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Could it be possible that the physical universe is orthogonal to the spiritual realm?
Q. Just some weird thoughts i would like to share with anyone out there who may have some ideas- could it be that the physical and spiritual universes are orthogonal to one another, and that from an observer looking in at us from the outside, both realms appear to be two dimensional? could there be (random) areas which connect the two universes, ocassionally making it possible to have so-called "paranormal" experiences? thanks guys- you're great!
Asked by fermion_gas - Sat Apr 21 17:35:51 2007 - - 4 Answers - 0 Comments

A. Actually there is some evidence that the situation you describe is false. If the people in this other dimension can "see" us, this means that photons are leaving our universe and travelling to theirs. We would notice that sometimes energy is disappearing in physics experiments or that electric forces do not drop off exactly like the radius squared. This has been measured very carefully for electrical forces. In contrast to electricity, gravitational forces have not been tested at small distances (less than a millimeter or so) so the existence of parallel universes that are very close to us and with which we can only communicate through gravitational forces has not been ruled out. This might not be the kind of spiritual realm you are… [cont.]
Answered by b_physics_guy - Sun Apr 22 05:22:46 2007

How do you prove that orthogonal matrices in three dimensions are either a rotation or a reflection?
Q. How do you prove that orthogonal matrices in three dimensions are either a rotation or a reflection?
Asked by Lynsey - Tue Feb 19 13:38:50 2008 - - 1 Answers - 0 Comments

A. Start out with a 3x3 orthogonal matrix A. Suppose it has determinant +1 and lets show it is a rotation. There is a real eigenvalue (because the characteristic polynomial is cubic). That eigenvalue must be 1 or minus 1, because the matrix is orthogonal. Take a unit length eigenvector u for that eigenvalue, and then extend to an orthonormal basis u, v, w of three dimensional space. (Just let v be any unit vector orthogonal to u, and let w be a unit vector orthogonal to both u and v, for example take the cross product u x v.) Now write the matrix M of the transformation with respect to the basis u, v, w. The Matrix looks like 1 0 0 0 a b 0 c d OR -1 0 0 0 a b 0 c d where the matrix P= [a, b; c; d] is a 2 x… [cont.]
Answered by okdan - Tue Feb 19 14:17:56 2008

How do you determine if a vector is parallel, orthogonal, or neither?
Q. How do you determine if a vector is parallel, orthogonal, or neither?
Asked by NewYear2008 - Thu May 8 02:10:47 2008 - - 2 Answers - 0 Comments

A. 2 vectors v, w are parallel if there is a scalar c with cv=w. this regards the 0-vector as parallel to anything, two vectors are orthogonal if their dot product is 0. if neither of these conditions hold, then the vectors are not parallel and not orthogonal.
Answered by holdm - Thu May 8 02:17:29 2008