Quote:
Originally Posted by Bombadil
So would the new  after being changed to a new frame still describe the behavior of the element if we had the correct solution for  or would the new function no longer describing the correct behavior of the elements. It also seems to me that the new function would no longer expand in a spherical manner but would expand in an elliptical manner.
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It seems to me that you have a misconception of the issues here. My fundamental equation was designed such that any flaw-free explanation could be cast in a manner such that it fulfilled that equation. The issue “correct” then falls to the question, “are the expectations yielded by

consistent with your expectations”. The momentum adjustment provided by

does not change the predicted expectations at all; it merely changes your perspective on the circumstance. Go back and look at my analysis of the moving clock.
Essentially, I am looking at the solution from exactly the same frame as was used to analyze the rest clock. The only difference is that oscillator's momentum to the right is higher than it's momentum to the left (there is a significant change in momentum when the oscillator reflects off the mirror). I think you need to understand
“Doppler shift”. The analysis is not how the solution looks from a new frame but rather, the issue of changing the momentum of a specific solution.
Quote:
Originally Posted by Bombadil
So what happens if we don’t ignore the effect of the Dirac delta function?
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Then you have to include all the interactions with the rest of the universe (or at least some aspect of it). Go look at my deduction of Schrödinger's equation. The solution is then a very complex thing and depends very intimately on “what you are trying to explain”. I made it quite clear that I was talking about a very specific circumstance here: “if the data belonging to a given observation could be divided into two (or more) sets having negligible influence on one another”. The “influence” is a direct consequence of the Dirac delta function.
If influence is allowed, all bets are off! This is in stark contrast to Einstein's theory of relativity which postulates that the speed of light is c. My presentation is based entirely on the lack of influence between the two collections of information being explained.
Quote:
Originally Posted by Bombadil
So we are considering an expanding sphere for each set of elements that make up an object
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No, we are hypothesizing the structure of a specific object, ignoring how the structure of that object is maintained (essentially assuming that such an object as I describe, my clock, is a possibility). Since such objects appear to be possible in our universe, it seems reasonable that there could exist a solution to my fundamental equation which would explain such an object (most of the individual interactions would have to be approximate solutions to Schrödinger's equation, where rest mass of the elements are momentum in the tau direction). “We are totally free to make these assertions as we are defining an object and, in the absence of contradiction, such an object could certainly exist.”
Quote:
Originally Posted by Bombadil
But, what if they can‘t be considered separately? Will the Lorenz transformation still need to be applied, or will we no longer be able to apply the Lorenz transformation to the objects?
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If the two collections of data cannot be considered independently, then the rest frame of the collection is a definable thing and my equation is only valid in that rest frame: i.e., if the data cannot be considered independently, it can't be considered independently and no “transformation” can be defined.
Quote:
Originally Posted by Bombadil
So is this due to the only possible function that describes the objects that make up your clock must have a constant derivative to  as a result the object will have a positive mass?
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Mass is momentum in the tau direction and thus can be either positive or negative just as momentum in the x direction can be either positive or negative; however, the energy associated with that momentum can only be positive. Secondly, you seem to have lost sight of the fact that the structure of my object (my clock) is only bound by the fact that, “We are totally free to make these assertions as we are defining an object and, in the absence of contradiction, such an object could certainly exist.”
Have fun -- Dick