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Decoding Ed's Writings
The Original System of Maxwell's Equations: Is it Consistent and Self-sufficient?
edited October 29
The methods of LeGrange feeds through to Einstein by two routes. The first route is through Hamilton and through his quaternions. Hamilton produced the quaternion algebra which was readily adopted by Maxwell in the early days.The second way was via Grassmann whose early work the Ausdehnungslehre was adopted by Peano and Peano was responsible for Levi and Ricci development of tensors.
LeGrange's method was simply to sit down all the variables of a situation or a system and then to set up constraints upon those variables and see what system was produced by those constraints. That LeGrange was able to derive the Newtonian laws in a different way which revealed the symmetry and also the underlying assumptions have been made.
When Hamilton provided his quaternion algebra Maxle was very pleased because it was a way of dealing with the complex relationship between variables that work in rotation within his systems. However there was some deep indeterminacy in using these methods, and a careful account of the sign was always necessary and very difficult to track. In addition Hamilton had made some simple mistakes in assuming that the angle that was being discussed in a rotation was the angle that his formulas actually depicted. It turned out that in fact is angles with twice the angles that were being depicted and that was not realised until Rodrigueuz work was brought forward and half angle measures of rotation were established.
This situation did not affect the Grassman version of the algebraic geometry that was being established in this time. And indeed games used Grassman's version to establish a form of vector algebra that became supported by Lord Kelvin and which was used to supersede the Hamiltonian vector algebra and the quaternions.
Meanwhile Levi and Ricci using Peanos work developed the tensor description of forces and also geometries in space
Newton was a Pythagorean or of the Pythagorean school and at the time Euclid who was also the chief proponent of the Pythagorean School in Alexandria was being discredited as being outmoded out of date with modern understanding of geometry . But he Had successfully established the use of geometrical forms and figures to represent the quantities of force and of energy.
So Einsteins bold new idea was simply to replace the Euclidean geometry with the established none Euclidean geometry of his day.
However we now know that the none Euclidean geometry is a fiction. The Euclidean geometry which was depicted it as being flat was in fact the geometry of our space. The use of four dimensions was sufficiently radical to move the Cartesian coordinates system into a non-Euclidean John geometrical situation. From that position using a mint Kowski geometry and Levi and Ricci notation Einstein was able to depict a non-Euclidean geometry as a system of gravitational forces.
Space time then is this none Euclidean geometrical form of the gravitational system. However the form of the gravitational law which Newton derived is equally valid for both Electro static and electro magnetic as well as magnetic forces. Therefore I understand equations do not depict a system of gravitational forces only but every known force to man whether it be nuclear or whether it be electrostatic dielectric these forces are all covered under the Einstein system of representing forces by a non-Euclidean geometry.
Both Newton Einstein's systems lacked a medium for propagating these forces throughout the space. In fact when the new attempted to deal with the fluid dynamic version of his system he came up with immense calculation difficulties which led him to simplify to the extent where it became an usable unusable. system.
Although space-time has many aether like properties, it is not usually represented in a aeher like form. Rotation within the aether is very obviously missing
Maxwells attempt to use the rotational dynamics of the vortex as a basis of his explanation of electricity and magnetism failed because number one he didn't understand the quaternion algebra well enough and number two Lord Kelvin forced him to use the Gibbs version of vectors which destroyed the underlying links to the rotation. .
However JJ Thompson in his sequel to the treaties on electricity and magnetism by Maxwell attempted to correct for these failures by going back to faradays tubes. In so doing he really explained maxwells findings and equations in terms of the motion of faradays tubes. This would have been hopefully something that faraday would have appreciated more than Maxwells attempt to use Liniell forces to explain his concept.
I want issue with JJ Thompson which is issued due to the form of electricity and magnetism. JJ Thomson rightly points to the chemical evidence and the electrolyticall evidence for using electrostatic tubes of force. He does this by way of justifying why he would use Electrostatic tubes of force as opposed to magnetic tubes of force the second being a complete and justifiable alternative.
Today we can use nuclear magnetic resonance imaging and also nuclear magnetic resonance to demonstrate that there is a justifiable observable base for using magnetic tubes of force in the same manner as JJ Thomson describes.
It is my opinion that this is a sounder base to developing our understanding of physics in the physical world then the electrostatic version.