I've been working on this topic of the twin paradox for the last few days and after referring to the posts I received earlier and from references on other websites, I've finally come to a conclusion.
Here goes...
Firstly, the relativistic doppler effect (RDE)---this is basically a cumulative result of the classical doppler effect (CDE) and time dilation (TD) ,since Einstein first checked the CDE and found, when dealing with light waves, that it wasn't in accordance with his Special relativity (SR)and Maxwell's postulate for the constancy of the velocity of light,and so he edited the formula so that the modified formula gives result in accordance to SR--in other words, if we apply the classical relativity to a particular situation and then slightly modify the result by using lorentz transformation,we eventually get the same result that the RDE gives us.
(reference:
http://redshift.vif.com/JournalFiles/V12NO1PDF/V12N1HAM.pdf)
In his post(https://www.physicsforums.com/showthr...76#post1384776 ), George states that the result,whether obtained by RDE or Lorentz transformation,is the same--it has to ,since the RDE was tailor-made for SR.
However,if we leave the formulae of RDE,and,as I said use CDE first,followed by time dilation formula,we see that the individual results for the doppler effect is 3 times more 'powerful' than time dilation effects.So, for a rapidly receding star, we would have TWO effects, Doppler and Time Dilation, both of which would cause us to see the spectral lines to be shifted toward the red end of the spectrum. Einstein made a Relativistic adjustment to the Doppler Effect equation to account for this Time Dilation effect.
If the star was rapidly moving toward us, The Doppler shift would be toward the BLUE end of the spectrum, while the Time Dilation shift would still be toward the red. Einstein's Relativistic Doppler formula calculates this, too, and gets a resulting red shift that is smaller that the non-Relativistic Doppler red shift would have been. It turns out that the Doppler effect is always at least three times as great as the Time Dilation effect, so Doppler always prevails.
(reference:
http://mb-soft.com/public/reltvty1.html)
Now, as
Sylas pointed out,in one of the previous threads, what we observe is nothing but the reception of light photons(I think page 3 of Twin paradox,a quick(ish) problem),time dilation is not what we see-the visual perception of light is governed by the doppler effect,since the doppler effect alone tells us about,'how' I may say,the light is received by us and thus it tells us exactly what we see.
In
sylas' post(which is more elaborately dealt with in another thread,referring to
https://www.physicsforums.com/showthread.php?p=2217788#post2217788), he dealt emmaculately with the observations of the twins--in which,therefore,the role of the doppler effect becomes very emminent.The reason why the star suddenly appears 12 light years away to the traveling twin, at the start of the outward journey,instead of the 6 light years that it appeared to be at in the star's rest frame, is basically due to the "way" in which light is recied or percieved---this is explained very well in the example of the pin-hole camera example,given by
sylas(on
https://www.physicsforums.com/showthread.php?p=2217788#post2217788).
In this example,it clearly states that the change in observation of objects,like the star,is all due to the way our perception of the light from the object changes, once there is relative motion.
I will not go into the detailed description of
sylas' example,but I found a simpler approach to it(which does not,however deal with what the twins individually see).
Suppose there is a pulsar (flashing star) at a certain distance from earth,which to an earthbound observer flashes 1 time per sec.Now, a twin moves staright toward this puslar,leaving earth, and due to doppler effect,observes a greater frequency of light,2 flashes per second,and when he returns home,observes a lower frequency of 0.5 flashes per sec (=1 flash per 2 secs).
The earthbound observer sees 20 flashes from the beginning of the other twin's journey to the instant that he reaches home--so the journey took 20 seconds to the earthbound observer.
However, to the traveling twin,he sees 16 flashes while going and only 4 while coming. Thus, the outward journey took him (in his reference frame) 8 secs and so did the return journey(this comes from the different frequencies observed by him during the journey.)
Thus, by the end of the trip,the traveling twin thinks he is 16 secs old,but the earthbound observer thinks he is 20 secs old.(reference:
)
This is a much more simplified version of
sylas',explanation,but its purely in the point of view if the doppler effect,just like
sylas said.
The explanation in the Virginia Tech website ( link provide in post 24 of this thread),is,on the other hand completely in terms of lorentz transformation---but,as
George Jones said, they end up to the same result.
Now, coming to my original question, the twin paradox is very different from the train-tunnel experiment because --in the train-tunnel experiment,the two observers are only receding from each other,whereas in the twin paradox,the twins first reced from each other,then move toward each other---and,thanks to the doppler effect,they 'recieve' the light waves responsible for the visual perceprtion of these events,very differently on either journey.
The explanation on the Virginia Tech website described the entire story based on time dilation and length contraction only--that was just an alternate,but equivalent description.
sylas also stated in one of his posts that "Furthermore, the star ship passengers KNOW that that they are the ones who have changed perspective -- not the remote star -- because the star cannot have moved a large distance in negligible time. They must be looking at it from a new frame of reference. " (pg 1
https://www.physicsforums.com/showthread.php?p=2217788#post2217788)
He says that in the case of the twin paradox,we can tell which person is moving,as opposed to other situations in SR where due to relative uniform motion,we can't tell which person is moving and which isn't---but this is again,not due to any breach of the laws of SR,but it is due to a common sense explanation,that a massive nonliving object like a star can't move all of a sudden. If we lacked this common sense,or if the star had the capability to move,like a giant living object,we could not have told who actually is moving.
This is what I think it is all about,please tell me if my basic concepts are alright,even if I haven't gone into the details.
