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m/h/p distance/ratio; q = angle to magnetic vector v ([1, 2, 3][4] from 7) A force that varies with the square of the distance means that the force will increase with the square of the distance if we reduce the distance, and it will decrease with the square of the distance if we increase the distance. As a result, this author concluded that a force that varies with the square of the distance can be considered as a conventional 1-dimensional force vector (x-axis) that is scattered into 2 additional dimensions (y, z) due to the 3-dimensional nature of space. The square power of the distance indicates the number of additional dimensions we must add to a 1-dimensional force vector in order to get the number of dimensions of the whole field of force (here, 3):
[5]
Where: N = number of dimensions of the whole field of force a = number of dimensions of the force vector (usually 1) n = power, the force varies with the distance (in this case, 2)
In the above case: N = a + n => N = 1 + 2 = 3. This means, a 1-dimensional force vector varies with the square of the distance in a 3-dimensional space.
In an analogous way, a force that varies with the fourth power of the distance (Casimir force) can be considered as a 1-dimensional force vector that is scattered in a 5-dimensional space (N = a + n => N = 1 + 4 = 5). Therefore, it is evident that the field that originates the Casimir force is a 5-dimensional field, i.e. that it is in fact a hyperspace field that produces the corresponding effects in our 3-D universe.
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