Question about length contraction

[peterspencers]

I am on a spacecraft as it makes a journey between two planets. I use a lightpulse to measure the distance before I set off, I then accelerate to a speed that is close to the speed of light and measure the distance again. I find that the distance when I am stationary (relative to the planets) is much grater than it is when I am moving very fast.

I think I understand the equations for length contraction, but I have a few nagging questions...

Does space 'actually' contract for the fast moving craft, relative to the planet? And is space considered to be a separate entity to matter and energy?

 

[bgq]

Hi,
Before special theory of relativity much of things have their own identity which is represented by its properties, but special relativity makes things somehow loses some of their properties. That is distance between two objects is NOT anymore something that is absolute property of two objects the distance in between, but the distance is something that every frame can measure it differently. Referring to your question, you measure a larger distance; but this is not to mean that the distance is larger, other observer may measure it smaller.

 

[haael]

Does space 'actually' contract for the fast moving craft, relative to the planet?

The geometrical interpretation of that fact is most closely related to rotation. The spacetime is "rotated" along the axis of the fourth dimension and you see it from a different angle, that's why it looks contracted.

Suppose you have a circle. When you look at it from a different angle, it will look as an ellipse. One dimension is contracted.

Lorentz transformations look strikingly similar to rotations. The difference lies in the measure that they leave unchanged.

When x is an angle, for normal rotations you have: (sin x)^2 + (cos x)^2 = 1
For Lorentz transformations, you have: (sinh x)^2 - (cosh x)^2 = 1
Another approach is to say that normal rotations leave a unit matrix unchanged:
R(x)^(-1) [[1, 0], [0, 1]] R(x) = [[1, 0], [0, 1]]
Lorentz transformations leave the matrix that have one diagonal element negative:
L(x)^(-1) [[-1, 0], [0, 1]] L(x) = [[-1, 0], [0, 1]]

This very fact led to the interpretation of special relativity as a geometry of a 4-dimensional space and to the concept of spacetime.

 

[harrylin]

I am on a spacecraft as it makes a journey between two planets. I use a lightpulse to measure the distance before I set off, I then accelerate to a speed that is close to the speed of light and measure the distance again. I find that the distance when I am stationary (relative to the planets) is much grater than it is when I am moving very fast.

I think I understand the equations for length contraction, but I have a few nagging questions...

Does space 'actually' contract for the fast moving craft, relative to the planet? And is space considered to be a separate entity to matter and energy?

"Space" in one direction is in SR simply the measured length, based on an assumption of simultaneity (Einstein: "rulers" and "clocks"). See if you can follow the elaborations here:

"physicsforums.com/showthread.php?p=4016947"
"physicsforums.com/showthread.php?p=4019235"

 

[peterspencers]

So from the given replies, firstly, in regards to Bells spaceship paradox. This gets at the heart of my question, is length contraction real enough to break strings? or is it just a perspective issue? With Bells paradox, it all depends on how you accelerate the two ships. Simultaneity would seem to be important, however if the acceleration of the ships was equal then the string will accelerate equally and thus contract equally with the ships as though the string were as much a part of the ship as the ships were! thus the string will not break.
Comparing Bells paradox to the Ehrenfest Paradox, where we have a train with its carriages connected by strings traveling along a circular track. As the track and the train are in two separate reference frames the contraction will only apply to the train, thus the strings will break, as now the strings arn't sufficient to cover the circumference of the track.
If i apply this to my question regarding my ship as it travels between two planets. And now ask how long it takes for the ship to get from planet A to planet B. I would take the speed of my craft, divided by the now contracted length between the two planets.

So this would seem to suggest that the the answer to my question is, 'yes' the length really does contract.

However my limited understanding of Haael's response suggests that length contraction is a phenomenon of perspective?

What is the current definition of 'spacetime'?

 

[peterspencers]

Would it be fair to say that space is a creation of time through movement. Movement of information at the speed of light, information in the form of bosons interacting with fermions. Time being cycles of boson interaction through fermions?

 

[pervect]

Would it be fair to say that space is a creation of time through movement. Movement of information at the speed of light, information in the form of bosons interacting with fermions. Time being cycles of boson interaction through fermions?

Ummm - I don't think so. Where did you read this? It sounds like a personal theory I hope you're aware of the status of personal theories here at PF...

Earlier you asked

What is the current definition of 'spacetime'?

Spacetime is a 4 dimensional manifold.

Manifolds are built from the underlying concept of topological spaces.
Topological spaces are built from the notion of "open balls" or "open sets"

The exact definition of manifolds (and the rest) is somewhat technical, alas. But as an example, the 2d surface of a 3d object would be an example of a 2d object. If you visualize such a curved 2d surface as having "extra dimensions", you'll get 3d and 4d manifolds. That's really just a visual aid, but it may be helpful. A really rigorous treatment of manifolds and topological spaces would be quite long, and I probalby couldn't do it justice in a post, especially as there are a lot of tiny but vital details to "get right".

 

[harrylin]

[..] if the acceleration of the ships was equal then the string will accelerate equally and thus contract equally with the ships as though the string were as much a part of the ship as the ships were! thus the string will not break.

To the contrary! I only linked my two posts there which directly answered your original question and more, here once more:

- Yes, the accelerated observers will, if and after they re-synchronizes their clocks, measure a contracted distance between the planets.

- The stay-at-home observer who uses a reference system in which he is in rest, will measure that the rulers of the accelerated observer have contracted and that he now de-synchronised his clocks ("measurements" depend on system-dependent convention).
In this way the stay-at-home can explain why the accelerated observers measure all unchanged distances as if they are contracted.

However, as explained everywhere in that thread, length contraction is a physical effect: for it to happen to the whole system of ship-string-ship, the string should pull the ships together. And as the string is defined as not strong enough, it must break.

Comparing Bells paradox to the Ehrenfest Paradox, where we have a train with its carriages connected by strings traveling along a circular track.

That's a funny variant. See a discussion with the original paper (no train) here:
https://www.physicsforums.com/showthread.php?t=503462

[..]
If i apply this to my question regarding my ship as it travels between two planets. And now ask how long it takes for the ship to get from planet A to planet B. I would take the speed of my craft, divided by the now contracted length between the two planets.

So this would seem to suggest that the the answer to my question is, 'yes' the length really does contract. [..]

Do you think that your acceleration contracts the universe??

However my limited understanding of Haael's response suggests that length contraction is a phenomenon of perspective?

Confusion about that reigns, even in the literature; and I ascribe that to the erroneous question of asking if it is one or the other. My 2 cts: it's both, as follows from my earlier explanations.
- a change of velocity induces real effects, as proven with clocks; real effects on rulers and clocks necessarily affect measurement systems.
- if your measurement system is affected and you make a new synchronization with those instruments then what you next measure is a phenomenon that is a matter of perspective.

 

[peterspencers]

So when the ship accelerates it 'actually' contracts and has its time dilated. But the planets around it don't 'actually' become length contracted and time dilated, they just appear to. And the 'real' length contraction/time dilation only becomes apparent when the craft slows down to the planets reference frame and you compare clocks?

 

[harrylin]

So when the ship accelerates it 'actually' contracts and has its time dilated.

No: that is from the perspective of the stay-at-home. From the perspective of the end rest frame of the ship, the ship expands to the un-contracted length and its clocks speed up to the "normal" speed. There is only agreement that real physical things happen. There is no absolute reference frame for us to base absolute statements on such as that something that is in inertial motion is "actually" contracted.

But the planets around it don't 'actually' become length contracted and time dilated, they just appear to. And the 'real' length contraction/time dilation only becomes apparent when the craft slows down to the planets reference frame and you compare clocks?

See above: no inertial reference frame is preferred, so that we cannot establish any "absolute frame". The "planet's (rest?) reference frame", if such a thing existed, has no special status (except perhaps for ease of calculation); that is the meaning of the relativity principle.

 

[peterspencers]

Ok...but when the passanger onboard the craft returns after a long, high speed flight, he finds that he has actually aged less than the people on the planet. Theifore surely one must conclude that the time dilation 'did' actually happen and it was dependent on the reference frame that experienced acceleration.

 

[harrylin]

Ok...but when the passanger onboard the craft returns after a long, high speed flight, he finds that he has actually aged less than the people on the planet. Theifore surely one must conclude that the time dilation 'did' actually happen and it was dependent on the reference frame that experienced acceleration.

Quite so... More precisely, that one of the two changes velocity (and not the other) is responsible for the asymmetry in the accumulated clock times when they meet again. That is the so-called "twin paradox" scenario which is currently (for the Nth time ) being discussed here:
https://www.physicsforums.com/showthread.php?t=642784

Perhaps you want to join the discussion there, if these things are relatively new to you; by now I walked away as it's like a soap opera that I have seen plenty of times, and just as superficial.

 

[nitsuj]

Does space 'actually' contract for the fast moving craft, relative to the planet? And is space considered to be a separate entity to matter and energy?

Comparatively, yes it does actually contract, but that's just from moving so fast (time slows)... What makes that statement true is comparatively.

How else could spacetime account for the length traveled in reduced time, but with a reduced length as well. So does it actually contract? I guess the word contract implies spacetime physically shrunk, and if that's the question then no it doesn't actually contract.

One of the coolest ways to interpret spacetime is to consider we don't ever measure spacetime it self, it's un-possible. So spacetime itself doesn't contract. If you accept time dilation, just consider contracted length as the other side of the coin. This all helps ensure that causes & Effects happen in the right order

From an observation perspective yes spacetime is separate from the stuff within it. (SR/GR yes, QM maybe not so much)

For me "Bell's Spaceship paradox" demonstrates that contraction/dilation is separate from spacetime itself.

That said whether you call c a "speed limit" for spacetime, or a "speed limit" for the fundamental forces is a matter of taste imo. Bottom line seems to be about how we define/observe spacetime (and most specific the relationship of length/time).

 

[peterspencers]

by now I walked away as it's like a soap opera that I have seen plenty of times, and just as superficial.

Well... I'm very appreciative of your help, if that makes the mononity any easier to bear :p

I've been back and read through most of the link you posted, in regards to the bells spaceship paradox, and I want to make sure I've understood it by running it past you in this thread, the other thread is way too crowded and a lot of people seem to be in dissagreement about a few things.

So basically the string breaks! It breaks because:

Consider the situation at the moment that the ships take off, as viewed from the reference frame that is moving at the final speed. Because both ships take off at the same time in the ground observer's frame, relativity of simultaneity means that they don't take off at the same time in that moving frame. In fact, in that frame the lead ship takes off first, lengthening the distance between itself and the trailing ship (which breaks the string between them). Lorentz-contract that increasing distance and you'll get the constant distance that the ground observer sees - but of course the ground observer also sees the string Lorentz-contracting so that it can no longer span that constant distance, so again the string breaks.

So... does the string break because its a 'relatively' weak object? If we did a thought experiment where there was no string, just one big ship with engines at the front and back (like the lead ship and the following ship), would there be forces of tension in the middle of the craft due to the same reasons that make the string break?

 

[harrylin]

Well... I'm very appreciative of your help, if that makes the mononity any easier to bear :p

I let myself be dragged back into it.

I've been back and read through most of the link you posted, in regards to the bells spaceship paradox, and I want to make sure I've understood it by running it past you in this thread, the other thread is way too crowded and a lot of people seem to be in dissagreement about a few things.

So basically the string breaks!
[..]
So... does the string break because its a 'relatively' weak object? If we did a thought experiment where there was no string, just one big ship with engines at the front and back (like the lead ship and the following ship), would there be forces of tension in the middle of the craft due to the same reasons that make the string break?

Right - and as a result the ends of the ship will move closer until the engines have stopped and the forces have equilibrated to obtain the contracted length of SR. That is all very theoretical of course; in practice, until the engines stop their forces and perhaps slight differences in "identical" engines will be more important.

 

[peterspencers]

ok, and in Bells situation, would the fact that, once the ships have finished accelerating, there is a broken string between them, be evidence that they have physically contracted? What other forces, other than 'actual' atomic contraction, could explain the broken chord?

Also... the quote I lifted from the other thread containing the statement:

Lorentz-contract that increasing distance and you'll get the constant distance that the ground observer sees - but of course the ground observer also sees the string Lorentz-contracting so that it can no longer span that constant distance, so again the string breaks.

Why would the increasing gap become length contracted? I thought space itself remained unchanged?

 

[harrylin]

ok, and in Bells situation, would the fact that, once the ships have finished accelerating, there is a broken string between them, be evidence that they have physically contracted? What other forces, other than 'actual' atomic contraction, could explain the broken chord?

Replied in post #10: I said No. Please try to understand other perspectives. From all inertial frame perspectives the length changes, but differently. From the point of view of the end rest frame the string even de-contracts, and the broken chord is than explained by earlier departure of the front rocket.

Why would the increasing gap become length contracted? I thought space itself remained unchanged?

Not sure from where you quote it, so I must guess a little. Probably with "Lorentz-contract that increasing distance" was meant "do a Lorentz transformation to the launch pad frame from an accelerating frame". I don't use accelerating frames with shrinking rules, but some others do; with a shrinking ruler (assuming force equilibrium, which is doubtful!), you would measure an increasing distance - that's all. According to the launch pad frame's perspective, the distance is not changing and neither does the string contract, but its equilibrium length contracts so that it is increasingly in a stretched state (ignoring any dynamic effects).

 

[peterspencers]

so if I stayed in the reference frame of the ships the entire time, what reason would I give to explain why there is now a broken chord? What would the captain tell his crew, an ensign reports "sir the chord is broken" to which the captain replies "yes, that's because..."

According to the launch pad frame's perspective, the distance is not changing and neither does the string contract, but its equilibrium length contracts so that it is increasingly in a stretched state (ignoring any dynamic effects).

I understand that you have alreday answered my question with this answer, what do you mean by 'its equilibrium length contracts'? What is physically happening to the string in the ships reference frame?

(Eli Botkin *16) (from the first thread you posted)

So, if the string does break it needs to be because it is being accelerated, which is a feature common to all observers

So is the answer to my question, the string breaks because the engines can never be 'perfectly' balanced in their acceleration, leading to real and unavoidable tugging from both craft?

with a shrinking ruler (assuming force equilibrium, which is doubtful!), you would measure an increasing distance

This has also confused me :p can you spell out to me the situation where one measures the increasing distance. I thought, as one accelerated all distances measured become shorter. Unless you accelerate to be in the same inertial frame as something that was previously moving, then that thing would appear to de-contract.

 

[harrylin]

so if I stayed in the reference frame of the ships the entire time, what reason would I give to explain why there is now a broken chord? What would the captain tell his crew, an ensign reports "sir the chord is broken" to which the captain replies "yes, that's because..."

The reference frame of the ships is a magical frame - just think of it, it looks as if the whole universe is accelerating due to the rocket engines.
A captain who would tell his crew that "the rocket engines accelerate the whole universe", might tell his crew that the chord broke "because the distance between the ships increased". I'm not sure if you are such a captain.
A neutral announcement would be that the chord broke because it was put under too much strain.

I understand that you have alreday answered my question with this answer, what do you mean by 'its equilibrium length contracts'? What is physically happening to the string in the ships reference frame?

See above: I'm not sure if you reason like the captain. The "accelerating ship's reference frame" is not suited for describing "what physically is happening". With 'its equilibrium length contracts' I described it from the launch pad frame. Bell gave his spaceships example to highlight that the atomic bonds are electromagnetic, so that at high speed the inter-atomic distances are reduced except if the material is prevented from contracting.

(Eli Botkin *16) (from the first thread you posted)
So is the answer to my question, the string breaks because the engines can never be 'perfectly' balanced in their acceleration, leading to real and unavoidable tugging from both craft?

I find that a bit too vague - acceleration is required to produce this kind of effects, but different acceleration scenarios have different results [edit: I notice that most of that post is wrong anyway, as also next elaborated there]. And I meant the contrary of what you understood: with perfectly identical engines and rockets that take off synchronously according to the launch pad frame, the string should break.
It is similar as with electromagnetics, which was an important motivation for relativity: depending on your reference frame an event can be said to happen due to electrostatic attraction or due to a combination of electrostatic attraction and magnetism.

This has also confused me :p can you spell out to me the situation where one measures the increasing distance. I thought, as one accelerated all distances measured become shorter. [..]

That is a lethal confusion.
Picture that I "see" that you are moving and that your ruler is contracted to half its original length, and that the distance between you and the other ship is unchanged. Now I "see" you measure that unchanged distance with your shortened ruler; based on that ruler it will be double the original distance.

 

[peterspencers]

A neutral announcement would be that the chord broke because it was put under too much strain

And what was the cause/causes of the strain from the ships perspective?

I asked earlier if the broken string was evidence of actual atomic contraction, and you replied, no. But now you have just posted

Bell gave his spaceships example to highlight that the atomic bonds are electromagnetic, so that at high speed the inter-atomic distances are reduced except if the material is prevented from contracting.

"at high speed the inter-atomic distances are reduced" well the ship 'is' at high speed, an onboard accelerometer will confirm this.

Are you saying the chord breaks under circumstances that appear different depending on your frame, but they all involve too much tension upon the string?

Picture that I "see" that you are moving and that your ruler is contracted to half its original length, and that the distance between you and the other ship is unchanged. Now I "see" you measure that unchanged distance with your shortened ruler; based on that ruler it will be double the original distance.

Ok, but from the ships viewpoint, my ruler dosent change, and the gap also dosent change (as you earlier stated), but the chord still breaks! why? From the ships viewpoint does the length remain the same but the gap appears to increase in line with the way it was before the ship accelerated (ie unchanged gap from the viewpoint of the stationary frame)?

 

[Nugatory]

Are you saying the cord breaks under circumstances that appear different depending on your frame, but they all involve too much tension upon the string?

Harrylin can speak for himself, but that is exactly what is going on.

In ground-guy's frame, the two ships maintain a constant distance while the cord shrinks. In the lead spaceship frame, the cord maintains a constant length while the two ships move apart. In the frame of an observer moving relative to both lead ship and ground-guy, there will be a combination of these two effects. In all cases the cord is subject to tension and breaks.

 

[harrylin]

And what was the cause/causes of the strain from the ships perspective?

I replied that from the weird perspective that the ship is in rest so that the rockets accelerate the whole universe in opposite direction, the chord broke because the distance between the ships increased. And you did not reply if you think like that.

Are you saying the chord breaks under circumstances that appear different depending on your frame, but they all involve too much tension upon the string?

Yes, I have been explaining that throughout that other thread, just as others did.

Ok, but from the ships viewpoint, my ruler dosent change, and the gap also dosent change (as you earlier stated)[..]

No, I tried to explain that if your ruler on the ship shrinks a factor two, necessarily you will next measure the same distance as doubled. I literally wrote: "based on that ruler it will be double the original distance." Everyone including you yourself can see you measure that; and what you measure is "the ship's viewpoint". Please read again what I explained.

 

[peterspencers]

So, just so I am completely sure, you are saying that, when the bells ships accelerate, they measure an increasing gap between themselves, that the string can no longer cover? If the bells ships were on a journey to a distant word and they measusre the distance to that planet with a pulse of light before setting off, they will find that, once accelerated, that distance has decreased. is this correct?

I replied that from the weird perspective that the ship is in rest so that the rockets accelerate the whole universe in opposite direction, the chord broke because the distance between the ships increased

I thought that if it looks as if the entire universe is accelerating, then it would also look as if the entire universe was contracting. If this was the case, then the gap between the launchpad, which was addequate to house the vessels and the string before setting off, would now appear to be to short from the ships viewpoint after setting off. In the Bell's scenario, if i measured the gap between the launchpad before setting off, with a pulse of light, I would find that when I measured the gap again, after accelerating, it would appear to be too short. If I am measuring that the length has decreased, then why does my string break due to an increasing gap?

The above paragraph, is why I am confused.

Is the answer to my question that, the apparently increasing distance between the ships, is not the decreasing length measurement of the apparently shrinking launchpad I came from?

 

[harrylin]

So, just so I am completely sure, you are saying that, when the bells ships accelerate, they measure an increasing gap between themselves, that the string can no longer cover?

That is correct, and no doubt you could follow my explanation why this must be so. The best way to understand SR is to stick to logic and common sense, and for this case it is very simple. As a reminder: If, as analysed from the launch pad frame, you measure while you accelerate the original distance with rulers that are shrunk by a factor two (neglecting forces and the length change during measurement), then you must necessarily measure double the original distance.

The analysis with other inertial frames differs but must give the same answer as to what you (and anyone else) will measure; although there are different "views", there is just one universe.

I thought that if it looks as if the entire universe is accelerating, then it would also look as if the entire universe was contracting. If this was the case, then the gap between the launchpad, which was adequate to house the vessels and the string before setting off, would now appear to be to short from the ships viewpoint after setting off. In the Bell's scenario, if i measured the gap between the launchpad before setting off, with a pulse of light, I would find that when I measured the gap again, after accelerating, it would appear to be too short. If I am measuring that the length has decreased, then why does my string break due to an increasing gap?

The above paragraph, is why I am confused.

The probable cause of your confusion, "in one word" (one concept): relativity of simultaneity. See next!

Is the answer to my question that, the apparently increasing distance between the ships, is not the decreasing length measurement of the apparently shrinking launchpad I came from?

I'm not sure to understand that phrase, but probably that's right. You will be able to answer that for yourself next, if I manage to explain it clearly enough. Allow me to get back to my clarification to which I linked in post 4:

"One may better understand length contraction as a physical contraction of bodies. This cannot affect the distance between accelerating rockets. However, in combination with a different synchronisation of clocks, the result is that for a reference system that accelerated from rest to a certain speed, after re-synchronisation all space in the stationary system appears to be contracted."

The key word is re-synchronisation. The result is what is called "relativity of simultaneity". If you stopped accelerating then you can take your time to get out of your ship and count how many times you can fit your nominally "1 m" long measuring rod in the space between the ships; time is not a factor here. So, in my illustration you can place twice as many times that rod in that space.
It is different for measuring moving lengths: you must determine what points are simultaneous. If you use the simultaneity of the launch pad frame then you will necessarily also measure the for you moving launch pad frame length as now being doubled in length. Same for the universe: it would seem to be expanding! I hope that you can follow that, as it is just common sense.
As a matter of fact, if you start out with to the launch pad synchronised clocks in both spaceships, they will keep the launch pad synchronisation (assuming perfect clocks).
The "trick" happens when you synchronise your clocks such as to make the one-way speed of light the same in both directions relative to your ships (that only works well if you stop accelerating). Then you created the conditions in which you will measure the "moving" lengths as contracted.

More on the one-way speed of light and clock synchronisation in this thread:
https://www.physicsforums.com/showthread.php?t=641102

 

[phyti]

I am on a spacecraft as it makes a journey between two planets. I use a lightpulse to measure the distance before I set off, I then accelerate to a speed that is close to the speed of light and measure the distance again. I find that the distance when I am stationary (relative to the planets) is much grater than it is when I am moving very fast.

I think I understand the equations for length contraction, but I have a few nagging questions...

Does space 'actually' contract for the fast moving craft, relative to the planet? And is space considered to be a separate entity to matter and energy?

No. You don't influence the behavior of the universe when you move.
You do experience motion induced phenomena, time dilation and length contraction. You can't detect the length contraction because everything moving with you contracts in the same proportion.
Similarly your clock and all light related processes, including biological, slow by the same proportion. Your sense of time is as slow as your clock, so you arrive earlier at a destination outside your frame of reference. Since you can't detect your slow time rate, you interpret it as a contraction of the universe, i.e. it's altered perception.

 

[peterspencers]

You do experience motion induced phenomena, time dilation and length contraction. You can't detect the length contraction because everything moving with you contracts in the same proportion.

Many thanks, this statement has cleared things up for me. Earlier in the thread I asked...

So when the ship accelerates it 'actually' contracts and has its time dilated.

To which harrylin responded...

There is no absolute reference frame for us to base absolute statements on such as that something that is in inertial motion is "actually" contracted.

I took this to mean; no, there is no 'real' contraction, there are only observations. It seems to me that there is 'real' length contraction, even if the ship dosent notice directly that it has contracted, it nonetheless knows it has contracted due to the fact that the string is broken. The ship knows the universe remains unchanged.

No. You don't influence the behavior of the universe when you move

Thankyou both to harrylin and phyti for helping me with this, I hope I have done your patient explanations justice with my above post.

 

[harrylin]

[..] I took this to mean; no, there is no 'real' contraction, there are only observations.

I'll try a last time.
I stressed that an observation must have a cause. Exactly because our "observation" is affected by real physical effects (and even convention) we cannot usually know what is "real" and what only "appearance"; we should expect a combination of both. And we do not have access to an absolute reference - see next, adding blue for emphasis.

It seems to me that there is 'real' length contraction, even if the ship dosent notice directly that it has contracted, it nonetheless knows it has contracted due to the fact that the string is broken. The ship knows the universe remains unchanged.

Almost correct. In post #4 here I referred you to post https://www.physicsforums.com/showthread.php?p=4019235 :

"according to observations in a [final] co-moving frame this is so because the first spaceship took off earlier. Note that also from that point of view length contraction plays a role; however in this case the spaceships are seen as slowing down, so that now the string would hang loose (due to length de-contraction) if according to that frame the ships had taken [STRIKE]of[/STRIKE] off simultaneously."

In other words, people on the ship can not "know that the ship has contracted". However, if we consider descriptions that are based on the total of all inertial reference systems as "real", then we may still say that its length has "really" changed.

Thankyou both to harrylin and phyti for helping me with this, I hope I have done your patient explanations justice with my above post.

You're welcome.