They say the human brain uses 12 watts of power. So you'd think pushing physics thoughts around all day would burn more calories than watching sit-coms all day. You'd think they'd make a study on this and reveal the results of how many more calories you burn thinking about physics over the philosophy which appears in the science gossip rags. Anyway, I must burn most of my energy while asleep because when I have a problem, I put it in for processing before I konk out and usually wake up with the solution. This morning I had to deal with a great deal of solution.
I was having a ton of difficulty resolving the right hand side of my STD. It just wouldn't work out in the same way the left hand side did. So I thought I'd go back and try to solve it using Einstein's method of employing length contraction and time dilation (Lorentz transforms) to see if it would give me any insights.
Then I remembered the battle between cranks and relativists on all physics forums. Both sides have little to no math skills but one side at least asks questions while the other blindly quotes art history philosophical theologian dogma from scripture thinking that's what science is all about. The question I remembered from the cranks was why do Einstein's derivations have terms such as (c+v) and (c-v) if in Einstein's relativity those terms should always equal c. Those terms are Newtonian, not Einsteinian.
So I went back into the left hand side of my STD to see if (c+v) appears there. It does but it's written as (pink c) + v = (yellow c). I've had to swap the colors of the light lines on the right side to match this equation.
So look within the triangular area bounded by the numbers 0, .67 and 0. The pink light signal always uses up .5 Bobs seconds to reach Alice and crosses .5 ls of invariant space to do so. (Space is invariant unlike what Einy's un-physical length contraction assumed.) Alice's .6c velocity starts simultaneously to the light pink signal no matter what the perspective and is given the time to cross the required distance to meet the pink football. So from Bob's line of simultaneity, she is given .4 sec Alice time = .5 sec Bob time to cross .3 ls to catch the football. Since the green line represents causal simultaneity, she is given a head start of .2 ls from Bob's perspective. Causality is the sun going out before the Earth's perspective goes dark. There is a delay between causal simultaneity and perspective simultaneity and that is how Alice's head start to the blue line works.
Speaking of causal simultaneity, Alice is given .67 sec Alice time = .833 sec Bob time to cross .5 ls to catch Bob's football. From Alice's perspective simultaneity, she is given 1 sec Alice time = 1.25 sec Bob time to cross .75 ls to catch the pink ball.
The equation is (pink c) + v = (yellow c). Bob's time for pink c is .5 sec. Bob's time for v from the blue green and red perspectives is .3, .5 and .75 sec. Bob's time for yellow c from the blue green and red perspectives is .8, 1 and 1.25 sec. The distance for pink 5 is .5 ls. The distance for v from the blue green and red perspectives is .3, .5 and .75 ls. Distance for yellow c from the blue green and red perspectives is .8, 1 and 1.25 ls. So the equation becomes:
Pink c distance / pink c time + v blue, green or red distance / v blue, green or red time = yellow c blue, green or red distance / yellow c blue, green or red time.
Obviously the equation Einy should have come up with instead of his lame Lorentz transforms.
Now let's apply it the the right side of the STD except the equation is now pink c - v = yellow c. Velocity will now subtract from pink c because it takes longer for the light to catch up.
So pink c distance = 2 ls
pink c time = 2 sec
Blue v time = 2 sec
Blue v distance = 1.2 ls
Green v time = 1.67 sec
Green v distance = 1 ls
Red v time = 1.25 sec
Red v distance = .75 ls
Blue yellow c time = .8 sec = Blue yellow c dist = .8 ls
Green yellow c time = 1 sec = Green yellow c dist = 1 ls
Red yellow c time = 1.25 sec = Red yellow c dist = 1.25 sec
Plug these values into the equation and see c-v is always = c but the catch is pink c and yellow c have two different time and distance values. This is how the MMX works to conclude velocity towards or away from light does not add or subtract from a relative velocity which is always c. Hopefully armed with this understanding I can come up with a much more powerful mathematical description of how velocity relative to c really works.
PS. You may wonder why I always use Bob's time for the calculations. This is because velocity uses Bob's time (v=x/t). If I wanted to use Alice's time, velocity is expressed as Yv = x/t'.
Edited by ralfcis, 12 September 2019 - 09:27 AM.