Originally posted by Dollard, E. P. (N6KPH)
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I have just been reading in your symbolic representation of alternating waves ( http://www.tuks.nl/pdf/Eric_Dollard_...%20Dollard.pdf ). I read your statement above before and I wondered what you meant by that. As you can read in one of my posts just above, I do believe in conservation of energy. So, your statement of producing energy out of the square root of minus one did raise my eyebrows so to speak.
Now that I am reading your paper I see what you mean. However, IMHO you have to keep in mind what you are describing with your equations. As far as I understand now, you essentially describe propagating waves in two dimensions. When you go to a transmission line kind of model, one of them is the length of your transmission line, which is also the propagation direction of your wave(s). The other one is your complex wave model, which only describes part of reality, cause physical reality is in 3D, of course. So, what your model describes is a complex 2D surface projection of phenomena that actually occur in 3D space.
And therefore, what you call "reactive energy" which is "imaginary" and therefore "not real" is very real in 3D reality. It is not imaginary at all, it literally flows in dimensions that are not part of your 2D complex model. It flows in the 3D reality of which your model only describes a 2D projection!
Let's illustrate this with an example. When you throw a rock in a pond, you get 2D transverse waves on the surface of the pond. However, in 3D reality these are longitudinal waves underneath the surface as well as in the air above the surface. There are no transversal waves inside 3D reality fluid/gas media, they are at the boundary of two adjacent media, while most of the energy flows under the surface by means of longitudinal waves. So, when you only describe the transverse wave you totally ignore the energy contained in the longitudinal waves that are hidden under the surface (literally in this example), unless you include a "projection" of that 3D phenomenon in your 2D model using an "imaginary" component in your wave model.
And that is essentially what you do with complex math. It's in essence a trick to take two (mathematical) dimensions together into one equation.
So, it may seem that you can produce energy out of a non-existing imaginary energy field, that is just an illusion which is the result of the limitations of your 2D model. The energy you can "produce" that way does not come out of the square root of one. It comes out of the real 3D energy floating around in space, of which your model literally only scraps the surface.
Now please don't take this wrong, your model and work is really awesome and goes far beyond anything you can find in the University textbooks these days.
I just can't live with the idea of "producing" energy out of a non-existing "imaginary" component. I mean, just look at how Einsteinians managed to screw up with "virtual particles", "dark matter" and God knows what.
Really, you don't want to go there!!
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