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If we add an additional orthogonal spacial dimension, w, to the usual 3 spacial dimensions plus time, x, y, z, t, does any one know if the physics of this x, y, z, w, t -space is different in fundamental ways?

For example: suppose a hypersphere rotates around the axis w, producing an angular momentum vector parallel to w, what would be seen if our space intersected this space?

Would we see the hypersphere as spinning? If it was a hyper gyroscope and we pushed on it in our space, would the spin on the w axis that we couldn't detect affect the properties of part that intersected our space?

Is there any book about this 5-D physics?