What is the relationship between the unit circle and relative motion? Is there a unit circle background for the rest frame and a relative motion unit circle for the object with relative motion? http://s1061.photobucket.com/user/p...tiveMetric001_zps1d4cd274.jpg.html?sort=3&o=1 Some more stuff: http://s1061.photobucket.com/user/prismgreenpb/media/STnotes001_zps7d8e3569.jpg.html?sort=3&o=3 http://s1061.photobucket.com/user/prismgreenpb/media/ST0001_zps2187ab47.jpg.html?sort=3&o=4 http://s1061.photobucket.com/user/prismgreenpb/media/MISC001_zps7f85c177.jpg.html?sort=3&o=2 http://s1061.photobucket.com/user/prismgreenpb/media/ST4001_zps90e4f54d.jpg.html?sort=3&o=5 http://s1061.photobucket.com/user/prismgreenpb/media/ST3001_zps0576c992.jpg.html?sort=3&o=6 http://s1061.photobucket.com/user/prismgreenpb/media/ST2A001_zpsbee76e4b.jpg.html?sort=3&o=7 http://s1061.photobucket.com/user/p...estionMark001_zps9217f15e.jpg.html?sort=3&o=0
You've been busy with your drawings and photobucket. My impression of your post is, given your photobucket slide with notes, that if you start with a light sphere which can be defined from a rest position, and then transition to a moving position relative to the rest frame light sphere, there are some adjustments based on relativity of motion and the effect of length contraction as you approach the speed of light? Why not cut and paste the notes, and or use the "image" link provided by Photobucket?
Why is it that "Alternative theories" are so often presented in an unstructured manner, often with poorly reproduced photos of handwritten scribblings or scans of documents that look like they were typed on a typewriter back in 1975? The reader is apparently expected to do all the work - to dig through archives of photos posted on other websites, or to read through obscure web pages or blog posts - in the hope of being able to deduce (somehow) what the poster's amazing and revolutionary new theory of everything is supposed to be. The purpose of posting to a forum is to communicate something to other people, is it not? If you have a new and important theory, why don't you take 10 minutes to present it in a manner that people might want to read?
The geometry is what it is. It's all a matter of what meanings are given to the lines and which one sets the scale. The geometry shows why the relative motion is parallel to reference radius AB to get the correct values. The unit circle can show the value of gamma, but not the Lorentz factor. You have to go outside of the unit circle to show the reciprocal. The distance between the observer and the object of interest is set to unity and sets the metric. https://www.mathsisfun.com/algebra/trig-interactive-unit-circle.html
The only thing you can possibly be referring to is the Lorentz transformation, which involves a rotation of spacetime coordinates. But this has nothing to do with the unit circle; not unless you set out to define a unit circle which relates to that rotation. But that would only be contrived, not something essential to defining how dilation and contraction are known to manifest themselves. So why bother?
Why bother? Too much time on my hands this winter. The 1 in the unit circle equation is a radius of the unit circle doubling as a hypotenuse. What does the 1 in the gamma equation stand for? Unity? See Fig. ST3: http://s1061.photobucket.com/user/prismgreenpb/media/ST3001_zps0576c992.jpg.html?sort=3&o=6
The path along the circumference is interesting. Don't know if it has any real importance. See Fig. ST0: http://s1061.photobucket.com/user/prismgreenpb/media/ST0001_zps2187ab47.jpg.html?sort=3&o=4
