# Re: A Symmetric Twins Conundrum

*From*: Mike Fontenot <mlfasf@xxxxxxxxxxx>*Date*: Sat, 02 Sep 2006 10:10:28 -0600

(For context, parts of my previous question are quoted below).

I found the error I was making when I tried to adapt my CADO

equation to the symmetrical twin paradox (that was causing

results that were inconsistent). My initial conjecture about

the correspondance between the ages of the two twins (according

to one of the twins) is correct: a plot of twin 2's age, versus

twin 1's age, according to twin 1, starts from the origin as

a straight line (of some positive slope 1/gamma < 1). Working

from the other end (when the twins are reunited, say, at ages

40 and 40), the plot is another straight line with the same

slope 1/gamma, ending at the point (40,40). At the midpoint

(age 20 years old for twin 1), the plot jumps discontinuously

from the lower straight line to the upper straight line.

This plot is just like the plot for the standard (aymmetrical)

twin paradox (plotting the home twin's age versus the traveler's

age, according to the traveler), except that the magnitude of the

discontinuity is smaller.

But I had wanted to adapt my CADO equation to handle the symmetrical

problem so that I could obtain the plot without having to work

from both ends. (In a more complicated scenario (with multiple

speed changes), the twins would not necessarily be reunited, so

that working backward from the reunion wouldn't be possible).

That's one of the advantages of my CADO equation (for problems

in which one of the twins is perpetually inertial): it allows

the magnitude of the discontinuity to be computed directly, without

using information about the future parts of the trip.

I wanted to be able to do the same thing in the symmetrical problem,

but when I tried to adapt the CADO equation to do that, my first

attempt produced inconsistent results (because of mistakes I made).

It MAY be possible to adapt the CADO equation to handle the

symmetrical case, but my first attempt was incorrect. It may be that

any such adaptation might not be very useful...the utility of the

CADO equation in the standard (asymmetrical) case lies in the fact

that the quantities on the RHS of the equation are all based on the

conclusions of the home twin, which are much easier to compute than

the corresponding quantities based on the conclusions of the

accelerating twin. But in the symmetrical case, both twins

accelerate, so most or all of the utility of the CADO equation may

be lost.

Mike Fontenot

_______________________________________________________________

I wrote:

.

I previously wrote:

I quantified this effect in a previous posting. The equation in

that posting applied to an accelerating twin and a stay-at-home

twin. But it can be adapted to handle the symetrical case also.

I've been trying to do what I claimed (in the last sentence above)

could be done, and it's not as easy as I had expected...so far,

I haven't gotten a consistent result. Has anyone ever seen a

description of the symmetrical twin paradox, in which one of the

twins determines the correspondance between their two ages?

I.e., for each instant in the life of one of the twins, what

is the corresponding age of the other twin (as concluded by

the first twin)? (I'm of course talking here about the DEDUCED

simulataneity, NOT the way a TV image of the other twin would

appear to the first twin to be ageing). What does that plot

look like?

**Follow-Ups**:**Re: A Symmetric Twins Conundrum***From:*Mike Fontenot

**Re: A Symmetric Twins Conundrum***From:*xilog

**References**:**Re: A Symmetric Twins Conundrum***From:*Mike Fontenot

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