From Bell’s theorem and the Kochen-Specker theorem we know that any hidden variable model hoping to reproduce the predictions of quantum mechanics must be both non-local and contextual. What model satisfy these conditions and what research is being done?
Also is de-Broglie-Bohm theory contextual?
Hi, can someone please explain to me if the two 3-ohm resistors on the right are in series or parallel? I thought that they would combine and create a total resistance in parallel with the voltage source of 1.5 ohms. my.mixtape.moe/caqjug.png
Hi. Does anyone know whether Lubos still does research? I am curious because he writes such detailed and intense reviews of many of the latest string theory papers that I can't believe that someone could be that active and up-to-date with the field and still be inactive on the research front.
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Would any of you guys be willing to take a few minutes to sort out the links in the above answer?
@q3d Neither. The one on the top is in series with the sub-network consisting of all the rest of the resistors. And in that sub-network the otehr is in parallel with the sub-sub-network consisting of the rest.
@dmckee Okay. But in one of the blog posts, he even claimed to have obtained some restricted proofs to the ER=EPR conjecture. I just can't understand why would he not publish. :/
@Dvij I've got to say it - I have issues with his blog. Maybe his String theory posts are all right (I have no interest whatsoever in stringy stuff), but the other things he writes... I'll stop now before I violate the 'be nice' policy.
I think the thing you have to understand is that there is no cosmic rule book that said "And thou shalt only consider velocity as a function of time!".
We can go ahead and try treating velocity as a function of position and then check latter to make sure it doesn't have any horrifying consequences.
These things are basically a tool box, and a bunch of early physicist spent about 200 years thinking them up, so it is no surprise that most of us have to be told about them.
So when we see $F(v)$, we should actually think $F(v(t))$
(second picture)
and this is something that was pointed to me too; say we have $F$ as a function of $x$. In the case of oscillatory motion, that is going to give us problems, because we could have two possible values of $F$ on some $x_0$
@ShaVuklia Well... F is a function of v, so if you give it a value of v, you'll get the value of F out. If however, you give it t or x instead, then you need to think of it as $F\left(v\left(x\right)\right)$ or $F\left(v\left(t\right)\right)$ - I'd say that it depends on the context
@ShaVuklia That could be a problem (although not one I remember experiencing). At that point, you can either say that it's double-valued for the data that's been given, or you need more information (i.e. the time and $x\left( t\right)$ or something similar), if that makes sense
Later on, in more complicated oscillating scenarios (with horrible-looking solutions), it does get to a point where such a thing possibly does happen, but at that point, you're usually not bothered with analytically coming up with horrible-looking solutions, but in numerically solving it to see what it physically looks like
(or at least, that's my experience, although I do remember having to come up with horrible analytical solutions anyway :/)
I wonder how those solutions look like. I just finished [I think a basics to] oscillations, and in the case of the driven damped oscillations, the solution was already getting huge :P
but yea, I just can't do mathematical tricks. not sure if that's a good thing or a bad thing. I really need to work from the definitions/theorems from math. so whenever I see a "separation of variables", I either theat the $\Delta$ "something" as a finite nonzero entity and take a limit at the end, or I just apply the actual theorems. My brain just shuts down when I try do apply a trick, even if I know the trick works
@ShaVuklia I was a bit like that once (although not as bad). Not doing tricks can be useful when you come across a really long calculation, which there aren't any (known) tricks for. Doing tricks does improve with practise, but If you're looking more at the physics than the maths side, I'd say it's well worth the effort. It feels really, really good when you spot a trick that cuts the calculation way down :) But this is just my view...
Yea, I get what you mean. But honestly, I was traumatised by not having been introduced the proper math behind the tricks. I almost quit physics a month ago (I didn't do any physics for 5 months, because I refused to do seemingly random tricks), but the past week all I've been doing is revising my old physics courses of this year,
and I realise it's really just a couple of simple math theorems (integration by substitution, chain rule) that we're using, where we've adopted some intuitively nice notation.
@ShaVuklia I did some differential geometry last year and actually got annoyed with it for the exact opposite reason - so, so many words that at first seemed so confusing, that were much more simple to think about in a 'physics' way, yet when done in maths, was just a rabbit hole of increasing detail. It's nice to do it just 'cause, but when trying to put it in physics, the technical details (and even words) just made it complicated for no reason
@Mithrandir24601 I agree to an extent. I find his anti-climate change posts annoying. I also don't agree with his political views for the most part. But still, I love his blog overall. His physics posts are really nice - not just the stringy ones.
@Dvij Hmm... I stopped reading after I read a post where he completely and utterly mis-interpreted what someone did, when they explicitly wrote in the paper that they didn't do what he accused them of doing
OK - if he'd just mis-interpreted, fine. But he completely tore into them for doing the very thing that they explicitly said that they didn't actually do :/
Guys, so we have $$ a(t)=\frac{dv(x(t))}{dt}=\frac{dx(t)}{dt}\cdot\frac{dv(x(t))}{dx}=v(x(t))\frac{dv(x(t))}{dx}. $$ However, if we write $$ F(x(t))=mv(t)\frac{dv(x(t))}{dx}, $$ then how does the integral make sense? Shouldn’t it then be: $$ \int_{t_0}^t F(x(t’))\ dt’? $$
@ShaVuklia my answer is that you again need to look at what I'm going to call the context - what do you want to integrate over? x, or t? Forgetting about what the function is a function of, what do you want to end up with - integrating over t gives you the change in momentum (by definition), integrating over x gives you 'work done' (also by definition)
yea well, I wasn't looking at it from a physical pov. Obviously $\int F dt$ won't yield work. I was just sort of trying to show the technical difficulties I had.
Yeah, I sleep. I'm actually not far from bed now. Drinking some tea first. Went to bed at about half past midnight last night, then woke up at 5.30 am. Don't normally do that, but anyway... It's now half-past midnight again
so finding the longest path to 1 using the collatz function where the starting number n is under 1,000,000
collatz conjecture: take a number n; if n is even, do n/2; if n is odd, do 3n+1; n will always reach 1 (this has not been proven but tested on many numbers)
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