(December 25, 2022 at 10:32 am)polymath257 Wrote:(December 24, 2022 at 1:25 pm)LinuxGal Wrote: The cosmological constant corresponds to a non-zero vacuum energy, which causes an acceleration in the expansion, and the total of this energy is integrated over the (increasing) volume of the universe. Money for nothing and chicks for free.
Once again, the problem is that energy is NOT a scalar quantity. It is one component of the four-dimensional energy-momentum vector. As such, it simply doesn't have a well-defined value at each point. Even observers moving at different speeds will measure the energy of an event as different. For a flat spacetime, this can be resolved frame-by-frame. When curvature effects are also brought in as well, you can't even make a common frame of reference at different points.
In the case of dark energy (old school, the cosmological constant), the easiest local frame to use is the co-moving frame. And, in that frame, it represents a type of energy density of the vacuum. But that doesn't allow to 'integrate over the volume' to get a meaningful answer.
Sorry. It was a good idea, but the details simply don't work that way.
Well, it also fails for perfectly practical reasons: If your source of energy is the lowest energy state of the universe, then you've got nowhere to dump your waste photons and take advantage of the differing quantities of degrees of freedom to do work. This seems to elude the folks with pi in the sky notions of tapping "zero point energy".
