In the case of condensed matter, the sea of electrons is actually there, and holes is just a convenient mathematical trick that obviously works. You do not have a degenerate amount of matter for this trick to work in the universe.
In the case of Dirac equation's trickery, that is even worse. There is no way to make that trick work.
I think, particles with negative mass cannot have charge, color charge, nor parity. Perhaps that's why we have never detected them.
By lacking charge, they don't interact with light, and by lacking color charge, they don't interact with gluon, and by lacking parity, they don't interact with W/Z... right?
I mean... Consider the "paradox" about a positive mass and a negative mass being tied to a wheel. The paradox claims that the wheel will angular-accelerate forever. But if the negative mass consists of chargeless particles, it cannot be tied to the wheel from the first place, because normal force is an artifact of EM.
@ACuriousMind I don't know why you said that. The 21cm line is pretty important to astronomy. Even without astronomy, precision measurements of the H atom is so important to so many parts of physics that I'm sure we have covered all kinds of, say, finite nuclear size and mass, high order QED corrections, proton spin, etc.
@imbAF You keep asserting that $\left|j,m\right>$ is an eigenstate. It is not even a possible state. The only possible state that you are referring to is $\left|j_1,j_2,j,m\right>$, and you should stop asserting wrong things.
@SillyGoose you too
@SirCumference That is partly because there is no possible way to make a tolerable presentation of the same thing in SR and/or QM. In SR, you would need to already know the full energy expression in order to show that the theorem works, in which case it is absolutely useless. In QM, you cannot define forces. There is simply no place for that in modern physics.
@SirCumference First year, first sem, end of first module of classical mechanics, in UK. And never returned to. It is not actually useful; except that once a person sees how ugly it takes to derive both Coriolis and centrifugal effects, one finally understands why pre-university physics ought to never invoke that concept.
@AdityaKrishnaPanickar if you only care about physics,then one strategy would be just study physics books and pick the required tools simultaneously from books like Byron fuller/hassani etc..when it comes to linear algebra for eg r Shankar's first chapter does the job pretty well
@naturallyInconsistent im not sure what you mean. the vector $[1, 0, 0, 0]$ is an eigenvector of $S^2$ and $S_z$. what is the need to additionally label with $S_z^{(1)}$ and $S_z^{(2)}$?
the simultaneous eigenstates of $\{S^2, S_z\}$ are organized in spin sectors, though. so it automatically computes the "addition of angular momentum" business
Do the math for studying physics..have you done it the mathematician way studying all the stuff rigorously or you took some other approach like taking the less rigorous math methods kind of courses
@SillyGoose again, I think you haven't really given enough context on what you're doing; I, for one, don't understand what the issue is or what the (1) and (2) labels here mean
I was just trying to reorganize a hilbert space of $N$ spin-$1/2$s $\mathcal{H} \cong \mathbb{C}^{2^{\otimes N}}$ into the irreducible representation space decomposition
@SillyGoose Again, you should be careful. The first is the $\left|\frac12,\frac12,0,0\right>$ and the remaining are the $\left|\frac12,\frac12,1,m\right>$ states for $m=-1,0,+1$
@naturallyInconsistent well, as long as we fix the two leading 1/2 (the goose is not changing them anytime soon afaics) we can omit them, I'm not sure why you insist on that part so much
@SillyGoose Okay, so what is the discrepancy now that you wanted to initially ask about?
@ACuriousMind because they keep writing $\left|j,m\right>$ as if they are actually realisable states. This is definitely not the same thing when adding angular momenta of different types, e.g. when one of them is the orbital angular momentum.
@naturallyInconsistent they're just writing $\lvert j,m\rangle$ as a shorthand for $\lvert 1/2, 1/2, j, m\rangle$ because in their context there are only spin-1/2s, I don't understand the problem
@ACuriousMind no... It's just that these things being wrong can cause problems. E.g. if someone tells u that oils cure cancer and they pull up a paper, and all u can do is pull up another paper urself. How do u settle this argument
The first question is always whether the debate is actually of a scientific nature - is it really the case that we just read different research, and if one person convinced their other that their research has more merit, the other will change their mind?
Because very often people who believe in pseudoscience will cite (bad, faked, misinterpreted, whatever) studies as if they were the support for their beliefs
but debunking the study will not actually lead to anyone abandoning their belief - they had the belief first and just produced the study to act as if they were arguing scientifically
Even a paper that is perfectly fine from a methodological standpoint can just be...wrong. Many fields have a p-value threshold of 0.05, so even for a correctly calculated, non-hacked p-value, it is to be expected that the findings of 1 study in 20 are just random noise and not actually a pattern
@RyderRude I mean, the paper should contain some discussion of the reliability of its results. In many fields, one standard for this is the p-value, and in a field where this is the standard, a paper making no mention of it is a red flag.
I mean, in specific cases you can see problems without understanding the topic, like ridiculously small sample sizes - but if this was easy, don't you think we wouldn't have such a big problem with misinformation? :P
@naturallyInconsistent People not trained in research are generally extremely bad at questioning information they read "somewhere" as long as that "somewhere" has the outer formal appearance of a trustworthy authority, this isn't unique to ChatGPT
And they can put as many figleafs on it as they want ("Double check information", "ChatGPT can make errors", whatever), the fact remains that the answers from LLMs usually sound as if they know what they're talking about and are written in a tone people associate with news articles and scientific reporting, i.e. trustworthiness
@ACuriousMind I dont think it has anything to do with "trained in research". It would be better for a society if it is not always verging off cliffs at the slightest suggestion of every charlatan there is. And people who have been trained in research are not faring particularly well either, just much less worse than the layfolk
I stumbled upon a lecture note on MIT OpenCourseWare, as I was trying to read up on antisymmetric and symmetric wavefunctions of two particle Fermions and Bosons, respectively.
Interestingly, I came across a sentence that said the following:
... fermions can be described by both symmetric wave f...
@ACuriousMind extremely bizarre. which is why I was particularly interested in whether he had a version of the 2nd quantised fermion system using symmetry rather than skew-symmetry, yet he had omitted just that alone. like, WTF
It's interesting in that the A-B dialogue in that section shows he had a valid complaint about the standard presentation - the significance of "the phase" is unclear in the standard treatment. Now, I would remedy that by pointing out how this is related to representations of the symmetric/braid groups as the groups of exchange operators, but he instead went and invented a strange symmetric representation for 2d fermions and apparently is convinced this works in general?
@ACuriousMind exactly; I had trouble seeing how that would have worked in general, which is why the 2nd quantised version would have been really interesting if he had managed to produce it
was not expecting Wen Xiao-Gang, of all ppl, to be making an argument this bad
I'm kinda confused as to the current state of QED. Prof Wen Xiao-Gang is one of the few people who is actually worried about how we could even make sense of QFT in general. However, it seems like he does not know that QED can have both its UV and IR divergences go away at every term, and thus only the summation of the perturbation series may give rise to a problem.
In view of this, I am not sure what would be the central challenge to the interpretation of QED as currently understood.
@naturallyInconsistent Central challenge of QED as a standalone theory is probably the Landau pole/UV triviality, see also physics.stackexchange.com/a/359627/50583
that thing goes into the definition of configuration space. e.g. if i have two particles and i define configuration space to be (x1,y1,z1,x2,y2,z2), then i am identifying the first three numbers wirh the first particle, and the last three with the second particle
@123 The Hamiltonian formulation of GR in the form of the ADM formalism is widely used in numerical GR and frequently the starting point for quantum approaches. You can't just in general say that any field uses Lagrangians or Hamiltonians more, it always depends on the concrete use case
I'm sorry, but given for how long (five years) you've been asking questions about elementary classical mechanics in here, I don't think there's a realistic timeline for you to learn GR in this way
@ACuriousMind :D you are right. Because i didn't understand the basic ideas of newtonian mechanics previuosly. And i found that all these ideas energy etc.. used in QM , QFT etc..
@RyderRude Yes i know the experiments and ideas, i am postgraduate in chemistry , we had applied chemistry peter atkins. which is not the foundation of QM. I learned on my own, but not mathematics.
@RyderRude May be in your country government support all the fields and give money to that students. In my country we have to do some industrial work to earn money (no government support)
I think only those peoples take QFT and GR who are enthusiast. First it required a lot of learning and consume a lot of time of your life to understand the subject in better way other than memorizing thing only or accept things as definition.
HELLO. for stat mech, im seeing that there is a concept of state space, similar to classical and quantum mech. however, i am confused how we determine the dimension of state spaces in stat mech. for instance, wiki says the dimension of the state space for a monatomic gas with fixed particle number is 2. how would i know this a priori ?
@ACuriousMind the answer you linked to, is not using Causal Perturbation; under CP the usually renormalised quantities are simply fixed by us inputting the experimentally obtained values, and so there is no freedom, say, for $e$ to go to zero. Not to mention that it also says that the argument likely doesn't happen. I suppose at some point in myow learning miao miao will get there myowself
@naturallyInconsistent There has to be some confusion here: Causal perturbation theory merely sidesteps the usual presentation of renormalization in terms of infinities, it does not remove renormalization altogether (hence why it's also called Epstein-Glaser renormalization). The Landau pole (or whatever happens in the non-perturbative UV) of QED is a feature in the RG flow that doesn't vanish just because you do causal perturbation theory
@Relativisticcucumber not necessarily, you can also see it in chat accounts (and before I wrote the 5 years above I actually also briefly searched the transcript for @123 to confirm they did indeed start posting back then)
@ACuriousMind yes, I know it still does renormalisation. But miao miao have no understanding of RG, so that must be why miao miao is mistaken. Will learn it some day far in the future
@Relativisticcucumber errr... that is standard checking...
@naturallyInconsistent In causal perturbation theory, the necessary ingredient is called the "main theorem of perturbative renormalization theory", showing that any two renormalization schemes (i.e. ways to specify the experimental values one needs to fix the renormalization) are related by a transformation (the RG transformation).
This one needs to discuss in some form even if you are not particularly interested in RG flows because one needs to know how to translate the values obtained from different choices for the renormalization parameters into each other
@naturallyInconsistent because if you fix a choice at low energy your perturbation theory is useless at high energies - remember that the perturbative corrections essentially scale with "how far" the diagrams you want to evaluate are from the ones you used to fix the parameters (this is known under various names, in many schemes in manifests as the "problem of large logs" since certain logarithms become big)
ok technically it can work; just because work is a path function does not mean that changes in energy, which is what WET is talking about, cannot be a state function
@Relativisticcucumber careful: In the thermodynamic context where we talk about state and path functions, you usually have that energy is the sum of work and heat.
instead, the issue is that work and heat are incredibly bad conceptions in thermodynamics. There exist quarrels about what is work and what is heat in thermodynamics especially in the magnetic case
You would be far better served completely ignoring what is work and what is heat, and instead discuss only well-defined quantities
the problem is simply that the word "work" does not mean exactly the same thing in these cases: If you consider accelerating something with friction from rest to a certain velocity $v$, then the "work" in the sense of the "work-energy theorem" is $\frac{1}{2}mv^2$. But the "real work" you did working against friction is larger - and depends on how long you accelerated the object and not only the final state, i.e. is a path function!
i find thermodynamics lacks structure. its very confusing. been doing some ising/heisenberg model stuff with master equations, and im quite interested in quantum stat mech/these topics. problem is i cant understand basic thermodynamics in a sensible way
even getting to the ensembles and making sense of their results has been a struggle for me. i only have some notions of partition functions as moment generating functions and free energy as cumulants SORT OF blebs
but bc of this i always struggle to understand simple things like derivation of BE and FD stats. trying to once and for all get it but alas no luck so far
even more problematic is the connection btwn thermo and stat mech is just not even clear to me
Well, if you really wanted to understand classical to statistical thermodynamics, there is an axiomatisation if you like to do it that way. It is just very challenging to learn it that way. And you need to know the basic physics prior to learning the axiomatised version.
@Relativisticcucumber why is this a problem? Like, by the time one gets to the partition function, it is mostly an exercise in mathematics: differentiate, and get the correct answer.
i am a big fan of master equations thus far, i also am very interested in these models that condensed matter teaches. but yes i am not excited by thermo indeed XD
For example, anybody who thinks that they understand quantum theory, but does not understand what stat therm is saying, is lying to themselves. The best evidence and understanding of what quantum theory is saying, is via stat therm
Well, it is easy to motivate partition functions: work without it for a few times, and then you will fully appreciate how magically effortless it is compared to the direct integration otherwise.
that is, I understand QFT well enough in general to be able to make sense of a lot of basic condensed matter, but I've never learned it as a topic on its own
and my approach to statistical mechanics is similarly rather "I understand what a probability distribution on phase space is, ignore all the weird "microstate", "macrostate" etc. stuff and just stick to doing classical mechanics on phase space" :P
Well, you know miao miao lived in a place that is extremely hot. And then studied in a place that is known for cold winters. The god-emperor of miao miao land once asserted that the most important invention in the history of humanity is the air-conditioner, and this is quite correct. Keeping food fresh with refridgeration, enabling hot places and cold places to still keep people in employment, are incredibly important to history. Even the mRNA vaccines needed great cooling to deploy.
Why is there no factor of $e^{ \pm i p_i \cdot x}$ in the above? This is a proper Feynman amplitude, right? So it should contain all the external line factors (won't there be polarizations if we were doing spin-1 theory instead of spin-0?)
$x_i$ is a free variable if you just add $\mathrm{e}^{\mathrm{i}p_ix_i}$ terms. Free variables have to occur on both sides of an equation. Where is there an $x_i$ in $\mathrm{i}M(p_1p_2\to p_3 p_4)$?
@SirCumference Yeah or being able to extract paper elements from the pdf file or whatever it's stored in, so you can edit it yourself
i.e., u can unpack & put it in some local software vs. having it in some better format which you can access instead of the pdf, one with all the options you specified.
idk who would fund the tech upgrades i guess the journal ppl
