yogi said:
When you include changing velocities, SR can be used to predict the behavior of the accelerated phase so long as, in the formulation, the analysis takes the view of the inertial (unaccelerated clock). So if you want to stick to a pure comparison between SR and LET (which is what i thought we were discussing), my challenge to you is to work the problem from the standpoint of the K' clock at rest.
So, you can't solve the problem and you ask for me to give you a solution? Interesting...But more about your "answer" later. For the time being, the solution is readily available in many course notes and papers (I may have even quoted a few in my other posts). Done from the point of view of calculating and comparing the proper times of BOTH twins, the right way to do it.
When you include accelerations using LET,
Stop right here, LET does not deal with accelerated motion, only SR does. Sooo, LET CANNOT be used to solve this problem Unless CHEATING is involved. But more about this later...
the K clock is considered at rest wrt the ether - and SR takes the position that the K clock remains in an inertial frame - both give the same result (In LET however, the presupposition is that both acceleration and uniform velocity are absolute wrt to the K frame (which is the ether frame) whereas in SR the uniform velocity increment is relative).
LET doesn't have a treatment for accelerated motion, ONLY SR does.
While I have a firm conviction in the sui generis properties of space as a medium, I am not going to take up the defense of a theory which is based upon physical changes in lengths and time brought about by absolute motion.
...but this is what LET IS all about. You were supposed to produce a solution based on LET, as you have been challenged. Instead, you "produced" ...nothing but a bunch of deflections and this :
If you want the problem worked by an LET type - see
http://redshift.vif.com/JournalFiles/V10NO3PDF/V10N3KHO.pdf
Regards
Ahh, what do we have here? A "paper" from the very famous crank journal Apeiron, by the resident crank co-editor who quotes an even more famous crank, Tom van Flandern (Chris is going to have a ball with this, wait until he gets loose on the garbage in the paper) having "proven" the twin paradox in LET.
But ...what do both Kholmetskii and TvF use? Lo and behold, hyperbolic motion (reference [2]) from...Special Relativity. So, by plastering to the original LET the results of SR (80 years later notwithstanding), messrs K. and TvF "prove" that they can "solve" the twin paradox using LET. So, with a little bit of historical forgery , one can prove anything, right?
Now, let's not be so hard on you , mr. K and mr. TvF, let's admit that LET can copy from its younger sibling SR. Problem is , that the "solution" from the paper you quote is wrong, mr.K does not understanf hyperbolic motion well enough to solve the problem. How do I know this? Because the correct results computed using SR are readily available in many other places.
But again, let's give you one more chance, given a, A and T from my previous post , you try to find the correct solution to the problem and correct the stuff botched by the illustrious messrs K. and TvF. I'll give you a hint: it takes about 1 page to do it right using SR.
Phase 1: Rocket (with clock K') embarks with constant proper acceleration a during a time A as measured by clock K until it reaches some velocity v.
Phase 2: Rocket keeps coasting at velocity v during some time T according to clock K.
Phase 3: Rocket fires its engines in the opposite direction of K during a time A according to clock K until it is at rest w.r.t. clock K. The constant proper acceleration has the value -a, i.o.w. the rocket is decelerating.
Phase 4: Rocket keeps firing its engines in the opposite direction of K, during the same time A according to clock K, until K' regains the same speed v w.r.t. K, but now towards K (with velocity -v).
Phase 5: Rocket keeps coasting towards K at speed v during the same time T according to clock K.
Phase 6: Rocket again fires its engines in the direction of K, so it decelerates with a constant proper acceleration a during a time A, still according to clock K, until both clocks reunite.I know (and most everybody else does) that it CANNOT be done in LET. Unless...CHEATING is involved. Even with cheating, it should take you about 1 page, not the many pages of nonsense from Apeiron. Time for you to hit the equations, enough of the runaround.