>11329422
It does. Why do you think you weigh more on Earth than you would on the Moon?

[Anonymous No.11329455]

>>11329441
Because the gravity field of the earth exerts a greater force on my body than the gravity field of the moon.

[Anonymous No.11329461]

>>11329455
but both objects (Earth and your body) have fields of gravity.

two earths would collide faster than you and the earth

[Anonymous No.11329463]

>>11329422
very unintuitive result, indeed. me and yo mama so fat in free fall would reach the ground at the same time (no, air cant resist her)

[Anonymous No.11329544]

>>11329461
https://www.youtube.com/watch?v=KDp1tiUsZw8

[Anonymous No.11329788]

>>11327783
>1
In general given a measure-preserving ergodic map [math]T\in\operatorname{End}(\Omega,\mu)[/math], Koopman's lemma says that the unitary [math]U_T = T^* \in \mathcal{B}(L^2(\Omega,\mu))[/math] has [math]1\in\sigma(U_T)[/math] with multiplicity 1; namely [math]\operatorname{dim}\operatorname{ker}(U_T - 1)=1[/math]. Now ergodicity, by deifinition, also implies that [math]\{T^n x\mid x\in\Omega\}\subset\Omega[/math] is dense for some [math]n\in\mathbb{N}[/math], whence at some point in the application of [math]U_T^n[/math] you will hit the one-dimensional eigenspace and stay there; convergence in finite time occurs because the singular dimensionality means that there is essentially "no where for the image to go". See also Poincare recursion.
>2
I presume you're referring to the time evolution operator [math]\alpha_t[/math] generated by the complete SA Hamiltonian vector field [math]X_H[/math]. By the criterion above, [math]\alpha_t[/math] is ergodic when the induced map [math]U_\alpha(t)\in \mathcal{B}(L^2(\Omega,\mu))[/math] has a simple eigenvalue 1. Hence we examine [math](U_\alpha(t)-1)\psi = 0[/math] whence by Stone's theorem implies [math]\psi\in\operatorname{ker}X_H[/math]. If [math]X_H[/math] is elliptic, then the existence of [math]\psi[/math] can be proven with the spectral theorem. By Fredholm alternative, either this [math]\psi[/math] is unique or [math]X_H^{-1}\in\mathcal{B}(L^2(\Omega,\mu))[/math] exists, but typically the Green function [math]G = X_H^{-1}[/math] isn't bounded.
>>11328853
That's not how it works hun.

[Anonymous No.11329953]

>>11321242
PEP <- anticommutation relations <- spin-statistics theorem <- Lorentz invariance <- empirically observed constancy of the speed of light (causality) in all inertial reference frames

[Anonymous No.11329979]

>>11327744
Lie group is a smooth manifold with a group structure. Lie algebra is the tangent space of Lie group at the identity. For connected Lie groups, you can obtain any Lie group element by exponentiating a Lie algebra element.

Coincidentally I have been writing some notes recently

https://mega.nz/#!COBD3KZJ!3dDwY4-89giS98PeBlRFGUJ_Xcv7t9LDuUPnewyEGXc

[Anonymous No.11329986]

>>11329422
F=ma
-mg=ma
a=-g

Note that higher mass objects do "fall" faster, in that they pull up the earth towards them, decreasing the time needed to hit the ground.

[Anonymous No.11330149]

comp sci major fresh out of uni and I'm tired of being a physics brainlet.

what's a good classical mechanics book to get me started with? I do have a decent math background.

[Anonymous No.11330219]

>>11330149
just read Feynman lectures on physics.

[Anonymous No.11330251]

>>11330219
thanks, friend.

[Anonymous No.11330332]

>>11325652
It's crazy to see people you've seen in real life appear on 4chan.

[Anonymous No.11330354]

>>11330149
Classical Dynamics of Particles and Systems by Marion was my baby during my classical mechanics sequence. I don't know how it stacks up against the other popular undergrad texts, but I loved it. I'll still pick it up from time to time and work on a problem from it for fun.

[Anonymous No.11330641]

>>11330149
Classical Mechanics: John R. Taylor
or the one by marion and thornton

[Anonymous No.11332095]

Bump.
https://arxiv.org/abs/1712.02952

[Anonymous No.11332842]

>>11330332
Yup.

[Anonymous No.11333562]

>>11330332
imagine if people you've seen in real life POSTED on 4chan.

[Anonymous No.11333582]

>>11313811
Best textbook for waves and also for EM? Math isn’t a barrier but correct statement of equations and lucid clean writing would be preferred. I have Griffiths for EM but I’ve seen people calling it shit, is there a better alternative?

[Anonymous No.11333588]

>>11333582
also preferably no L&L I have most of the series but without undergrad exposure to EM or Waves im worried id lose a lot of the intuition.

[Anonymous No.11334705]

>>11333562
I know a lad who posts on /a/.

[Anonymous No.11335299]

>>11333582
>>11333588
griffiths is good, just doesnt appease some people. for undergrad, another good one is purcell (nobel laureate).
for grad level, the absolute reference is jackson.

[Anonymous No.11336516]

shut down the thread

[Anonymous No.11336557]

>>11336516
Not so fast, Bog.

[Anonymous No.11336741]

>>11313811
im taking an EM class and it's the first time i feel challenged what do

[Anonymous No.11336981]

>>11320681
They gaslit me and refused to give me grades I deserved because they prioritized those in three grades above me. They would also arbitrarily mark things wrong on my homeworld hoping I wouldn't come back to correct it.

Then I showed them my iq, and solved a problem not even the grads could do.

Lmao I fucked my professors daughter that fucked me over and did her homework for her in 30 mins and made her feel like an idiot.

[Anonymous No.11336991]

>>11336981
Basically I stopped taking physics courses and did electrical engineering or engineering physics and got As. They really fucked my gpa though.

[Anonymous No.11337015]

>>11336981
>>11336991
I'll be honest.
You sound extremely hard to get along with.

[Anonymous No.11337023]

>>11337015
I used to be. Pretty much have little chance of getting into a good university and only have like 1 good academic letter of rec. Humbled me and am pretty quiet and shy and recognize the importance of hierarchy.

I just hate that my family was paying money so that my profs could fuck me over and deny me opportunity that I repeatedly received.

I got denied a school change to a better school because of my professors. If I'm paying money you better believe I'll stir shit up if it isn't fair. However if you pay me I'll sit quiet. Profs dont understand the value of money at expensive universities because they are soaked in privilege and 9/10 came from affluent families.

[Anonymous No.11337027]

>>11337023
Edit: I had already been accepted to the other school and they fucked it up for me.

[Anonymous No.11337297]

blogs are the other way