A Simple Example, and a Test

Dec 2012
81
4
Boulder, Colorado
Here is an example that I posted to a UseNet group that might be of interest to people on this forum:

First, I wrote:

The MCMIFM (the Momentarily Co-Moving Inertial Frame Montage) is the uniquely true and meaningful reference frame for the accelerating observer, because it is the ONLY reference frame that agrees with the observations and first-principle calculations that he himself can make. [...] My CADO reference frame is completely equivalent to the MCMIFM.

Then, I wrote:

I've given numerous examples that show how easy the CADO equation is to use ... MUCH easier than directly using the Lorentz equations, and much easier than using a Minkowski diagram. To refresh your memory, first read Section 2 of my webpage, which defines the CADO equation and its variables. Then read Section 3, titled "Idealized Instantaneous Velocity Changes", which shows in detail how the CADO equation is used. Be sure to read about the "delta_CADO" equation (which is only valid for instantaneous velocity changes), because it is especially easy and fast to use. All of the above is just a few pages ... shouldn't take you long. When you are done reading that, test your understanding by using the delta_CADO equation to determine how much the home twin ages (according to the traveler) if, when they are 40 ly apart (according to the home twin), the traveler instantaneously changes his speed from 0.8 ly/y, going toward her, to 0.9 ly/y, going away from her.


-- https://sites.google.com/site/cadoequation/cado-reference-frame
 
Last edited:
Jun 2016
1,253
598
England
I have to admit that I am relying on my experience with other consequences of accelerating reference frames (e.g. the Coriolis effect) rather than direct (mathematical) experience with the time dilation issues, however...

I suspect that a rigorous mathematical analysis of the MCMIFM will show that there is a missing term for the "rate of change of MCMIFM".

This will mean that for modest accelerations your MCMIFM algorithm will work well,
but for larger accelerations, you will find there will be discrepancies.

My personal mathematical dexterity is very unsophisticated,
(I can usually follow someone else's route, but struggle to find my own)
so I will have to leave it to others to either support or put down my argument.
 
Dec 2012
81
4
Boulder, Colorado
[...]
I suspect that a rigorous mathematical analysis of the MCMIFM will show that there is a missing term for the "rate of change of MCMIFM".

This will mean that for modest accelerations your MCMIFM algorithm will work well, but for larger accelerations, you will find there will be discrepancies.
[...]
I'll quote from my previous posting:

"The MCMIFM (the Momentarily Co-Moving Inertial Frame Montage) is the uniquely true and meaningful reference frame for the accelerating observer, because it is the ONLY reference frame that agrees with the observations and first-principle calculations that he himself can make. [...] My CADO reference frame is completely equivalent to the MCMIFM."

The fact that the CADO reference frame agrees with the accelerating traveler's OWN observations and OWN first-principles calculations, for ANY accelerations (large or small), is enough to convince me that it is correct. And it is the ONLY frame that agrees with those observations and first-principles calculations.

Those observations and first-principles calculations are explained in detail in Section 10 (entitled "Empirical Determination of the Current Age of a Distant Perpetually-Inertial Person") of my webpage,

https://sites.google.com/site/cadoequation/cado-reference-frame