/sci/ - Science & Math

I'm really interested to compare how various universities in various countries compare in terms of the study load.

If you're a physicist, mathematician or a chemist,

1. What's your country and uni (at least like some tier)
2.. What's your major?
3. What courses did you have in BSc? (a lot of unis have some site for course schedules so if you're too lazy to write it all out, just post a screenshot)

>>11492814
In QM on a lattice, you assign a local finite-dimensional Hilbert space [math]\mathcal{H}_x[/math] to each lattice point [math]x\in\Lambda\subset \mathbb{R}^n[/math], then you construct observables [math]\mathcal{A} = \operatorname{cl}\bigcup_{X\subset \Lambda}\mathcal{B}(\mathcal{H}_X)[/math] as the closure of the direct limit of local nets of bounded linear operators where [math]X\subset \Lambda[/math] is a finite subset and [math]\mathcal{H}_X = \bigotimes_{x\in X}\mathcal{H}_x[/math].
A state [math]\Psi[/math] determines measurements [math]|\langle \Psi,A\Psi\rangle|[/math] for observables [math]A\in\mathcal{A}[/math] only up to its projection [math]\tilde{\Psi}[/math] onto the unit sphere [math]S\mathcal{H}_\Lambda[/math]. For a short-range entangled state [math]\Psi \sim_{\text{unitary equiv.}} \bigotimes_x \psi_x[/math], the measurement clusters [math]|\langle \Psi,A\Psi\rangle| = \prod_{x\in \operatorname{supp}A}|\langle \psi_x , A_x\psi_x\rangle|[/math] and hence is determined by [math]\sum_{x\in\operatorname{supp}A}\operatorname{dim}_\mathbb{C}S\mathcal{H}_x \leq \sum_{x\in\Lambda}\operatorname{dim}S\mathcal{H}_x[/math] number of variables. If [math]\operatorname{dim}_\mathbb{C} \mathcal{H}_x =\frac{1}{2}\operatorname{dim}_\mathbb{R} \mathcal{H}_x= K+1[/math] is uniform, then measurements are determined by at most [math]\sum_{x\in\Lambda}2K = 2K \cdot |\Lambda|[/math] number of real parameters. This is in general untrue if [math]\Psi[/math] is long-range entangled, however.

>>11493089
Jesus, that's a higher level answer than I'm at right now. I'm only in my second semester of QM.

But the thing is, it was said about some general QM system as far as I understand, hence my question is where does the lattice come from and what it actually is?

>>11493243
>Jesus, that's a higher level answer than I'm at right now. I'm only in my second semester of QM.
HEY everyone, look, he did it again !!!!

>>11493243
>where does the lattice come from
The tight-binding hypothesis in condensed matter. Besides, field theories are the continuum limits of lattice systems so it's useful to study them in general.

I hate this board on so many levels.

>>11493260
> Besides, field theories are the continuum limits of lattice systems so it's useful to study them in general.
But wouldn't such a limit-case lattice have infinite points for any finite part of space?

>>11493307
Indeed, that's why you shrink the dimension of the local Hilbert space along with it, at least formally. Here's what I mean: instead of taking point-wise local finite-dimensional Hilbert spaces and observables in our definition, we take them associated to each space-like open set [math]U\subset\mathbb{M}[/math] in the continuum spacetime [math]\mathbb{M}[/math]. We must do this, in fact, otherwise our QM definition above would lead to non-local interactions (things that couple faster than light) at some point in the continuum limit.
Since Minkowski spacetime is locally compact, we can find countably many such local space-like covers such that [math]\mathcal{H} = \bigotimes_{U\in\mathcal{U}}\mathcal{H}_U[/math] is at most seperable. This is the Haag-Kaster construction of QFT, via local operator nets.

>>11493563
>Kaster
Kastler*

yukari-poster, you aren't welcome here. you're a mathematician, admit it.

if you are so smart, then answer this question. it's actually real physics instead of abstract math crap

If ron maimon can't make it in theoretical physics, what hope is there for any of us?

So black holes are 4d spheres right
like a ball resting on the ground if the surfaces were perfect it would be resting on a singularity
when a star gets too big or dense or whatever to support itself it collapses and breaks through somewhere

right?

I don't even want yukariposter in the math general,if he wastes a few posts here good

>>11493585
I distinctively recall him answering that exact maymay image once. BRB looking through the archive.

>>11495306
Bingo.
https://boards.fireden.net/sci/thread/10331062/#10331062

I'll leave now, catch you later.

>>11494140
jon snow believes in cold fusion

>>11493089
>>11493260
>>11493563
You absolute retard, how the fuck do you go to the construction of lattice QFT just from somebody asking basic questions about mechanics? Your answers are useless.

>>11492814
In non-relativistic classical mechanics, the state of a particle is fully determined if we know it's initial position in the phase space (and Hamiltonian describing the system, of course). That is, we know it's momentum [math] \mathbf{p} [/math] and position [math] \mathbf{x} [/math], since the evolution is then determined by the equations of motion, I believe that is clear to you. The move towards quantum mechanics lies in the fact that a precise state in the phase space is not well defined, which is most easily seen through the uncertainity relations. These tell us that, at best, we can localize the state in the phase space to the phase space volume [math] \Delta \mathbf{x} \Delta \mathbf{p} = \hbar / 2 [/math]. In quantum mechanics, the evolution of the physical state happens within the Hilbert space and is fully determined by the Schrödinger equation, therefore all you need to know to fully describe a quantum particle is the initial value of the wave function, at each point in space, which is in principle infinite numbers. The number L^3 * 2K is the result of spatial discretization, which can be context dependant, physical (see Yukari fag mentioning lattice QFT) or non-physical, but since the book talks about digits, I'm going to assume that it relates to numerical discretization, therefore L^3 is the number of nodes within your discretized grid at which you read the value of the wave function.

>>11495338
>lattice
>QFT
>FT
Anon... time to stop pretending you know what you're talking about. You've tried it before in /mg/ and it's not gonna work again here.

>>11495359
I don't know about lattice QFT and I don't need to. I didn't bother reading past your first sentence, which immediatelly assumed spatial discretization, so that's what I assumed you are talking about. If you want people or actual physicists to interact with your posts in other ways instead of just instantly dismissing them as mathematical word salad, especially in physics threads, you need to get your head out of your ass and stop relating everything to useless AQFT, TQFT or whatever the fuck it is you study.

You continute to post redundant information on basic topics and degrade the quality of physics discussion on this board. Not a good sign of character.

Are cellular automata /pg/ related, especially if they are behaving like Ising spin-glasses?

>>11495470
Fucking based. The 2hu avatarfags' answers are 95% useless because they think it's fun to ignore the level and context of the actual question/asker. Someone needs to put them in their place.

Just know that I literally don't care what you think of me.

>>11494427
The blackhole is a point singularity. Its event horizon is a 3-sphere at past/future infinity, namely any geodesic near it evolves to [math]t=\pm\infty[/math] in finite proper time.
>>11495506
That sounds interesting; can you give an example where people model spin-glasses, or some other long-range order, with cellular automata?

>>11492814
Seems like it's just the discretization lattice, which they assume in this case is uniformly cubic. (More sophisticated methods use less trivial geometries, e.g. finite element.)

Basically they're just talking about the amount of information required to store a single state in the classical vs. quantum setting.

The classical state is basically just an element of [math]\mathbb{R}^6[/math] for the reasons you stated (technically phase space is the cotangent bundle of the configuration space, but let's not be a Yukarifag here...). OTOH, a pure quantum state is an element of a separable Hilbert space [math]\mathcal{H}[/math], usually in the case of infinite-dimensional spaces we choose a faithful representation being square-normalizable functions, in this case [math]\mathcal{H} = L^2(\mathbb{R}^3)[/math]. Thus in principle you need a continuum of information to describe the continuous functions ("wavefunctions) of this space. In order to work with this numerically, we discretize the *spatial* information into a lattice [math]\Lambda \subset \mathbb{R}^3[/math] and basically just assign/calculate values of the wavefunction at only these points.

It's really no different from doing any type of numerical discretization to solve PDEs and so forth.

>11495645
lmao literally seething
cope you fucking autist, you're not as helpful as you think you are

>>11495645
>Just know that I literally don't care what you think of me.

Why do you then even bother replying to threads with useless informatiuon? Why not just write a diary? I don't understand.

>>11495645
>Just know that I literally don't care what you think of me.
You're clearly fishing for ego validation. Do you actually think about yourself that you don't care they think of you?

>>11495695
>>11495706
Of course he cares, he's a fucking avatarfag for christsake. That's evidence enough, before any of this even started.
By the way, isn't avatarfagging a bannable offense? Why is hiromoot suddenly okay with it?

>>11495727
Sure it is. Go ahead and report him.
But I'd like to remind you that off-topic meta discussion is also against the rules.
>>11495677
Good post.

>>11495645
>That sounds interesting; can you give an example where people model spin-glasses, or some other long-range order, with cellular automata?

Of course, even the simplest automata may work.

https://en.wikipedia.org/wiki/Toom%27s_rule

>The 2-dimensional majority vote cellular automaton (CA) is analogous to the Ising model. The majority vote CA evolves each site in the lattice by taking the spin value of current site plus that of the 4 neighboring sites and makes this spin +1 in the next time step if the sum is positive and -1 if the sum is negative.

However, there are few models who approximate well to the 2D square-lattice Ising model's Curie temperature. For instance, Mehta and Schwab wrote a deep neural network that approximates the coupling J to 0.4352, where my automaton with far fewer lined of code approximates to 0.4443 (actual value is ~0.4407). Pic related - the critical point acts like the critical attractor of the automaton.

https://arxiv.org/pdf/1410.3831.pdf

https://github.com/goktu/ADama/blob/master/cellularautomata.py

https://github.com/goktu/ADama/blob/master/cellularautomata.py

>>11495645

>That sounds interesting; can you give an example where people model spin-glasses, or some other long-range order, with cellular automata?

Of course, even the simplest automata may work.

https://en.wikipedia.org/wiki/Toom%27s_rule

>The 2-dimensional majority vote cellular automaton (CA) is analogous to the Ising model. The majority vote CA evolves each site in the lattice by taking the spin value of current site plus that of the 4 neighboring sites and makes this spin +1 in the next time step if the sum is positive and -1 if the sum is negative.

However, there are few models who approximate well to the 2D square-lattice Ising model's Curie temperature. For instance, Mehta and Schwab wrote a deep neural network that approximates the coupling J to 0.4352, where my automaton with far fewer lined of code approximates to 0.4443 (actual value is ~0.4407). Pic related - the critical point acts like the critical attractor of the automaton.

https://arxiv.org/pdf/1410.3831.pdf

https://github.com/goktu/ADama/blob/master/cellularautomata.py

>>11495790
That's pretty neat. I've also heard form a friend that any 1 and 2D quantum order can be simulated with a space of localized quantum dots and you by tuning interaction parameters, I guess this is similar. Though maintaining the coherence of local quantum dots is pretty taxing.
Thanks for the links, I'll have another thing to talk about with my cond mat sims colleagues

>>11495790
I tried to detail the bifurcating phase transitions and their trigonometric representations in >>11495716

>>11495802
Awesome, I'm up for feedback anytime.

>>11492874
All I'll tell you is that I had zero fucking load whatsoever. Absolutely no homework, on exams you could brows internet, nobody gave a fuck. I only studied whatever I found fun from couple of books and video lectures, besides studying shit load of other stuff like programming, machine learning, little bit of game development. I somehow made it to PhD and now I'm publishing papers on higher dimensional algebra related stuff. Whenever I see stuff like this
https://www.youtube.com/watch?v=iBvm6RCISO8
I feel like a fucking imposter.

>>11495338
> which can be context dependant, physical (see Yukari fag mentioning lattice QFT) or non-physical, but since the book talks about digits, I'm going to assume that it relates to numerical discretization

By numerical discretization do you mean arbitrarily breaking up space into points with effectively infinitesimal distance in-between?

>>11495830
Math or physics? How did that happen? Were you in some super shitty uni?

We have a department of metals which is where you can be a total retard and not ever read, but I never heard this about MSc and especially PhD.

>>11495677
Thanks, thought so.

> It's really no different from doing any type of numerical discretization to solve PDEs and so forth.
Is that the same method as when solving integrals by a computer? Just taking some finite differentials that give accurate enough answer.

>>11497072
>numerical discretization
>>effectively infinitesimal
You'll regret ever having such a thought if you end up working with numerical PDEs. Poor convergence rates, numerical instabilities, and memory bottlenecks are all basically due to the fact that, no matter how hard you try, 1e-n >> "infinitesimal" for all finite n.

>>11497098
>1e-n
What does that mean?

>>11497088
On a spiritual level, I guess? I mean, that's always the basic goal to solving diff. eqs. But if you're doing any sort of practical calculation, finite difference simply isn't going to cut it. Even when doing ODEs, something like Runge-Kutta converges so much faster than naive finite difference it's not even funny.

Numerical analysis is really a fascinating subject and definitely does not get attention/appreciation from us physicists who rely daily on it. It really is a deep branch of mathematics. I've always been a fan of implicit methods myself, even if I've never personally implemented one myself (I'm a shit coder).
>>11497116
Sorry, lazy scientific notation for [math]10^{-n}[/math].

>>11497135
Runge-Kutta is a finite difference method.
>naive finite difference
Euler's method.

>>11497086
>Math or physics?
physics
>Were you in some super shitty uni?
I'm in a quite shitty country
>you can be a total retard
I can't tell you I'm retarded, I pick up stuff from books pretty well and pretty fast, the thing is I just missed lot of books and I do my work with huge gaps in knowledge. But to be honest you don't need much EM phenomenology and thermodynamics when doing QFT, isn't it right? At least half of my professors don't know what a Lie group is and can't tell Poincare group from Lorentz group. That's the unfortunate reality I live with. I'm working on my gaps though. But education system I went through was nothing but a disaster.

Question to physics folk here. I was reading about why there are a lot physics phds in finance and many answers were along the lines of "Physics grads can create mathematical models and find sensible ways to compare it to the real world system being modeled. Math grads while capable of creating mathematical structures don't have mich experience in modifying it to match anything else so they're found less in finance".

>>11498064
Oops, forgot to add the question. How accurate is that assessment?

>>11498064
>>11498070
Seems like a bullshit explanation to try to categorize people based off of a singular aspect of them. I see literally no reason for that to be even remotely true, it's almost caricaturizing mathematicians as being non-human.

More likely, there are just fewer math PhDs than physics PhDs in general, and those who do go into a math PhD typically have only 1 goal in mind, a tenure track position. Whereas physicists have more options outside of academia, and so are more open to looking for a wider variety of jobs. But I should stress that the difference is not as drastic as you might think.

>>11498109
Thanks. In general, I am curious about this how do physics grads land such high paying jobs in a completely different field like big finance and consulting companies? Is there any area of study that overlaps with physics?

>>11498141
Not really. It's more the fact that physics PhDs do lots of numerics and are open to learning whatever fancy mathematics they need to get the job done. I'd reckon that math PhDs simply don't do as much coding. But I might be biased.

Are all physicists bitter failed mathematicians or do I have bad luck?

>>11498585
In my experience being a physicist is very different from being a pure mathematician and I have no real interest in becoming the latter. But I think that depends on what you expected to do when you got into physics. I certainly wouldn't have minded becoming an applied mathematician or a computer scientist from what I see of those fields.

Bump with an interesting article https://arxiv.org/abs/1811.08182..
>Moreover, the Rashba SOC can produce a topological phase rather than hinder it, in contrast to the honeycomb lattice.
Quite surprising, since a honeycomb of 1/2-spins is lattice homotopy equivalent to a Kagome of 1-spins; I wouldn't expect the topology hosted by a given lattice homotopy class [math][\Lambda][/math] to change just because the Rashba SOC parameter is tuned, but [math][\Lambda][/math] doesn't contain such data anyway so I can't say for sure.

>>11494140
>ron maimon
I.. I love him... I love this nigga more than I've ever loved before

>>11494140
Are you gonna post any story or what?

>>11500192
Autistic super-rationalist who knows a whole lot about theoretical physics but keeps sticking to his ideals so that he always gets fired and banned from all his academic and job positions and all the forums. One of the few people outside of academia anymore who know a lot of string theory proper.

https://physics.stackexchange.com/users/4864/ron-maimon?tab=answers&sort=votes

Going through his SE pages boxes is fun:

>Math
My mathematical prejudices: 1. I don't accept choice on the continuum 2. I accept choice on countable collections, as well as countable infinity. 3. I don't think of the continuum as small enough to be a set, 4. I think every subclass (subset) of the real line is measurable, 5. I prefer constructions to abstractions. In this, I hope I am following Paul Cohen in spirit.

my dream theorem is a proof of the consistency of ZFC from a countable computable ordinal, as explicitly describable as possible, which plays the same role for ZFC as 𝜖0 does for PA. This would complete Hilbert's program, giving what I would consider a finitary proof of the consistency of set theory. If you think this is impossible because of Godel's theorem, you haven't understood Godel's theorem fully. The problem is that ordinal naming schemes crap out much too early for this to work with an explicit construction with today's methods.

>Hermaneutics
I like translating the Hebrew of the Bible, and I think it can be done accurately and honestly, better than extant translations, so long as you ignore the theologically minded people completely. They generally are not honest enough, you can't trust anything they say.

>TCS
I like computer languages, and hope to one day make an engineering language of my own. I think the current languages are not very good, the last major positive development for me was Perl, but Perl 6 isn't around .

etc.

His recorded writings on the web are actually a kind of treasure

>>11493089
Congrats, you just fucked the page for mobile users

>>11497929
What country?

Give up physishits, your 'general' will never get close to /mg/ in terms of quality, intelligence and history.

>>11501548
>quality
Any evidence of quality there?
I mean don't get me wrong, I love hanging out there. It's a place to hang out when you're tired of reading.

>>11501537
[math]oh ~ no ~ no~ no ~ no ~ no ~ no ~ no ~ no ~ no ~ no ~ no ~ no ~ no ~ no ~ no ~ no ~ no ~ no ~ no ~ no ~ no ~ no ~ no ~ no ~ no ~ no ~ no ~ no ~ no ~ no ~ no ~ no ~ no ~ no ~ no ~ no ~ no ~ no ~ no ~ no ~ no ~ no ~ no noooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo[/math]

>>11498585
>bitter failed mathematicians
physicists have more prestige, are better compensated and are objectively more intelligent and creative than mathematicians

>>11501550
Aside from the high quality discussions that sometimes reaches research level? Aside from the fact that we literally solved a 20-year unsolved problem using anime? We also got the tohou poster, he's a mathematician not a physishit

>>11501562
>Aside from the high quality discussions that sometimes reaches research level
I call that into question

>Aside from the fact that we literally solved a 20-year unsolved problem using anime?
That's like saying we won the world cup if the team wins. It was one guy many years ago who happen to also be an anon.

>We also got the tohou poster
I'm not saying it's not the best thread on /sci/, but it's still just coarse grained chatting. And the tohou poster would be better if he was anonymous and not fishing for admirers like give it to him here

Bump.

Bump.

What is HAPPENING?

>>11503723
It's just the [math]G=SU(3)\times SU(2)\times U(1)[/math] Yang-Mills-Higgs functional. Given a [math]G[/math]-equivariant Hermitian vector bundle [math]E\rightarrow M[/math], the action
[math]S[D,\phi]= |D\phi|^2_{L^2(M,E)} + |F_D|_{L^2(M,E)}^2 + \frac{1}{4}|\phi^* \otimes \phi - 1|^2_{L^2(M,E)}[/math] is a functional on the moduli space of holomorphic connections [math]D \in \overline{\mathscr{A}}(M,E)[/math] and the Higgs field [math]\phi \in \Omega^0(M,E)[/math]. Given a choice [math]\rho[/math] of an irrep of [math]G[/math], after a move into the associated vector bundle [math]E\otimes_G V_\rho[/math] it's just a matter of trivial rearrangements and rewriting [math]S[D,\phi][/math].

In quantum mechanics. Angular momentum ladder operators. We have a minimum and maximum eigenvalue of [math]J_z[/math], j' and j. Since this commutes with [math]J^2[/math] we have [math]j'(j'-1) = j(j+1)[/math]. This has two solutions [math]j'=j+1[/math] and [math]j'=-j[/math].

We throw away the first solution [math]j'=j+1[/math] because j' is the minimum so it can't be greater than the maximum j. But this equation does make sense for modular arithmetic. Say for Z/3Z the minimum is 0 and the maximum is 2, then 2+1=0. Is this in any way physically meaningful?

>>11503780
How the fuck do you know this? How old are you?

>>11504009
he just copied a bunch of latex...

>>11504004
>Is this in any way physically meaningful?
I don't know physically but it's mathematically meaningless. Generally irreps of semisimple Lie algebras form Verlinde algebras over [math]\mathbb{Z}[/math]. Projection into [math]\mathbb{Z}_n[/math] makes you lose information about certain irreps so the entire Verlinde algebra structure breaks, which makes the whole representation theory of Lie algebras via Verma modules meaningless. In particular the non-zero character of [math]\mathbb{Z}_n[/math] leads to non-unique singular vectors in the Verma modules which makes your vacuum sector degenerate and zero-point energy blow up, even for finite-dimensional Lie algebras such as [math]\mathfrak{su}(2)[/math], which is absurd.

>>11504062
I've thought about it some more. I don't think it makes any sense. It would mean that applying the raising operator so many times would eventually loop back around, but to obtain j in the first place we assumed it stopped at some point.

My knowledge of Lie algebras is still very limited. I know some books, Cahn, Georgi, Hall, Fulton and Harris, and Bump. Do you have any recommendations?

>>11504172
Introduction to Lie Algebras and Representation Theory by Humphreys

I've read that according to the Higgs theory (is it a part of SM by the way?) mass is just basically potential energy of interaction with the Higgs field.

That seems like it gives physics more symmetry.

Because full energy is all of the potential energies of interaction with different fields and kinetic energy. But if you account for the fact that m is proportional to potential energy, then the full energy is JUST a sum of all of the potential energies, including that of the Higgs field.

Also, considering the energy-momentum vector, you see that it's really a vector, all components of which "come from" potential energies.

Am I being sound here? I don't know the details of the Higgs Mechanism.

>>11504222
If you read griffiths particles there is, in like the last chapter or so, a very concrete explanation of the higgs mechanism. Very approachable. I'd recommend reading it.

>>11504264
or maybe it was spontaneous symmetry breaking which he described. I forget. They're very closely related notions at any rate.

>>11504222
The secret symmetry chapter in Coleman's aspects of symmetry is a good explanation.

>>11504222
Masses ares dynamically generated by a [math]choice[/math] of the Higgs vacuum. This means that yes, with the Higgs potential your theory has an additional (typically [math]U(1)[/math]) symmetry, where other fields couple to the Higgs [math]\phi[/math] but are for the moment massless. Once the Higgs field settles to a specific vacuum configuration [math]\langle\phi\rangle \in\mathbb{C}^*[/math], the masses of the fields are dynamically generated and are proportional to [math]\lambda |\langle\phi\rangle|[/math]; however, this spontaneously breaks the [math]U(1)[/math] symmetry of the Higgs potential, hence we must return to the same symmetry as we had started with (without the [math]U(1)[/math] Higgs symmetry).
>>11504278
Yes, Coleman's text is great in general.

Bump

Hi, I have a question about special relativity velocity addition (and no this isn't homework rather a question I made up in my head).

Let's say I have a train with a reference frame [math]S'[/math] moving relative to an observer on the ground in reference frame [math]S[/math] at constant speed. I fire a bullet from the back of the train when the front passes the observer (in the train's frame, so then in the observer the firing happens a factor of [math]\frac{Lv}{c^2}[/math] seconds ago). I want to find how long the bullet takes to reach the front in the frame of the observer. Obviously I have to use a velocity addition formula to find the relative velocity of the bullet in [math]S[/math]. But then the train is still moving relative to the observer, the bullet would have to not only travel the length it was fired from before but also the length the front of the train made by continuously moving. Would I have to use another velocity-addition formula except with a negative speed of the train, or can I just subtract the train's speed from the relative velocity of the bullet, and say it has to cover the distance of the train [math]d[/math] (which will not be its proper length but Lorentz contracted)?

>>11505606
btw by 'subtract the train's speed' I mean using a standard algebraic subtraction rather than a relativistic one

basically how do I find when the event of the bullet hitting the front happens, do I have to use a composition of velocity addition formulae, or what, how do I do this

These two continue to blow my mind, moreso the first.

https://www.youtube.com/watch?v=fynuCLQp1TE
https://www.youtube.com/watch?v=EzZGPCyrpSU

I'm especially curious about the first guy. I watch his videos a lot. Is he right? He insists stars dont form from gravitational collapse, and he's pretty convincing.

>>11505889
>PICTURE THE MEME: Bill Nye huddled in a corner, trembling and sucking his thumb, repetitively muttering, "Make him go away!"
Based YouBoobers dabbing on Bill Gay.

Bump.

>>11505889
>Is he right?
Yes.
>>11506612
Thanks anon

>>11505610
>>11505606
A simple way of thinking about problems in SR is that when you fix a particular frame and you know your values, you can do physics as you knew already. The observer in the ground sees a train moving and someone firing on the train and he measures a speed U of the bullet. He doesn't really see any weird relativistic effects untiñ the guy on the train shows his measurement and see that it wasn't a simple gallilean adition. That means that if you know the velocity measured by tye rest frame, you can calculate their paths as seen by this observers in the usual way. He sees the bullet and the train as different objects and so you only need to know if there is a time when the front of the train and the bullet have the same x value. My point is that these exercises are to get tou acustomed to the fact that mamy things we thought were universal from classical mecanics are frame dependent in relativity, but that doesn't mean tye concepts can't be applied in a per frame basis. Just like with ficticious forces, there are non trivial transformation rules, but you still can use it if you specify the frame. Basically all you are doing is assuming that the rest observer somehow only knows the velocity measured by the guy in the train. This is odd, but I think its sometimes not emphasized enough that in SR of you are not accelerating things or whatever, observers still see classical stuff, but there is going to be a disagreement with the measurements if you try to apply usual Galilean transformations.

How do I derive the Standard Model Lagrangian?

what made you guys choose physics over mathematics? assuming you can only pick one.

>>11507213
Unironically, my undergrad professors, and their research.

>>11495330
So did Julian Schwinger

>>11495338
Thank fuck someone actually understands physical principles ITT

>>11501516
He's clearly a genius but I don't see why consistency proofs are useful at all. If a set theory is inconsistent then it could plausibly prove itself consistent anyway.

>>11492814
Im an EE with some training into real analysis, what do I need to learn in order to start properly leearning quantum mechanics

>>11508169
Properly? [math]C^*[/math]-algberas.

>>11507198
I'm not sure it's derived per se

>>11508169
IIRC the situation with QM is that, technically, it has a bunch of requirements (specifically, at least some functional analysis on Hilbert spaces, Lie algebras, Lie groups and knowledge of electrodynamics and hamiltonian dynamics), but you *can* go into it with multivariable calculus, linear algebra and some Fourier.

>>11508169
If you know abstract linear algebra it and some pde theory that would be great. But most important is to have a good backround in different classical subjects of physiscs.

>>11508189
>>11509076
>>11509086
Soo.. basically math until functional analysis? This info is a bit conflicting.
Right now I know calculus from one variable to multivariable and complex variable.
Linear algebra ofc.
All the math involved in signal processing, both discrete time and continuous time.
First 5 chapters of baby rudin.
Physics wise I know from newtonian dynamics and engineering thermo to electromagnetism, obviously I know the most about electromagnetism as im a EE

>>11509109
You might want to brush up on hamiltonian dynamics, but otherwise you're good.

>>11509109
Not even graduate texts on QM will use functional analysis. If you want to know QM in mathematical rigorous setting then yes, otherwise its linear algebra, some pde theory and some fourier analysis. Note that is best to understand linear algebra in an abstract setting though, but its not that hard.

>>11509172
Never seen anything about hamiltonian dynamics, if you mind me asking, where is a good place to start?

>>11509192
The lin alg I know I learnt on an abstract setting, when I had to take it in university I did a real oopsie and erroniously selected the lin alg course math majors take in my uni instead of the engineering course.
I spent the first few weeks wondering what the fuck was going on. After realizing my up I just talked to my department head and they validated the class.
I would need to learn about pde theory tho, where can I get started on this.

Sorry about the annoying questions lads, I just really wanna have everything clear before starting

>>11509231
The pde theory is just thd typical techniques such as separation of variables, eigenvalue methods and integral transforms, greens functions. Its ok to just be familiar with this methods as in QM you kinda generalize this methods. So any mathematical methods for physics/engineering text should be fine if it covers methods for pdes. For hamiltonian dynamics try Goldberg.

>>11509231
>>11509531
>>11508169
They literally teach you these things in intro textbooks. What, do you think physicists go through a rigorous math degree before they get to learn their first physics subject? Just pick up a fucking book and learn.

>>11509531
Ok bro thanks

>>11509622
Obviously not, but I dont know when in undegrad physicists start learning qm so knowing what you should grasp beforehand imo is important

>>11508169
Don't worry about it. Start reading Sakurai, Shankar, Susskind, and Weinberg's books on QM. You'll pick up the math you need as necessary. You will probably never bother with functional analysis.

Bumperooni.
https://eudml.org/doc/164885

>>11510438
I literally never seen any of those recommended. Mostly it's Griffith, Landafshitz and Feynmann.

Our professor, head of QFT department, recommended Messiah, Dirac and Fermi actually. Plus we have pdf of lecture notes (incomplete unfortunately).

>>11513137
>I literally never seen any of those recommended.
That's because you're an undergrad. Sakurai/Ballentine are grad-level QM books and Weinberg/Bertlmann are grad-level QFT books

>>11513137
>Dirac
*opens Monster energy drink*
*loud pshhhh*
Now THAT's a good QM text.

>>11492874
In contrast to the other post, my courseload was intensive and extremely difficult.

Students in the honors course rarely had a gpa of higher than 3.5, especially if they double majored. Problems were maxed out and highly mathematical, and questions were intentionally vague and lacked exposition in order to both weed people out and "cultivate independent thinking".

Freshman year 500 ish people started the major, but my graduating class was like 40ish people.

>>11513145
Sakurai is upper level undergrad at top schools

>>11513145
But he clearly needs an undergrad QM.

BTW anybody studied that String book by Michio Kaku? Some grad student made a guide for textbooks where he says it's total shit,

>>11513317
>strings
Try Polchinski

>>11513159
Fuck those drinks. They taste kinda cool, but I drink 2 cans and go to sleep anyway.

>>11513229
What country and did you have any courses extra to what people normally take?

>>11513690
US university

>>11514076
> intensive and extremely difficult.
What uni?

>>11514088
Phoenix

>>11514088
Dont want to dox myself but it was top 5 in physics worldwide

>>11504282
I know that U(1) is a unitary group of order one, but what are it's elements in this case?

>>11514099
[math]U(1) = \{ u \in \mathbb{C} ~ : ~ |u| =1 \}[/math]
The group is multiplicative btw.

>>11514117
Ok I should've asked: what do it's elements mean physically?

>>11514131
Rotations of [math]\mathbb{R}^2[/math].

>>11514131
It's the symmetry group of the Higgs Mexican hat potential [math]V(\phi)[/math]. What this means is that, if the Higgs potential [math]V[/math] achieves a minimum [math]V(\phi^*) =V^*[/math] somewhere at [math]\phi^*\in \mathbb{C}[/math], it must achieve [math]V^*[/math] at every point in the orbit [math]\operatorname{Orb}_{U(1)}(\phi^*)\cong S^1 \subset\mathbb{C}[/math] of [math]\phi^*[/math] under [math]U(1)[/math]. A specific choice of [math]\phi^*[/math] in this orbit you take as the vev [math]\langle \phi\rangle = \phi^*[/math] in the quantum theory spontaneously breaks this [math]U(1)[/math] symmetry.

What do physicist mea when they write [math]|\phi \rangle[/math] or something like that? Most similar thing ive seen is writing vectors like that (e .g [math]\vec{x} = \langle x,y,z \rangle[/math]) or to denote an inner product

>>11515249
It's literally just a column vector.

>>11515249
https://en.wikipedia.org/wiki/Bra%E2%80%93ket_notation

>>11515249
The other answers seem to be missing the physical ingredients.
In general we start with the (generally field-theoretic) Hamilton-Jacobi equation [math]\delta_\Phi S_E(\delta \Psi,\Psi) = 0[/math] on [math]L^2(\mathcal{A})[/math] with [math]S_E[/math] the Euclidean action, where [math]\mathcal{A}[/math] is the space of "boundary conditions" (i.e. field-theoretic data on codim-1 submanifolds [math]\Sigma[/math]). Completing [math]\mathcal{A}[/math] it in the convolution product, we invoke GNS to obtain a *-representation [math]\mathcal{A}\rightarrow \mathcal{B}(\mathcal{H})[/math] on some Hilbert space [math]\mathcal{H}[/math] with a distinguished cyclic vacuum vector [math]|\Omega\rangle\in \mathcal{H}[/math] (in fact, GNS says that there is an equivalence between states [math]\Omega: A\mapsto \langle\Omega|A|\Omega\rangle \in \mathcal{B}(\mathcal{H})^*[/math] and *-representations into [math]\mathcal{B}(\mathcal{H})[/math]). For each "boundary wavefunction" [math]\Phi \in \mathcal{A}[/math], we wish to associate a state vector [math]|\Phi\rangle\in\mathcal{H}[/math] to the Schwinger functional [math]W[\Phi] = \int_{\Psi|_{\Sigma} = \Phi} D\Psi e^{-S_E[\Psi]} {\equiv}^{\star} \langle \Phi|\Omega\rangle[/math]. If this is doable, we can invoke the cyclicity of [math]|\Omega\rangle[/math] to write this as [math]\langle \Omega|\hat{\Phi}|\Omega\rangle[/math], where [math]\hat{\Phi}\in\mathcal{B}(\mathcal{H})[/math] is the second-quantized quantum field operator of [math]\Phi\in\mathcal{A}[/math] under the GNS *-representation. These state vectors [math]|\Phi\rangle\in\mathcal{H}[/math] are what we mean by the kets.
There are many [math]many[/math] mathematical subtleties to this construction of Schwinger correlations in QFT, however, but it is the foundation of non-perturbative methods in QFT.

>>11515259
>>11515260
Thanks bros

>>11515917
Pls kys jesus christ

>>11494140
>>11501516
https://vocaroo.com/23WUZ934W2r

>>11515917
Fuck this is terrible lmao

>>11514131
It's a circle.

>So far, for various reasons, these models are not realistic.
https://arxiv.org/abs/2001.06582

When solving brachistochrone problem (x, y - coordinates of the thing sliding down a rope without friction) this is what they propose. However, how do we know that c*y's absolute value is no larger than 1? c is an arbitrary constant from previous integration.

>>11518359
c is an arbitrary scalar. You can have it equal whatever you like.

>>11517521
>masses for the second and first generations are produced respectively by one-loop and two-loop radiative corrections
Wtf why?

Think about this. We have no idea why the physical constants have the values they do. We dont really know if they are static or not over the history of the universe, we dont know if they might change again.

>Whats the most apocalyptic thing that can happen by suddenly changing a physical constant?

>Suddenly G is a billion times stronger and humanity instantly tuns into a paste of hydrocarbons on the flattened earths surface.

suddenly hbar = 1 and everything becomes incredibly uncertian

alpha turns up and the universe turns into empty space

Bump.

>>11497929
Why do you assume professors need to give a fuck about poincare or lorentz groups? Get the fuck out of the hep bubble dude

>>11519621
How do physicists outside the "hep bubble" think of spin, if not through representations? I don't know any condensed matter theorists. Not the same guy.

>>11503780
>>11504009
gay samefag

>>11519871
Anyone worth their shit knows spins are irrep labels of the Spin group, which fits into the central exact sequence [math]1\rightarrow U(1)\rightarrow\operatorname{Spin}_{1,n}\rightarrow SO(1,n)\rightarrow 1[/math], or at least know that spins are reps of the universal cover of the homogeneous Lorentz group. HEP theorists know, cond mat theorists know, QC theorists know, and even some soft matter people know. It's an integral part of understanding what spins are.

>>11519971
Yeah I know this. I was asking >>11519621 why it was only a HEP thing.

>>11520023
Probably because he's just an undergrad, or an experimentalist.

>>11519871
I doubt anyone in biophysics, atmospheric physics, geophysics or nonlinear physics thinks of spin at all. Classical optics and some astronomy people probably don't deal with it on a highly technical level either.

>>11520186
Good job sidetracking and shifting the goalpost. The question was obviously referring to people that study quantum systems with spin, and if you think non-linear physics/NLSE people don't look at spin I think it's clear that you're too inexperienced to comment on this.

>>11520442
You realize non linear physics is a bigger field than just non linear optics and QM right? The post was clearly asking about people outside the hep bubble.

>>11520442
For a source you don't even have to look further than the first hit on google for non linear physics:
https://www.nature.com/subjects/nonlinear-dynamics

Bump.

>>11492814
Nash's final lecture. What was he working on?

My neighbor is on his last year of MSc, he hasn't been studying shit for like 3 years at this point, but he got himself hired in a small science company doing all sorts of cool stuff getting decent money. He's specialty is nuclear physics on the experimental side. He says he doesn't know shit about electrodynamics and he doesn't need it.

Is this normal? To me it's crazy to do one field of physics and be so ambivalent towards another field - that is so fundamental. Like I get how you could see metal physics as boring, but electrodynamics!

>>11522609
It's not that weird. What matters the most when you are a researcher is the subfield of physics that you actually work in, you'll probably have lots of gaps in lots of fields and it's unproductive to try to cover them all.

>>11522482
Looks like second-order GR. In particular if you treat [math]F = [D,D][/math] as the curvature of a principal [math]SO(1,n)[/math]-bundle on a 4-fold [math]M[/math] with spin connection [math]D = d + [\omega,\cdot][/math] acting on the vierbeins [math]e\in T^*M[/math], first order GR is [math]\int_M \operatorname{tr}(F\wedge\ast F) = \int_M R[/math] while second order GR is [math]\int_M \Lambda\left[\operatorname{tr}(F\wedge \ast F)^2 - (\operatorname{tr}F\wedge\ast F)^2\right] = \int_M \Lambda[R\wedge \ast R - R^2][/math], with [math]\Lambda[/math] the map dual to multiplication by the Kahler/metric 2-form [math]\lambda[/math]. These are Kahler [math]SO(1,n)[/math]-Yang-Mills theories with topological vacuua [math]c_1(TM) = \int_M \operatorname{tr}R[/math] or [math]c_2(TM) = \int_M \left[\operatorname{tr}(R^2)-(\operatorname{tr}R)^2\right][/math] bounding them from below, respectively, so Nash was probably looking at the compatibility of the Riemannian structure on [math]TM[/math] with the spin structure on a principal [math]SO(1,n)[/math]-bundles on homologica 4-spheres [math]M[/math].
In particular you can see in the slides the requirements [math]c_1(TM) = 0[/math] in dim-4 and [math]c_2(TM) = 0[/math] in dim-2 from the field equations, which are obvious from a first course in GR.

>>11522609
This is already pretty well ingrained, most people fall into that category. Not just physics, math too. The fields are so large and advanced now that average students just can't learn it all. The average undergrad in math or physics knows almost no math or physics, by modern standards at least.

One of my older professors was teaching a course on quantum computing a couple years back. Of course most of the people taking it were computer engineers and computer science grad students. The only real prerequisite he listed was linear algebra, everything else he would teach. But problem was, it was clear from the first day that most of the students didn't know enough linear algebra. Specifically some knowledge of dual spaces was necessary. I talked to him after class about it. It turns out that he knew that linear algebra was a course everyone took now, but he assumed that it was the same linear algebra course he took when he was young, a course taken after a basic algebra course on number theory and rings/fields. He thought that standards had gone up, so many young students taking more math than they used to. But sadly that's not the case.

I doubt things will change when it comes to a proper broad study of fields like math or physics. Either we would have to make courses harder, so more people fail, or take many years longer. The second one might actually be possible, I know the engineering college at my school required 3 semesters of coop so the standard was 5 years to graduate, so it could definitely be possible to expand math and physics degrees as well.

>>11523132
Who the fuck are you?

ill resurrect this just to say that i find it interesting that math general goes quite well while physics general either dies or has a bunch of disconnect posts.

>>11493260
Tight binding is not what it seems. All of its results are a simple consequence of the linear algebra eigenequation that is constructed.

>>11524823
There aren't any relevant physics questions I could ask here. They're too context dependent and not typically things that can be solved online.

>>11524833
yeah, the same kinda of happens in reddit too. /r/math is a lot more informative and interesting than /r/physics, which is mostly a news feed.

>>11524823
Physicists are less autistic than mathematicians on average, thus less likely to be here.

>>11524842
There's /r/physicsstudents which is more people asking stuff. Another aspect is that there are a lot of purely pop sci people on physics, while math enthusiasts are a bit more serious.

>>11523132
based smart retard

>>11525195
>There are a lot of purely pop sci people on physics, while math enthusiasts are a bit more serious.
This is sadly true. normies think they can understand physics just by having it explained to them by known sconners such as Brian Cox. the boundary to entry of pure math keeps the riff raff off the lawn.

>>11524823
we need a joint project to work on. that will get this board moving.

>trips makes our research proposal

>>11525751
Collectively make an actually good chart telling the lads how and what books to study.
>isn't that a pretty low bar you're setting
No.
I'm willing to edit it if needs be.

>>11525777
Feel free to use this as a model or inspiration.

>>11525777
I'll start. Maybe we could get a spreadsheet going. Here's some I like

Schutz's GR book
Sakurai's QM
Weinberg's QM
Lahiri and Pal QFT
https://www.damtp.cam.ac.uk/user/tong/qft.html
Peskin and Schroeder QFT
Weinbergs 3 QFT volumes
Bertlmann. Anomalies in QFT
Zinn-Justin. QFT and critical phenomena
https://arxiv.org/abs/math-ph/0204014
Coleman. Aspects of symmetry
Hori et al. Mirror symmetry
Georgi. lie algebras in particle physics
Cahn. semisimple lie algebras

>>11525783
this seems like a good list, but most in most grad schools you skip the "advanced" entirely

btw, never used schwabl, how does it compare to sakurai?

>>11527771
Sorry I think you got the wrong thread, /mg/ is that way

>>11527785
i thought this might be it, but i should know that /pg/ aint gonna work.

What are the physics' memebooks, like Spivak's Calculus?

>>11503723
>show that the Lagrangian describing all observed physical processes (sans gravity) can be written:

Yet it does not describe neutrino masses, dark matter (it if interacted with SM particles) or the cosmological constant.

>>11527852
Any book by Weinberg

>>11527852
Landau

>>11527867
Do you have something better for the material in Weinberg volume 3?

>>11527879
I don't know too much about SUSY, I only did some work with it in my undergrad. I used Fernando Quevedo's lecture notes to learn the basics of using superfields to derive supersymmetric Lagrangian and their transformations:
https://arxiv.org/pdf/1011.1491.pdf

They're pretty introductory in my opinion. A nice book that I really only used as a reference is 'Theory and phenomenology of Sparticles' by Drees, Godbole and Roy.

You can also check this one, but it doesn't deal that much with SUSY and it delves more on other things like extra dimensions:
https://arxiv.org/pdf/1602.04228.pdf

>>11527852
>memebooks, like Spivak's Calculus?
>>11527867
>Weinberg
yes
>>11527879
>Landau
fuck off. unlike weinberg, it is not a waste of time to decipher landau's books, you get a lot back.

>>11528272
Which of Landau's books are worth going through in your opinion?

>>11528285
Not him, but I liked Volume 1 and Volume 2. Volume 1 usually covers things in Mechanics that you can't find in usual Mechanics books, like Goldstein. Volume 2 is a nice introduction to GR, imo.

bump

>>11518359
if you notice the the numerator cannot go negative (or else you would be in imaginary territory), and the denominator can't either. This effectively sets our limits on what cy can be. Remember that c is an arbitrary constant, so y can still be much greater if c is small.

If you want to convince yourself further, solve that first equation for y: cy = x'^2/(x'^2+1) and think about what happens as x gets very small (goes to zero) or infinity (goes to 1), since the denominator is bigger it will never go above 1

>>11528285
1,2,5 and 6 are great.
never touched 7 and 8.
i used 3,4,9and 10 as complements, also worth it.

>>11527907
>Quevedo
https://arxiv.org/abs/0712.0868
Good stuff.

creating another topic here...

how do you self study a book? be explicit (nothing else going on anyway): do you read the whole chapter then problems? or bit by bit? many hours a couple of days of the week or a little every day? do you take notes similar to the book or try to write your own? pen&paper or laptop? many book at once or just that one? do you throw those notes away later or? ...

>>11497929
slav?

>>11530682
I usually search for a syllabus from a good university and touch on the topics that it says in the syllabus with the books that they list.

Usually, just one book, read the chapter if there is a derivation I try to do it myself while looking at the book (making sure everything is right) and do some of the excercises that I find interesting.

https://arxiv.org/abs/1607.08422
>It is natural to ask how to obtain global observables on a closed surface. The answer is provided by the theory of factorization homology. We compute the factorization homology of a closed surface [math]Σ[/math] with the coefficient given by a unitary modular tensor category, and show that the result is given by a pair [math](H,u_Σ)[/math], where [math]H[/math] is the category of finite-dimensional Hilbert spaces and [math]u_Σ∈H[/math] is a distinguished object that coincides precisely with the Hilbert space assigned to the surface [math]Σ[/math] in Reshetikhin-Turaev TQFT.

I had to deliver this on Thursday but I couldn't do it. Am I really that stupid?

Also, I want to do phenomenological particle physics. Should I worry about differential forms and what not?

>>11530754
Use graded commutativity and cyclicity of trace. You'll get something like [math]\sum_{i=1}^{2q} (-1)^i \operatorname{tr}(dF \wedge F^{2q-1}) = 0[/math].
>I want to do phenomenological particle physics
Theoretical HEP is much simplified by differential forms and you probably can't catch up to your peers if you don't know how they work.

>>11530779
Why is that trace zero?

>>11530798
>why is [math]\sum _{i=1}^{2q} (-1)^i A = 0[/math]
Because shit cancels out.

>>11530817
Shit, I think I am really that stupid. Thank you

>>11530798
Lmao anon it's not the trace that's zero.
Also the "square-root" of that quantitiy computes the q-th Chern number [math]c_q(E) = \int_M \operatorname{tr}F^q [/math] of the principal [math]G[/math]-bundle [math]E\rightarrow M[/math] on even dimensional [math]n=2q[/math] manifold [math]M[/math] and these label the topological vacuua in the Yang-Mills theory so you have to know these things.

>>11530828
Yeah, it kinda talks about it in the next exercise. Two of my classmates said they didn't have to go through the solution because they said it was 'straightforward'. I thought that they said that because they want to be string theorists, so the dig this shit.

I'm gonna try and do the rest myself.

>>11530841
It's a very elegant result of Chern-Weil theory that allows you to write the Chern characteristic class [math]c_q: K^\ast(M) \rightarrow H^\ast(M,\mathbb{Q})[/math] (paired with the fundamental class [math][M]\in H_n(M,\mathbb{Q})[/math]) as a local integral.
Good luck anon.

>>11495470

Fucking lol. As a physicist myself, I agree. I didn't bother reading shit after the first line. Not that it doesn't make sense though. I spent a good amount of time in string theory. lmao.

>page 9
you guys are so useless

Is Helsinki University a good place to get my PhD from?

>>11532535
probably. at least for particle physics they have good connections and good metrics/citations.

>>11524823
Dude look at the catalog. There are like 15 threads on physics at any point. But people don't know /pg/ exists now, so they just keep creating new threads for every question.

Literally all we need to do is instead of answering in those threads just give them the link to this thread, it's gonna be on the first page more often and people will catch on soon.

Stickying it for a couple of days at least will help as well.

>>11529977
I see. Thanks.

>>11531341
Why did you leave string theory?

>>11532812
String theory is useless. Not him btw

>>11532754
>Literally all we need to do is instead of answering in those threads just give them the link to this thread
Any particular reason why you want to concentrate all physics discussion in the board into these threads?

>>11532875
I'd say it's a good idea. You know where to come back to, where to hang out with your favorite weebs and the /mg/ is also good.

How does a spectrum of molecular hydrogen look like? I know how does atomic spectrum look like (Lyman, Balmer, Paschen series etc.) but I newer saw a spectrum of [math]H_2[/math]

>>11533293
im sure you can find it in some chemistry book.

Bump.

>>11492874