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I have been reading that the quantity called "Weyl curvature" can exist independently of any matter, or energy, in the universe?

This seems to contradict Heisenberg uncertainty which says there can be no 100% vacuum, because uncertainty in position and uncertainty in momentum must be greater than zero:

Mach's principle seems to say that the distribution of matter-energy determines the geometry of space-time, and if there is no matter-energy then there is no geometry.

The Weyl tensor vanishes for a constant curvature if there are no

tidal forces. So it appears that a Weyl curvature, which is described

as 1/2 of the Riemann curvature tensor[where it is split into two

parts, the Ricci tensor and the Weyl tensor] is dependent on

matter-energy -"existing" in the universe also?

Thanks for the help.

This seems to contradict Heisenberg uncertainty which says there can be no 100% vacuum, because uncertainty in position and uncertainty in momentum must be greater than zero:

**DxDp >= [Planck's constant]/[2*pi]**Mach's principle seems to say that the distribution of matter-energy determines the geometry of space-time, and if there is no matter-energy then there is no geometry.

The Weyl tensor vanishes for a constant curvature if there are no

tidal forces. So it appears that a Weyl curvature, which is described

as 1/2 of the Riemann curvature tensor[where it is split into two

parts, the Ricci tensor and the Weyl tensor] is dependent on

matter-energy -"existing" in the universe also?

Thanks for the help.

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