In the QHO in regular quantum mechanics the creation-annihilation operators connect the energy eigenstates but they don't (obviously) affect occupation number like those used in QFT. Does there exist operators in QFT that do this? i.e. $$a^\dagger(k)|0\rangle=|k\rangle\in \mathcal H,\quad A^\dagger(z)|k\rangle=|k+z\rangle\in\mathcal H,$$ something like this? Essentially an operator that gives a particle more or less energy
@NiharKarve hi, the question reminds me of the thermodynamic heat death of the universe which states entropy is always increasing and that all the stars will eventually burn out. and another theory that black holes will eventually swallow all other matter. anyway think the no-cloning thm is one of the deep principles of QM but speaking freely here, think it has questionable elements. was looking for anyone else questioning it, but nothing seemed to turn up on a cursory search.
@NiharKarve The quantum "no-X theorems" are overhyped and usually don't say anything interesting in their standard formulations, see physics.stackexchange.com/q/296678/50583 :P
I have a confusion if a rod lying on horizontal which is always perpendicular to one end of rod dow the com remains at rest if yes then how to prove it
@PrateekMourya I have no idea what sort of situation "if a rod lying on horizontal which is always perpendicular to one end of rod dow" is supposed to describe
is the rod lying on a table (why "horizontal"?)? what does it mean for that to be perpendicular "to one end of rod"? Things can't be perpendicular to points, only to vectors/lines/directions. What's a "dow"?
I have tried to prove the fundamental theorem of calculus:
Assuming: f,g,F are continuous,differentiable in the appropriate range(s)
By definition,
$$ \int _{x=a}^{x=b}g(x)dx=\lim_{n \to \infty} \sum_{r=0}^{n}\dfrac{b-a}{n}g(a+ r\dfrac{b-a}{n})----------->E-1$$
Now consider the integral:
$I= \int...
I have a confusion whether we take amplitude or principal argument in euler form of complex number
@ACuriousMind suppose a rod is lying on a horizontal table or in x-y plane and a force coplanar is is such that it is always perpendicular to one end of the rod
@fqq Yeah I guess that would make sense, thank you
Maybe this is obvious, but if the quantum field operators obtained during second quantisation satisfy an "operator version" of the classical field equations, i.e. we can literally just replace the classical field solutions with the operators in the equations of motion: $$(\partial^2+m^2)\phi(x,t)=0\quad\rightarrow\quad (\partial^2+m^2)\hat \phi(x,t)=0,$$ does this mean that the classical gauge freedom of the $A_\mu$ 4-vector in electrodynamics gains exactly the same freedom as a qft operator?
Yeah, but even in Gupta-Bleuler you have to be careful how you implement the gauge
if you just implement the full gauge $\partial_\mu A^\mu = 0$ you just kill all the photons, that's why there's this "positive part" $(\partial_\mu A^\mu)^+ = 0$ you end up enforcing
Could I just have a sanity check, two objects of the same mass travelling upwards from the surface of the Earth at different velocities (no acceleration) require exactly the same amount of energy to get $x$ distance from the surface of the Earth, they only differ in the power input required to get them there
@Charlie by "no acceleration" you mean that they propel themselves with a variable acceleration that exactly cancels the gravitational acceleration at the current height?
@PrateekMourya what?
if you form complete sentences the probably of someone getting what you're talking about usually increases :P
not parallel transport, you know, the most common form of it
I actually can't for the life of me remember its name right now
there are three common ways to get around the vectors at different points being part of different tangent spaces: the Ehresmann connection, covariant derivative and ...?
if you're asking if the idea of a connection as a horizontal/vertical split as in the Ehresmann formalism is ever physically more relevant than the idea of a connection form, I don't think so
but an Ehresmann connection is equivalent to having a connection form or a notion of parallel transport, so it's a philosophical difference, not a technical one
I think the Ehresmann viewpoint is much more geometric and better to visualize, but physically we're not really motivated by the aesthetic of the geometry, but by the idea of having local gauge fields, i.e. we get the bundle by a clutching construction, not by starting with the bundle as the central idea.
so physically the "geometry" of the bundle is more or less accidental, so there's little gain in emphasizing any geometric intuition a mathematician might be interested in
the connection form is essentially the projection on the vertical part
so you go from the Ehresmann assignment of horizontal/vertical split to a connection form by projecting onto the vertical part at each point, and you go the other way by defining the horizontal space at each point to be the kernel of the connection form
@RewCie Why the facepalm? You literally said "The question claims it's an "assumption"", and I just pointed out the word "assumption" was not mentioned anywhere on the page. You really say a lot of stuff that doesn't seem to follow. I don't see why you're facepalming me when it's the same stuff I keep pointing out.
March is generally when I would realize that I had fallen behind in concepts in most of my classes, and May is generally when the exams finished up, so that timeline makes sense to me.
It's really about time someone actually did the math on a Mach 5 cooking method. Cooking in my ultra-high velocity convection oven is a mess because apparently most people don't cook like that or something.
I have no idea what you mean by that, and I'm on a work computer so I don't think I'm going to search the internet for "slapping a turkey" cause that seems like it will be a bad idea
That's fair, probably a good way to make mashed potatoes too
The real crazy thing is that I can run a joke simulation of a turkey on my workstation in a few hours, when a comparable-sized simulation for my thesis work just a few years ago needed a supercomputer.
In 2016, I needed something like 128 processors for a problem of this size and let it run for a day or two. The turkey ran on my workstation that has 80 cores for about 3 hours
Although 40 of the cores are hyperthread, which took some work for the code to make use of without killing the regular cores. I think it's only 2x20 physical cores
Oh okay at first I was thinking something like double Xeons, then I looked up "80 core CPU" and actually found a company making one in a single processor apparently.
I'm skeptical they will work well for scientific computing though, last time the supercomputer people built an AMD supercomputer it was really a disaster... but, they seemed to repress that and there's 2 new AMD-based clusters coming online in the spring
So I'll have to make the code work on those... Right now, the Intel compiler suite gives us much faster code than GNU. But, on AMD, Intel compilers intentionally slow down the code they generate so I'm going to have to redo a lot of the optimizations
Yeah, although we don't actually thread our code yet. We just treat each thread as it's own process instead
We use the Message Passing Interface (MPI) to communicate between processes. So we explicitly send/receive data when needed.
The MPI library, depending on the vendor, is smart enough to recognize when it's all on the same machine (threaded) or when it's across different machines, and optimize how it does the sending/receiving based on that
So it avoids the need for us to worry about whether we're on 5 threads of a single CPU of 20,000 cores distributed across an entire cluster. But, that comes with an overhead of not being optimal for the threaded case
I will try thank you. I hve tried ask it on mathematics stack exchange because it seemed more a mathematical problem, but I will where you suggested .Thank you.
@BioPhysicist Yeah... what? "In experiment the shape of bodies is very significant. Newton's law has been studied by billions and trillions of people in past 335 years. The law is applied right from the applications of colliding bodies to fireworks and launching of rockets," he said." Apparently there have only ever been ~100 billion humans over the history of Earth... so that seems wrong
I can't really trust someone who thinks trillions of humans have studied Newton's third law in 335 years.
@JMac Sorry, had to hop on a call to offer somebody a job... This is a finite volume code. Finite element doesn't see much use in fluid dynamics actually, although the new hot research area is discontinuous Galerkin methods that sort of unify finite volume and finite element
@tpg2114 Oh okay. My knowledge on that stuff is pretty jumbled. I had a fluid dynamics course that did get into some CFD methods, but because I was non-co-op and we were a pilot year for our program, we took that course before we took numerical methods. So basically all the CFD stuff got into math that I was supposed to understand, but didn't. And I took a FEM course I kinda understood so I'm probably primed to think everything is that lol
It's pretty interesting how the structural mechanics world and the fluid dynamics world developed in parallel but isolated, even though the governing equations take the same form at the end of the day. FEM confuses the heck out of me, but then I did some structural mechanics work for my MS thesis using peridynamics, which to me is just finite volume for structures, but to structures people it's like some abomination that breaks all the rules of structural simulations
I surprisingly understood what was going on in FEM better than I expected. I suck at matrix math, so doing any of it by hand was basically out of the question. But I did actually have a good idea about what methods were good where, and how to do some basic FEM using the program we had at university. That was one of those classes for me where I wound up surprised when I came out of it and wasn't clueless.
The math is weird to me, but it's a very useful skill. I find myself projecting onto orthogonal mode shapes surprisingly often when doing data analysis or reduction, or doing uncertainty quantification. Glad I took the class on it, but it still is bewildering to me how it works
I've never been able to get a good grasp on matrices, and how to relate them to basically anything. Like to this day I need to look up matrix multiplication. It just will not stay in my head in a way that actually allows me to grasp the math well. I'm okay with like "this matrix times another matrix gives us this useful matrix"; but when it comes time to do the operations I have like no intuition on why it works like it does. It's like my mind just can't deal with it.
I had a horrible calc3 / linear algebra / differential equations teacher in undergrad, so I really didn't learn any of the intuitiveness behind those classes
I can't really get into educational video series I find. I've watched some of those videos (not sure if they were the linear algebra ones though) and my issue is that it "makes sense" when I watch the video; but then afterwords it basically all leaves my mind. I've "understood" matrix math a few times, only to have to disappear from my mind the next day basically.
I remember learning matrix multiplication in grade school. What is the point in that?
Like they definitely are not teaching the motivation behind the process. So you are just following this weird rule of multiplying a bunch of numbers in boxes and adding the products together
@BioPhysicist Yeah that didn't help. And then when I took an actual linear algebra course in University my professor was like one of those "crazy genius" types, who writes with one hand while erasing with another, all while talking about some weird abstraction of the subject that no one understands at the time. Though when he did that with DE random rants of his came back to me when I was studying and suddenly made sense.
My DE class was so bad that we also did Gaussian Elimination in that too. And I know there could be applications to DE, but that isn't what happened in that class
@BioPhysicist Lol literally all the testing I remember from the class was just elimination using different algorithms basically. It's just the professor would talk about really complicated aspects of it while teaching us. I'm pretty sure I got an A+ in the class because I could remember the simple algorithms, but the theory was still a total wash.
And I had gotten a 5 on the AP Calc B/C test, so I took Calc 2 as an "easy" grade to get started rather than waive it. But that meant I was bored and didn't go to class, so I missed most of the transition to LA and the material until I was very surprised on the final...
I got 5's on the calc / physics AP tests, but my advisor recommended I still take calc 1/2 and the intro physics classes to help build the foundation. I am glad I did it
It's actually kind of ironic that all of my work deals with linear algebra (which I never took a proper class), chemistry (which I haven't taken any class since high school since I AP'd out), and system dynamics (which I got a D in when I took it)
I actually really enjoyed my DE class. I was doing terrible at it at first; but once I hunkered down to study for the exam I would literally like think of random phrases my prof said that were nonsense at the time, and a bunch of them clicked as I was studying, so that was actually pretty cool.
I'm kinda glad my school didn't really offer AP or anything, because I probably would have been tempted to skip classes and it would have been bad.
@tpg2114 2.3, suck it. (apparently our GPA reset after second year so all my good marks on the intro classes didn't factor into my average for my degree lol)
I don't think it is that competitive here. I did get pretty good grades in HS, but not like "work my ass off" good; and got into the program I wanted at the school I wanted without issue. It may have gotten worse in the last 10 years, but I don't think it's too bad here. My province has a really high rate of universities per capita.
Yeah my undergrad wasn't a competitive university, so no issues there. In terms of grad school, I got accepted into 2 places (forget how many I applied to). But I am still surprised I got into the school I am at now given that my undergrad was weak on the research side.
I never did anything past undergrad, but I did get to make an automated beer brewer for my capstone project... so I'd say things worked out pretty damn well.
I... exaggerated... my skills a bit when I applied. I knew how to program, but mostly C or C++, and the post said they wanted Fortran. So I figured if you know one language, you can learn others easily and said I knew Fortran. The professor called me into his office on a Friday and said "Since you know Fortran, you can start on Monday. We have some code that needs updated, talk to X on Monday and he'll give you a copy."
So I went to the campus bookstore and bought the only book on Fortran they had
Hi, I am working on a problem and I really cannot move on. It is not really physics, so sorry if i post it here, but in case you want, could you please give it a check. Thank you in advance. The problem is:math.stackexchange.com/questions/3919495/…
@ACuriousMind Sadly it wasn't mine alone. Our capstone projects were group projects, and my project was even more so, because they decided to test out a "cross-discipline" capstone project where we worked with a group of Chemical Engineers who basically laid down what kinds of targets we had to hit with our system to get different beers.
It was pretty automated. We were going for load it up and leave it; but there were a few steps that were by hand. Mostly adding the hops and putting it into cooling. And the hops was supposed to be automated but the small part we made for it wasn't consistent enough. Overall though it was fairly automated. You just loaded up what you wanted into a raspberry pi and it controlled the pumps and stuff.
Definitely a very interesting project. Plus we were a pretty popular project among classmates... given that our project meant that we had several kegs stashed away in a fridge that we had a key to access and a supply of plastic cups.
Our engineering campus was literally isolated from the rest of the school; besides architecture students. It's a campus that's like a 10 minute walk away from the main campus; because they didn't have engineering until they took over the old government founded "technical university". So sadly you likely would have still been screwed out of free beer.
True enough. Plus on a Friday afternoon the campus was still very much open while people didn't have a lot of classes, so it wouldn't have been hard to make the walk over and manage to find your way to the fridge. Also Friday was "Engibeering" so being a little buzzed on campus did not suggest that you had been drinking in a lab.
Literally one of the first activities we did on our first day was go from the main university campus to the engineering one while chanting a song they gave us the lyrics to. The chorus was "We are, we are, we are, we are, the engineers. We can, we can, we can, we can, demolish 40 beers. Drink rum, drink rum, drink rum, drink rum, and come along with us. Cause we don't give a damn about any old man who don't give a damn about us." I can't believe I remember that.
I feel like it was pretty iffy to get us to chant that 10 years ago, and it might not fly anymore.