Physics challenge: stringy ships

[Kuroneko]

Alice and Bob are in two spaceships away from you, with a delicate piece of string tied between them. They accelerate gently and smoothly enough not to break the string due to inertial forces, in completely identical way, so that at every instant, their velocities relative to you are equal. The string is not strong enough to affect the accelerations of the ships in any way.

However, they disagree on what will eventually happen to the string, and each of them is trying to convince you to take their side in their dispute. Their arguments are as follows:
-- Alice: "The string will break. It will want to Lorentz contract and be unable to do so because it's tied down to the ships, and not strong enough to pull them together. Eventually, the velocity will be great enough to overcome the tensile strength of the string."
-- Bob: "The string won't break. Lorentz contraction is a purely coordinate effect, so there will be no additional tension on the string no matter how fast we're going relative to you."

Does the string break? Please post your reasons in spoiler tags. I'm very interested in people's intuitions on this question, so "Alice/Bob's argument makes sense to me" or similar is quite fine (or if you agree with Alice/Bob's conclusions but not the argument). If you tried to work out the problem in detail and have gotten a different answer than your initial impression, please make a note of it as well

[bilateralrope]

Spoiler

At first I thought that the string won't break, because the distance between the ships remains the same from either ships reference frame. Then I realised that the ships might not observe each other to be at the same relative speed, so until I do the calculations I can't be sure.

[bilateralrope]

Is the string parallel or perpendicular to the direction of acceleration ?

[Kuroneko]

Parallel (or really, any direction not perfectly perpendicular to). Apologies for the ambiguity.

[Ariphaos]

Spoiler

No point on the string is going to be contracted from the frame of reference of the point ahead or behind it, since contraction only occurs in the direction of motion, and every point along the string is receding from every other point, as in the expansion of space. Once the ends of the string are far enough apart and the ships are moving fast enough, the ends of the string will effectively be beyond each others' horizon simply due to the expansion of space, and calling it 'whole' at that point is probably a bit facetious.

So I'd go with 'Alice is right for the wrong reasons', assuming I understand the question correctly.

[Lord of the Abyss]

Spoiler

My guess as a non-physicist; the string doesn't break, any more than a relativistic ship is squashed by being flattened by Lorentz contraction. In its own frame of reference it isn't even stretching, just like the "flattened" ship looks unflattened to people inside. A "purely coordinate effect" like Bob says.

[ThomasP]

Spoiler

I said yes based on my complete layman's understanding of relativity, with my understanding being that the change in coordinates via Lorentz is equivalent to a real force being placed on the object, when talking gravity.

That's a total guess though, because I don't understand it well enough to say meaningfully and I wouldn't know where to begin number-crunching.

[Sriad]

Spoiler

The string does not break; relative to itself the string is stationary and doesn't actually "feel" any stretching, any more than a human being gently accelerated to .999c would "feel" like they'd been mashed into a millimeter thin red paste.

[Spoonist]

Spoiler

The string will break.
You are saying that it is delicate and that it is a string. Not a cable or wire but a string. To me that implies a thin rope.
Scenarios that come to mind:
1) A string would not be stronger than its weakest point and since we are talking spaceships I will assume that it is a long string. Especially since it needs to be a very long string to prove the Lorentzie thingie, if it is too short it will simply be impossible to break of the contractions.
2) The friction of space (yes its almost negligent but at the speeds necessary for spaceships it is not) will make the string go from a straight line to a curved line which puts tension on the string and eventually it will break.
3) Wherever we are going we will eventually have to break, again the scenario above, or if they are behind eachother then the length will have so much inertia that it will snap. (It being much harder to provide as smooth decelaration as accelleration).
4) It being thin and not protected will lead to microhits, which if we are going far, which spaceships seam to imply, then the string is going to get weakened further.
5) The string will however not break due to the lorentz contraction since this applies to the whole operation and not just the string itself.

[Zixinus]

Spoiler

As someone who never heard of "Lorentz contract": I don't think that the string will brake.

Possible effects would be radiation, heat change and solar wind, but if they had any sense, they chosen a material that will resist these forces.

In my mind, there is nothing to give additional tension to the string aside the spaceships themselves. I could imagine that the vibrations of the two different spaceships could also effect the string, but I don't know whether it would be strong enough to brake it.

So in essence, if the spaceships behave as you say they will, then the question is purely reliant on the properties of the string.

[Glass Pearl Player]

Spoiler

I'll vote "Don't know", because the problem contains a subtle but important ambiguity: They try to keep their acellerations equal at every instant, but to do that, they have to agree on a reference frame. Remember, in special relativity, simultaneity depends on the observer.
If they use my reference frame (I'll assume I do not acellerate), their distance will remain constant from my point of view, but if they use, say, Alice's frame, I will see their distance undergo Lorenz contraction.
From my point of view, the string does contract as well, so they cannot use my frame of reference without breaking the string.

[Twoyboy]

Spoiler

My feeling is that Bob is correct and the string will not break. I look at it like the thought experiment I once heard to explain that all things fall to earth at the same speed regardless of their weight. Imagine 2 objects, 1 heavy, 1 light. Tie them together with a thin piece of string and drop them both from the same height. If the heavy falls faster than the light then the heavy pulls the light one down. Then imagine instead of the string you welded a metal rob between them, effectively making them one object. This should fall at the same speed as the 2 objects tied with string, but it should also fall faster than the original heavy object given it weighs more. There's a contradiction and thus the assumption that heavy objects fall faster than light ones cannot be true.

Well, if we then imagine not a string joining the spaceships, but one long spaceship in the same space, we don't theorise that it would be torn apart, and thus I imagine the space between the ships must also shrink.

However, my basic first year engineering physics knowledge gives me little inkling into how it actually works.

[The Grim Squeaker]

Spoiler

If I understand it correctly, the string has no pressure/external forces applied to it at all, due to both ships having a set acceleration (the same), so the T(tension) applied to the string would be zero, and it would never break. (the speed of the system as a whole is irrelevant, the relative frame of motion is all that applies).

I'm probably misunderstanding the situation though

[Thanas]

Spoiler

Not being a physicist, I remember reading somewhere that the Lorentz effect is only a problem at higher speeds. As they are in two spaceships and can (I assume) accelerate to close to light speed, I would think that this qualifies as high speed and therefore the string would break.

Again, me not being a physisicst.

[Steel]

I would intuitively say that the string does not break, however
Spoiler

my mathematical intuition says otherwise. I get the feeling the constraint of matched acceleration at all times from *my* reference frame will cause a problem... But I haven't done any maths so that could be completely wrong

[Surlethe]

Spoiler

No. Lorentz contraction is a purely coordinate effect obtained from transforming observations of the string from Alice/Bobe to me; from the perspective of the string, Alice, and Bob, the string remains exactly the same. Their acceleration (I assume the problem is about acceleration?) will simply bow the string's shape.

I haven't done the math on it, so the answer is intuitive. The basic intuition I'm applying is that, in SR, one observer should not see a "physically significant" event if the other does not (eventually) see it as well. The string snapping would count as a "physically significant" event.

[Darth Holbytlan]

Spoiler

The string breaks.

From your point of view, Alice and Bob maintain the same velocity at all times. Therefore they maintain the same distance at all times in your frame of reference. But this means the distance is increasing between Alice and Bob's vessels in their frame of reference*. (For the distance to stay the same in their frame of reference, it would shrink in your frame of reference.) So the string stretches and will break.

*Technically, Alice and Bob are in different frames of reference, but theirs are far more similar to each other than they are to yours, so it's a good enough approximation.

Edit: Spoiler

Actually, Glass Pearl Player is right that the problem is ambiguous. I was reading the "their velocities relative to you are equal" as from your POV, but the problem isn't actually clear on that point. It could be from Alice and Bob's POV, in which case the string doesn't break.

[Covenant]

Spoiler

Outside of silly variables like "oh the string gets hit by an asteroid" the string does not break. It's not actually being tugged by the ships (which are still apparently stationary to it) and the situation of a pair of spaceships connected by string is not different than a single spaceship tied together by it's hull. Just as the hull does not undergo shearing friction from the contraction, so will the string endure despite the acceleration of it's two matched halves.

This contraction is an entirely observational effect, so it's also relative to the frame of reference. It's possible the string would spaghettify and snap if parts of it were not moving at the same frame of reference to each other, but this circumstance seems to assume nearly equal acceleration on all parts. If there was an inchworm on the center of the string, observing both halves might become confusing, but as the string is not actually being acted on by the kinds of stresses that would tear it, the string will endure.

[Kuroneko]

Yes, the acceleration profiles are identical in your (inertial) reference frame--the problem is completely from your point of view. It's not my intent to hinge the answer on ambiguities or factors like the interstellar medium, etc., though I should have been more explicit in stating so.

[Ariphaos]

Spoiler

Well no matter what, there is no part of the string that perceives another portion of the string to be contracted (and the same goes for the ships) - how they see the rest of the Universe is irrelevant to the problem.

Assuming an infinitely elastic string, though, without the expansion of space there doesn't seem to be any particular reason for the string to sever.

[Steel]

Yes, the acceleration profiles are identical in your (inertial) reference frame--the problem is completely from your point of view. It's not my intent to hinge the answer on ambiguities or factors like the interstellar medium, etc., though I should have been more explicit in stating so.

Spoiler

Ok, so then we have that the string does break, as your surface of simultinaeity is different to theirs, and thus in their frame they apply different acceleration profiles where one nearer lags the other and they do genuinely move apart in their frame snapping the string?

[Darth Holbytlan]

Yes, the acceleration profiles are identical in your (inertial) reference frame--the problem is completely from your point of view. It's not my intent to hinge the answer on ambiguities or factors like the interstellar medium, etc., though I should have been more explicit in stating so.

OK. Then I change my vote back to my pre-edit answer.

[bz249]

Spoiler

Since time have to be transformed also from "so that at every instant, their velocities relative to you are equal" one can conclude that they have different velocities in the system moving with Alice at every instant. Thus they are getting farther and farther away from each other, the string will break.

[bz249]

Spoiler

BTW note that Alice and Bob are two different frames, because of the different origins, thus the two Lorentz transformations are different. If they have moved with constant velocities than transition from Alice to Bob be would be a simple translation. Since they are accelerating a full fledged Lorentz transformation is required between the two also.

[Terralthra]

Spoiler

Bob is correct, and his argument seems more or less accurate. If we were to consider a double-hulled spaceship with an engine on each hull, and Alice and Bob are on separate hulls, we would not even be asking the question of whether or not the ship tears itself apart through Lorentz contraction. Lorentz attraction affects the ship as a whole as a coordinate effect. The situation as given is a case of that, with the firm connection between the hulls replaced by a thin string. So long as the initial conditions are met (force applied by the engines such as to produce equal acceleration, exactly parallel acceleration, etc.), the string will not break.