@Obliv Short-wave can bounce off the ionosphere. So you can listen to short-wave broadcasts from the other side of the world, when conditions are right.
Clearly I'm not welcome here anymore. I don't think I'm going to come back here. I used to find this chat productive and I learned many things but I’ve felt some hostility recently (almost completely from naturallyInconsistent but also to a lesser extent someone else (/two people) who I don’t want to name).
In the later case, most of this comes from the nature of this chat mainly being hep-th meanwhile my interests are mostly in lower energy phenomenon and them interpreting all my statements in that context.
@DIRAC1930 you can click on their name and hit "ignore this user (everywhere)"
it's no ones fault, imo. Sometimes people just don't mesh well. I also apologize again if my jokes earlier offended you. You're welcome here in my eyes (And I'm guessing everyone elses)
This chat is mostly general physics. There is no lack of crystaliine physics questions. In fact, I brought my own copy of Ashcroft & Mermin from overseas because there were people asking about it here and also on the main site.
I mean, isn't the echo chamber right here with bolbteppa and the rude one entertaining your L&L fanboyism more than enough goodness for you to stay?
@Obliv no, it cannot be this. Like, there are also massless gluons and gravitons if you want to go that direction, and then you cannot explain why they must be massless
If we have a closed system with countable number of states/configuration and we have perfect information: we don't need an arbitrary parameter like time to "evolve" or keep track of the system per se. Is time mostly useful when we have incomplete information or an uncountably large number of states? Like why do we have time in physics in the first place
worrying about lorentz transformations & SR.. do we really need time
Yeah I guess if we don't know how the system is going to evolve, we need to discern states with some sort of index like time, and then consider it acting like in a positive direction
to describe the systems evolution/physics
I just want to jump into QM and uncertainty principles >_< but I should do this homework
Let $A = \{0,1\}$ be a set of two states and let $T = \{t\mid t \in \mathbb{R}=(-\infty,\infty)\}$. $A\times T = \{(0,t),(1,t')\}$ we can partition $T$ into two sets (if that works with $\mathbb{R}$ idk) and say $t \neq t'$ for all $t \in T$.
Ohk ... Well if anyone wants me for anything feel free to ask ... I really think ppl are too hard on themselves ... Like this bunch of ppl haven't experienced failure ... I experienced for more than a decade of it
@Obliv how is this supposed to be useful for eliminating the time variable?
@MoreAnonymous no, you are only considering kinetic energy.
@Obliv near perfect is not the same as perfect, by far. You need perfection to remove the time variable. But all real systems are actually open to environment and you cannot control that interaction to perfection.
As of right now, I do not know of any fundamental particle that does not have a magnetic dipole component, and thus they should all interact with photons, at least to some extremely weak degree. But of course you shouldnt take this into some random philosophical tangent.
@bolbteppa Looking back at this, asking a basic question to confirm with you: the fact that the $U(1)$s are commuting that implies that it is a "factor" in the subgroup, right?
@MoreAnonymous The issue is that even in the ideal gas scenario, your result is still wrong. If you did statistical thermodynamics properly, they will teach you what the result actually is supposed to be.
I'm too sneepu but I will look more into the history of electron&atomic nucleus. I want to understand better the concept of mass for atomic/subatomic stuff. Also eventually how the standard model works.
@naturallyInconsistent yea ... I remember working on this ages ago ... And wondering how do I talk about a Lorentz invariant version of the hard ball potentials ... I did consider a 4 vector
Nothing specifically. It went like: studying string compactifications after ACM suggested Duff's article on $G_2$ holonomy but then to understand that I had to read complex geometry, got sidetracked by studying black hole microstate counting and mock modular forms and then heterotic string theory (most compactifications are based on these nowadays), and then to understand $E_8$ stuff, some group rep theory (mostly Dynkin diagram stuff), then a bit of GUTs, and now back to actual CY compactification...
@Sanjana I didn't ... But maybe I'm not imaginative enough to think of alternatives ... I think Einstein's musing of how much choice there was in choosing the laws of the universe is a deep one
@Obliv bah! Ppl don't get group theory in physics ... You can't just say I rotate an equilateral triangle by 60 degrees and get the same triangle ... You have to mention relative to what? The vaccine or the piece of paper etc etc
@Obliv I don't think that makes sense personally :/// if it were relative to itself it would be a sphere in spacetime and not something that moved with the particle
@MoreAnonymous We typically work in relative coördinates and thus do not have any problems with Lorentz invariance. If the ideal gas is so hot as to be relativistic, the usual equations are all wrong anyway. Hot to the point of relativistic means that pair production is possible, and then the conservation of number of particles approximation is violated.
@MoreAnonymous There is absolutely nothing confusing about that. If you replace the usual kinetic energy expression in the usual ideal gas integral with the SR counterpart, you just get a Bessel function. The results will resemble the Maxwell-Boltzmann (or what other case you choose to deal with) results for low temperature, but the high energy parts are all physically nonsense because, again, there must be QFT corrections to them.
@naturallyInconsistent you seem to be a boss at statistical physics :))) I had a pretty good stats teacher myself who had really good intuition ... Though I was surprised his area of research was actually DFT
i feel like it should offer one avenue of directly computing the expected eigenvalues for a density matrix. but the computation might be unwieldy as you go higher and higher dimension--there is probably a slick way of doing the computation in general...
Usually I end up phrasing the problem in a way I think is intuitive ... I always have a contextual understanding relative to the problem I'm solving ..
I never have all the details worked out and am not really that quick on my feet ... Especially while world view hopping
@MoreAnonymous That cannot be the case. Quite many people are not so fortunate. Otherwise, everybody should already be quite good at stat therm and there wont be so many questions on the topic.
@naturallyInconsistent true ... But even the best teachers will pale in front of the lessons of life ... I never went to an Ivy League college .. I was thought of as a joke by most profs and I was treated rather unkindly but I still believe in my potential and the importance of having gratitude to whomever tried to.give you their time
Not trying to pick a bone fyi
@naturallyInconsistent doesn't your QFT considerations naturally have infinite particles? I'm not sure how Obliv is thinkjng about the problem though
(just a thought ^ )
From here: MoreAnonymous There is absolutely nothing confusing about that. If you replace the usual kinetic energy expression in the usual ideal gas integral with the SR counterpart, you just get a Bessel function. The results will resemble the Maxwell-Boltzmann (or what other case you choose to deal with) results for low temperature, but the high energy parts are all physically nonsense because, again, there must be QFT corrections to them.
I also think so. Btw I derived a covariant form of wave equation involving field strengths using Maxwell's equations (including Bianchi identity), and it looked like $ \Box F_{\mu \nu}=0$ without sources.
Taking a partial of the Bianchi identity and using $\partial^\mu F_{\mu \nu}=0$ along with antisymmetry of $F_{\mu \nu}$ specifically. This is valid in all gauges.
i guess the Lorenz gauge makes it immediately clear that an electromagnetic potential satisfying the Maxwell's corresponds to an electromagnetic field satisfying the wave equation that you write since if $\square A^\mu = 0$, then $\square (\partial_\nu A_\mu) = \partial_\nu (\square A_\mu) = 0$
Pls see the equations of 1st page and read the 5th line from the last of 2nd page. Is says "This results is true for any system of particles, not just for those fixed in a rigid objects, as long as the forces between the particles obey Newton's third law."
My question is that if N2L also applicable when system of particle do not interact each other. If system of particles do not interact each then there will be no use of N3L between particles of system. So in this way the above equation can also be possible in a scenario to center of mass of translational motion like.
Suppose my system has 3 particles with different masses "$m_1 \neq m_2 \neq m_3$" with no interaction between them. I calculated CoM of the system "$R$" with respect to some inertial coordinate system. and applied three different external forces on each particle separately in such a way that direction of all three forces are same but magnitude will be set such that acceleration of each mass will be same $a_1 = a_2 = a_3 = a$.
So my system will also behave same way as mentioned in book. Does in such situation the i can apply above equation?
@Mr.Feynman i was just making the observation (after realizing what naturally stated) that the Lorenz gauge makes it especially clear that the corresponding EM field also satisfies a wave equation
Can we call the spacetime Poincaré symmetry an internal symmetry of the Polyakov action? Because e.g. a translation changes the parametrizations which are the "fields"
What would the linear span mean? Like, if you just want to parametrise them, then consider the case of spin half. The Pauli matrices with the identity matrix form a basis for the Hermitian matrices for the su(2) space, and by exponentiation you can parametrise the entire SU(2) unitary matrix space.
If you really want it to be linear, then I think ACM's confident tone means that it is simply not possible.
hm well the papers that the note cites seem to be constructing a basis for a hilbert space or algebra such that the basis elements are unitary. but the note seems to be talking about a basis for unitary operators suc h that the basis elements are unitary.
I don't understand this above equation of work-energy theorem. How integral evaluate and limit change from position to time.
Pls help me in understanding this.
If force is a function of position. why knk wrote acceleration as function of time $\frac{d^2x}{dt^2}$ in relation $F(x) dx = m \frac{d^2x}{dt^2}$ or $F(x) dx = m \frac{dv}{dt}$
@Obliv But the limit are time. How can he used time limit put in the velocity. But here velocity is a function of position. Which he said in below text of the equation.
@lucabtz it's related to it, but the reason Mr. Feynman asks is precisely because in a straightforward Fourier expansion you would not get the linear dependence on time
@Obliv But knk says here velocity is taken as a function of position "$x$". few line above this text he shows $s(x) \equiv s(t)$ , $v(x) \equiv v(t)$ etc.. Why?
Okay, let's start with position, velocity, acceleration, which are all functions of time $x(t),v(t),a(t)$ and are related by $a(t) = \frac{d}{dt}v(t) = \frac{d^2}{dt^2}x(t)$
When we integrate w.r.t. position we have $$\int_{x_1}^{x_2}F(t) = m\int_{x_1}^{x_2}\frac{d^2 x}{dt^2} = m\int_{x_1}^{x_2}\frac{dx}{dt}\frac{dx}{dt}=m\int_{x_1}^{x_2}\frac{dx}{dt}\frac{1}{dt}dx$$
@ACuriousMind Hello. Pls help me in solving the equation force as a function of position $F(x)$. Where position, velocity, acceleration parametrization is not defined.
@ACuriousMind Pls see these knk pictures. where it $F(x)$ force is a function of position.
but i don't understand velocity is a function of position or time. Because knk said velocity is taken as a function of position. but he is putting limit of time in the place of velocity. Why?
I really can't tell what you're trying to say, but when you have a trajectory $x(t)$ then you can express any function $F(x)$ also as a function $F(t) = F(x(t))$
conversely at least locally you can invert the trajectory to get a $t(x)$ to express functions of time as functions of position
@ACuriousMind Pls clear me. How force as a function of time equal force as function of position $F(t) = F(x(t))$. In my sense both should be different.
@123 read what I wrote bro. $\int vdv$ is what you use for work energy theorem. To get this you change variables from $dx$ to $vdt$ by $dx = \frac{dx}{dt}dt$
$y(x) = mx$ but if $x(t) = t^2$ then $y(t) = mt^2$ if we integrate $\int y(x)dx$ we have $\frac{mx^2}{2}+C=m\frac{t^4}{2}+C$ but that's different from $\int y(t) dt = \frac{mt^3}{3}+C = m\frac{x^{3/2}}{3}+C$
@ACuriousMind But in this case $F(x) = 1^2 = 1N$ and $F(t) = v^2 (1)^2 = v^2N$ here $v^2$ is multiplying. How can $F(x) = F(t)$ in your example. Pls explain or give me hint.
@ACuriousMind ;P Yes you are right. Thanks to all of you make me better and better in physics. When i found no answer from books, threads, self thinking etc. then i wrote here.
What i think until i properly understand all the basic ideas of newtonian mechanics i can never fully understand LM, HM, QM etc.. Because the same concepts used there with different ideas and experiments. But basics are same.
Anyone know what i'm doing wrong? For an EM question: When $R\ll z$, $(R^2+z^2)^{3/2} = R^{3}(1+\frac{z^2}{R^2})^{3/2} \approx R^3(1 + \frac{3z^2}{2R^2})$ so $$\frac{\mu_0 I}{2}\frac{R^2}{(R^2+z^2)^{3/2}}\approx\frac{\mu_0 IR^2}{2R^3(1+\frac{3}{2}\left(\frac{z}{R}\right)^2)}=\frac{\mu_0 I}{2R(1+\frac{3}{2}\left(\frac{z}{R}\right)^2)}=\frac{\mu_0 I}{2R+3\frac{z^2}{R}}$$
