I suppose "we just need anti-gravity" is equivalent with "we just need to violate energy and momentum conservation".

It could also mean: We only have to feed the escape energy of the rocket itself into the rocket while it is on the ground, and without also carrying fuel upwards.

The “anti gravity” was just zero altitude momentum all along. Just use that big washing machine thing. Can’t stick humans in it though :-(

> The question is how much power the anti-gravity requires.

This is essentially a case of "draw the rest of the owl".

I would assume (with good reason) that the amount of energy needed to generate a counter to the gravitational field would be the same as the amount of energy required in thrust to do the same thing.

Still, having a drive that doesn't need to push stuff out of its back would be very interesting, IMHO - even if it doesn't work out better energy-wise.

Gravity is the shape of spacetime. Why would antigravity be a thing.

Can be a defect in spacetime. See: https://arxiv.org/abs/1803.09736

Alcubierre drive essentially changes the shape of spacetime, doesn't it?

Everything (that has mass or energy) changes the shape of spacetime.

Sure, my point is that the changes made with Alcubierre drive are controllable.

Not really. The Alcubierre "drive" is closer to a "shape", a static solution to Einstein's equations. There is no proposed device that actually achieves this shape. The only idea along those lines implies a kind of Alcubierre railroad - you set up a path of negative mass matter (which almost certainly doesn't exist) and then move this with regular means as the ship is approaching, thereby continuing the bubble for the ship.