orthogonal reflection

[AntonioLao]

In any physical dimension, four successive orthogonal reflections (ORs) complete a cycle of a rotational transformation thus implying a rotational invariance. This type of invariance cannot be used to distinguish between clockwise or counterclockwise rotations. This raised the reality question between an object and its image behind the imaginary mirror in a four dimensional space-time continuum. This is similar to the reality between matter and antimatter. At the local infinitesimal domain (LID), it can be conjectured that all local infinitesimal motion (LIM) exhibit these types of OR. Moreover, a theory of quantum space-time at the level of LID can be formulated using the LIM of squares of energy.

Consequently, if the imaginary mirror planes are not orthogonal then the result affected the minimum number of Ors needed to reach rotational invariance. Analogous to entropy, this number can only increase. These imaginary mirror planes are equivalent to the axes of symmetry of regular polygons. For a regular equilateral triangle, there can be three axes of symmetry. The angle of rotational invariance is 120°. For a square the angle of rotational invariance is 90° for two possible axes of symmetry. For a regular pentagon there are five axes of symmetry and the angle of rotational invariance is 72°. It seems that the number of axis of symmetry increases as the number of sides of the regular polygons increases. However, for reflection only one axis of symmetry is needed to reach reflection invariance assuming parity is conserved between left and right which are fundamentally equivalent to a partial state of directional invariance. Surprisingly, although one axis of symmetry is needed for reflection invariance of the circle, it is not necessary if the circle is reflected about its center. This is analogous to the existence of a big bang singularity. On the other hand, the angle of rotational invariance for the circle is exactly zero. Since a point of a big bang singularity and any arbitrary circle are both reflection and rotation invariance, it is preferable to use the circle for formulating physical theory because of its embedding orthogonality of circumscribing a unit square lattice of the quantum space-time continuum.

[mkirkpatrick]

"Oh" to see ourselves as others see us! What sort of reflection would we see,and would it cause us shame?

"LIFE" reflects in on itself and "appears" as energy, we are
life too,but looking for energy is our unfolding task,as we
open up as a bud before the rising sun,we then reflect more of the life potential embedded within us.



regards michael.