- Lengths do not 'appear' contracted! -
In the sketch I show how relative moving travellers experience reciprocally a moving contracted train car.
A moving train car does not 'appear' (as if an optical illusion is involved) to fit between the passenger's fingertips. The observer feels both ends of the train touching his fingertips simultaneously: the signals (information of the two events 'front of train hits fingertip' and 'rear of train hits other fingertip') reach the observer's brain simultaneously (the signals travel from his fingertips through his arms and reach his brain simultaneously). There is a shorter train between the fingertips at the end of the passenger's arms. One may call this 'measuring from the passenger's frame', it simply means what the passenger's 3D space of simultaneous events (his 3D reality at one moment in time) is made of.
If you consider a train car at rest in front of you, you do not say the train car at rest 'appears' x meters long. You don't do this because you do not refer to any 'optical illusion'.
Stating that a moving train car 'appears' contracted insinuates there is some optical illusion involved. But there is no optical illusion invoved. Therefore there is also no reason to state that a moving train car 'appears' contracted. If the moving train car 'appears' contracted, then a train car at rest also only 'appears' measuring a certain length.
The reason why people often think the contraction only 'appears' as such is because the contraction is reciprocal. How can relative moving train cars be contracted reciprocally if it's not an optical illusion effect?
Because the 3D worlds of simultaneous events of both passengers are different. Consider the train cars as 4D spacetime structures instead of evolving 3D objects. The different contracted train cars are different objects of simultanous events, cuts with different 'direction' through the 4D spacetime train car structures (like cutting a loaf of bread in different directions results in different dimensions of 'objects'/slices of bread). Minkowski or Loedel diagrams visualize this very well.
If you are a 'realist', then these cuts are different but 'real' 3D spaces, part of 'real' 4D spacetime 'existence'. Whatever your definition of 'real' and 'existence' is. If you are a solipsist, then all the above is only a mathematical calculation with no reference to any 3D or 4D object 'really existing' out there. But then your own arms and fingertips, your body and braincells do not have any 'real' existence out there either.
If you do not consider the physical experience of feeling the other train car ends at stretched arms length a valid measurement to find out what is really in front of their body, then you consider the whole proces of 'experiencing' apparent and/or illusionary! And if there is in fact ('actually') no short train between stretched armes, then what is there between (or at) the stretched arms of Green and Red passenger?
Stating that a train car at rest is 'real', and the contracted train car only an optical effect or mathematical frame feature without any 'real' content (and therefore only 'appears' contracted without relly being contracted), does not make sense.
Why not simply calling the moving (contracted) train length the 'moving length'? Rest length vs moving length makes a lot more sense than rest length vs 'apparent' length.
Is there a full train between the passengers hands or not? Let's be more specific: will the passenger himself confirm his physical experience of feeling the full train between his hands -i.o.w. feeling the ends of the cars simultaneously? Yes. Is the length he measured (twice his arm length...) an 'apparent' length? Of course not. Does the passenger had to choose a frame to feel the train? No. Nature did it for him. He feels the events at arm length simultaneously. Period.
The fact there are on the internet search '20,900,000 results where a length is described as "apparent" in the context of special relativity' does not impress me at all. They all copy-paste text from each other, because they all think the reciprocal length contraction can not make sense if no form of optical illusion is involved. And trust me, it's because they do not grasp the essence of the real observer independent 4D spacetime existence.
'Apparent' does make sense if it's interpreted as 'as it shows', or 'as it is'. But in that sense it would be logical to call the rest length also 'apparent'. Nobody does this. Why? Simply to make a distinction with 'rest'? No, because why is it then that in so many -probably another 20,900,000 results on the internet- the moving train SEEMS contracted/shorter? Does -for the train passenger- the other train SEEM to fit between his hands? Obviously not. The train simply does fit between his hands.
I bet the use of 'apparent/appears' is used in the same semantic meaning as 'seems'. In other words: erroneously.
Note . Actually the 'appear' vocabluary originates in the translation of the german 'erscheinen'. In his 1905 paper Einsteins used two different verbs: 'scheinen' and 'erscheinen'. He doesn't mix these at random. They have specific different meanings:
'Sheinen' means: illusion - an appearance that does not correspond to reality - it appears so, but it may not be true - what you see is mere appearance - only outward show, things are not what they seem to be, etc.
'Erscheinen' is: as it shows, come to light, as it is, etc.
In the english version 'sheinen' and 'erscheinen' are translated by one verb only: 'appear'. Strictly speaking the translation is not wrong (ask google to translate and somehow you will find 'appear'), but the very important difference in meaning in german disappears in the english word for word translation. Prove is that in thousands of texts dealing with Special Relativity the english 'appears' is often replaced by 'seems', which is a synonym of 'appears', but not the correct one to match the german significance of 'erscheinen'.
The contracted green train is not the green rest train 'but measured differently'.
The contracted green train (simultaneous events for red) is made of completely different events (different content) than the events of that train for a co-moving observer/passenger.
That's the reason for reciprocal length contraction (and time dilation...).
For Red the green REST car is made of non-simultaneous events. But Red does not measure that car (those events) contracted. He measures simultaneous events, i.e. OTHER events of the green 4D spacetime train. (No wonder for so many people not grasping the essence of realtivity the moving train only 'appears' shorter... )
Passengers of different relative moving trains consider completely different events of the 4D train as being part of their respective 3D world reality. The simultaneous green car events are 'really' 'physically' out there between the red passenger's hands. Similar reasoning for the green observer/passenger feeling the red car.
What the red observer thinks about light signals from the green rest train is irrelevant. (Draw on the diagram the light paths from the rear and front of the green rest train and see where they end at red's head. That's a complete different story, irrelevant for red's measurement of a shorter green train.)
The contracted train has nothing to do with the events of the train at rest of the co-moving observer, strictly speaking the train does not really get contracted. Unfortunately when one says or reads that the train at rest in fact does not contracts, then everybody will interpret this erroneously as: the contracted moving train is only an illusion, or only a mathematical frame feature, or only 'appears' as such, etc.