Thursday, August 6, 2009

Back-reaction and Time Symmetry

Although the observable universe does not suggest Time Symmetry as an inevitable, inescapable law, the physical laws themselves exibhit an indifference to the direction of flow of time.

Time symmetry itelf is a highly important condition for physical laws.
Indeed, there is no apparent reason for which such symmetry should be broken, and therefore one time direction has no privilege to be more important than the other. Thus, a theory that respects this symmetry appears, at least, more elegant than theories with which one has to arbitrarily choose one time direction over the other as the preferred one.
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General Relativity is a time-reversible Lagrangian theory. The Wheeler-Feynman absorber theory assumes that it is happening. Maxwell's equations also exhibit time symmetry i.e. symmetry of results whether we assume time to flow forward or backward. A mathematically rigorous solution of Maxwell's wave equation for EM waves would produce two possible solutions commonly labeled retarded and advanced solutions.

The Maxwell equations and the wave equation for electromagnetic waves (and the accel-gravitic waves we are deducing via the analogy between electricity and mechanics - Ravi) have, in general, two possible solutions: a retarded solution and an advanced one.
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This means that if we have an electromagnetic emitter which generates a wave at time t0 = 0 and point x0 = 0, then the wave of the first solution will arrive at point x1 at the instant t1 = x1 / c after the emission (where c is the speed of light) while the second one will arrive at the same place at the instant t2 = x1 / c before the emission.

I propose that the advanced wave is physically significant for only those situations involving time scales and length scales comparable to that of the resonance frequency of the caacitor-inductor arrangement involved.

Under such circumstances, the wave travels into the past and brings energy with it. In the case of the gyro, the no-nutation condition shows that just the slightest nudge right as we start the inductive suspension is all thats necessary. (i.e the effect isn't travelling into the 'distant' past, for example, I dont need to already give the gyro that nudge several seconds before I release it in inductive suspension).

Besides, this only seems proportional and fair to the way the effect behaves in positive time - Suppose you were to release the gyro at rest, (rather than in the nonutation condition), beyond a few wave lengths of the inductive-capacitive circuit, there would be no noticeable nutation - ie. the tight damping of the nutation is also a measure of the tight damping of the energy travelling backward in time.

Its only that if we appropriately design a RelMachine, we can harness this backward flowing energy to amplify the thrusting torque to significant levels. In the case of non-inductive suspension, it would be capacitance that would be dominant (and capacitive interactions can be analyzed using Newton's Laws) and this would reduce to Newton's Third Law.

The Wheeler-Feynman absorber theory explains the resistance of a charged particle to changes in its state of motion as being due to advanced waves emanating backwards in time from an all-encompassing array of absorbers in the future, whose waves are excited by the retarded waves emanating forwards in time from the particle.

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Therefore, similarly, we may postulate that inertia of any object is due to the advanced waves emanating backwards in time from an all-encompassing array o absorbers in the future, whose waves are excited by the retarded accel-gravitic waves emanating forwards in time from the particle. Further we may also postulate that in the case o the Relativistic Machine (as also in the case of the LC circuit), in operation at its resonant mode, this backward travelling feature of energy is being built up to create a large response.

Thus we see that the Wheeler-Feynman absorber theory helps explain the self-interactive nature of an inductor (and now, we extend it to an inductively suspended spinning wheel) and the backreaction generated by inductive-capacitive arrangements as arising due to the time-symmetry of natural laws.