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Light is a scalar. This is the reason we talk about the speed (scalar) of light. This is al;so the reason the Michelson-Morley Experiment was a deemed a failure, though it was a success. M-M assumed as did most scientists that light was a vector and would compound like a vector. When light had the same speed in all directions, which a vector would not do, the experiment was said to fail, when in fact it succeeded in showing light to be a scalar. What failed was the expectations of the experimentors and rather accept that light was a scalar they invented the shrinking of space in the direction of motion.
Light is related to the fourth dimension of Quaternion Space:
Q= r +Ix +Jy +Kz
where I, J and K are vectors and the scalar is r=ct where c is the speed of light and t is time. Light c is related to the real scalar distance r=ct.
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A scalar times a vector is a vector.
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