Rotation and Time, Part 5 – Angular Momentum and the Parity of the Universe
Since I wrote the “Afterthoughts” section, I’ve realized a couple of things about angular momentum and how it fits into my concept of a universe of five spacetime dimensions manifesting to us as four dimensions of space (one of which would be too small to detect) and one of time.
Again, I’m using a Euclidean approximation. However, angular momentum exists in other geometries also, so this may still have value.
Angular momentum is a vector arising from a rotation. Like linear momentum it is conserved. Unlike linear momentum it requires at least two spacial dimensions to exist because rotation occurs in a plane. (Measuring angular momentum or any rotational motion also requires choosing a point of reference. Throughout I have assumed that point to be the geometric center of the universe considering all existing dimensions.)
Mathematically, the direction of the angular momentum vector is at right angles to the plane of rotation. This not just a convention but an expression of the physical fact of gyroscopic resistance of a rotating body to a change in its axis of rotation. This means there is an extra dimension intrinsic to any rotation. This dimension need not be a significant part of the mass that is rotating, but it is real and must exist for the rotation to happen. Sounds a lot like time.
This implies two things.
First, the minimum number of spacetime dimensions for rotation to exist is three. That’s true of any rotation. It doesn’t have to be the whole universe that is rotating. If one spec of two-dimensional dust is rotating anywhere in a 2d universe, a third dimension must exist. Its angular momentum requires it. This could be an unobserved third spacial dimension—in which case time is a fourth dimension—or, perhaps, it’s actually time itself.
Second, if time is a manifestation of rotation, like angular momentum, the parity of the dimensionality of the universe must be odd. In my concept, some rotation must manifest a dimension orthogonal to all existing spacial dimensions. This can only happen if the number of spacial dimensions is even, because all rotations define planes. Multiple rotations, happen in or around 2d planes intersecting at a point. Generally, rotations around a unique point only happen in even numbered dimensions. The universally orthogonal time dimension would intersect that point and add one dimension to that even number, making the total number of dimensions an odd number.
NOTE – Our spacetime is not neatly divided into separate dimensions of Euclidean space plus time as noted before. That makes this discussion highly oversimplified. However, if rotation is the part of the engine of the universe that creates time, angular momentum and its gyroscopic effects could be part of the observed resistance of mass to approaching the speed of light—resistance to its motion becoming more light-like by tilting its axis of rotation.
Since we observe three spacial dimensions, the total number of spacetime dimensions (including our time) would have to be greater than that, so, as my earlier discussion also concluded, the minimum number of spacetime dimensions consistent with my model is five, and if the number were larger, it would have to be an odd number.
August 11, 2021