Guido "Wugi" Wuyts @ Dilbeek, Belgium, Europe, World, Solar System, Milky Way, Local Cluster, ...

Meet MySRT and the Paradox Twins

Note.

These lines are intended, not as an explanation of the Twin Paradox (TP) -and other SRT features- to the non-understanders, but as an afterthought for those who get the hang of TP and SRT, or think they do. An attempt to show how one can always find new, surprising, aspects upon something that is generally considered an established body of knowledge.

Click on the pictures below (or on the text reference) for full size.

See also my page qbRelaty where some of the programs discussed here are illustrated with animation.

Again that Twin Paradox?

At a first glance TP may seem a relativity feature that is, if surprising, “relatively” straightforward.  Quite a few e-sites deal with it, and some will be referred to in this one.  When I included the topic in my <Relaty> Qbasic program (*), the first version of it went like this (Relaty.exe, Relaty.bas) , see illustrations below

(*) Pardon me for still using Q-Basic. I'd love to learn about 'Flash'-ier or mathwizier environments, but the time it's going to take me will outpace what, amongst others, I want to communicate here and now. See also my QBasic-page.

 RelatyHometwin.PNG,    and     RelatyTravtwin.PNG :

       

As you can see, its looks are a quite simple Minkovsky representation, if more telling (the animation within the program, that is) than your average explanation elsewhere .

Then after some time, having come across the odd question (or answer) in the occasional topic-related news group or web site, and having pondered further about it, I came to realise that I wanted a better, more explicit and detailed description of TP (*).

(*) Caution  I wish to stress that I do not at all intend to prove anything “Einstein didn’t see or got wrong”, as I consider myself adhering to the SRT (and otherwise science-minded) community, and not to any revolutionary crackpot scene !
It’s only that I haven’t encountered yet an explanation of TP (and other SRT features) that I liked better, than the one I'm "trying out" here myself.
It’s also that I’m graphics-biassed, all the more regarding a geometric theory par excellence, when many scientists seem to think of graphic representation as cumbersome burden:-\

First, I wanted to better show the status of each twin, and of his kin, with respect to himself, and with respect to the other, throughout their respective "Oddissey" ;-).

Second, I realised that TP was absent in my <Relasee> program (*) (Relasee.exe, Relasee.bas), and needed definitely inclusion there as well.

(*) I'll say a bit more about Relaty and Relasee and the respective features of SRT they're concerned with in the next section.

Third, I felt that, besides a Minkovsky representation of TP, a visual “real time” simulation -in the style of the relativistic trains in <Relasee>- would give a feel of the "actual phenomenon".

So I developed (still in QBasic;-)  
1) a version of <Relaty> with a slightly completer description of TP ;
2) a version of <Relasee> including TP, in a similar Minkovsky description ;
3) a separate <TwinTy> program doing a visual simulation “in real time” of TP, as counterpart of <Relaty> ;
4) another <TwinSee> program doing ditto, as counterpart of <Relasee> .
Some other ideas are expressed in yet other programs <TwinTest> and <TwinRev>, see later.

Each of these programs is discussed in one of the next paragraphs. But first let me introduce you to my SRT pet topics, say, to MySRT :-)

 

MySRT.

My first struggling with SRT at university resulted from noticing (who hasn't?) an apparent contradiction between relatively easy algebra and geometrically counterintuitive statements such as constancy of light speed. The impression that even my teaching prof had no full understanding of the geometrical properties didn't help much either.

After seeking for quite some time by myself, I found my way to a geometry-based axiomatism that could trigger one's intuition, and that would come up with constant c as a there-you-are result, not as a hard-to-swallow presupposition. Others have tried out or achieved similar axiom schemes  (*), but the scientific establishment seems to shun geometry-biassed approaches. Tant pis for them, and honni soit qui mal y pense.

(*) A good article on this aspect can be found in Science & Vie (october 2000 issue p 71 "Tout est relatif, absolument tout!").

My Relativiteit page deals with my "relativistic geometry" (TAK), after explaining the historic development of SRT "from Galileo to Einstein" (TIK), which could be summarised as kind of going through all the wrong assumptions possible, in the reverse way ;-)

My apologies for its being in Dutch (notice the tick-tocking of the klokje in the titles). 
So, let me just mention here my set of axioms, sparing the intuition yet yielding correct relativistic results:

1.   There exists a system holding "solid bodies", this meaning, bodies keeping their dimensional ratios constant (internal=sizes, external=distances) .
tak2 axiom1.gif

.

(admittedly, along rather fuzzy space and time axes x,t, yet to be defined).

2.   Light clocks in that initial system relate to each other homothetically, ie they keep "running in pace" .
tak4 axiom2.gif

(or the other way: world lines of light behaving like this define light clocks)

Definition: inertial systems follow parallel (world)lines in the initial system, obeing x=vt+const, or v=dx/dt=const. The initial system is inertial with v=0 to itself. results:

(inertial world lines can be followed up by light clocks and vice versa)

3.   A solid body in an inertial state has world lines in some inertial system, ie keeps its dimensional ratios constant 
tak13 axiom3.gif

(Solid bodies belong to inertial systems and can be gauged by light clocks)

4.   In all inertial systems isotropic light clocks mean equal time, ie isotropy of time in each inertial system.
tak16 axiom4.gif,     tak17 axiom4 b.gif

     

(And hence, of material distances. What seems obvious in the initial system, thought at rest, is 'cleverly' imposed upon any inertial system)

5.   Perpendicular to motion, length measurements between inertial systems are symmetric.
tak20 axiom5.gif

(Hence, length equality means material equality, perpendicular to motion)

Only by now can we specify and gauge the space and time axes for the various systems.
tak14 axes.gif

Axiom 4, put to comparison between different inertial systems, yields differential simultaneity.
Axioms 4 and 5 yield length contraction and time dilation.
Another result is the constancy of light speed, as a common feature of all light clocks, their isotropy meaning same light time for same distance, but being aware of what 'distance' means in different systems.

Actually, understanding the properties of light clocks, and their role as basic gauge tools for measuring length and time in any system, with any ruler and clock equipment, is my cornerstone for an intuitive and geometrical understanding of SRT. The Michelson-Morley experiment may with hindsight be re-interpreted as an attempt to prove light clocks not being true (isotropic) clocks !  

My program <LichKlok> (Lichkl9e.bas) displays the behaviour of lightcone clocks as "seen" by
moving (LichtklokRuster.png) and their own (LichtklokBeweger.png) systems. 
           

The following (pseudo-) animations (*) can be run :

(*)  Extract the ZIP files to a single folder, sort to name, and open the first picture with some program allowing browsing through them at speed (even cycling back when at the end) by holding down a mouse or key button, to get the (cycling) 'animation' effect.
PM.  Since then, I've also made the GIF animations that follow.

Moving lightcone clock according to system at rest:
Minkovsky description (xyt) liteconeclok xyt restsys.zip ; and 
space description (xy) liteconeclok xy restsys.zip .  
Also,
lightclk_restframe_xyt.gif,     and     lightclk_restframe_xy.gif    
           

Moving clock according to its own system:
xyt description liteconeclok xyt cloksys.zip ;
and xy description liteconeclok xy cloksys.zip . 
Also,
lightclk_movframe_xyt.gif,     and     lightclk_movframe_xy.gif  
           

The second pet topic of MySRT is the distinction between measuring and watching, both being often referred to as "observing", and many an explanation confusing one with the other in its line of thought !

Length contraction, time dilation and differential simultaneity describe relativistic objects according to the rules of the Lorentz equations, which render the relationship between an object's system and an observer's system.
An object thus described can be viewed as being "laid out" along a space-like axis, of its own or of an observer, evolving along the corresponding world lines. I will call this a "Lorentz object", obeing as it does the Lorentz equations.
Now, space-like axes, and objects laid out along them, can never be perceived instantly !  They result from measurements and back-calculations of corresponding positions and times, using Lorentz equations and the necessary knowledge of the various light paths involved.
So, a Lorentz object could as well be called a measured object, or back-calculated object, or space-like object.
Observe that an object moving along an observer has two different Lorentz "manifestations" (besides third party ones) : one along a space axis of its own, and one along a space axis of the observer. So does the observer's measuring rod in the object's system. That's how length contraction is made to be a reciprocal feature.  

My QB-program <Relaty> deals mainly with basic SRT, somewhat revisited geometrically, and Lorentz objects. (Admittedly, the "Measuring ain't seeing" chapter would belong rather to the program of the next section)  
The derived and completed picture
LorentzObjects.PNG 

shows the key features of Lorentz properties between two 'equal' moving objects : differential simultaneity, length contraction and time dilation, and the reciprocal nature of those. It gives also a hint to the solution of the so-called Pole-Barn paradox.

When it comes to perceiving an object instantly, it will "appear deformed" according to the different paths it takes light to reach the observer at a given moment from the object's various parts. An object thus perceived can be viewed as laid out, not along a space axis, but rather along a light cone that connects to the observer at the moment of his perception. Light cones are the media of instant perception, not space axes (*).
I will call such manifestation of the object an "Einstein object" (**).
We could call it as well the perceived object, or the light cone object.

(*) It is ironic that space axes, the basis of our intemporal, instantaneous conception of space, should be forever beyond our instantaneous perception. What we see all the time is light cone spaces.

(**) Why Einstein object?  I read that Einstein asked himself early on: what would I see if I "sat" on a light front?  Although he doesn't seem to have answered this question explicitly (a photon "lives" a single moment and place, condensating thus all energy it encounters and scatters, correct me if I err:-), the general question "sees" beyond Lorentz and results in Einstein objects. 

Observe that where two observers would meet, they would see the same Einstein object, sharing the same light cone. They would see it however differently, being themselves in different states: see what follows.
Indeed, there is actually a third manifestation of the object, linked with its manifestation of being perceived and with the observer doing the perceiving. It is the manifestation of perception, of one actively perceiving the object. This manifestation is instantaneous, at the moment of perception, and the perceiver therefore "projects" the object along his space axis of that moment (but with its parts belonging to various earlier events, it not being a Lorentz object).
We could call this the perception object (or object of perceiving), to distinguish it from the perceived object (or object of being perceived), but generally either manifestation represents an Einstein object.  

My QB-program <Relasee> deals with Einstein objects (ie relativistic objects as SEEn).  
(Admittedly, the "Measuring ain't seeing" chapter of the previous program should be transported in this one as it treats about linear Einstein movements as well; it was meant as a 'mise en garde' in the Lorentz-object explanation there. The derived and completed picture LinearMovin.PNG shows the results, in agreement with the formulas mentioned hereafter in "Relasee, TP-wise")

Besides TP, the program discusses some other basic inertial movements. Examples: 

a frontline before passing (frontline1.PNG) and after having passed (frontline2.PNG) the observer, 

         

a passing squadron (animate with SeeSquad.pps, SeeSquad.zip), 
Squad.gif

a train simulation ( trains.zip). 
TrainSimul.png     Animation : RelaTrains.gif

     Animation:    

When watching the squadron at work you'll understand my frowning upon the so-called Penrose-Terrell Rotation (***) (http://www2.corepower.com:8080/~relfaq/penrose.html)

(***) Roughly speaking it corresponds to a square of pawns passing by the observer, stating that it appears rotated by a same angle along (i) the direction of movement (due to Lorentz contraction) and (ii) the perpendicular direction (due to light needing time to reach from there). Bringing thus a 'Lorentz object' value (i) and an 'Einstein object' one (ii) into a same explanation, a thing I complained about before. But the 'real' picture Squad.gif hereabove does show rotation-like deformed squares...

Let us now return to our Paradox Twins.

 

Key events in the Twin Paradox.

When looking at the graph of the Twins (taking the symmetrical case: velocities v and ‑v), at first sight it seems alarmingly simple :
 TPKeyEvents.PNG 

A = departure of traveler
B = turn-back point of traveler
C = arrival of traveler

AC = world line of home twin with corresponding xt axes
ABC = world line of travelling twin, ie
AB = outbound leg at velocity v with corresponding x't' axes
BC = homebound leg at velocity –v with corresponding x"t" axes

Yet, some other events enhance matters along the homestayer's worldline:

M = halfway event between A and C
D = simultaneous with B in traveler's outbound system, defining space-like line BD
E = simultaneous with B in traveler's homebound system, defining space-like line BE

Rv = home twin, when perceived by traveler twin at his turn-back
Rh = home twin, when perceiving turn-back of traveler twin
(RvB and BRh = light lines, at velocity c and –c respectively)

M, D and E are Lorentz object events, linked by Lorentz equations to event B;
Rv and Rh are Einstein object events, linked to B as one twin perceives the other with a delay.
Notice also that in the symmetry case AM= MB, DM= ME, and RvM= MRh.

Calculation of these special events is straightforward. Let us use the beta-velocities beta= v/c and, Minkovsky-wise, put c= 1 (expressing distances in lightyears when time in years). The traveler twin switches instantly between a "beta" and a "–beta" frame at B.

Let us call total travel time, in home twin's system :
tC== 2 t0,
say, 2*50 = 100  Y (years),
and the distance reached :
xB== x0= beta*t0  LY (lightyears).
This happens at the moment t0= tC /2, so that
tM= tB= t0= 50 Y.

To the traveler, his voyage lasts 2 t'0 and his homestaying twin reaches distance x'0, so that
x'0= ‑x0/gama, and
t'0= t0/gama, with
gama== 1/SQRT(1-beta*beta).

Now let us calculate Lorentz events D and E.
Whereas for D, according to the traveler’s "beta" frame
t’D= t’B= t’0,
according to the homestayer, the Lorentz transformation yields
tD= t0 /(gama*gama)= t0 (1-beta*beta).
The distance reached at turnback, according to the traveler is
x’D= x’0= -x0/gama.
Similarly for event E, according to the traveler’s "‑beta" frame
t"E= t"B= t’0,
so that according to the homestayer we get
tE= t0 (1+beta*beta),
and again, the distance starting from turnback
x"E= x'0= -x0/gama.
Note that the intervals
DM= ME= t0 *beta*beta.

As for the events of perception, they are linked to B by light, covering the distance x0= beta*t0 with velocities c and -c.  So:
tRh= t0 +beta*t0= t0 (1+beta)
tRv= t0 -beta*t0= t0 (1-beta)
Here also, equal intervals
RvM= MRh= t0 *beta.

Notice the absence of acceleration in this description of TP. Indeed, although often described with accelerations, TP is essentially a non-accelerated SRT feature that only gets complicated, perhaps even slightly countered, by calling for the effects of acceleration.

Nevertheless, the notion that there is more to TP than my initial description, came precisely to me when realising that the voyager twin's instant switching from outbound to homebound system is not to be dismissed as a mere gap in his world description. Thinking of it as the limit case of a smoother description involving acceleration, it can be thoroughly detailed so by a proper investigation of the transitional systems at work. This too was to be an additional feature of my "new" TP programs.

Let us now have a closer look at those programs and the Twin's story they tell.

 

Discussion of each program.

Each program comes in two stages.  First is shown the standpoint or observation of the homestayer, secondly that of the traveler.  The velocity has to be chosen initially, or rather the beta= v/c factor, generally between 0.1 and 0.9+.  Travel time is set to 100 years, 50 outbound and 50 homebound, both at speed (+ and -)v, or beta.  The return is thought instantaneous at the return point, the traveler swapping continuously, but “instantly”, inertial systems between bet= beta and bet= -beta.  This transition, which would be taking zero time, is however developed in detail when in the standpoint of the traveler, and gives "limit case" information about how a continuously de- and ac-celerated transition would look like, and also in the event of different speeds in the going and the return trips.

The traveler's inertial outbound or "beta" frame, is represented in orange; his homebound or "-beta" frame in green.  The "instant" turnback event whith the transition between "beta" and "-beta" frames, sliding through a series of "bet" frames (bet= beta TO –beta), is shown in magenta.

 

Relaty, TP-wise

The program is at Relaty8.bas. A pseudo-animation can be obtained with relaty_tp.zip. A slide show with some more explaining is at relaty_tp.pps. An animation of both standpoints is here:
Relaty.gif

Standpoint of homestayer.

RelatyHometwin2.PNG

The traveler leaves in A at speed beta, reaches distance x0= beta*50 LY (light years) in B (homestayer in M), and then comes back at speed –beta until return C. 

Standpoint of traveler.

RelatyTravtwin2.PNG

The traveler accelerates, switching instantly/continuously inertial frames bet= 0 to bet= beta, the outbound frame.  He then starts off and considers the homestayer, not himself, as receding.  He reaches his return point at proper time t’0; the homestayer at that, traveler's, time has reached event D prior to his midpoint M! 
The traveler then switches instantaneously to his homebound "-beta" frame as described before, then "suddenly" detects his twin at event E ulterior to his, homestayer’s, midpoint M!  The traveler, still at proper time t'0, starts off back, meaning that now he considers the homestayer as approaching. A final decelerating maneuver lets the traveler instantly switch between inertial frames with velocities –beta and 0, and be back again at 2 t'0.

Remark: the homestayer’s events between D and E (including M in-between) are not “covered” by either traveler’s system! All homestayer’s “life” between D and E would seem to have been “dismissed” in the instant turnback maneuver of the traveler.
This shouldn't be too far-fetched: remember that we are dealing with calculation features involving space axes, rather than with 'seeing and not seeing' things. (Though, be warned, we'll 'see' hereafter that what the traveler is going to see is bad enough; he'll see it not in D or E however, but in Rv :-)

What I want to go deeper into here is the question of what is 'really', if instantly, going on between travtwin's system pointing to hometwin at D, and then at E? That's where I came to see there must be more than a mere gap.
If travtwin were to de- and accelerate smoothly to accomplish the turnback maneuver he would be going through a series of instant inertial systems whose space axes would sweep all along the D-E interval of hometwin's worldline. So, in our limit case, we can consider all positions X between D and E as really belonging to a particular space-axis XB, corresponding to an intermediate reference system with velocity bet (between beta and –beta) that's easy to determine.
To each X then, corresponds an instant distance
x' = x'(bet)= BX= x0/gam   [ where gam= gam(bet) ]
that will vary starting from
x'= BD= x'0= x0/gama
to a maximum of
x'= BM= x0  [ X=M: traveler at rest, bet= 0, gam= 1 !)
and then down again to
x'= BE= x'0.
So, even when jumping very quickly, instantly, from a velocity beta to its contrary –beta, in-between there is a split moment when travtwin 'really' is at rest to hometwin, and finds the same distance x0 between them. (Well, he would be too busy suffering accelerations to care much for backcalculating these results :-)

I have added these findings to the <Relaty> program, TP part, displaying x' throughout the turnback maneuver. You'll hardly notice it since it's an 'instant' feature. It's more visible in the <Twinty> program, as the perspective view there renders the changes of x'.

 

Relasee, TP-wise

See program at Relase9.bas. Pseudo-animation of TP with relasee_tp.zip. Slideshow at relasee_tp.pps.

As said before, this program reckons with light taking time to reach the observer, who as a result SEEs an object with its parts in “previous” locations and ages w.r.t. the moment of perception, ie he SEEs an Einstein object. 

The "Measuring ain't seeing" section of <Relaty> discussed already the seeing process of a movement along the line of observation, of an object with length L0 and velocity v : 
LinearMovin.PNG. 

This gives the following observed or "Einstein" speeds and lengths (as compared to beta= v/c, and L= L0/gama= contracted length):  
At approach:
L- = L /(1-beta)
bet- = beta /(1-beta)
At recession:
L+ = L /(1+beta)
bet+ = beta /(1+beta)
(At approach there appears an increased speed as bet- >bet; length L- proves to be even a length dilation, ie L- > L0. At recession the speed appears diminished as bet+ <bet, length appears extra contracted.)

Let us apply this to our TP case (dismissing lengths L along the line of movement, TP describing mainly one-dot twin positions). Either twin is seen by the other, during the outward trip, receding at a diminished speed bet+, Doppler redshifted, and growing old at a lower than "Lorentz" pace. Then, during the homeward trip, approaching at an increased speed bet-, blueshifted, and growing old at a higher than "Lorentz" pace.  It works both ways, but the intervals of perception away and back again differ considerably for either twin: remember Rv and Rh being quite apart !

Standpoint of homestayer.

RelaSee_ObsvHome.png     Animation :     RelaSee_ObsvHome.gif

     Animation :     

The homestayer, then, sees the traveler recede for the larger part of his 100 Y waiting time, up to event Rh, when he gets to see the turn-back. After that, the traveler is seen coming back for the shorter part of the 100 Y. The traveler appears to grow old more slowly in the first half of his trip than in the latter, totalling up the same aging time in either half.

Standpoint of traveler.

RelaSee_ObsvTrav.png     Animation :     RelaSee_ObsvTrav.gif

     Animation :     

On the other hand, the traveler sees his hometwin both recede and come back in equal intervals (his proper time t'0, both away and back again), but he sees him recede for the smaller part of the hometwin's time, ie while growing old more slowly, until event Rv; and then approach for the greater part of ditto, ie while growing old faster. As the Einstein speeds apply, the recession is seen at diminished speed bet+, and hometwin so reaches a distance in the outbound system of 
x'- = BRv- 
at the traveler's turnback ; after his instant maneuver, the hometwin appears to have got at a different, greater distance (now in the homebound system, and corresponding there to an "earlier" event)
x"+ = BRv+ (*), 
and from there on his approach is seen at an increased speed bet- until return !
Rv- and Rv+ are two Einstein perception events, at-before and at-after turnback, of the single perceived event Rv.

(*)  This came as a surprise even to me. Imagine two observers passing by each other, (an alternative for a single observer switching frames instantly) actually SEEing the same event (their twin counterpart at a previous, light-linked location) at a different distance according to their frame of reference !  Imagine your looking at the sun, and your twin passing by at relativistic speed looking at it as well, seeing the same sun in the same state 8 odd minutes back, but seeing this same event from the same place at another distance, ie with another view angle !  I still find it hard to swallow, but that's the way it is.

Let us now turn to the "simulation" programs, with another approach and feel, but trying to tell the same story of the Paradox Twins.

 

Twinty and Twinsee.

Programs at Twinty21.bas and Twinseen.bas. 
Pseudo-animations with Twinty.zip and Twinsee.zip. 
Slideshows at Twinty.pps and Twinsee.pps.
Also:
Twinty_StandpHome.gif     and     Twinty_StandpTrav.gif

         

TwinSee_ObsvHome.gif     and     TwinSee_ObsvTrav.gif

         

The <Relaty> and <Relasee> programs give, talking about TP,  Minkovsky spacetime descriptions. Moreover they show the story "unfolding with time" within a Minkovsky frame, adding in my opinion to a better understanding, but kind of contrary to the very concept of Minky's spacetime, where a world line ought to just "be there", and not "unfold with time", this appertaining to a purely spatial description.

What I missed yet, was a feel of actually experiencing the mutual observations, as the Paradox twins would experience them themselves. A simulator, that is. In addition, I sought to answer not only the question "How would one twin see the other?" but also "How would the other be seen seeing himself and watching his twin?".

<Twinty> and <Twinsee> are tentative simulation programs, displaying such 'duplex' data at the same time.

The twins are represented as squares. The observing twin is the "foreground square", with constant size (though changing position in the case of the traveler, so as to have him always in the upper part of the screen, the hometwin being kept in a fixed reference position in the lower part). The observed twin is seen as the "remote" square, decreasing and increasing size through the recession and approach stages, according to requirements of perspective.

The first cycle shows the observation of the hometwin, the second that of the traveler twin.
The data to the left are the hometwin's, to the right the traveler's.
At any moment "t", four twin data are shown: "home by home", "trav by home", "trav by trav", "home by trav".
For instance, in the case of hometwin's standpoint:
1. position (0) and time (t) of hometwin in his own system (event H),
2. position (x) and time (t*) of traveler in hometwin's system (event T, "Lorentz" or "Einstein"!),
3. position and time of event T in traveler's appropriate system (*),
4. position and time of event H in traveler's appropriate system (**),

(*)  outbound or homebound system according to where event T belongs
(**)  outbound or homebound system, or the appropriate transitional system at turnback, according to where hometwin's event H belongs with respect to key events D and E

Events 1. and 2., and 3. and 4. respectively, allow determining and displaying the distances between them, better called space gaps as, generally, either pair of events would not be simultaneous.

As said before, the story these programs tell is mainly the same as their "Minkovskyan" counterparts. The (cognitive) effects are different though. Some other aspects I've thought of since then are shown in yet other little programs (the task of incorporating everything is getting a bit "forbidding" :-).

 

TwinRev

In the Minkovsky descriptions, the traveler twin's standpoint is displayed without quitting hometwin's reference system. One could think of projecting travtwin's systems onto a single frame (travtwin following a single, his, worldline), wherein hometwin would be following a compound worldline. I have done this revisiting of Travtwin's viewpoint, in the <TwinRev> program (Twinrev3.bas ; use '+' and '-'  keys to change velocity, and SPACE for END).

By now only the Einstein-description is shown, but that's the interesting one. The dramatic transition of hometwin's position in Rv, seen by travtwin just before and after his turnback, is now "better seen" as if through travtwin's eyes :
TravtwinSee  pt-of-vw.PNG

The left half is the "perceived" story, the right one travtwin's instant perception.

 

TwinTest.

I wanted some evidence of the aging process of the twins. One could consider changing height or size of the squares or showing a kind of gasoline fill gauge, but that would interfere with the perspective aspect of the squares. So I thought of a simpler, linear alternative with this program <TwinTest> (Twintes2.bas ; use '+' and '-'  keys to change velocity, other key to repeat present cycle, and SPACE for END).

As yet, only a Lorentz description of hometwin's point of view is displayed :
TwinLineGrowin.png

 

Other TP websites.

There are sites legion and one has to pick them to one's liking. Here I merely mention some sites where I came upon picture representations alike or nearly to the ones I found meaningful in my approach.

http://www.sparknotes.com/physics/specialrelativity/applications/section2.rhtml

See picture 
Sparknotes.png

 
See the simultaneity lines of the outbound and inbound systems, leaving a 'blind' triangular area (my DEB) corresponding to the blank home-interval DE.

http://physics.nmt.edu/~raymond/classes/ph13xbook/node46.html

Similar accelerated scheme
PhysicsNmtRaymond.png

 
as mentioned under the math.ucr.edu site.

http://www.answers.com/topic/twin-paradox

Finds almost the same scheme 
AnswersCom_Simult.png

 
(simultaneity lines and gap) as mentioned under the Sparknotes site.
Finds also the 'Einstein' description 
AnswersCom_LightPaths.png

 
with Doppler (blue and red) shifted zones seperated at Rv resp. Rh.

http://physics.syr.edu/courses/modules/LIGHTCONE/LightClock/

TP explained through light clocks or, better, light cone clocks. 
The relation between moving clocks is put in evidence, eg 

rest clock cycle in 
PhysicsSyrSalgado_Restclock.png ,

 
moving clock cycle in 
PhysicsSyrSalgado_Movinclock.png .

 
Compare to my Lightclock program <LichKlok> discussed under MySRT, featuring moving light cone clocks as seen by rest and moving systems 
(LichtklokRuster.png,      LichtklokBeweger.png).

           

http://physics.syr.edu/courses/modules/LIGHTCONE/java/TwinParadox.html

You can run a simulation looking like 
PhysicsSyrSalgado.png

 
showing the 'Lorentz' and 'Einstein' positions of the sole traveler.

http://faraday.physics.utoronto.ca/PVB/Harrison/SpecRel/Flash/TwinParadox.html

Various pages with simulations like
FaradayPhysicsUtoronto.png , 

 
 
if a bit messy. 
Well, mine too perhaps :-)

http://www.phys.unsw.edu.au/einsteinlight/jw/module4_twin_paradox.htm

Picture PhysUnsw.png


suggests the dramatic effect of Travtwin's seeing the 'Einstein'-course of his home twin, but not in a complete way (not linking the proper return events, compare my

TravtwinSee  pt-of-vw.PNG

discussed under Twinrev).

http://webphysics.davidson.edu/physletprob/ch10_modern/twin.html

You can run a simulation looking like 
WebphysicsDavidson.png
 
 
and giving Lorentz+Einstein positions of the sole traveler.

http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html
especially the "Too many explanations" page
http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_vase.html

This site offers a thorough description of TP, starting from a basic worldline graph like 
MathUcr_Worldlines.png , 

passing by a Doppler ('Einstein') scheme
MathUcr_Doppler.png , 

working out the accelerated scheme
MathUcr_GR.png 

with space-lines like I argued in my remark under Relaty, TP-wise , to come to the instantaneous case 
MathUcr_TimeGap.png 

but leaving the gap unexplored.