Sunday, July 12, 2009

On Assigning Cause and Effect in Inductively Suspended Objects

First it might be useful to take a quick refresher of forced oscillations in harmonic systems. Here's a good one I found after a quick search. Although written for a spring pendulum, this applies also to spinning wheels in inductive suspension.

Forced oscillations. (@
Begin Quote
On the whole you can see three different types of behaviour for forced oscillations:

case A: If the exciter's frequency is very small (this means that the top of the spring pendulum is moved very slowly), the pendulum will oscillate nearly synchronously with the
exciter and nearly with the same amplitude.

case B: If the exciter's frequency agrees with the characteristic frequency of the spring pendulum, the oscillations of the pendulum will build up more and more (resonance); in
this case the oscillations are delayed about one fourth of the oscillation period compared with the exciter.

case C: If the exciter's frequency is very high, the resonator will oscillate only with a very small amplitude and nearly the opposite phase.
End Quote

The gyro and the Rel(ativistic)Machine (that I contend will be able to fly) contain spinning objects. Any spinning object that is inductively suspended can be harmonically excited. Now, case B is the case of such a harmonic system at resonance. i.e. a Rel(ativistic)Machine.

Case C is the gyro in precession under the influence of gravity. The precession exists only as long as a rate of change of angular acceleration exists and cannot exist in the absence of it. Gravity is a high frequency exciter when compared to the characteristic resonance frequency of a spinning gyroscope suspended in inductive conditions. Thus, the gyro responds with a small steady precession & in the opposite phase (i.e. cancelling out gravity).

How do we assign cause and effect in analyzing interactions? Lets analyze the situation. Under routine Euclidean conditions, in analyzing cause and effect, if Y changed when I meddled with X, it can perhaps follow that X is the cause of Y. You would be correct in the sense of action - reaction (i.e. for a gyro on the ‘Eiffel Tower’, even if the physics says precession came first – that’s what the cross-product formula is saying- we 'know' that we initiated the torque first).

Now normally that would work just fine. But in looking at the Gyrscopic interaction that way, one will have missed the temporal aspect. What really matters in interaction analysis in this situation is that we label what comes first as the cause and what comes second as the effect.(And NOT to assign what you 'know' yourself to be doing as the cause and what happens then as the effect.) Otherwise one is liable to become deceived.

Lets look at how, if it were up to a Newtonian, s/he would label the energy flowing into the gyro (in the form of the torque) - S/He would call the torque the cause (lets label it event 1) and the precession as the effect (lets label it event 2). S/He would insist that event 1 came first and event came next.

But according to relativistic analysis, the energy contained in the wheel has a shorter spacetime distance between events. Therefore the energy of the wheel in the present is not in the same phase as the energy of the frame. (Recall this diagram below from this post.

That phase difference bestows upon it (the spinning wheel) a variable ability to oppose or reinforce the arriving energy that can be harnessed most efficiently, if we make the appropriate arrangements (i.e. it’s normally a limited ability but can be harnessed best when we induce resonance), in analogy with a properly tuned LC circuit. For a rate gyro its case C, the lower limit that is applicable.

For spinning wheels (for instance, for the prototype), under inductive resonant conditions, we activate case B, the ability of the momentum in the wheel to push more and more strongly (like a rider on a swing kicking the ground at exactly the right intervals over and over to acheive high amplitude.) against the frame, even as the frame's momentum attempts to act upon the wheel and drag it around, under the influence of that vertically mounted motor.

That means that under resonance conditions of reinforcement, momentum is delivered cyclically from the 'future' of the spinning wheel to the 'present' of the frame. (alternatively we can say energy from the 'present' of the spinning wheel is adding momentum to the 'past' of the frame. - the naming is irrelevant - also note that this doesn't imply time travel of any extended degree, in practical terms its merely saying the phase can be adjusted to be positive). If the cause is in the future and the effect is in the present, then it means the effect will be recorded first and only later the cause, when viewed from an inertial frame.

Since there is a process in play in which energy from the 'future' is influencing energy in the 'present', the actual temporal order of occurrence would be 2-1. That is the energy transfer would temporally execute in the order 2-1, but action-reaction accounting of the entire interaction would run 1-2. THAT mismatch in the ordering (between the temporal perspective and the interactive perspective) of events leads conventional Newtonian analysis of Gyroscopic action into a dilemma.

An analysis that conforms to Newtonian Laws can be achieved only by hewing to the temporal order of manifestation (so as to record the forces, play by play as and when they are manifest). However, in such an analysis, since we label what comes first as the cause and what comes second as the effect, that would also mean accepting cause as effect and vice versa in the situation of the gyroscope. (et voila,.. there you have the formula t = w X L - you gave up what should be the logical choice of what is cause and what is effect in order to preserve Newton's Laws)

Alternatively, we can break the temporal order i.e. we adopt the method of assigning the torque as the cause and precession as the effect. We say torque is the cause and precession is the effect - in which case, we would be forced to write w = t X L which does not conform to actual behaviour, thereby bringing all Newtonian analysis to a halt.

One cannot keep both logical and Newtonian order.
The formula t = w X L allows us to keep the Newtonian mathematics by reversing the logical order i.e. the order that we 'know' we are initiating and replacing it with the opposite situation i.e. the formula assigns cause and effect by temporal order - but at least in return for it, a simple Newtonian analysis of the motion is possible. (But only a limited one any how, because while Newtonian analysis has allowed the exploitation of the gyroscopic principle in constructing useful rate gyros etc, it has also deceived us into thinking we understand everything about the phenomenon. In fact, much more can be done if we harness the effect in a resonant mode.)

Suppose we assigned the torque as event 1 and the precession is then event 2 AND we also incorporated the insight (provided by relativistic analogy between Electro-Magnetism and Accelero-Gravitation) that the effect is in the present and the cause in the future, then we can do a modified Newtonian analysis as follows:

We introduce a fourth force (temporarily) right at the beginning of the interaction, equal in magnitude and direction to the effect, to hold the place of the effect until it actually kicks in. This force would account for the fact that the effect will itself be recorded (and will itself be the cause of activity) BEFORE the cause is manifest. In such a situation, we could preserve Newtonian analysis. Such a situation has striking similarity to the No-Nutation condition:

Lets say you have a spinning toy gyro. You've just spun it up. You are positioning one end of the axis on top of the 'Eiffel Tower'. How do you set off the gyroscope without causing nutation? The way to set a gyro precessing without causing any nutation is to give it a gentle nudge even as we let it go and the nudge but be equal in magnitude and direction to the precessive velocity that will be introduced. Then there will be no nutation.

That is we are compelled to introduce that exact 4th force we discussed in the above paragraph. i.e that fourth force is not a mathematical artifice but an actual, real necessity if you want behavior that strictly and smoothly adheres to Newtonian prediction. If not you MUST deal with perturbation (nutation) - perturbations open the door to Quantum Mechanical analysis of energy exchange.

By giving the gyro a velocity in the exact direction and magnitude as the precession would, we are ensuring that temporally, there is in existence exactly as much momentum and angular velocity -both amplitude and direction - identical to what would exist if there was precession - i.e. precession already exists before there is torque effect - or at least a
simultaneous start)

Finally let us analyze the situation where we don’t give it that fourth force. What happens if you don’t give it that extra push? Then you get nutation i.e. precession + torque.

In the best case (we give the push), the precession is already in existence before the torque came into existence. And in the worst case scenario, they are simultaneous. What we deduce is that the physical situations all work smoothly in accordance with Newtonian predictions only when built in the following fashion:

The precessional velocity comes FIRST and THEN the torque appears OR they are simultaneous. Its also how the precession formula works too - with the counterintuitive cross product.

Thus the real test that helps assign cause and effect in a way that conforms to Newton’s Laws is what comes first and what comes second. And in this we find that the precession comes first and then the torque OR they come together. But never torque first and precession second.

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