@ACuriousMind how is this statement agreeable? For example, consider any quantum system with "large quantum numbers" occupying an entangled state. this would exhibit non-classical behavior. of course, there can be other factors which preclude or make less likely that an entangled state can be occupied, but that is not necessarily about the largeness of the quantum numbers, to my understanding. it should be an effect of a combination of conditions. one of which might be "large quantum numbers".
in electrostatics, a common approach is to use poisson/laplaces equation to solve for the potential, then to use the potential to get the field. however, if we leave the realm of electrostatics, we no longer have such equations since we can not write the electric field as the gradient of a scalar field/potential. what is the main strategy for tackling problems in this case? with nonstatic electric fields i mean
@Relativisticcucumber depends on the situation, use Lenz law etc. generally for tougher cases, you see a "quasistatic" approximation, where, yes, you do use maxwells equations, but you assume the field B's contribution comes statically, i.e you use biotsavarts law , good old amperes law on B. Things become a little easier here. You are not assuming steady current, but at every instant you will be assuming the current's B will be from the biotsavart's law
This approx is good if you're dealing with not insanely varying currents
Or if you're far from currents
I have seen many a magnetohydrodynamics people apply this "quasistatic" approximation. I used to hold that field in high regard smh
@Relativisticcucumber Oh, you are worrying about something that happens to apply way further than you think its applicability is. If you look at the general full set of Maxwell's equations, you see that Gauß's law is part of it. More suggestively, if you express them in terms of potentials, in the Coulomb gauge you get Poisson's equation yet again; the price to pay is that the magnetic vector potential will be horrible to find. Or you can use Lorenz gauge and both potentials will be under D'Alembert's
wave equation, you know, the same equation satisfied by light waves, just having a source term this time. So, first of all, there is a choice in the gauge condition. On top of that, you have a choice of how to partition up your $\vec E$ field, because now $\vec E=-\vec\nabla\phi-\partial_t\vec A$; we tend to put the basic charges into $\phi$ and boundary terms into $\vec A$, but this is another choice. Once you are done with these, solving is pretty straightfoward.
@SillyGoose ACM had said many times that there cannot be a way to state the thing agreeably. Large things can be put into entangled states, as you correctly point out, and so he never attempted to state any set of conditions as you seem to think he was.
@naturallyInconsistent so i take it generally $A$ cannot be found reasonably? what do you mean by "Or you can use Lorenz gauge and both potentials will be under D'Alembert's"?
@Relativisticcucumber If you use Coulomb gauge, then $\vec A$ is quite horrible to obtain. But if you chose Lorenz gauge, then you have the simultaneous equations
@SirCumference What is most wild is that covid is now a fact of life. Sars never became a fact of life. We made it go away just by being reasonable people.
Now, $\left[\left(\frac1c\partial_t\right)^2-\vec\nabla{}^2\right]$ is called the D'Alembertian, and is crucial in the EM wave equation, and also obviously related to both Laplacian and the Poisson equation.
@Relativisticcucumber techniques are not in the textbooks. They are in another set of textbooks that specifically cover techniques as applied to EM. They can get extremely intricate.
@naturallyInconsistent covid is crazy. went the entire pandemic without getting it, then i got it last summer and i literally felt like i might die. had a fever just under 40 for like a day and felt like i was m e l t i n g. thank god the sickness was only a few days for mine -- i know many people had it worse ;((
miao miao took 6x moderna and yet got it 3x. The severity keeps fluctuating; this last one was horrid. However, the jab does relieve long covid, so that is nice
yeah i was like the only person i knew besides by gparents who didnt get it during the pandemic. i was staying w my gparents during the bulk of the pandemic so i didnt really go outside. they live like in a forest XD
but i did move to abu dhabi when things were still improving but not quite better. i was in shanghai when it actually broke out and things were wild. the markets were empty! when i took the metro to the airport i was the only one the entire time. living in shanghai ive never seen anything like it! the metro is always packed nonstop
@naturallyInconsistent i do recall you saying you were sick many times. hope you are okay :(
Recently miao miao got overworked. murican colleague gave lecture, and miao miao had to give live lecture translations. Didn't get lunch, and that turned into acid reflux.
I have a thought and I want some criticism on it: In General relativity, there are runaway solutions when you include both negative and positive mass. The negative mass creates a repulsive potential while the positive mass creates an attractive one. As a result (assuming equivalence principle), they both accelerate in the same direction and run away to infinity. This is known from 1950s.
These instability inducing solutions are regarded pathological. But can't this be a good explanation of why there is no negative mass in our universe anymore?
What I was thinking is that, there's no negative mass because some positive mass chased them off to infinity?
@Sanjana I don't understand what you imagine here: The runaway motion in question is that the negative mass chases the positive mass with constant accelerations on both of them, but the distance between them doesn't grow.
we are very obviously not in that universe where all positive mass is constantly accelerated by some negative mass
the pathology here is precisely that what you present - the positive and negative masses flying off to different directions of infinity - does not happen
@SillyGoose what nI said: Again, no one claims that this is a law, it's just a heuristic: The classical limit will be found among the limits of large quantum numbers/large size, but no one is claiming the converse (that all such limits produce classical behavior). I will also repeat again that there is no universal characterization of the classical limit of arbitrary quantum systems known today.
@naturallyInconsistent This sounds as if you think the spread of covid could have been prevented by the same measures we took against the original sars, but this is probably not true: One crucial difference between the two strains is that the original was most infectious when the carrier was already visibly sick, so "quarantine sick people" was a successful strategy to eventually eradicate it (and that still took ~2 years). This could not work with Covid and its asymptomatic spreaders.
@ACuriousMind You completely misunderstand her. She is saying that the lack of negative masses in the universe that we see around us could be explained by this. All of those negative masses have already chased some positive masses away to infinity and we are left with the net leftover positive masses.
Ahh...that seems to require a very specific initial configuration so that we are in the end left with a bunch of positive masses (our observable universe) in one spot
because you could equally well assume that this leads to all positive mass being chased off to infinity by negative masses and the universe hence being mostly empty :P
@ACuriousMind Yes, what you are saying is a problem, but living through sars, we also had asymptomatic spreaders back then too. It was, however, rather important to keep the R value low enough, fast enough, and long enough, that the asymptomatic spreading variants did not grow to become dominant. Basically, starve the disease of mutation possibilities.
also I feel there's an issue here where the "to infinity" can't really mean the things disappear - even eternal constant acceleration can't accelerate you to FTL velocity, so we should see these near-lightspeed negative-positive mass pairs zipping around the observable universe
> Moreover, our experience does not only appear to be temporally limited, it is so: we do not perceive the future, and we do not continue to perceive transient events long after information from them reached our senses. Now, there is a very simple answer to the question why we do not perceive the future, and it is a causal one.
> Briefly, causes always precede their effects; perception is a causal process, in that to perceive something is to be causally affected by it; therefore we can only perceive earlier events, never later ones. So one temporal boundary of our experience is explained; what of the other?
@user85795 i think this part is incorrect... future is casually connected to the past as much as past is to future. causality does not pick out a time direction.
but they proceed to give the correct explanation : Evolution has ensured that we do not experience anything other than the very recent past (except when we are looking at the heavens). @user85795
thye do disagree with the causality explanation.. i just saw
If we consider two operators, where one of the two has a time dependency. How is this different manifested when considering a quantum mechanical system at some arbitrary state $\Psi$ ?
Is it the fact that the time derivative of the expected value of the time dependent observable, additionally depends on the expectation value of the time derivative of this operator?
@user20458579510081670432 In big universities, when profs become old the uni celebrates their birthday in a festival way... I was thinking that when ACM turns 70 or something, we should make a "Curious Fest" or something happen :p
@SirCumference These sites (All SE sites) exists because its developers and user understand the 'why' behind these sites. We should be thankful to SE Group for letting us use these sites for free.
@SirCumference @ACuriousMind do you guys read short stories by Arthur Conan Doyle? Yeah, I'm talking about Sherlock Holmes haha
