Page 9 "The change in the size of the unit with the number of dimensions is unknown in our experience."
Might be unknown in legacy science, but it IS known in the RS. Outside the time region, the numerical value of displacement represents the TOTAL displacement, whereas inside the time region, the numerical value represents only that part of the displacement. This “unknown” may have to do with the additive properties of displacement inside the time region. For example, compare the first 5 speeds in these regions:
t-s region = 1, 2, 3, 4, 5…
t region = 1/1, 1/1+1/2, 1/1+1/2+1/3, 1/1+1/2+1/3+1/4, 1/1+1/2+1/3+1/4+1/5…
This may also work for the temporal dimensions... I’ve been treating the temporal dimensions as three independent, polar dimensions, and this may not be the case. Consider the possibility of dimensions “wrapping” around one another within the time region, such as what Xiaodong Chen came up with, using three temporal dimensions to do a quantum model. (See “Modified Kaluza-Klein Theory, Quantum Hidden Variables and 3-Dimensional Time”):
Quote:
If this is the case, we may view temporal geometry a bit differently than expected from a purely polar-Euclidean system:Now let’s try to understand spin. As we see in 6-dimensional time-space metric of 0-spin particle, 5th dimension is diagonal. There is no components between 4-dimension and other dimensions. In time-space metric of 1-spin particle, 5th dimension wrapped around 4 dimensional time-space, no components between 5th dimension and 6th dimension. In time-space metric of 1/2-spin particle, the time-space geometry become more complicate, 5th dimension wrapped around all other 5 dimensional time-space. In our knowledge of 4-dimensional world, if an objects moves around some space dimensions, it is a rotation movement. It is reasonable to interpret that the spin is the particle rotating the other dimensions through 5th dimension.
1d (Chen 4th) = 1/1 (linear, spin-0, “beyond atomic zone”, thermal vibration)
2d (Chen 5th) = 1/1+1/2 (single rotation, spin-1, atomic zone, energy levels, “C” in A-B-C notation)
3d (Chen 6th) = 1/1+1/2+1/3 (double-rotation, spin-1/2, nuclear zone, “A” and “B” in A-B-C notation)
Chen is suggesting that what we view as “rotational” and “rotational vibration” would just be the addition of temporal dimensions in a polar geometry, and we view spatial rotation as a direct consequence of temporal displacement from unit speed.
One of the more interesting facets of GSM's work is how imaginary roots connect unbounded and bounded states of rotation (see Section 4, p. 12).
For all ‘s’, the roots are exp(2*pi*s/n) where 0
