Can anybody please recommend someone that I can talk to, who is knowledgeable about the consistent histories interpretation of QM? I would be truly grateful 🙏
@Amit No worries. Here's an example that does a 3D plot of a potential surface. It also does a little bit of symbolic differentiation. space.stackexchange.com/a/57679/38535
@nickbros123 Hmm you're asking a non academic person remember? My understanding is that it makes it easier, i'm sure peer review puts some weight on your creds
@123 we've had this convo here not long ago. It depends on the rules / precedents in your area and on whether you can get an advisor that will help you do it
@Amit that sucks because though my institute is considered premier in my country, the course structure is a massive massive joke. Grad students don't even see a line on L&L vol 8 related stuff (they do have a condensed matter 1 and 2 module, but I don't think they cover this)
@nickbros123 But isn't vol 8 kind of narrow? I mean, isn't it the kind of stuff very few people need when they actually start doing research? I always think that's why the educational aspect of an institute should be mainly judged in how it handles the core subjects that is most useful in everyday work
@123 Never wrote a paper, no idea, lol
I barely even write grocery lists (I just remember, who can bother)
I self study physics and math because in my student career even no one topic is understandable and we don't have any teacher here who clear the concepts. We all here just memorize the books in every class
@Amit bs here is a joke. I feel very very bad for the wannabe physicists in their BS who subscribe to the teaching that happens here. They don't know they're getting severely handicapped
They treat Newton mechanics like I'm a 9th grade kid, waste the entire 1st sem, on just Newtonian stuff, not even making it to free axis rigid body motion. This sem, they are doing Griffiths in the worst way possible, skipping essential points on E fields in matter and their teaching of potentials is a joke.
I'll give you an example: the electric field inside a conductor, which has a hole in the middle with some charge in it, experiences no field due to charges outside the conductor, including the shell. This "shielding" must be proved using uniqueness theorem arguments
My teacher cut copy pasted Griffiths sub heurestic argument of saying " this is what happens with the conductor extending to infinity " and called it a propf
Now that I've set the stage of roughly what happens in the first 2 years, (there's then optics and stat mech ), they directly jump to L&L vol 2 treatment, Goldstein treatment immediately in the 3rd year
I don't know if I should for my own safety (?). After all, they do have a substantial amount of power on my grades, some of which are evaluated subjectively. At any rate I don't really care, the profs are kind enough to allow me to skip their class, and I'm only doing what you're doing but inside an institute
@nickbros123 Ah I didn't mean it in a bad way. First of all going to the professor can be great to ask questions... you don't really have to complain explicitly, but just go and pester him/her with questions because what they don't address during class they should at least address when you come to them personally
If you want to skip class that's a different matter
@Amit the prof that teaches me (or to put it correctly, my batch) tells my questions are not worth caring much about and that they aren't familiar with the material I'm speaking of. The otherr profs, esp ones working on stat mech and fluids, and another guy on string theory seem to care, though, even they are saying the questions I ask are currently unsolved and they haven't put too muc thought into it
@Amit What is the benefit of looking angular momentum at different origin?
If at some origin "A" angular momentum is constant in magnitude and direction then torque is also zero. In the same example if we take angular momentum at different origin "B" it look angular momentum changes in direction but not in magnitude, and found torque.
The (oriented) area of the triangle swept for unit time is $\mathbf{r} \times \dot{\mathbf{r}}$ and if you $\frac{d}{dt}$ that you get the torque (I'm leaving out masses)
Because from some origins $\mathbf{r}\times \dot{\mathbf{r}}$ is not constant
you lose symmetry for example
Take $\mathbf{r}=R(\cos \omega t, \sin \omega t, 0)$ and calculate $\mathbf{r}\times \dot{\mathbf{r}}$ , then transform by $\mathbf{r} \rightarrow \mathbf{r} + \mathbf{d}$ for some $\mathbf{d}=(d_x,d_y,d_z)$ and repeat the exercise
Pls explain and take any example you want. What happened why torque different.
What is in my mind if i look conical pendulum at origin of circle it looks constant angular speed. But if i look at pivot the conical pendulum has torque and changing angular speed looks. Does it correct or not?
What is this symmetry idea to look angular momentum and torque at different origin?
Because you don't really need to change the entire coordinate system. You just calculate with respect to a different point. You don't have to translate the origin
(in the states) though a PhD is meant to train one to become a physicist, my impression is that top programs accept people who already have a precise direction of interest and experience to back it up :P
So only when you have a physical knowledge of where the pivot of something is for example, you can say that this is a "real force" that generated a torque. Otherwise, all kinds of forces can generate the same torque
Because torque has two degrees of freedom, the position vector and the acceleration
@naturallyInconsistent pre academic education here is garbage. But regardless, if I had a good academic institute near me (there are a few) I would probably go attend some lectures. It's just a geographic issue
The problem is that self-study is many orders of magnitude more difficult than getting good instruction and having peers to discuss with.
Like, if someone told you that the thing you are looking for simply isn't rigorous and nobody has managed to make it rigorous, you would stop looking for resources to find out a rigorous formulation of it.
You can be buried under a lot of reading if you do not realise that the thing you are looking for simply doesnt exist (yet)
Instead, now that you know it is an open problem, you might want to tackle it yourself.
But then you would need to read up all the different schemes available, and it is pleasant to find that, actually, the broken schemes that we have, give incredibly good agreement with results.
@naturallyInconsistent I would have to take your word for it, I've never had a proper teacher whose class I respected enough to attend.
And peers ofc are important, to know whether one is going mad or is still sane, at the very least. In this case i guess, the situation I am in right now is most optimal; at an institute , degree is a confirmed, don't have to attend classes, have access to profs, and peer(s?) Exist But really, if ones willing to spend like 10+ Hourzs a day, a primary book and internet access would be completely sufficient imho
There's hardly any depth in the teachings in my country. Everyone just parrots Griffiths word for word. One is simply better off reading Griffiths then
No doubt, a good course and in general studying in a good program can save you months/years of struggling with textbooks, it's not so much that it saves time but rather you're less "in the blue" about the state of your own knowledge because you're getting constant feedback from your environment
That's why I always think assignments should be much harder than the exam, but the exam should still allow you to pass the course. Because getting feedback is most important imo, the hardest exercises tell you where you're at better
@Amit, you're talking about a perfect course. In my country such a thing doesn't exist. My real analysis course was near perfect, and guess what I attended all of them diligently, solved all the problems sheets etc. If such things exist obviously it's a no brainer. But here, you only find people cut copy pasting textbooks words into their lecture notes, as a result covering almost always less than or equal to what the book the course is based on does.
I think the live lecture format is a bit outdated, especially if it is a big group of students. For small groups where the lecture can be more of a discussion it is okay
But I think some lectures should be recorded in their perfect form and then the professor should be available to address questions etc. online
I mean live
Just imagine the wasted time professors spend preparing the same lectures over and over again
And surely someone did it nearly perfectly already
@nickbros123 Ive had the good fortune to meet great teachers. A course is not something you can replace with books; you would not know what you do not even know you have to look for, until someone introduces it to you and you realise you have been missing that all your life.
Also, self studying is just not for anyone. And it is a skill you need to work on, as opposed to the academic framework where you're more like a fish in water without being always aware of the water
I mean, even shitty courses can give you some orientation
But the grass is always greener on the other side, scattering of spectrum is a messy ride, and when the phase shift's gonna occur you want to ride the tides
I am trying to understand angular momentum and torque rigorously about different origin.
In example of conical pendulum taking origin at point A (which is the center of circle of rotating bob) found angular momentum constant in magnitude and direction. And torque is measured zero at A.
If we take origin at B (B is pivot point which is at the one of string and another end of string attached with bob) . Angular momentum at B constant in magnitude but changing direction. And torque at B also constant in magnitude but changing direction.
@Amit i am trying to understand change of origin give different results of angular momentum and torque. How to see these values rigorously and their meaning. May be ACM or naturallyInc could help me more in understanding these if they want . along with you. I know I will come to the conclusion after discussion with them.
I agree it depend on origin , because we defined angular momentum and torque this way. I want to know rigorous meaning of changing magnitude and direction or both.
Again, the question is very little to do with physics and almost all to do with maths. If you want to study the maths, you can start by deriving the conditions for which we may prove that the quantity involved does not depend upon the choice of origin.
The meaning is not rigorous. You are looking for intuitive meaning of what it means for the quantity to depend upon origin or to be changing. But from the chosen new origin there is net torque, so it had to be changing.
@naturallyInconsistent My english is weak. When you write sentence compact i am finding hard to understand the sentence. I don't understand the question properly.
@naturallyInconsistent possible hint that may be necessary, if i understand what you're getting at, this condition can't be satisfied for a single point particle.. (right?)
i have a potential defined as such, when they solve the schrödinger equation, they get a solution of some Constant * sin(kx) for psi 2. in order to find k , they put in the condition, that at +a the function is zero and get an equation kx = n pi.
@Mad When n is a negative integer, you get the same physical state as positive integers, and so to avoid double counting, it is necessary to only consider positive integers.
This is what my math mechanics book says couple does not depend on choice of origin. But moment (torque) does depend on choice of origin which is in below pic. Otherwise i don't know the condition. You can tell me
@123 I can easily make 3 forces get the behaviour; by restricting to couples you must have pairs of forces, and that is not the answer. If you have worked it out you would have been able to tell me directly what the simple answer is.
@Mad Yes, it is the same solution, just changed by a global phase, and global phases are un-observable because all the observables are found by $\psi^*A\psi$, and in that formula, the global phase cancels out. We may only see a phase difference if it is an overlap integral $\phi^*\psi$
@naturallyInconsistent The picture i sent you above moment of force which i have read. Which say torque/moment depend on choice of origin. otherwise equilibrium condition says if moment at 3 different points is same then it is in equilibrium. Let me share you picture
@naturallyInconsistent I think where ever moment arm is same torque is same
And so as long as the net force is zero, you can pick the origin anywhere. If the net force is non-zero, then you can choose the origin anywhere along the line of action of the net force, and you will get the same numerical value of the torque.
That is the simple answer, derived with very little maths.
And now I want to go back to sleep. Your kind of questioning always makes me very angry, so I will stop now.
i have one doubt tho. if instead of the Schrodinger eqn, one uses Heisenberg's eqns for a particle in a gravitational potential, one gets a time independent state vector and a position operator which evolves according to $m\frac{d^2X}{dt^2}= - m\nabla \phi$. $m$ cancels out from both sides.
so the Heisenberg picture says that the equivalence principl DOES hold in quantum mechanics?
i will try, but for now, i do have a proof that different masses produce the same interference pattern. is this proof what u r asking for ? @ACuriousMind
let's do the same experiment in a gravitational field with two particles of different masses. the initial state is the same in both experiments $\psi_i$. The final state in Heisenberg picture is $\psi _i$ and $X(t)$ given by $\frac{d^2X}{dt^2}=-\nabla \phi$. so the position measurement expectation values are $\langle \psi _i|X(t)|\psi _i\rangle$, which is the same for both particles
because $\frac{d^2X(t)}{dt^2}=-\nabla \phi$, X(0)=X$ actually does not have any solution, because we dont have $X'(0)$, and $X'(0)$ shud be the $\frac{P}{m}$ which is mass dependent!
also how on earth did you even get $\partial_t^2 X(t) = -\nabla \phi$? The Heisenberg equation of motion is $\partial_t x(t) = \mathrm{i}[H,x] = \mathrm{i}[\frac{p^2}{2m} + m\phi, x] = \mathrm{i}[\frac{p^2}{2m},x]$
the $\phi(x)$ just drops out because it commutes with $x$
i am thinking that if we have $\psi _i$ and $X(t)$, we have the position expectation value at time $t$?. am i wrong in sying that interference pattern is position measurement?
again, just do this for the normal double slit first
unless you know how to compute the normal double slit in the Heisenberg picture, how could you be confident that you can correctly apply the Heisenberg picture to the gravitational case?
in the normal double slit, i have $\psi _i$ as a function peaked at two locations. and i have $X(0)=x$, $X'(0)=\frac{-i}{m}\frac{d}{dx}$ and $\frac{d^2X}{dt^2}=0$
which means i have $X(t)= x-t\frac{i}{m}\frac{d}{dx} $
then i can take the expectation value of this $X(t)$ with the state function that is peaked at two locations
