Perspective on Relativity and Length Contraction

[universal_101]

There is no contradiction at all. Note that there is an invariant measurement (muon reaches the ground; rocket can complete journey without astronaut dying). The measurement just has a frame variant manifestation (time dilation, length contraction, or mixture, depending on frame). Measuring time in one frame, or distance in another, are both equally valid measurements.

I think we can agree to disagree, as long as there is no observed length contraction effect(direct).

 

[PAllen]

I think I don't understand what direct local measurement stand for, and if this measurement involves only the frame of rocket then how are we going to measure speed of rocket. Since speed must be w.r.t some other frame if it has to be non-zero and the only other frame here is of beacons, so the measured speed must be w.r.t beacons frame.

Exactly, you must ask who never accelerated.

I can measure the speed of beacon going by: I just have it interrupt two laser beams 5 meters apart (for example), and time the interval between the interruptions. Rocket can 'easily' do this with some apparatus mounted outside the rocket. So, all within rocket frame (only one time rate involved, no comparisons), I measure beacon speed, and time interval between beacon's passing. Distance is v*passing_interval. During the whole time of these measurements, all in the vicinity of the rocket, the rocket is inertial. I find that on each passing, the beacons are getting closer together.

[edit: to be even clearer: the rocket uses only clocks on the rocket and one ruler for all its measurements. Thus no time dilation involved. ]

You really want to argue that if you've ever accelerated, you can no longer make valid local measurements?

 

[universal_101]

I can measure the speed of beacon going by: I just have it interrupt two laser beams 5 meters apart (for example), and time the interval between the interruptions. Rocket can 'easily' do this with some apparatus mounted outside the rocket. So, all within rocket frame (only one time rate involved, no comparisons), I measure beacon speed, and time interval between beacon's passing. Distance is v*passing_interval. During the whole time of these measurements, all in the vicinity of the rocket, the rocket is inertial. I find that on each passing, the beacons are getting closer together.

I think the laser beams that the rocket interrupts are lying across the path of the rocket.

Now, I think you would consider the beams to be stationary in the beacons frame.

This implies, the frame of lasers is none other than that of beacons.

Therefore, your speed is w.r.t the non-accelerated frame, and it is exactly what we need.

 

[PAllen]

I think the laser beams that the rocket interrupts are lying across the path of the rocket.

Now, I think you would consider the beams to be stationary in the beacons frame.

This implies, the frame of lasers is none other than that of beacons.

Therefore, your speed is w.r.t the non-accelerated frame, and it is exactly what we need.

Wrong. There is no measurement of rocket speed. The rocket is measuring speed of passing beacon. There is no acceleration in the rocket during a whole cycle of measurement. The lasers are mounted on the rocket outside the rocket. The clocks are mounted on the rocket. The sensors to detect lasers are mounted on the rocket.

<Rocket---->
R1-------- R2
|----------|
L1---------L2

R1 and R2 are receivers and associate clocks on the rocket. L1 and L2 are lasers. Their mounting is simply offset or angled so the beacon can go by without hitting the mounting.

 

[universal_101]

Wrong. There is no measurement of rocket speed. The rocket is measuring speed of passing beacon. There is no acceleration in the rocket during a whole cycle of measurement.

What is so special about it, its a simple setup you are describing.

Now, the rocket measuring the speed of passing beacon is same as the measurement of rocket speed w.r.t beacons. Since relative velocity is frame invariant. It does not matter how you measure it, it is same for all the inertial frames.

Ofcourse we don't need any acceleration in the rocket during measurement, I never implied anything like that

 

[universal_101]

You really want to argue that if you've ever accelerated, you can no longer make valid local measurements?

Never implied anything like that, what I said instead that your measurement are w.r.t a frame which has never accelerated, and I think it is fairly easy to see through it.

 

[PAllen]

Never implied anything like that, what I said instead that your measurement are w.r.t a frame which has never accelerated, and I think it is fairly easy to see through it.

Nonsense. All measurements are local measurements in a rocket inertial frame. We measure speed of a passing beacon, and time between one passing and then the other. One pair of local clocks, one ruler, all on/in rocket are all that are used.

 

[nitsuj]

The same applies to the later part, they both are time dilating w.r.t each other as long as they are in motion w.r.t each other, but it is hard to recognize which frame experienced less/more/equal time compared to the other frame.

Ah I see, thought you gave preference there. Seems you mean just from an interpretation perspective. George's graphs (spacetime diagrams) show that stuff very clearly, and the acceleration is made irrelevant via duration, and that specifically really clears up the hard to recognize part. In other words considering the acceleration in this kinda of scenario trying to determine "which frame experienced less/more/equal time compared to the other frame." adds no value to the results.

 

[nitsuj]

Never implied anything like that, what I said instead that your measurement are w.r.t a frame which has never accelerated, and I think it is fairly easy to see through it.

Are you saying that an object that has accelerated in the past is physically(geometrically) different from an object that has not?

 

[Nugatory]

your measurement are w.r.t a frame which has never accelerated, and I think it is fairly easy to see through it.

The bolded text above represents a confusion about what a frame is. There's no such thing as accelerating a frame; when you hear people talking about an "accelerating frame" they really mean "a frame in which an accelerating observer is at rest".

Thus, the frame in which the ship is at rest when it passes the beacon at constant relative speed is not the frame in which the ship was at rest while it was accelerating through the takeoff.

 

[nitsuj]

your measurement are w.r.t a frame which has never accelerated, and I think it is fairly easy to see through it.

The bolded text above represents a confusion about what a frame is. There's no such thing as accelerating a frame; when you hear people talking about an "accelerating frame" they really mean "a frame in which an accelerating observer is at rest".

Thus, the frame in which the ship is at rest when it passes the beacon at constant relative speed is not the frame in which the ship was at rest while it was accelerating through the takeoff.

im sure universal_101 knows a frame actually isn't an object, so doesn't care if a frame cannot technically be said to be accelerating; due to the definition of a frame.

 

[Dale]

So it is hard to find any mainstream reference for the criterion.

Then it doesn't belong here.

 

[Dale]

Agreed, but there is inherent contradiction between the three underlined, "A frame dependent falsifiable prediction which is not illusory(i.e. a physical effect)".

I don't suppose you can produce a reference illuminating this supposed contradiction either?

Note, "physical effect" is your term, and is not in PAllen's comments.

 

[Dale]

I think we can agree to disagree, as long as there is no observed length contraction effect(direct).

There is plenty of evidence for length contraction. Whether or not you choose to call it "direct" depends primarily on your definition of "direct" and not primarily on the quality of the evidence. The MMX, muons, and bunch length are all good solid evidence for length contraction. The bunch length, in particular, is in my mind what I would call "direct" evidence since it involves length contraction of the object moving relative to the lab.

 

[universal_101]

Nonsense. All measurements are local measurements in a rocket inertial frame. We measure speed of a passing beacon, and time between one passing and then the other. One pair of local clocks, one ruler, all on/in rocket are all that are used.

Never implied that measurements are not local, instead the resultant speed that you get with this measurement is w.r.t the beacons, because those lasers you are using, which the rocket needs to interrupt(pass through) are stationary in beacon's frame. So laser's frame is none other but the beacon's frame, and the speed you get is also w.r.t the beacons.

Edit: And ofcourse speed of passing beacon is same as the speed of rocket w.r.t beacons. Its the relative velocity between the two, which is invariant..

 

[universal_101]

Are you saying that an object that has accelerated in the past is physically(geometrically) different from an object that has not?

No, I'm not saying anything fancy like that, instead my point is local measurements does not give you the speed independently from other frames, since the speed must be relative to some frame, what I'm implying is that the speed is w.r.t the frame of beacons which is stationary and never accelerated.

 

[universal_101]

Ah I see, thought you gave preference there. Seems you mean just from an interpretation perspective. George's graphs (spacetime diagrams) show that stuff very clearly, and the acceleration is made irrelevant via duration, and that specifically really clears up the hard to recognize part. In other words considering the acceleration in this kinda of scenario trying to determine "which frame experienced less/more/equal time compared to the other frame." adds no value to the results.

duration in which reference frame, and how does it work(maybe an example).

 

[universal_101]

The bolded text above represents a confusion about what a frame is. There's no such thing as accelerating a frame; when you hear people talking about an "accelerating frame" they really mean "a frame in which an accelerating observer is at rest".

Thus, the frame in which the ship is at rest when it passes the beacon at constant relative speed is not the frame in which the ship was at rest while it was accelerating through the takeoff.

OK, I should have replied to this first, I think that is exactly the source of confusion. Then again I thought it was lucid enough, that a frame which never got accelerated is different from the frame of an object which was accelerated and then put in inertial motion.

Nonetheless there is no real meaning to the phrase accelerating a frame in SR, it is always the object accelerating and then analyzing the infinitely many instantaneous frames in between the acceleration or the frame of the object after the acceleration ceases.

 

[universal_101]

I don't suppose you can produce a reference illuminating this supposed contradiction either?

Note, "physical effect" is your term, and is not in PAllen's comments.

OK let me put it another way,

TD and LC are frame dependent, both effects are present in muon's as well as Earth's frame. [Keeping in mind that the only physical effect that we have is number of muons reaching Earth measurement, at two different heights.]

From muon's frame, the Earth is time dilated and the space is length contracted. From Earth's frame muon is time dilated and the space is length contracted.

So, instead of choosing muon to be time dilated in Earth's reference, we can choose the space to be length contracted in both frames(E's and M's), and we would easily be able to explain how muons got to earth.

Next, we can choose both of them to be time dilated w.r.t each other and explain the results from their respective frames, it is easy to see how time dilated muons would make it to the surface of Earth in more numbers than expected, but the same follow if we analyse the situation from muon's frame and consider Earth to be time dilated, since in muon's frame Earth is slow in time whereas muons are perfectly fine and not time dilated, the particular number 'n' muons would reach the surface of the Earth in less time because clocks at Earth are Time Dilated. That is the Earth's clock would register 'n' muons reaching in less time due to Time Dilation which is same as more muons reaching Earth than expected.

This means we can explain the results by using any of the above combination, but this does not validate that the co-ordinates(time and space) we used to explain the invariant effect(number of muons reaching earth) are somehow related to the reality. They are just co-ordinates of a transform!

 

[PAllen]

Never implied that measurements are not local, instead the resultant speed that you get with this measurement is w.r.t the beacons, because those lasers you are using, which the rocket needs to interrupt(pass through) are stationary in beacon's frame. So laser's frame is none other but the beacon's frame, and the speed you get is also w.r.t the beacons.

Edit: And ofcourse speed of passing beacon is same as the speed of rocket w.r.t beacons. Its the relative velocity between the two, which is invariant..

This is pure and simply a lie. The lasers are attached to the rocket, moving with it, and the rocket does not cross them. No measurement is made in the beacon frame.

Since this has been explained multiple times, and is a simple fact of the set up, there is no longer a discussion going on.

 

[PAllen]

OK, I should have replied to this first, I think that is exactly the source of confusion. Then again I thought it was lucid enough, that a frame which never got accelerated is different from the frame of an object which was accelerated and then put in inertial motion.

This is nonsense for local measurements. There is a sense in which for events distant in time and/or space, such that the difference in the past between the motion of two observers affects later observations, that you cannot ignore the difference. However, none of this is matters to local measurements.

Again, we are at the point of ludicrous, unsupportable, and unsupported claims being made.

 

[PAllen]

OK let me put it another way,

TD and LC are frame dependent, both effects are present in muon's as well as Earth's frame. [Keeping in mind that the only physical effect that we have is number of muons reaching Earth measurement, at two different heights.]

From muon's frame, the Earth is time dilated and the space is length contracted. From Earth's frame muon is time dilated and the space is length contracted.

So, instead of choosing muon to be time dilated in Earth's reference, we can choose the space to be length contracted in both frames(E's and M's), and we would easily be able to explain how muons got to earth.

Next, we can choose both of them to be time dilated w.r.t each other and explain the results from their respective frames, it is easy to see how time dilated muons would make it to the surface of Earth in more numbers than expected, but the same follow if we analyse the situation from muon's frame and consider Earth to be time dilated, since in muon's frame Earth is slow in time whereas muons are perfectly fine and not time dilated, the particular number 'n' muons would reach the surface of the Earth in less time because clocks at Earth are Time Dilated. That is the Earth's clock would register 'n' muons reaching in less time due to Time Dilation which is same as more muons reaching Earth than expected.

This means we can explain the results by using any of the above combination, but this does not validate that the co-ordinates(time and space) we used to explain the invariant effect(number of muons reaching earth) are somehow related to the reality. They are just co-ordinates of a transform!

This is total nonsense. The rate of Earth clocks is completely irrelevant in the muon frame. A bunch of muons are sitting at rest. The Earth is approaching at a given speed. The muon's have certain half life T. In time T, the Earth moves by vT. This is 600 meters. None of this can be impacted in any way by what clocks on Earth are doing compared to muon clocks. The only thing that can cause the Earth to reach the muons before T when the muon rest frame measures the Earth's speed as v (no Earth clocks can affect this speed measurement) is for the Earth to be closer than vT.

 

[nitsuj]

No, I'm not saying anything fancy like that, instead my point is local measurements does not give you the speed independently from other frames, since the speed must be relative to some frame, what I'm implying is that the speed is w.r.t the frame of beacons which is stationary and never accelerated.

Ah okay, then I'm not sure what you are suggesting. Reading through the thread it seems you are looking for "hard evidence" of length contraction. Dalespam listed a number of solid popular examples.
imo the postulate and support for c being invariant is proof enough.

 

[TheBC]

Length Contraction is observer dependent(i.e. it is not Lorentz invariant), same as Time Dilation is observer dependent. But because, Time Dilation exhibits measurable physical effects(differential aging-Twin Paradox-fast moving muons) which are ofcourse Lorentz invariant, whereas unlike Time Dilation, Length Contraction has no measurable physical effect, it is safe to say it is an apparent effect(or observer dependent).

In other words you do not consider the physical experience of the other train car ends at stretched arms length a valid measurement to find out what is really in front of their body?
Do you consider the whole proces of 'experiencing' only apparent and/or illusionary?
Do you mean there is in fact ('actually') no short train between stretched armes?
If not, then what is there between or at stretched arms of Green and Red passenger?

 

[dvf]

In other words you do not consider the physical experience of the other train car ends at stretched arms length a valid measurement to find out what is really in front of their body?

Nice diagram!
Fwiw, note that :
(*1) in the top figure, where Red touches the green car simultaneously with both hands, Green protests and says that Red is cheating because he does not touch his green car simultaneously. According to Green, Red touches the green car's front too late and the back too soon, so no wonder that Red thinks that the green car is shorter than the red car.
(*2) in the bottom figure, where Green touches the red car simultaneously with both hands, Red protests and says that Green is cheating because he does not touch his red car simultaneously. According to Red, Green touches the red car's front too late and the back too soon, so no wonder that Green thinks that the red car is shorter than the green car.

 

[TheBC]

Nice diagram!
Fwiw, note that :
(*1) in the top figure, where Red touches the green car simultaneously with both hands, Green protests and says that Red is cheating because he does not touch his green car simultaneously. According to Green, Red touches the green car's front too late and the back too soon, so no wonder that Red thinks that the green car is shorter than the red car.
(*2) in the bottom figure, where Green touches the red car simultaneously with both hands, Red protests and says that Green is cheating because he does not touch his red car simultaneously. According to Red, Green touches the red car's front too late and the back too soon, so no wonder that Green thinks that the red car is shorter than the green car.

Fwiw? I think it's worth nothing at all. I do not like the way you formlate it. Sounds as if experiencing the shorter train is 'cheating' or 'incorrect thinking' of the observer train passenger. You get nowhere with this approach. No train passenger is cheating or thinking in a wrong way...

 

[Nugatory]

Nice diagram!
Fwiw, note that :
(*1) in the top figure, where Red touches the green car simultaneously with both hands, Green protests and says that Red is cheating because he does not touch his green car simultaneously. According to Green, Red touches the green car's front too late and the back too soon, so no wonder that Red thinks that the green car is shorter than the red car.
(*2) in the bottom figure, where Green touches the red car simultaneously with both hands, Red protests and says that Green is cheating because he does not touch his red car simultaneously. According to Red, Green touches the red car's front too late and the back too soon, so no wonder that Green thinks that the red car is shorter than the green car.

Of course these protests are misguided, as they are both overlooking the relativity of simultaneity. Understanding how that can be is the key to resolving this and many related paradoxes.

 

[dvf]

Fwiw? I think it's worth nothing at all. I do not like the way you formlate it. Sounds as if experiencing the shorter train is 'cheating' or 'incorrect thinking' of the observer train passenger. You get nowhere with this approach. No train passenger is cheating or thinking in a wrong way...

Fwiw--not much apparently--I think you missed the point, but feel free not to lose any sleep over it

 

[Simon Bridge]

Of course these protests are misguided, as they are both overlooking the relativity of simultaneity.

It's a bit like two observers disagreeing about the height of a a building (say) without taking into account the (Galilean) laws of perspective.

It's just that we would intuitively expect the train observers to get the same measurement. It's natural, in that situation, think we've already corrected for perspective.

The diagrams in post #59 are, in fact, demonstrating the error in that intuition.

This is why the disagreement between the observers is fairly described as "apparent".

It is also fair to point out that the different measurements are quite real just like the different measurements of the heights of the buildings are real. The mistake, then, is equally described as lack of care in defining the "real" length being measured. In the latter case, it is the length measured by an rulers right next to the building.

I gave a link right at the start of this thread which explains this.
There's four chapters and an introduction.

 

[Dale]

I don't know why there is any need to add poorly-defined descriptors like "real" or "apparent" or "illusion" or "physical" or whatever else. Why not just stick to the well-defined and accurate terms like "frame variant".

Length is frame variant. Scientifically that is complete. Any additional non-scientific terminology you might choose to use is either wrong or must be defined so that it means "frame variant".

I wish people wouldn't make a clear concept fuzzy and confusing this way.

 

[Simon Bridge]

I don't know why there is any need to add poorly-defined descriptors like "real" or "apparent" or whatever else.

Well that's easy:
1. the above debate demonstrates the need for specific, specialized, descriptors;
2. the terms are in common use and so need to be addressed. At the very least, we have to demonstrate the need for a specialized term or people will wonder why they have to say "frame dependent" when they have "perfectly good" words like "real" and "apparent".

I think "apparent length" as distinguished from "true length" is reasonable.
People using the terms do need to make sure the listener is using the same definition though.[*]
In this sense, "apparent" just means "measure in a frame that is not at rest with respect to the thing".

It is too easy to confuse that meaning with the use that describes an optical illusion, or something that is not real for the person doing the measuring. The apparent length of the rail car (for example) is what you'd use to make sure you cross the rails just behind it as it passes you. If the length reduction were not real, you'd bang into car.

--------------------

[*] there's nothing new about this - we have the same problems when introducing newcomers to "force", "work" "color" "strangeness" etc.

 

[PAllen]

But why pick on length for apparent? Kinetic energy is frame variant in both Galilean relativity and SR. Do we say that the only 'non apparent' KE is zero (that measured in the rest frame), and all other KE's are apparent?

Neutral, objective terms like rest length, and length avoid such judgments. These can be considered to correspond to rest mass and total energy (no one calls this 'apparent' because it is frame variant). (length=rest length in rest frame; total energy = rest energy = mc^2 in rest frame).

 

[Dale]

2. the terms are in common use and so need to be addressed.

The way to address them is simply to point out that they are not scientifically well defined. Then you can proceed to explain the scientific terms, which you cannot avoid anyway.

I don't remember any of my professors using terms like "apparent" or "physical" when teaching me about momentum or forces or velocity, despite the fact that they are common terms. And when they did use words like "real" and "fictitious" in teaching me about forces they were careful to point out that the scientific meaning is different from the common meaning.

 

[Simon Bridge]

You'll find the FAQ I link to earlier is also careful in the same way.
And for much those reasons.

I believe we are in agreement here.

I agree with PAllen: Nobody calls frame variant things "apparent" - but they do refer to a measurement that is not made in the rest frame "apparent". A quick trawl through the net yields about 20,900,000 results (0.44 seconds) where a length is described as "apparent" in the context of special relativity.

If you want to know why they are inconsistent in their labelling, you'd have to ask them. Probably things like kinetic energy do not get called "apparent kinetic energy" for the same reason nobody says "rest kinetic energy": the former is a tautology and the latter an oxymoron ... the nature is already included in the usual definition in a way that it is not included in the usual definitions for length and time.

i.e. Famously: Vladimir Varićak (1911) asserted that length contraction is "real" according to Lorentz, while it is "apparent or subjective" according to Einstein.[1] Einstein replied:

[Vladimir] unjustifiably stated a difference of Lorentz's view and that of mine concerning the physical facts. The question as to whether length contraction really exists or not is misleading. It doesn't "really" exist, in so far as it doesn't exist for a comoving observer; though it "really" exists, i.e. in such a way that it could be demonstrated in principle by physical means by a non-comoving observer.[2]​

Which, I think, sums up the POVs and puts them into perspective.

The use of the word "apparent" to refer to observation by a non-comoving observer is all through the literature and through undergraduate textbooks teaching relativity. However, I don't think very many people familiar with relativity use the word "real" very much - though I see the word "true" used a lot for the rest-values.

I agree with DaleSpam about the way to address the use of these terms.
The confusing and argument we have seen in this thread is due to this approach simply not being followed.
Which is pretty much what I hoped people would take away from my last two posts.
Maybe I should have spelled it out more - but I wanted to hear from OP before launching into a lecture.

-------------------------------------

[1] Miller, A.I. (1981), "Varičak and Einstein", Albert Einstein's special theory of relativity. Emergence (1905) and early interpretation (1905–1911), Reading: Addison–Wesley, pp. 249–253, ISBN 0-201-04679-2

[2] Einstein, Albert (1911). "Zum Ehrenfestschen Paradoxon. Eine Bemerkung zu V. Variĉaks Aufsatz". Physikalische Zeitschrift 12: 509–510.

 

[ghwellsjr]

I read a quite a few 'appears'/'appearance' vocabulary in this thread. Why should a moving train car 'appear' contracted (as if an optical illusion is involved), and not simply 'be' contracted? It does not make sense.
In the sketch I show how relative moving travellers experience reciprocally a moving contracted train car.

Unfortunately, a static sketch of a dynamic situation can lead to some false conclusions. Spacetime diagrams can clear up these false conclusions. Here is a spacetime diagram depicting the scenario you describe. The vertical red lines depict the red train car and its passenger. The endpoints of the train car are shown as the dark red lines on the left and on the right with another dark red line in the center showing the brain of the red passenger. The light red lines in between the dark red lines show the fingertips of the red passenger. Similarly, the long diagonal green lines depict the moving green train car and its passenger. The shorter darker red and green lines depict the signals traveling from the fingertips of each passenger to their brains. Note that each signal starts at the coincidence of a dark line of one color and a light line of the other color. I have chosen to make these signals travel at a little less than one-half the speed of light (44.7%c) just to keep the diagrams small enough to fit on a page although the same correct conclusions can be drawn no matter what their speeds are or even if they are different for each passenger (but the same for each arm of each passenger):

The moving train car does not 'appear' to fit between the passenger's fingertips (and does not 'appear' contracted to be able to fit between his fingertips). The train car simply does fit between his fingertips. The signals (information of the events) of the front and rear of the moving train at his fingertips are traveling simultaneously, from his fingertips through his arms and reaching his brain simultaneously. That's no illusion or arbitrarily chosen frame calculation.

I agree it's no illusion but the statement that the two signals for each passenger are traveling simultaneously from their fingertips to their brain is based on an arbitrarily chosen frame calculation. In this case, it is true for the red passenger but not for the green passenger. And that is the point of length contraction. It is frame dependent. In the rest frame of the red train car, the green train car and its passenger are length contracted and his signals are not simultaneous except at the point where they become coincident at his brain. The fact that each passenger senses in his brain the two signals simultaneously (true for any frame) does not mean that the signals started out simultaneously at their two widely separated fingertips. The top image in your sketch shows only the instant that the two signals started out simultaneously in the rest frame of the stationary red car on the railroad tracks, in other words, at the Coordinate Time of zero in the above spacetime diagram. That image does not show how the signals propagate along the arms of either passenger on their way to their brains. In fact, it does not show where the signal is in the left arm of the green passenger nor where the green car is when the red passenger senses the two signals in his brain.

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 its 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 'objects'/slices of bread). Minkowski or Loedel diagrams visualize this very well.

Now I want to show the above spacetime diagram transformed to the rest frame of the green train car and its passenger to show the reciprocal effects that you are talking about but first, I have to correct the bottom image of your sketch to show that the train tracks are also length contracted:

And here is the corresponding spacetime diagram. All of my comments regarding the rest frame of the red train car apply in a reciprocal nature in the rest frame of the green car:

And since you mentioned a Loedel diagram, I show another spacetime diagram transformed such that both trains are moving at the same speed in opposite directions:

The point of all these diagrams is that they are all equally valid and all depict exactly the same observations that each passenger and each object makes in the different frames. None of the frames are preferred, not even the rest frame of each passenger. In all of them, they each detect in their brains the signals from their fingertips simultaneously even though they may or may not start out simultaneously and may or may not travel along their arms simultaneously.

And as I said earlier, a static sketch of a dynamic situation can lead to false conclusions. If you had made animations showing the sensing by the fingertips of the opposing train cars and the propagation of each signal along each arm and the simultaneous arrival of each pair of signals in the brains of the two passengers, then the false conclusions could have been avoided. Your sketch depicts just one snapshot of such an animation.