controlgroup

@TobiasFünke Just a particular shape, it's sort of like a polar harmonic but not

Very pretty function that I enjoyed graphing

there we go

Can't get the image to upload right

@Feynmate Whatever the opposite of spinors is

Had a thought -- in the proton + boron-11 to three-alpha-particle fusion process, is there an intermediate carbon-12 nucleus that immediately fissions into three helium nuclei? that at least preserves proton/neutron count (not necessarily conserved but whatever) -- or does the proton just immediately fission the boron nucleus

probably just its own fundamental force

@SillyGoose maybe 1:2 depending?

@ACuriousMind and now my nightmares will be almost-entirely hairy metal, thanks for that

@DanielSank if I am not mistaken it is a tone marker of sorts

@TobiasFünke I have seen many episodes of it but have not watched it in a while

*and Google Chrome

@SirCumference I was just able to download the version successfully on Windows 11

Quite possible. Set $f(x,y,r)=x^2+y^2-r^2$ and then this becomes $\int_\infty^\infty f(x,y,r)\,\text dx$ which can be solved immediately

I'd imagine that unless $r^2=y^2$ it would be zero, and one otherwise

as in $\int_\infty^\infty \delta(x^2+y^2-r^2)\,\text dx$?

The post itself seems fine though

and I thought it was pretty elementary that a system can evolve unitarily while a subsystem might not necessarily do the same?

@TobiasFünke they do

@PM2Ring Congratulations to the Parker Solar probe for, again, getting the #1 spot for Worst Job Missing the Sun

obviously these spaces are not simply connected, but is there any way to do a consistent coordinate mapping of a space with handles in some sense?

@RyderRude if it is or isn't marked, regardless, you can't draw a finite causal chain to show why, so the situation doesn't exist

@Blue A meter and a number around 3 feet both "represent" the same concept. They're just different units. The units don't matter, the quantity does.

Time is, at best, a really really good model of how the Universe works. Yes, it could just be a construct, or not really exist at all, or whatever, but the model works nonetheless.

I have no idea what youre referring to

"DO NOT INVEST IN THE UNREGULATED <anything>" and "DO NOT INVEST IN THE SPACEX <anything>" also work, depending on conditions

@ErinAnne I just saw the video. I hope everyone near the launch site is ok given that that's 330 tons of liquid methane

@TopMath "It does not matter if Ohm's law is nonrelativistic." -- Yes, it does. Try and apply a classical theory to the realistic atom, and you get absurdities, because you're applying a law outside its domain of applicability. The same goes for Ohm's law. I can't help you if you're just pointing out that category errors produce paradoxes.

But it cannot describe the circuit because the circuit is on a scale where relativity matters. I don't know how to help you if you're going to continually insist that I and everyone else are wrong and you are somehow right. Think like this: replace the wire with a beam of light, the bulb with a solar panel, and the battery with a lamp (this is almost identical in physics). Do you not expect there to be a delay between the lamp turning off and the solar panel stopping power generation?

@TopMath You should note that Ohm's law is nonrelativistic. You shouldn't expect nonrelativistic equations to apply to relativistic situations, e.g. where speed of light delay is relevant. The Schrodinger equation for example is not relativistic and thus breaks down when describing relativistic particles.

I would imagine that, as current begins to flow at ~lightspeed upstream, yes, things immediately upstream will be affected sooner than things immediately downstream. Perhaps my electronics logic is wrong...

Yes, sorry, that is also correct; didn't realize that's what you meant, but yes there will be a response just based on geodesic distance.

In the case of a realistic switch and bulb you'd be transferring power through an electric field restricted to the inside of a conductor (mostly, since parasitic electromagnetic fields might exist), so it will be dependent on distance through conductor

(Through the wire, yes -- e.g. the bulb and switch could be a meter apart but if the wire does a spiral with a length of a lightminute in the interim it would take a minute for the switch to toggle the wire)

@TopMath The light bulb isn't next to the disconnected area, no? So until causality catches up to the light bulb, the circuit as seen by the light bulb isn't disconnected. So there's no issue.

I highly doubt that you couldn't find the transient response Wikipedia page. Like I and others have said, you are operating from incorrect assumptions ("there is no such ... circuit where current would flow through a disconnected area.") Yes, obviously if you presuppose something wrong, you will get wrong results.

For example, in a transient circuit, which is a real thing. You not having heard of it doesn't mean it's not real, so take Prof's advice and look it up.

Why do you think a student giving a wrong answer would result in expulsion? How do you think high schools work?? And moreover, why is that last sentence at all relevant to the post?

It is not possible to measure the OWSOL. You can actually prove this. Moreover, there's no physical reason why it needs to be different from an isotropic speed of light, so it's a pointless measurement even if you could make it.

Is there a more natural choice that results in the particles being stationary?

But it has demonstrated that the particles will move apart with that natural choice though, hasn't it?

Perhaps I have been unclear in terminology, then, because I think we have disagreed on what we mean by at rest

Okay, then w.r.t. our chosen coordinate system, set it to $x,y\text{ at rest}\implies \text{for all times: }x^i=y^i$

So we have made no assumptions about the coordinates that would make them strange (e.g. the spatial coordinates being equal at all times implies being at rest w.r.t. one another, which is not necessarily an obvious condition), and yet we recover the observed recession effect from FLRW

Consider two particles at rest w.r.t. each other at different positions, and the metric is as given; then as $a(t)$ increases surely we agree that the proper distance between the particles increases as well, so both particles will begin to perceive the other as receding, yes?

Perhaps my answer was not sufficiently clear in that regard

(Or spherical, or cylindrical, ...)

You don't need to consider FLRW-specific coordinates, though, treating the metric in rectangular coordinates is sufficient to get all the same effects

As in, the Minkowski metric in those coordinates may not be trivial/it may not be related to rectangular/spherical/cylindrical coordinates trivially