(December 24, 2022 at 1:25 pm)LinuxGal Wrote:(October 25, 2022 at 8:51 am)polymath257 Wrote: For compact spacetime (finite, negatively curved), this is possible and gives a 'total energy' of zero. For non-compact space, this is still a problematic thing.
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.
