@Relativisticcucumber Grassmann numbers are heuristically “numbers” that anti-commute with each other. They are used to encode fermionic anti-commutation at a classical field theory level, among other things.
@SillyGoose Yupp I'm an undergrad,but I've already had an EM course based off griffiths,this time it's based off Landau n Lifshitz's second volume :')
But one good thing this time is there is no macroscopic electromagnetism stuff at all,it's just going to be point charges in vacuum,so no eternal stomach aches caused by averaging : )
@naturallyI Continuing our conversation about gamma rays... Photodisintegration is pretty important in stars that are burning neon (& beyond). It typically "knocks one or more neutrons, protons, or an alpha particle out of the nucleus".
Such reactions are endothermic (since they're fissioning small nuclei), so you get a negatve feedback loop: high temperature gives more gammas, causing more photodisintegration, which lowers the temperature. So this helps to stabilise the temperature.
Also, many of the heavier fusion steps involve fusing an alpha to a nucleus. But in the core of a star burning heavy stuff there isn't much primordial helium, or helium that the star produced while fusing hydrogen. So the required alphas mostly come from photodisintegration.
Those heavy fusion stages only last a few years, but they produce several fairly important elements. I have links to the relevant Wikipedia articles on the various stellar fusion reactions at the end of this answer: astronomy.stackexchange.com/a/43908/16685 Sure, it's only Wiki, but those articles are all quite good, with links to decent references.
Def: Sample space $ \Omega $ of an experiment or random trial is the set of all possible outcomes or results of that experiment. Is this equal to the set of microstates for a given Ensemble $\Omega(E,V,N)?$
@PM2Ring actually, we should be tagging @Loong about this. Hey Loong, I just commented on an answer of PM2Ring's, that you can read here and the comment thread underneath. In short, do you know of a definite advantage of the definition you like?
We're so used to stellar processes lasting billions of years, or millions of years for big stars. So it can be a bit surprising that some of the final fusion stages only last a few years, or even days.
@Relativisticcucumber it is a mess. It can be a superposition of both the fundamental electron field wave, and the Fermi quasi-particle wave. Clearly too long to fit inside the margins there, and thus omitted from discussion
A week or so ago, there was a news item about using carbon-14 diamond as an energy source. The idea has been floating around for a while. The news was about a successful test involving a thin layer of C-14 sandwiched between normal C-12 symthetic diamond, to create a betavoltaic device.
@PM2Ring oh. so symphony is used for the longer compositions
it is still a great tune from Beethoven. but there are parts that r disjoint
i think it is often in older classical music that the composer keeps repeating the same tune for long and then to spice it up adds something which feels like a different song
If I did the arithmetic right, 1 gram of fresh C-14 puts out ~1.3 milliwatts. That's going from the weighted mean beta emission energy, 49 keV, with an activity of 164.9 GBq/g.
@RyderRude that's Mozart's disdain for his contemporaries. Even his earlier works are like that, but it quickly evolved to emphasise a certain style of "sum is larger than parts" and smooth transitions and so forth.
@RyderRude The technology of the 20th century kind of warped our sense of how long a piece of music should be. It really focused on short pieces. The early early phonograph records could only hold a few minutes.
Long-playing records didn't really become available until the mid-late 1950s. And short pieces worked well on commercial radio. Of course, there have always been short songs, and short-ish dance tunes. But a lot of older compositions are quite long, which permits a much more elaborate structure.
@Madder Here's a crude example
@Madder Here's a crude example. Say you have 10 coins. You toss them all multiple times & record the outcomes. If you record the heads/tails state of each coin, then you have microstates. But if you only record the total number of heads each time, then you just have the macrostate.
@RyderRude Für Elise isn't an elaborate piece. As I said earlier, it's just a simple tune, probably intended to be suitable for someone who's been playing piano for only a few years, not an expert musician.
Ok, that transition to the 2nd theme around 0:52 is pretty abrupt. But that's ok, because it contrasts nicely with how the original theme later returns in an almost imperceptible way. :) Don't forget, Beethoven was considered to be pretty radical in his day. So we should expect stuff like that from time to time.
OTOH, the abruptness is partly down to how it's played. You can make it sound less or more abrupt by tiny variations in the volume and timing.
Also there's a subtle interplay between timing and volume on a piano. If you strike a key harder, not only do you get a louder note, but the note sounds slightly earlier, because the hammer hits the strings earlier
@RyderRude It is not a problem. People usually want music to have repetitions and minor variations. Mozart simply chose his way to tackle a perceived issue, and succeeded at making himself happy.
However, there's also a psycho-acoustic component. If you hear two notes of identical volume (and similar pitch) that start at almost the same time, the earlier note will actually sound louder. Good players take that effect into account, either consciously or subconsciously.
Some modern pieces do. :) Some modern composers do stuff that the old guys wouldn't have dreamed of doing. Or thought they could get away with doing. ;)
Every composer is a product of their time, and writes with some awareness of their potential audience. There's no point writing stuff that nobody else will be able to relate to.
One of the all-time experts in doing variations was J. S. Bach. The great jazz guitarist Pat Metheny, who's a brilliant improviser, says "compared to Bach, we all suck".
They can say what they like. But what counts is if people actually want to listen to their stuff. And I'm not talking about students & associates who politely listen because it's supposed to be good music.
OTOH, music can be an acquired taste. Eg, I love be-bop. But it just would not have made sense back in the 1920s. It needed several decades of older styles of jazz to act as the foundation, both for the writers & musicians and the audience.
@RyderRude I used to listen to Bach's Well-Tempered Clavier on a regular basis, especially the first book. At one stage I listened to it every day, for months. But of course you only scratch the surface by listening. To really get into a piece, you have to play it. And I never learned a whole Bach piece, just little snippets.
One day, a guy was at an outdoor cafe when Picasso dropped by. While having a coffee (or maybe something harder), Pablo began making small random pencil sketches in a little notebook. Eventually, the guy works up his courage, introduces himself, and asks "Senor Picasso, will you make me a drawing?" Picasso looks him over, says "Ok", and gets to work on a new sketch.
A few minutes later, he hands it to the guy, who gushes with thanks. But then the guy says "Senor Picasso, you didn't sign it". Picasso says, "I said I'd make you a drawing. I didn't say I'd make you rich".
@RyderRude Yeah, you mentioned it here a few months ago.
Here's a short music visualisation clip, from a more modern composer: Stevie Wonder. (His mum also has a writer's credit on it). Featuring wonderful improvisation from young Stevie on harmonica, and a brilliant bass line from the great James Jamerson. I Was Made To Love Her.
A longer piece from Stevie, Isn't She Lovely. In the last half of the song he plays a dozen or so variations on the main theme, each one unique and equally lovely. I think he repeats the main theme straight, once.
We know that in this Wheatstone bridge if,
$\bf{I_3 = 0}$, it can be derived that $\bf{\frac{R_1}{R_5}=\frac{R_2}{R_4}}$ . But could we prove it backwards, mathematicaly, that - if in such a circuit $\bf{\frac{R_1}{R_5}=\frac{R_2}{R_4}}$, then it will be also true that $\bf{I_3 = 0}$?
I a...
@RyderRude Or maybe they have someone else's purpose... and that someone else may have not been exactly sane. :) We don't really know what went down in anvient times, but from what we've seen of new religious movements that started in the last few centuries, founders of religion tend to have some pretty weird ideas. Delusional people can be very charismatic.
I prefer to think that the purpose of life is to construct your own purpose in life. That requires some understanding of yourself, human nature, and the world you find yourself in.
A prog rock epic composed by Yes, performed by The Band Geeks: And You And I
Here's another uplifting classic. The quality isn't great because it's from a TV tape from 1970. Melanie & The Edwin Hawkins Singers. Candles In The Rain
Ann Marie Nacchio (from The Band Geeks) is actually a classically trained singer. But she discovered that she prefers to sing prog rock, rather than opera. :)
i think calculus stuff can be analytically unsolvable, while computation stuff is always solvable in principle. so it may be good to rephrase physics in computational language
they call it "constructivist physics" analogous to "constructivist math"
@RyderRude Calculus is a very useful tool, and we developed a lot of mathematics to solve calculus problems. And a lot of important physics is amenable to that stuff. But yeah, it has its limitations. Even the 3 body problem isn't usually well-behaved.
And now we have computers that can easily do all sorts of algorithms. So maybe it's not a great idea to always try to put stuff in terms of Taylor series, etc.
@think_meaning_buildß Witten's work is in math and string theory. the latter, unless it is correct, will not be as relevant for physics as Russell's work has been for philosophy
@PM2Ring Wolfram's ideas also try to replace smooth spaces with discrete ones
@RyderRude Exactly. And once you get away from nice smooth every-continuous functions, you often have to be careful with numerical computation. Algorithms using actual real numbers may behave the way you want, but implementations using fonite precision arithmetic may not work so well, even when using large numbers of bits.
Modern computer algebra systems can do exact arithmetic with various kinds of algebraic numbers, which is helpful, but it doesn't get around that problem.
With chaotic systems, you can easily get different behaviour with arbitrary reals vs any given class of algebraic number.
ultimately, we can say that any theorem in math is a computation
also, all physics predictions arise from some computation
but saying that discrete things can reproduce continuum things is different. i liked the idea of constructivist physics, but it need not work for describing nature, especially chaotic system
Hopefully, we never need to worry about that really "pathological" stuff, and that we can make useful physical prexictions using the arithmetic of rationals and simple roots. But there's no guarantee that that will always be the case.
Eg, the function f(x): f(x) = 1 if x is rational, otherwise f(x) = 0. If you try to graph it on any normal computer system, it looks like the line y=1, even though it only has value 1 on a set of measure zero. ;)
When elliptic integrals arise, the traditional technique is to scream quietly, and try to express them with evil looking power series. Gauss himself found some great some for elliptic integrals using the arithmetic-geometric mean. But that's not convenient to work with when you're in a world where you do calculations using logarithm tables. But we're no longer in that world.
Cartesian everything is tremendously easier. Then you can quickly prove stuff and function well, even all the way deep into QFT, since people tend to only work with the simplest, i.e. Cartesian, stuff. GR stuff extends it by a tiny bit. This is as opposed to differential geometry, which can be a lot of learning before it pays off.
Feels like nobody here is interested in helping me out as usual. Instead of straight up ignoring, you guys should tell who you don't want to help directly (it saves a lots of time) but I don't think most of the guys here will take an advice from junior.
If your question is ignored, "this is an indication that no one active in this room (a) has the knowledge to answer your question, or (b) has the time and inclination to answer your question. When you do the same thing multiple times and get the same result, it is time to do something else."
@SineoftheTime (a) it is hard to imagine how so many people with degrees in physics find it hard to answer high school problem so I don't think this as a possibility. (b) Why is there no inclination to answer someone's question? Is the question wrong? They should guide what is wrong at least. Or they just don't feel like helping someone as i said.
@NOTEBook well, I'm rarely in this chatroom, but the point is that no one is "morally" obliged to answer you questions (in chats), even if they know the answers
@naturallyInconsistent Indeed. Bille Carlson was amazing. Sage & mpmath provide both Carlson & Legendre forms, but I'm pretty sure they just work with Carlson internally. I have some links to Carlson stuff here: physics.stackexchange.com/a/718837/123208
@NOTEBook Sorry. My electronics knowledge is a bit rusty these days (I studied that stuff ~50 years ago, in high school), and I didn't want to say something that would make you even more confused.
But yeah, the basic concept is that these kinds of circuits are linear. Do mathematically, so you can kinf of break circuits into sub-circuit parts, solve each part, and then superimpose the partial solutions.
@NOTEBook This is a chat room, not a help desk, and everyone participates here voluntarily as much or as little as they want. You have no standing to tell other users how to behave, and I find the entitlement that you expect other people who are just here to talk about other things to waste their time telling you they won't answer your question for whatever reason quite astonishing, given that you seem so concerned about a waste of your time.
So, there is a point B in a fluid. The elemental area is an infinitesimally small point in this fluid. A book I'm reading says this is dA, and that dF is the force on one side of dA. Why are we computing area if dA has sides? Sounds like 3d mixing with 2d and I don't understand
Should I take an intro physics course before I study aerodynamics
@Michael The idea is that you have an infinitesimal volume element (a tiny cube) and you can consider the force exerted on one side ("$\mathrm{d}A$") of this cube. Formally, pressure is the momentum flux, see e.g. this answer
@NOTEBook 1) you strongly underestimate how much labour and time it takes to tutor high school physics, have not considered that the exact content is different in different places and times. there is a reason that tutoring is a job and paid. 2) not all questions are interesting to all people for them to want to volunteer their time and they do not need to justify that to you or anyone else 3) you had already have number of answers on the main site
@NOTEBook ppl w physics degrees arent human repositories for physics problem answers. they are people with the ability to sit down and do a problem/the ability to look smth up and figure out how to do the problem. it's very possible for someone to construct physics problems that many people with a physics degree can't tell you the answer to a priori. [...]
[...] when you have only taken 1-2 physics courses, it's easy to overestimate the importance of smth that becomes a minute detail after 5+ years of studies. then, it's a matter of "i'm busy and this person is asking smth that will take me time to figure out, and i am not motivated enough (by either moral standards, interest, etc.) to spend my time in that way". i mean your recent q wasn't about a concept -- it seems to require one to actually invest in the problem and figure it out. [...]
[...] these questions are oftentimes less engaged with. whether this is desirable or not is beside the point, but i think your approach is definitely the wrong way to go about getting help.
@Relativisticcucumber well said. whilst I agree with what everyone else has been saying, I think you're getting to the heart of the problem with the "entitlement". sometimes I wonder if the hypercompetitive nature of some education systems and exams gives young people a massive misconception that solving physics problems should somehow be effortless "on the other side".
We know that in this Wheatstone bridge if,
$\bf{I_3 = 0}$, it can be derived that $\bf{\frac{R_1}{R_5}=\frac{R_2}{R_4}}$ . But could we prove it backwards, mathematicaly, that - if in such a circuit $\bf{\frac{R_1}{R_5}=\frac{R_2}{R_4}}$, then it will be also true that $\bf{I_3 = 0}$?
I a...
