Hi Tom,
The links work fine for me. I don't know what the problem might be, but oh well. You wrote,
"Let me turn this around. Why should we be interested in a theory that claims motion as a property of the geometry, with no mechanism or experimental evidence? Why should we be interested in Lynd's claim that motion is fundamental, which is demonstrably false?"
Ok, first of all, I know of no theory that claims motion as a property of the geometry, with no mechanism or experimental evidence. In the case of an RST-based theory, like mine, motion is defined as a change in space per change in time. The experimental evidence upon which this theory is based is the observation of the progression of time and the progression of space. We know that time is progressing, or increasing, because we can measure the increase of entropy associated with it. We know that space is progressing, or increasing, because we can measure the increase of wavelength in the light emitted from the hot elements of distant stars.
I have never heard of anyone insisting on the identification of a mechanism responsible for the observed increase of time, and I don't think that a reasonable demand can be made for identifying a mechanism responsible for the observed increase of space either. These two expansions are our fundamental observations of nature, the characteristics and properties of which we seek to explain in our physical theory.
As far as disproving the validity of Lynds' claim that motion is fundamental, you have your work cut out for you, because you can't escape the fact that space and time are the reciprocal aspects of motion. By appealing to Einstein's arguments for the fundamental role of spacetime, you establish the need for the space/time progression, which by definition is motion.
The problem here is clear: By insisting that motion can only be defined by something that is changing locations, we limit ourselves unnecessarily to 1D motion, driving us to search for order in the higher dimensions of complex analysis, for the greater degrees of freedom we need in our physical theories.
However, the natural order, commutativity and associativity of algebra based on the reals can be maintained in higher dimensions, if we recognize the proper dimensions of space and time and the reciprocal relationship they have in the equation of motion. The extra degrees of freedom we need are obtainable without resorting to the ad hoc invention of imaginary numbers, and this is why it's important to understand the n-dimensional geometry involved in the motion equation, not because we are trying to make motion out of the properties of geometry.
You wrote,
"The only really valid "why" question in physics, is why there is something rather than nothing. Any other "why" is philosophical, not physical."
That's right, and the RST-based system of theory addresses this question directly: Nothing is perfect, so something is not perfect. It is broken perfection. When we realize the key role that symmetry plays in both physics and mathematics, we see how that assuming motion is fundamental opens up the floodgates to understanding.
This is because a unit ratio is perfect, but a non-unit ratio can be non-unit in two "directions," which we can call "positive" and "negative." In this way, the unit ratio is also zero, because, like a pan balance, when there is no difference of magnitude between the two, reciprocal, aspects, of the ratio, unity is equivalent to zero. The question is, then, how is the perfection of the unit ratio broken? Is there a mechanism to do this? Is a mechanism required to do it?
Well, this is another philosophical question, but we can now see how related it is to the physical question. In theoretical physics, we invoke the idea of spontaneous symmetry breaking, and leave it at that. This spontaneous symmetry breaking is invoked philosophically, because the state of perfection is highly unstable, like a pencil balanced on its sharpened point.
However, as we discovered with gauge theory, local symmetry breaking is more powerful than global symmetry breaking, and it behooves us to explore that possibility. When we do, low and behold we find that we obtain a finite system of finite energy that should be completely describable by a set of finite real numbers, without the necessity of resorting to complex numbers and rotations in the complex plane.
This is a tremendous breakthrough, Tom, because, as you point out, we seek an algebraic description of reality, one which Einstein sought in vain. As he lamented to one of his former students:
"...the continuum of the present theory contains too great a manifold of possibilities...The problem seems to me [to be] how one can formulate statements about a discontinuum without calling upon a continuum (space-time) as an aid; the latter should be banned from the theory as a supplementary construction, not justified by the essence of the problem, [a construction] which corresponds to nothing "real." But we still lack the mathematical structure unfortunately. How much have I already plagued myself in this way." (see Stachel, 'Einstein from B to Z', pg 414)
I believe that the mathematical structure that we need is to be found in the discrete ratios of space/time, or motion, that we find in the tetraktys. We are accustomed to characterizing the mathematical structure of the tetraktys in terms of the reals, the complexes, the quaternions and the octonions, but these definitions depend upon the functionality of imaginary numbers, which in turn invoke the concept of rotation.
Hestenes has shed great light on the confusion involved in this structure, showing us how unnecessarily complex it has become, but his reduction of its complexity does not remove from it the concept of an imaginary number implying rotation, but rather only transforms it into an explicit operation.
However, when we see the mathematical structure of the tetraktys in the light of an expanding/contracting pseudoscalar, and we interpret its magnitudes in terms of space/time ratios, its algebraic structure is truly transformed into a suitable basis of physical theory.
Regards,
Doug
