Cause and Effect in Mathematics

Cause and Effect in Mathematics

Electromagnetic theory grew out of the perusal of such things as magnets, electrically charged bodies and the rest. This led to such concepts as electric charge and electric current, electric field and magnetic field. Much later, dubious mathematics was applied to such steady state things by Maxwell, expanding a little to slowly changing "electric currents" and thence to displacement current, the latter deriving from theoretical problems with slowly changing electric current and the capacitor. Displacement current led to the idea of sunlight as electromagnetic.

During this development of electromagnetic theory, there were no rapidly changing fields, and no electromagnetism travelling very fast, for instance at the speed of light.

Now supposing, instead of with static fields and devices such as stationary magnets, we had started with sunlight, which we have always known about. Had we had the appropriate instruments, we would have found out, if it was not already obvious, that sunlight was two dimensional energy, and travelled in the third direction at the speed of - light.

In the early case of Maxwell, the TEM Wave, or light, is the result of much mathematical manipulation, starting with magnets, electrically charged bodies and the like.

Now all this mathematical manipulation from electricity and fields to light is reversible, since mathematics ignores causality, or even direction in its equations. Since we know about sunlight (and monocromatic light), it is equally legitimate to start with sunlight, or the TEM Wave, and work backwards through the same mathematics towards electric field, magnetic field, electric charge and electric current. Only a historical accident caused us to progress in the traditional direction.

In this case, particularly if we accept Occam's Razor, each of the items we derive mathematically have to justify their existence as physically real, rather than merely the results of mathematical manipulation of things which really are physically real. It turns out that, in electromagnetic theory, electric charge and electric current remain merely mathematical manipulations of what went before from our starting point of light, or the TEM Wave. In the case of a battery connected by two wires to a resistor or lamp, they have no function. This is proved by "The Catt Question" and the dubious, contradictory "answers" to the Question by leading experts. We see that "electricity" is not quick enough to do the job in hand. This can only be done by the original sunlight, or TEM Wave, which has the necessary speed to get the energy from battery to lamp. This energy travels from battery to lamp at the speed of light.

Now we come to the difficult bit. It is pretty clear that the concept of electricity as perceived today started its life in the above role, of helping a battery to heat a resistor or light a lamp. I think that rubbing a glass rod with cat's fur only played a subsidiary role in the origins of "electricity". What are the other, surviving roles for "electricity" in today's science? I can think of the Bohr atom and the cathode ray tube.

The Bohr atom. Part of its role is to supply the "electrons" which expedite the flow of "electricity" from battery to lamp. But this role is discredited by "The Catt Question" . However, surely other roles remain today for the "electrons" in the Bohr atom.

The Cathode Ray Tube (CRT). First, a digression. My co-author the late Dr. Arnold Lynch told me he was giving the keynote speech in the IEE to celebrate the centenary of J J Thomson's discovery of the electron. When I asked him why he was chosen, he replied, "Because he told me about it." Now in Heaviside's "Energy Current" approach to electromagnetic theory, the energy current, or TEM Wave delivered by the HT power supply approaches the CRT sideways between cathode and anode, or in the case of the signal input, between the cathode and the grid. The movement is at right angles to the alleged movement of the "electron". Now the interaction between the TEM Wave arriving as "HT" and the TEM Wave arriving as "signal" is complex. However, since they collide at 180 degrees, their collision should be handled to some degree by the discussion in my book. However, the detail still has to be worked out. When we address the electron in the CRT, apparently travelling in the wrong direction at the wrong speed, it is useful to consider a wave in the sea sea approaching us. White foam on top of the wave appears to travel at a lower speed at right angles to the approaching wave.

Tradition

In case it should be feared that the transition descibed above moves us from a secure foundation to uncertainty, an analysis of the slovenly way in which the journey from "electricity" and fields to light was made, is called for. This is to be found at "Maxwell's Equations Revisited" and "The Hidden Message in Maxwell's Equations" . My article "The Heaviside Signal" discusses how academia cleave to two mutually contradictory versions of the TEM Wave and light, mostly keeping to the false "Rolling Wave". The flaw in "The Rolling Wave" is concealed by general ignorance about the relative phases of the E field and the H field. When we keep to the truth, that they are in phase, "The Rolling Wave" collapses.

Ivor Catt December 2008