@0celo7 :P Google the voltage across a capacitor until you understand it (Maxwell's equations -> voltage across a cap is easy), then the voltage across an inductor (which is less easy to derive -- basically the magnetic field inside a loop of wire is related to the current going through the wire. But this magnetic field has an energy associated to it, so it takes work to change the current)
add them up and it must be zero because you're looking at changes in voltages (electromagnetic scalar potential) and you wind up at the same point you started, so the sum of differences is zero
this "sum of voltages=0" equation is your EOM!
then you can figure out the canonical variables in the hamiltonian
and then I'm lost b/c I have no idea what the intent is there :p
maybe he wants it in terms of voltage instead of charge,
Could be it. $V(\hat{x})$ is an operator after all.
(you don't have to derive those cap/inductor formulas from scratch now, though you certainly will, over, and over, and over, and over again in any E&M class)
@Slereah Don't try to do resistance and quantum mechanics at the same time.
That's an advanced topic.
@JohnDuffield Ok, I read the question and answer you linked.
What would you like to me take away? Please note that as a practicing quantum physicist I have thought about wave-particle duality plenty. I'm not a n00b here.
@NeuroFuzzy The intent was to see that an LC circuit is a harmonic oscillator. We all know how those are supposed to work in quantum-land, and in fact if you make the circuit out of a superconductor so there's no scattering of the electrons you really do get a quantum harmonic oscillator!
This is really, really amazing. You can build an electrical circuit large enough to see with you naked eye which is quantum mechanical. You can measure the quantized energy levels, violate Bell's inequality, the whole works.
The high I got the first time I walked out of a nanofabrication clean room with a wafer on which I'd made quantum mechanical elements... it was really awesome.
The field of superconducting qubits revolves around the fact that this works.
It's great because you can literally use circuit designer thinking to engineer the Hamiltonian of your system.
You don't have to worry about finding some God forsaken hyperfine splitting in some random atom. You just decide what transition frequencies you want and engineer it in.
But then again, @JohnDuffield says this is pseudoscience, so maybe everything I'm telling you is wrong ;-)
@DanielSank So in the example you were leading 0celo7 on, I mean, you could choose voltage and then your conjugate to voltage... and then your $|\psi(v)|^2$ would be the probability of measuring a certain voltage?
It's a bit more natural to use charge and flux instead of current and voltage because the dimensions of charge times flux is action (i.e. hbar), but whatever.
@DanielSank That's really amazing. Can't wait until I can look at the quantum mechanics of decoherence/superconductors in a more big-picture view. I'm more in the stage of, "sure, that kinda makes sense with this hamiltonian, and I guess something analogous might happen for the tensor product of $10^23$ particles" :D
The individual electron states never change. The superconducting state has a gapped ground state. The energy excitation to the next excited state is typically something like 40 GHz.
@NeuroFuzzy we engineer the LC resonance frequency to be considerably lower. That way, the collective motion of the "electron fluid" has a low energy resonance, much lower energy than what you need to disturb the superconductor.
@NeuroFuzzy The problem is there aren't any books in our field!
I've more or less come to the conclusion that if I have to leave my job when my fiance finishes her post doc I'll spend a year writing a book. It needs to happen.
@DanielSank Yes. Don't pay attention to the -2, science is not a democracy, and we have down-vote issues here at stack exchange. Kids who believe in popscience woo downvote bona-fide physics with robust references. Also see this answer.
@DanielSank The dual slit experiment is explained simply via a wavefunction wavefunction interaction that acts like an optical Fourier transform. We just don't need Copenhagen or the MWI any more. So it's time to stick a stake through the heart of quantum mysticism, and bury it deep.
@ACuriousMind I just overheard someone say "definite antiderivative"
@ACuriousMind Moral of the story: every time you get upset at me for saying something derpy, there's always someone out there who thinks "definite antiderivative" is a thing.
> If photon have zero rest mass then the term E=hf should also be zero because if rest mass is zero then relativistic mass is also zero and so on by Einstein mass energy relation energy shoud be zero but it is not, why?
@0celo7 This is why one takes courses, instead of just reading books. In other news, I'm about 90% sure Carroll mentions this
It's actually historically very important, you see. Einstein was, for a long time, convinced there must be something wrong with the theory because the metric tensor only determines everything up to 4 parameters (in 4D). He didn't realize that this was actually what he needed.
I think it took about 1.5 years for him to realize this.
So the device is a Galvanometer.
According to the Lenz's Law, when we take the magnet towards the coil, the pole at the right end, should be north pole and when we take it away, the pole should be south. And the reason is inertia.
And my question(s) are-
1. If we take the magnet inside, due ...
The Question
I posted this question yesterday, but there was no "movement". So I write here, to kinda "promote" it for discussion. So please have a look at it.
And speaking of technique skills (e.g. working out that path integral) you have, sooner or later you will get there, I think what really matters is ideas, good ideas. It is something very hard to train yourself.
@JohnDuffield Now also, if you please, explain why in my laboratory I find that the rate of energy swapping between two harmonic oscillators goes as the square root of the amount of energy involved in the swapping. Please do it without quantum mechanics.
@0celo7 I'm really more interested in understanding @JohnDuffield's opinions. He seems to think he's got it all figured out and everyone else is muddled in confusion.
Part of the interpretation is that humans are magic boxes which break all the rules. The thing is, you have to do that to get a self-consistent theory, and I firmly believe that self-consistence is more important than sanity of a theory.
NB: I don't think that humans really are magic boxes, but I also think it's important to explain the data and not overextend an interpretation past what we really can say.
On a related note: I heard Sean Carroll talk about "deriving the Born rule" at the APS meeting last year. After the talk, I had the good luck to be called upon to ask a question.
I asked him if he thought anything he had talked about had even the slightest chance of influencing the design or outcomes of an experiment.
@JohnDuffield Have you ever considered the possibility that you actually might be wrong?
For whatever it's worth to you, I think that answer was down-voted because it's wandering and not particularly clear, regardless of the accuracy or relevance of the content.
I can't find a question that is, in general, about the relation between quantum mechanics, projective representations, universal covers, and central extensions. I'm thinking of a question that showcases e.g. $\mathfrak{so}(2)$ on the one hand, and the Witt algebra on the other, and asks why a central extension appears in one case, but not the other.
@ACuriousMind I hated the lectures for that course, but I had a lot of fun with the essarys. My final paper had a mobius strip with world lines stapled to it.
It had something to do with the notion of identity.
Whenever my buddy would bring up relativity in discussions of identity the prof just deflected. I thought the point of that course was to get some science up in philosophy's grill and see what happens. I was wrong.
There was actually an entire lecture on some issue X, in which the professor explained the positions of schools of thought A and B.
At the end of the lecture, I asked if it weren't the case that A and B think the same thing, but that disparate use of terminology lead to apparent disagreement.
He actually responded that this observation was inadmissible because it would render the issue trivial and then there'd be nothing to discuss.
Does quantum mechanics assume no law of causality?
Is that all the argument of interpretation about? A friend of mine insist on causality, and think qm has "fundamental problem". Not sure if he is a crackpot or what.
I'm not sure if this is the right place to ask this question. I realise that this maybe a borderline philosophical question at this point in time, therefore feel free to close this question if you think that this is a duplicate or inappropriate for this forum. Anyway, I'm an electrical engineer a...
@Shing your friend is not a crackpot (merely for that assertion alone). study "nonlocality" and "bells thm" etc which is related to causality. QM does seem to mix up the concept of causality, but not really admitting it directly; rather, it is swept under the rug so to speak.
So the device is a Galvanometer.
According to the Lenz's Law, when we take the magnet towards the coil, the pole at the right end, should be north pole and when we take it away, the pole should be south. And the reason is inertia.
And my question(s) are-
1. If we take the magnet inside, due ...
