{"id":435,"date":"2019-09-13T15:08:50","date_gmt":"2019-09-13T14:08:50","guid":{"rendered":"https:\/\/blogs.ncl.ac.uk\/alexyakovlev\/?p=435"},"modified":"2019-09-13T15:08:50","modified_gmt":"2019-09-13T14:08:50","slug":"is-energy-current-and-speed-of-light-vector-or-scalar","status":"publish","type":"post","link":"https:\/\/blogs.ncl.ac.uk\/alexyakovlev\/2019\/09\/13\/is-energy-current-and-speed-of-light-vector-or-scalar\/","title":{"rendered":"Is energy current and speed of light vector or scalar?"},"content":{"rendered":"

Yesterday, Ivor Catt effectively questioned whether it matters at all whether energy current, and its velocity, is a vector or scalar:<\/p>\n

”\u00a0ExH<\/b><\/span><\/span><\/span>: \u201c<\/span><\/span><\/span>ExH<\/i><\/span><\/span><\/span>\u00a0was the primitive …\u00a0<\/span><\/span><\/span>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<\/i><\/span><\/span><\/span>.\u201d Malcolm Davidson\u00a0<\/span><\/span><\/span>”<\/p>\n
Perhaps Malcolm made a mistake here. None of us is perfect.<\/div>\n
I prefer to not talk\u00a0about\u00a0vectors and scalars. In our book, we never mentioned them.\u00a0http:\/\/www.ivorcatt.org\/digital-hardware-design.htm<\/a>\u00a0. I have never mentioned them in any of my articles, including these;\u00a0http:\/\/www.ivorcatt.co.uk\/x18j1.htm<\/a><\/div>\n
I wonder\u00a0if anyone will venture that in that case, our writings (and seminars) are valueless. I suggest none of us three ever mentioned vectors and scalars in the seminars we gave for ten years.\u00a0http:\/\/www.ivorcatt.co.uk\/43.htm<\/a>\u00a0. We earned a lot of money for ten years not mentioning vectors or scalars.<\/div>\n
Seminars called “Digital Electronic Design Seminars” and no mention of vectors or scalars! One of us is called Dr. David Walton! Earlier he worked in Dublin with Nobellist Walton (no relative).<\/div>\n
I should finally mention that I do not object to anyone using the words. The above is just a smokescreen for my co-author Malcolm. The three of us spent decades designing digital electronics, and became quite sophisticated designing high speed digital systems.. None of the engineers I worked with in the UK and USA ever mentioned vectors or scalars.<\/div>\n
When\u00a0 I was Principal Lecturer in a college, I never mentioned vectors or scalars. Nobody else did either.<\/div>\n
Ivor Catt<\/div>\n<\/div>\n
<\/div>\n
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++<\/div>\n

Today Malcolm Davidson wrote in response to Stephen Crothers:<\/p>\n

Hi Stephen,<\/div>\n
<\/div>\n
You stated;<\/div>\n
<\/div>\n
\n

ExH<\/b><\/span><\/span><\/span>: \u201c<\/span><\/span><\/span>ExH<\/i><\/span><\/span><\/span>\u00a0was the primitive …\u00a0<\/span><\/span><\/span>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<\/i><\/span><\/span><\/span>.\u201d Malcolm Davidson<\/span><\/span><\/span><\/p>\n

If Malcolm means by ExH a cross product, the cross product\u00a0<\/span><\/span><\/span>x\u00a0<\/b><\/span><\/span><\/span>only has meaning when operating on vectors. Both\u00a0<\/span><\/span><\/span>E\u00a0<\/b><\/span><\/span><\/span>and\u00a0<\/span><\/span><\/span>H<\/b><\/span><\/span><\/span><\/p>\n

are vectors. The cross-product of two vectors is a vector that is orthogonal to both vectors, such as\u00a0<\/span><\/span><\/span>E\u00a0<\/b><\/span><\/span><\/span>and\u00a0<\/span><\/span><\/span>H<\/b><\/span><\/span><\/span>, and, by the<\/span><\/span><\/span><\/p>\n

right-hand rule, points in the direction of one’s thumb when one’s fingers curl from\u00a0<\/span><\/span><\/span>E<\/b><\/span><\/span><\/span>\u00a0to\u00a0<\/span><\/span><\/span>H<\/b><\/span><\/span><\/span>. The magnitude of the cross\u00a0<\/span><\/span><\/span><\/p>\n

product of two vectors\u00a0<\/span><\/span><\/span>A<\/b><\/span><\/span><\/span>\u00a0and\u00a0<\/span><\/span><\/span>B<\/b><\/span><\/span><\/span>\u00a0is AB times sine of the angle between\u00a0<\/span><\/span><\/span>A<\/b><\/span><\/span><\/span>\u00a0and\u00a0<\/span><\/span><\/span>B<\/b><\/span><\/span><\/span>, the angle between\u00a0<\/span><\/span><\/span>A<\/b><\/span><\/span><\/span>\u00a0and\u00a0<\/span><\/span><\/span>B<\/b><\/span><\/span><\/span>\u00a0being that which\u00a0<\/span><\/span><\/span><\/p>\n

is less than or equal to 90 degrees, A and B being the magnitudes of the vectors\u00a0<\/span><\/span><\/span>A<\/b><\/span><\/span><\/span>\u00a0and\u00a0<\/span><\/span><\/span>B<\/b><\/span><\/span><\/span>\u00a0respectively. Hence the magnitude\u00a0<\/span><\/span><\/span><\/p>\n

of the Poynting vector is EH, since\u00a0<\/span><\/span><\/span>E\u00a0<\/b><\/span><\/span><\/span>and\u00a0<\/span><\/span><\/span>H<\/b><\/span><\/span><\/span>\u00a0are orthogonal to one another.<\/span><\/span><\/span><\/p>\n

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!<\/span><\/span><\/span><\/p>\n

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\u00a0 has it’s own coordinate system built in I cannot think of where we would apply the basic rules of vector algebra.<\/span><\/span><\/span><\/p>\n

Any thoughts? Also is it useful ? If I take two microwave beams . at say 45o<\/sup>\u00a0angle how do the E & H fields add up to the scalar value that could be measured. anyway thanks\u00a0for keeping me honest!<\/span><\/span><\/span><\/p>\n

Regards,<\/span><\/span><\/span><\/p>\n

Malcolm\u00a0\u00a0<\/span><\/span><\/span><\/p>\n<\/div>\n

My response to that was:<\/p>\n

Hi Malcolm,<\/em><\/p>\n

I agree with you, likewise I agree with Stephen. The\u00a0notions 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\u00a0 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\u00a0makes 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.<\/em><\/p>\n

Kind regards<\/em><\/p>\n

Alex<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"

Yesterday, Ivor Catt effectively questioned whether it matters at all whether energy current, and its velocity, is a vector or scalar: ”\u00a0ExH: \u201cExH\u00a0was the primitive …\u00a0By definition, I think it is a scalar. It cannot be a vector because there … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":4763,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[16,12,1],"tags":[],"class_list":["post-435","post","type-post","status-publish","format-standard","hentry","category-causality","category-electromagnetism","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/blogs.ncl.ac.uk\/alexyakovlev\/wp-json\/wp\/v2\/posts\/435","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ncl.ac.uk\/alexyakovlev\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ncl.ac.uk\/alexyakovlev\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ncl.ac.uk\/alexyakovlev\/wp-json\/wp\/v2\/users\/4763"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ncl.ac.uk\/alexyakovlev\/wp-json\/wp\/v2\/comments?post=435"}],"version-history":[{"count":1,"href":"https:\/\/blogs.ncl.ac.uk\/alexyakovlev\/wp-json\/wp\/v2\/posts\/435\/revisions"}],"predecessor-version":[{"id":436,"href":"https:\/\/blogs.ncl.ac.uk\/alexyakovlev\/wp-json\/wp\/v2\/posts\/435\/revisions\/436"}],"wp:attachment":[{"href":"https:\/\/blogs.ncl.ac.uk\/alexyakovlev\/wp-json\/wp\/v2\/media?parent=435"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ncl.ac.uk\/alexyakovlev\/wp-json\/wp\/v2\/categories?post=435"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ncl.ac.uk\/alexyakovlev\/wp-json\/wp\/v2\/tags?post=435"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}