[MikeFontenot (OP)]

(The real title is "A New Simultaneity Method for Accelerated Observers in Special Relativity")
__________________________________

Until recently, I've been an avid proponent of the "co-moving inertial frames" (CMIF) simultaneity method (previously called the "CADO" method by me).  I had claimed to have proven that the CMIF method is the ONLY method that agrees with the accelerated observer's own elementary observations and elementary calculations.  But I recently concluded that there was a loophole in that proof, and therefore I had failed to prove what I thought I had proven.  I decided to take a fresh look at the whole issue of simultaneity for an accelerated observer.  In the course of doing that, I discovered a new simultaneity method that shows, with a very simple proof, that the CMIF method isn't correct.  My new method says that when the accelerating observer instantaneously changes his velocity, the current age of the home twin DOESN'T instantaneously change.  Instead, the slope of the age correspondence curve instantaneously changes its slope from a constant less than one to a constant greater than one.  And then after a well-defined passage of time, the slope instantaneously switches back to the same constant less than one that occurs in the first segment.  So the "curve" in the age correspondence diagram is always a continuous, piecewise-linear line of three straight line segments.  Unlike the Dolby and Gull simultaneity method, and the Minguzzi  simultaneity method, my method is causal, i.e., effects are always PRECEDED by causes.  My new method is explained in detail on my webpage referenced below (in front of the old information on my webpage, which I now know to be incorrect).

 Michael Leon Fontenot

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

  All you ever need to know about the twin "paradox".

[evan_au]

my method is causal, i.e., effects are always PRECEDED by causes

Preceded in whose frame of reference?
Are there other frames of reference where the cause and effect are not observed in that sequence?

[Colin2B]

Mike
You have introduced us to this before, and on other sites.
In keeping with our policy on nonstandard hypotheses we would prefer it to be in our New Theories section.

[MikeFontenot (OP)]

my method is causal, i.e., effects are always PRECEDED by causes

Preceded in whose frame of reference?

In the accelerating traveler's frame of reference.

[MikeFontenot (OP)]

Mike
You have introduced us to this before, [....]

No, that is incorrect.  I haven't posted this new simultaneity method anywhere before today.

[jeffreyH]

An observer A is in an accelerating frame and another observer I is in an inertial frame. From A's perspective he can assume he is in a gravitational field with I accelerating with respect to himself. This may not be the case but how would A know this? Apart from knowing he is in an accelerating craft. There are scenarios where the distinction is not possible.

You cannot circumvent relativity.

[MikeFontenot (OP)]

An observer A is in an accelerating frame and another observer I is in an inertial frame. From A's perspective he can assume he is in a gravitational field with I accelerating with respect to himself.

The equivalence principle CAN be used to define an alternate formulation of the twin paradox, one where at the turnaround, a gravitational field is magically switched on, that extends throughout all space.  When the traveling twin turns on his rocket for a brief time, he doesn't accelerate because the rocket thrust exactly balances the gravitational field.

That alternate view, while possible, just muddies the water.  Special relativity is perfectly capable of solving ANY scenario as long as there are no REAL gravitational fields affecting the twins.  That is certainly possible, even for a long space voyage ... space is mostly empty.

The equivalence principle is very valuable (and was very valuable for Einstein when he was trying to formulate his general theory) for understanding what the characteristics of general relativity must be.  But it is not of any use in helping to solve problems that arise in special relativity.