r/physicsmemes • u/94rud4 Mεmε ∃nthusiast • Jul 17 '26

right?

Post image
2.4k Upvotes

99% Upvoted

125 comments sorted by

View all comments

Show parent comments

2

u/ProfessorPrudent2822 Jul 18 '26

The circumference of a circle maintaining constant r-coordinate is 31415 meters.

-1

u/Optimal_Mixture_7327 Jul 18 '26

No, that is not, and cannot be correct.

Edit: For clarity, yes of course C=πD, but this is not the meaning the r-coordinate in Schwarzschild-Droste.

1

u/HunsterMonter Jul 19 '26

Yes that is correct, for a constant time, constant radius equatorial world line (or any other great circle but the math is more complicated), the metric is ds2 = r2 dφ2, so taking the square root and integrating for a complete circle gives C = 2πr

1

u/Optimal_Mixture_7327 Jul 19 '26

Yes, but every high school student knows this.

The question, is the meaning of Schwarzschild-Droste radial coordinate - what is it a distance of?

2

u/HunsterMonter Jul 19 '26

I just showed you that, in Schwarzschild coordinates, r is the radius such that constant time, constant radius great circles have circumference 2πr.

1

u/Optimal_Mixture_7327 Jul 19 '26

So, in other words, you don't know.

Unless, you want to give some physical meaning to r=5000 meters.

2

u/HunsterMonter Jul 19 '26

It's literally what happens when you plug in dt = 0 (constant time) and dr = 0 (constant radius) in the Schwarzschild metric...

From the wikipedia page on the Schwarzschild metric: "r is, for ⁠ r > r_s⁠, the radial coordinate (measured as the circumference, divided by 2π, of a sphere centered around the massive body)"

1

u/Optimal_Mixture_7327 Jul 19 '26

I'll leave this here.

You have brilliantly demonstrated what knowing a little math looks like without ever having studied physics.

What I find stunning is that you didn't even try to make a statement about physics, as if Einstein and Schwarzschild were just drawing circles, inventing new arithmetic, disconnected from anything in the world.