clues alpha

Last week ThursdayThoughts emphasized the importance of resolving disagreements with reality. This week we cover subtle clues that warrant exploration. There is no precise rule for this. Instead, we will look at an example of searching for the fine-structure constant.

The fine-structure constant (alpha) is a dimensionless physical constant related to the interaction between charged particles. It derives its name from the hyper-fine lines observed in atomic spectra. Much manpower has been devoted toward understanding the theoretical basis for this constant.

The fine-structure constant has been measured to about 10 digits of precision. This accuracy combined with unitary dimensions makes the fine-stucture constant an intriguing value for theoretical consideration. It is generally accepted that alpha has the same value for the interaction between charged particles and determination of the hyper-fine atomic spectra lines. It is not a given that alpha is identical in both cases.

A first step I frequently use for dimensionless numbers is to look for rational numbers that closely reproduce them. The results of this step are only useful if some reasonable logic for them can be uncovered. For alpha, the factors that work best are: (3^4 * 47) / (137 * 2^5 * 7 * 17). This gives us about 7 digits of precision so it clearly is not an answer. Is it even a clue?

If we rearrange the factors above, we get (1/137) * (138^2 - 3^2) / (138^2 - 2^2). 137 and 138 are the number of links in an electron and in space, respectively. This form of the factors can have physical meaning. The factors form compelling clues.

There is another interesting relationship. The fraction 355 / 113 gives Pi to about 7 digits of precision. It is the best Pi around! If we assume that nature is rational and apply the ratio of Pi to rational Pi to the alpha approximation, we pick up another digit of precision.

The Pi adjustment does not compel one to use it. It is reaching. This relationship I put in my back pocket in case it is needed for an exact answer and a compelling physical basis can be found. Otherwise, I ignore it.

In Thoughts 27 and 28, the ratio of gravitational force to electromagnet force contained a balancing amount of alpha squared. (I think the unresolved factor of 2 in Thought 28 comes from the electron interacting at both ends. This only leaves alpha squared.)

There is another effect to consider. As a slowing of time propagates through a chain segment, the link speed changes after contact with an adjacent link. This creates a fast-leg forward, slow-leg return effect. Remember, we still need precise synchronization.

The way to get a fast-leg, slow-leg effect without impacting synchronization is to have the fast-leg longer (i.e. more revolutions before contact). One should also be aware that phase-shifting between links works as long as the shift is a multiple of the number of links. This keeps the chain segment ends in phase.

The fast-leg, slow-leg relationships show promise. However, until results are meaningful it is just another clue.

A sample attempt at a solution would be, for example:

   Set J equal to 138 + 3;

   Set K equal to 138 + 2;

   Set M equal to 138 - 3;

   Set N equal to 138 - 2;

This is not presented as an answer. It simply means a number of relationships will be attempted and the results checked. In all likelihood, an answer will not emerge. However, a better understanding of the next step might emerge.

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