It depends which metric definition are you using. The one I wrote is a pseudo-Riemannian metric that is not positive defined.
Normally physicists use that generalized metric definition because spacetime in most cases has a metric signature of (-1, 1, 1, 1). Points with zero distance are not necessarily the same point, they just are in the same null geodesic.
You can make something like this properly by defining a different metric. For example with metric dl2 = dx2 - dy2 the vector (1, 1) has length 0, so you can make a "triangle" with sides of lengths 1, -1 and 0.
Yes, but that would be a lot less efficient. With a dielectric mirror you can get easily 99.9% of the maximum momentum gain from the light, while with a solar powered laser you would get for the emission the compounded efficiency of the solar panel + storage + laser, so way below 10%. So you would gain around 10 times more impulse from your solar panel absorbing light than from the actual laser.
The final momentum gain is a bit different as the maximum you can gain from a photon is double its momentum (because you can reflect it back with opposite direction).
Nowadays people use radical in political terms as another word for extremist, but it used to mean going to the root causes. Equality and justice, or the lack of, are the root of many political issues. So you are radical in a way, but that is good.
She definitely knew what she was doing. Carini is a policewoman with connections to the Italian alt right. She was paid 50k after the match by the IBA, the ones that disqualified Khelif in 2023 after winning the gold.
That should be an approximation. To get exactly pi the range of both integrals should be from minus infinity to infinity like this.
It's the integral of the 2D Gaussian, which is fairly known.
You can always buy a second hand one