My further discourse with Ed and Ivor last night has resulted in the following message from Ed.
your yesterday message to Ivor makes me consider once again the mathematical equations Ivor introduces in his paper “The Heaviside Signal”. I concentrate on the equation c(dE/dx) = dE/dt in Appendix 1 (ignoring the ” – ” on the right side). This formula is constructed by interpreting the propagation of a voltage step in space (first diagram) and in time (second diagram) as a velocity v of motion in the direction of time, v = dx/dt, that is, a vector quantity. In the diagrams, this velocity v is symbolized by the letter c. With dx/dt = v the equation c(dE/dx) = dE/dt results in c = dx/dt = v. This asserted equality of c and v then insinuates that the voltage step would really “travel” in space and time with a vector velocity v = c in the direction of time. As I see things, the equation v = c is mistaken, since v is a vector quantity, which c is not. c is a scalar, as is proven by the Poynting vector E when put over p, resulting in c: E/p = c. Vector E over vector p = mv; v is a vector, c is a scalar quantity. Q.e.d. So c does not symbolize some velocity of some motion in the direction of time. What else does this factor mean, as it is undoubtedly a quotient of a quantity of space, L, over a quantity of time, T, c [L/T] ? If you draw a diagram of Cartesian coordinates, space L in the vertical axis, time T in the horizontal, and you put the elements of space, L, over the elements of time, T, you get the constant quotient [L/T] to characterize the diagram as its parameter, or “grating constant”. Evidently this constant is not a vector, but a scalar. This shows that not every quotient dx/dt [L/T] represents a velocity of propagation in time, as the vector v does it. Rather it may be the case that such a quotient, the more if it is a constant (!), just represents the parameter of the space-time frame of reference wherein an observed phenomenon like the above-mentioned voltage step takes place. And this takes us into the middle of our finding that Poynting’s energy vector E = pxc differs from the classical scalar energy E = mv^2/2. This difference, as we can see now, is a consequence of not distinguishing between velocity v (vector, and variale), and the scalar constant c. Do you agree?
To which I have replied the following:
I am afraid I disagree with your conclusion that c coming out of the analysis of c(dE/dx) = dE/dt in Appendix 1 is a vector!
You raise a metaphysical story around it I am afraid.
This c is a constant coefficient. c is not a vector – its scalar.We have vectors around it dE/dt and dE/dx. These are vectors – one is force (or power in modern terms) and the other is momentum (as we agreed with you before).
Full stop here!
Then, we should acknowledge the fact that there is a physical element behind this c – and this is energy current, which emanates in the universe from its Big Bang!
This is the carrier of interactions in Nature. This wasn’t known to Artistotle, Galileo, Newton, Maxwell … Ivor was and is the first to give this carrier the appropriate place.
If you had known a bit of the physics of communication (I recommend you to read Hans Schantz papers and book for that) you’d realise that its completely natural for communication (or interaction for that matter) to have a carrier – and this carrier for ExH does not need massed matter – it can perfectly well live in vaccuum.
That’s my take on this. You played an important role in this discourse. We have identified what momentum is in Catt’s theory and Heaviside Signal. Eureka!
What I have also discovered thanks to Ivor is the potential way for future computing – which is based NOT on envelope characteristics – such as exponentials and sines, but on discretised steps – this can potentially give way to improving the speed of computations by 2-3 orders of magnitude – we just need appropriate devices to support this speed and react to changes transmitted in energy current. I am already working on this!!!