[AntonioLao]

This principle asserts that there is no preferred coordinate system and therefore it also implies that physical laws are invariant in any physical dimension. But still a mathematical equation for the physical phenomenon cough in 11th dimension will definitely appear complicated when compared to the same equation expressed in lower dimensions. Each additional dimension requires its unique unit vector to indicate a selectively chosen direction (from the infinite sets of possibilities). For the Cartesian 3-space, i,j,k are the unit vectors (these are selectively orthogonal vectors). For Euclidean n-space, there are n unit vectors, which can also be orthogonal vectors, strictly not really necessary, but for the 1-space, the unit vector is i and it is the same as the pure imaginary number .

[Brian Jakub]

Grand Master Antonio Lao,

Is it possible that the laws are the same in every dimension, but there is a yet unknown order to how the dimensions relate to each other,( are they parallel or are they imbedded in each other or both). And if you are working with imbedded dimensions instead of parallel, wouldn't the transformational math be different. I'm not a mathematician, but I could picture math in my schooling for engineering.

Brian

[AntonioLao]

brian,

I think we already exist in multidimensional space-time. Just look at the hierarchic structures of nucleus-to-atom-to-molecule-to-compound-to-inorganic-to-organic-to-planet-to-star-to-galaxy-to-supercluster-to-universe. The laws of physics are applicable at four distinct levels differentiated by the coupling constants of length scales. So, when we say dimensions we really mean coordinate system and the number of coordinates is then the number of dimension in that system.