This statement:
I'm not completely sure if this is what your w is...
Makes me think you're proof reading my post for math errors and not reading it for content or meaning. I'm also getting the impression that you don't accept c
^{2}=v
^{2}+w
^{2} as a valid equation of relativity.
Ok, to clear up confusion, I'm not going to refer to velocity through time as w anymore but as c/Y. c/Y is what you get when solving for w in the above equation. Gamma is a constant and c is a velocity therefore the velocity through time is a constant velocity as a factor of c even though it can also be expressed as time/time. A person moving at .8c velocity through space relative to you is also going .6c velocity through time relative to you. His relative velocity through space goes up and his relative speed of time slows down. That's because everyone is always moving at the absolute value of c (according to c
^{2}=v
^{2}+w
^{2} ) and their relative velocities (v and c/Y) are the space and time components of that absolute velocity c. This concept of splitting up the universal speed of everything of c into 2 relative components allows c to be c for all frames while allowing relative velocities through space to not be additive to c. This concept does not require the concept of length contraction to maintain the constancy of c for all frames as relativity requires.
So when you draw an STD and Bob is in the reference frame, both he and Alice are going at the absolute velocity c but Bob's relative velocity components are v=0c and c/Y =1c and Alice's relative velocity components are v = .8c and c/Y = .6c and vice versa when you draw Alice as the stationary frame. See c/Y (the velocity component through time) =1c for Bob, whose speed can be expressed as c or 1yr/yr.
I have an idea, what if I write my posts in blue and red font. The blue would be for standard relativity and the red would be for my non-standard relativity. Then you could read my posts using red tinted glasses so any non-standard relativity would be rendered invisible which it seems to be anyway. I know you're going to say there's no such thing as non-standard relativity but if I'm proposing new equations that fully comply with relativity and a new interpretation to add meaning to those equations then I am indeed engaging in non-standard relativity.
As for the Yv controversy, what you said was the only place you saw the term Yv in relativity was associated with 4-velocity or 4-vector. I went on wiki and indeed you were right but then I wrote a bunch of posts why my Yv was not related to your 4-vector Yv. (Yv also appears in relativistic momentum when proving E=mc
^{2}). I will find that exchange, which will take hours, when I have time.
P.S. Oops I found it right away:
Re: Ralfcis SR interpretation (Ralfitivity )
Postby BurtJordaan on June 12th, 2016, 12:11 pm
Ralfcis, although your math appears at first sight not to be in conflict with SR, your terminology is in conflict with SR and hence is bound to create severe confusion for readers who have learned a bit of SR. Examples:
The idea is gamma velocity (Yv) which is the total velocity vector through spacetime...
The term in relativity is the "four velocity" and in SR it equals the constant . Hence it is not a function of velocity.
P.P.S In case I really have to provide the proof that c/Y =W, here it is:
c
^{2}=v
^{2}+w
^{2}w= sqrt(c
^{2}-v
^{2})
Y=c/sqrt(c
^{2}-v
^{2})
so substituting c
^{2}-v
^{2} into the 2nd equation yeilds:
w=c/Y