Alcubierre Drives require an exotic matter that has a negative mass. since E=MC^2, this is synonymous with saying it requires a substance with negative energy density,
These substances work fine in our current formulas. they do weird things, but they do work mathematically, but we have never observed one in the real world.
The weak Energy Condition is a conjecture (unproven statement) or assumption (statement assumed to be true) that the reason we never observe negative mass/energy is that it is physically impossible for any region in our universe to have a negative energy density.
so since the Alcubierre Drives use negative mass, and the week energy condition assumes no negative mass exists, they are in conflict and only 1 can exist/be true
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