Yesterday, Ivor Catt effectively questioned whether it matters at all whether energy current, and its velocity, is a vector or scalar:
Today Malcolm Davidson wrote in response to Stephen Crothers:
ExH: “ExH was the primitive … By definition, I think it is a scalar. It cannot be a vector because there is no directional information inherent in it. It is a single constant for the medium.” Malcolm Davidson
If Malcolm means by ExH a cross product, the cross product x only has meaning when operating on vectors. Both E and H
are vectors. The cross-product of two vectors is a vector that is orthogonal to both vectors, such as E and H, and, by the
right-hand rule, points in the direction of one’s thumb when one’s fingers curl from E to H. The magnitude of the cross
product of two vectors A and B is AB times sine of the angle between A and B, the angle between A and B being that which
is less than or equal to 90 degrees, A and B being the magnitudes of the vectors A and B respectively. Hence the magnitude
of the Poynting vector is EH, since E and H are orthogonal to one another.
I agree with everything you state above, within the conventional way we were taught, however these days I look at it from a slightly different perspective. (and of course) for all these years we discussed energy current using the phrase “The Poynting Vector!
Because we can know only the value at any one point, the direction being defined by the inherent Tx Line itself isn’t the idea of a vector superfluous? Of course I immediately think of a microwave line of site Tx & Rx system. Given that the ExH “vector” is moving at speed c and has it’s own coordinate system built in I cannot think of where we would apply the basic rules of vector algebra.
Any thoughts? Also is it useful ? If I take two microwave beams . at say 45o angle how do the E & H fields add up to the scalar value that could be measured. anyway thanks for keeping me honest!
My response to that was:
I agree with you, likewise I agree with Stephen. The notions of scalar and vector are the the kind of mathematical quagmire which puts some pseudo-strictness on our way of thinking. Of course we can take the line of reasoning where we can say, well, a scalar value is a special case of vector value, where we don’t show the direction because the direction is given by an out-of-model assumption. In that way, your reasoning about the Tx giving us such a direction removes from us the liability for (not) talking about the direction. All this is a mathematical maze in which we can be easily trapped. And here, I am on Ivor’s side – does it really matter if it is vector or scalar? The point is about the Occam – it just makes us see the everlasting ability of universe to transfer energy at c. One might ask, in what direction? the direction is defined by the way how the EM (or gravitational …) field is perturbed in some point in space and the materials (including vacuum) surrounding this point.