Wednesday, July 29, 2009

The Good Professor Vs The Jabberwock

That last paragraph in the previous post bears repetition and reexamination: The back reaction of a particle's own field on itself is necessary to explain the friction on charged particles when they emit radiation.

Now, in order to understand the gyro's behavior in purely electromagnetic terms, it is necessary to see understand how this back reaction works when a gyro is inductively suspended.

Refer to "Roll Isaac Roll" (Laithwaite, 1979): In Professor Eric Laithwaite's paper, "back reaction" are the very words used by him to describe the behavior of a gyroscope.

So if the spin momentum remains constant (-for a spinning gyro-and why shouldn't it, if we postulate a wheel in perfect bearings ), then a torque T is seen to give rise to an angular velocity omega** (and for an electrical engineer it can easily be seen as the reverse way around, for a current can be seen as the cause of a voltage in a series circuit). Since when has an angular velocity been capable of producing a back reaction? I thought only an angular acceleration could do that...
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What the good professor is asking is this: Since the gravitational torque produced the angular velocity, any back reaction that the initiating gravitational torque suffers (in this case, it was gravity that initiated the torque and the back reaction cancelled the gravitational torque and kept the gyro horizontal) can only have been initiated by the product of the torque. Since the product of the torque was simply a precession, it means it was the back reaction of the precession that canceled out the torque – ie. A velocity produced an acceleration. That back reaction is identical to the back reaction of a particle's field on itself. That is, inductance is a field element. This is complementary to the fact that capacitances behave as point particles – both in Brillouin's development of electrical/mechanical filters and in Newtonian/Laplacian analysis of lattices. The two together form a harmonic circuit or arrangement – one which we can harness.

We can still continue to follow the analogy- this time with Quantum Electro Dynamics (QED). I propose that what we are seeing here is more commonly called the ‘jangle fallacy’ (Thorndike, 1904) -it refers to cases where two different terms are used for the same entity. That is, self-induction (in EM)/ back-reaction (of gyros) are analogous words describing one and the same phenomenon. ("the jangle") (As opposed to the “jingle” fallacy where we give two different phenomena the same name – thereby introducing another of confusion.)
There are already tantalizing hints that this is correct, from previous attempts to bring Gravity into the framework of the Unified Field Theory. For example, for one such alternate theory to work, it would need a decidedly non-Newtonian head-start:
The Abraham-Lorentz theory had a non-causal "pre-acceleration". Sometimes an electron would start moving before the force is applied. This is a sign that the point limit is inconsistent. An extended body will start moving when a force is applied within one radius of the center of mass.
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This is strikingly similar to the fact that pure Newtonian predictions would be unable to account for the 'lead' of the precession resulting from a torque over the torque itself. Newtonian predictions will likewise be unable to explain how a Relativistic Machine can function, as in pure Newtonian terms, such a machine would appear as in the Abraham-Lorentz theory, to be “moving when a force is applied within one radius of the center of mass”.

This it would seem that Abraham-Lorentz theory is lacking exactly the same thing that Newtonian Physics is lacking (when it attempts to explain how precession could lead the torque that produces it), when it comes to explaining how gravity fits with the strong and electroweak forces. Solve one and you just might solve the other.

It would also seem that the Abraham-Lorentz theory is implying that in order for a framework to be possible that integrates gravity successfully with the other three forces, it would also have to be possible to have “non-causal preacceleration” i.e. Precession leading torque as well as “an extended body to start moving under certain circumstances when a force is applied within one radius of the center of mass” i.e for a Rel Machine to be able to fly.
What is also being proposed in this discussion is that a gyro ( or a spin angular momentum which has been suspended inductively)'s behavioral response is the ultimate measure of "extension" or space. Therefore it dominates any discussion of field related formulations of gravity in ways that are analogous to inductive elements in Electro-Magnetism. In addition, all non-gyroscopic objects/arrangements can be dealt with as pure point masses without spatial extent.

Now, just how did QED solve the renormalization infinities problem when it first appeared?

The main idea that QED brought to renormalization is to correct the original Lagrangian of a quantum field theory by an infinite series of counterterms, each one of which is labelled by the Feynman Graphs that encode the perturbative expansion.

In this methodology, the divergences appear in calculations involving Feynman diagrams as closed loops of virtual particles in them.

A Feynman graph consist of loops and edges and satisfies certain conditions. Each loop or edge represents a segment of the worldline of a particle.
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Vacuum bubbles for instances are represented by a simple loop. Since in graph theory, a loop is an edge that connects a vertex to itself. Note that Feynman graphs consist of edges representing segments of the worldline of the particles involved.

Now, the spinning wheel going a-b-c- and-so-on-and-on and then forms vertices like at b over and over.
Thus spinning (a loop) is represented by a vertex with cyclical sets of two edges. (Figure 1) But in the case of a spinning wheel, we know that if a RelMachine is possible then it means that with respect to a stationary inertial frame (whose worldline is represented by a-c), the zig-zagging wheel and its support arrangement will move in space away from the inertial observer, ie there will be a divergence between them(Figure 2). Thus over time, the two sets of lines appear to diverge. Now, suppose both objects have spin – one simply has more spin than the other. Then, in such a case, we can modify the relativistic diagram further to Figure 3.

This is a cumbersome way of representing whats going on in the situation. A simple way would be as in Figure 4, where a single cycle of the spin is shown to both give the frequency and to represent that there is an inductive process at work. Then, we would connect the middle points d and b to indicate that there is an energy exchange going on. We could further encode information into the diagram by using color to indicate whether there is a large amount of energy interchange, color of the edge represents the type of energy of the particle, etc etc. This is infact what a feynman diagram does. (Figure 5)

Thus, the divergences that appear in calculations are implied to be inductive energy exhanges and are symbolically represented by loops. There are further useful deductions to be drawn from the analogy of spin/rotation with the Feynman Rules for loops in QED

Feynman Rule: Incoming and outgoing lines carry an energy, momentum, and spin.
Interpretation: The are inductive + capacitive arrangements (and therefore determined by their harmonic behavior.

Feynman Rule: each vertex where lines meet gives a factor derived from an interaction term in the Lagrangian
Interpretation: Each inductive interaction has its own entry in the Lagrangian.

Feynman Rule: A point where lines connect to other lines is an interaction vertex, and this is where the particles meet and interact--- by emitting or absorbing new particles, deflecting one another, or changing type

Interpretation: The vertexes are situations where an event is occuring with a decay and a collision (analogues of emission and absorption) involved.

It is proposed here that these closed loops that Feynman Diagrams refer to are nothing but representatives of the energy involved in harmonic arrangements involving inductively suspended spinning objects coupled to the capactive elements (point objects), in calculations.

Thus, in a Feynman diagram, the capacitive objects are being shown are particle (localizable) inputs and outputs, while the inductive objects/arrangements are shown only abstractly as a loop similar to a spinning wheel's spacetime trajectory. This would mean that the Feynman diagrams/graphs would be the best choice of schema to sketch the behavior of both inertio-gravitational oscillators and electro-magetic oscillators. Having a single schema to analyze both behaviors, in a way harmonizes the analysis of both phenomena.

A (inductively suspended object) gyro's behavioral response is the ultimate measure of "extension" or space. All non-gyroscopic objects can be dealt with as pure point masses without spatial extent.

The inductive property is disruptive to theories which are based on capacitive rules of interaction. Instead of the object going this way like a billiard ball would, it might go some other way, photons create virtual particles, etc etc. That is why they appear as "violations" of interaction rules which have been capactively founded. Much of this distortion has to do with the fact that most of our 'intuitive' interactions in daily life proceed capacitively (and all purely capacitive interactions can be analyzed using Newton's Laws).

We would expect that accordingly, the need for these 'loops' would coincide with situations where a large amount of inductive capability is trapped inside the particles/arrangments involved in the interactions. Indeed this is the case. Those situations for which the interactions are divergent are significant, which have large momentum/energy values.

While virtual particles obey conservation of energy and momentum, they can have any energy and momentum, even one that is not allowed by the relativistic energy-momentum relation for the observed mass of that particle. (That is, E2 - p2 is not necessarily the mass of the particle in that process (e.g. for a photon it could be nonzero).) Such a particle is called off-shell. When there is a loop, the momentum of the particles involved in the loop is not uniquely determined by the energies and momenta of incoming and outgoing particles.
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i.e., the inductance of the arrangement and the backreaction of that inductance's field upon itself, in response to local forces can play a large enough role in moulding the results of the interaction, even though they are largely invisible to the capacitively oriented Newtonian (Euclidean) laws.

A variation in the energy of one particle in the loop can be balanced by an equal and opposite variation in the energy of another particle in the loop. So to find the amplitude for the loop process one must integrate over all possible combinations of energy and momentum that could travel around the loop.
These integrals are often divergent, that is, they give infinite answers. The divergences which are significant are the "ultraviolet" (UV) ones. An ultraviolet divergence can be described as one which comes from- the region in the integral where all particles in the loop have large energies and momenta.
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(i.e. only those inductive processes are significant which have significant/large rotation energy and momentum) For such large energy processes (dubbed Ultraviolet divergences), the net result is calculated by adjusting the capactive laws to include an inductance (and the resulting harmonic oscillations term and its consequences) and its effects. The Feynman diagram is serving to document that adjusted calculation.

- very short wavelengths and high frequencies fluctuations of the fields, in the path integral for the field.
- Very short proper-time between particle emission and absorption, if the loop is thought of as a sum over particle paths
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Interpretation: Thats exactly what we showed for the rotating wheel- cyclical emission and absorption.
The faster the rotation, the shorter the proper-time between particle emission and absorption, if the loop is thought of as a sum over particle parths.

That is, the loop implies rotational motion of the object or constituents of the object. Infinite answers imply that for large inductances, the resulting precessive output will be large and is going to cause divergences. The formulas are merely reflecting the unsuitability of capactive techniques to analyze inductive phenomena.

Some Final Remarks
The Higgs field has a non-trivial self-interaction, like the Mexican hat potential, which leads to spontaneous symmetry breaking:
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That is, the Higgs field involved self-induction, which appears in the case of inductively suspended objects harnessed by a local variable torque.
So expect that in analogy, the weak gravitational force, inertia (capacitance) and induction arise through a Unified Field Theory with spin/rotation as a major driver.

In particle language, the constant Higgs field is a superfluid of charged particles, and a charged superfluid is a superconductor. Inside a superconductor, the gauge electric and magnetic fields both become short-ranged, or massive.
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Thus, this formulation of the Higgs field as the resonant excitation of inductively suspended spinning objects can form explanations of SuperConductivity as well.

Please note that n this and the previous post, I have quoted from

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