**Alternative Twin’s Experiment**

The traditional twins experiment is generally solved such that all agree the traveling twin is younger because of non-symmetric acceleration. However, this twin’s paradox will produce symmetric acceleration and force SR to exclusively explain reciprocal time dilation up against the SR clock synchronization method which is based on the universal truth of t = d/c. In short, SR fails.

Setup

O and O' are observers with clocks in the same frame in the vacuum of space.

Procedure

1. Both set their clocks to 0 and O instantly acquires v relative to O'.

2. O and O' are in relative motion for some agreed up time t' on the clock of O'.

3. After time t', O' will acquire v in precisely the same way as O in precisely the same direction.

4. At the same instant O' acquires v, O' enters the frame of O and O' sends a light pulse to O and records this as the end of the experiment at time t'.

5. O' receives the light pulse and records the time as te.

6. Since, O and O' are again in the same frame, O performs with O' the round trip speed of light calculation using a time trial to calculate the distance between the two. Let D be that distance. O then subtracts D/c from te and determines its proper for when O' entered the frame to determine the correct end of the experiment which will match the end for O'. Let this time be t.

7. Finally, O and O' perform the SR clock synchronization method to determine the ordinality of the two clocks. To do this, O sends its time t1O to O'. O' immediately sends its time tO' back to the clock of O. O receives this light at t2O. In particular, Einstein concludes the two clocks are in sync if tO' = ½ (t2O - t1O). Thus, the age ordinality is established as tO' - ½ (t2O - t1O).

http://www.fourmilab...in/specrel/www/

***Note, the above can be replaced with equal agreed upon proper burn times and proper accelerations and will produce the same results according to the SR uniform acceleration equations.

The steps above represent an effective procedure for deciding the age ordinality of O and O'. More specifically, step 7 determines the clocks of O and O' as one of the following.

· O is younger than O'.

· O is older than O'.

· O and O' are the same age.

Since each step of the procedure above is well defined and produces a unique outcome with the output at step 7 producing only one value, then this problem of determining the age ordinality of O and O' is recursive and thus logically decidable.

Now, LT will be applied to solve the problem above.

From O as stationary, its proper time is t. Hence, O concludes O' elapses t/λ and therefore concludes O' is younger.

From O' as stationary, its proper time is t'. Hence, O' concludes O elapses t'/λ and therefore concludes O is younger.

Now, Einstein’s clock synchronization method by his own admission is

*“free from contradictions”.*

http://www.fourmilab...in/specrel/www/

Therefore, we may conclude the effective procedure listed above produces one correct answer to the age ordinality of O and O' otherwise, the SR clock synchronization method does not work and hence LT fails.

On the other hand, LT produces contradictory results and thus provides an answer that is not logically decidable.

Hence, under SR, the problem above is logically decidable and not logically decidable depending on the method used.

Worse, at least one of the solutions provided by LT must contradict the results of the clock synch and therefore, LT must calculate at least one incorrect result. Clearly, this proves LT is not a reliable tool for mapping proper times between frames since at least one of its solutions must be wrong above.