Extra dimensions are not a prerequisite for understanding gravity's effects on space, as established by mathematical principles. The discussion highlights that a hyperplane can be intrinsically curved without the need for additional dimensions, countering the notion that gravity requires extra dimensions to warp space. Brian Greene's commentary suggests that while extra dimensions are a popular concept in string theory, they are not essential for explaining gravitational phenomena. This distinction is crucial for comprehending the foundational aspects of theoretical physics.
PREREQUISITESTheoretical physicists, mathematicians, and students interested in the foundations of gravity and string theory will benefit from this discussion.
Mathematically it is not necessary to introduce extra dimensions because a hyperplane (which is just a multi-dimensional plane) can be intrinsically, as opposed to extrinsically curved.tnadys said:But if gravity warps space doesn't it need another dimension to warp into?