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Slereah

07:51

Mathematica is of fairly limited use for solving PDEs, really

I can't really seem to think of any projective compactification of Minkowski space

Maybe I can check the Big List of Ideal Points in GR, maybe one of them is it

Since on its own, a projective geometry has no angles or length, I guess it may be tricky to do

But there is a projective structure, where geodesics are preserved

Which I guess relates to the preservation of collineations

Just not sure how you're supposed to get the completion of the space from there, though

Slereah

08:15

I think the trick is that the projective structure is pretty raw

It's determined by the pregeodesics, but they could be anything

They could be timelike, they could be null, they could be spacelike, no way to tell

So the completion is probably just the usual completion in the flat case, sphere at infinity

4 hours later…

Slereah

12:19

Apparently one may give back more structure to the projective space by setting some special subsets

Slereah

13:03

Let's go back to the good book

Tengri rejoices

@RyanUnger btw did you ever managed to get more pics of that thesis at your university?

2 hours later…

Ryan Unger

15:05

no, do you still want it

remind me on monday?

MethNoob

15:22

Q: Why is electric field zero in a wire with 0 resistance given nonzero voltage?

Why is electric field zero in a wire with 0 resistance given nonzero voltage and infinite charge inside a battery? It is true that for a wire with $0$ resistance there will uniform voltage across the wire. But comparing with an electron in an empty space it seems to be different. Imagine in a spa...

Ohm's law

Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equation that describes this relationship: I = V R , {\displaystyle I={\frac {V}{R}},} where I is the current through the conductor in units of amperes, V is the voltage measured across the conductor in units of volts, and R is the resistance...

Ohm's law holds for circuits containing only resistive elements (no capacitances or inductances) for all forms of driving voltage or current, regardless of whether the driving voltage or current is constant (DC) or time-varying such as AC. At any instant of time Ohm's law is valid for such circuits.

I am having doubt for the answer to that post.

1 hour later…

Slereah

16:27

I think that whole "Flags define light cone" is actually that they're defined by a null vector plus a hypersurface containing it

But in some cases it is possible to generate that hypersurface from smaller distributions

that would make more sense

I guess it's essentially defining a circle from its tangent?

sphere, anyway

Slereah

17:09

I think part of my confusion is that I'm not sure when the notation talks about an object in $TM$ and when it is in $TTM$

I think I need to diagram this out

Semiclassical

17:24

this feels like something that should be known but i'm not finding algorithms for it

i have an optical medium with some refraction profile $n(\vec{r})$. suppose I follow a light ray as it moves through this profile, starting at $t=0$ with the initial position $\vec{r}_0$ and the initial direction $\hat{v}_0$

it seems like I should be able to implement fermat's principle by some kind of forward propagation in time

4 hours later…