The Rocket & String Paradox 

Relativity is one of those things that just makes things weirder the more you explore its implications.

Einstein boards a train and asks, "Does Boston stop at this train?"

There's an alternate version where the string does not break. If both rockets accelerate in unison *from their own point of view* the string does not break. But to a stationary observer, it would look like the front rocket is more past-like and less accelerated, so the rockets appear closer together, relieving tension on the string.

I'm doing a MSc right now and largely feel like I've seen almost every "wow that's counter intuitive" common physics example. Not much amazes or tricks me anymore. I can say with confidence this properly blew my mind like I was in highschool again. Thank you for that :)

This is wild. I would not have predicted this. But your explanation is so clear that it almost feels intuitive now. Oh, and nice title and thumbnail!

You’re tearing me apart, Einstein!

Engineer: *Any real string would break from accelerating its own mass before relativistic effects are important*

"In some cases it's also whether you're torn apart, or whether you tear yourself apart." Apparently this guy understands more about life than my shrink.

Title and thumbnail sounds like minutephysics watched Veritasium's video on Clickbaiting. "Do Salt Lamps Work?" "No." 😂

Taking a page out of Veritasium's book for the title. I like it!

I remember watching your videos years ago! I never took a physics class in high school and here I am 10 years later at college taking electromagnetism

I've seen this video everyday since it was released and I learn something new each time.

I don’t understand your definition of “accelerates at the *same time* ” so I can’t follow why there would be any force on the string. The string also accelerates at the same time as the rockets and thus the length contraction works as a function of the velocity relative to an observer. If both rockets are equidistant from an observer, at rest relative to said observer, and that observer reports that they accelerated at the same time, where is the force? In the reference frame of the string, which is really what matters here, both sides started moving at the same speed at the same time. It’s equivalent to holding a rope at both ends and running or spinning. It’s not going to get taut just from the motion. Edit: the replies have made it clear that the question assumes that the ships are not accelerating at the same *rate* therefore, the “paradox” here is actually to do with the setup of the question. You don’t need relativity to understand that pulling both sides of a string by different amounts will break it. If they accelerated at the same rate, the distance between them will contract at the same rate as the string, and it will not break.

But if the rocket at the back accelerates ever so slightly sooner than the one ahead, have you then countered for this space time conundrum?

You can consider/create another point of view for "simultaneous": accelerating just enough both ships so the string stays stretched without break. In such case the string would look shorter.

Correct me if I’m wrong but from my understanding so long as the string has mass and the rockets are accelerated at the same time, direction and magnitude, the entire system would shorten length wise which includes the string meaning from an outside perspective the rockets should appear closer together

If the premiere feature is to be used, it should be reserved for long videos when it makes sense for me to 'save the date' and schedule my time accordingly. I can watch a 3 min video any time I sign in here. Just publish it, dudes.

"Can Length Contraction Tear You Apart?" thumbnail: "yes" alright then, i guess i don't need to see the video, i have the answer

Another note on why everyday objects don't tear themselves apart. The kind of acceleration and speeds we deal with for everyday things is relatively slight. So, it don't take much cohesive forces for everything to stay together. Even when they do experience this kind of tension, they have the strength to hold together. In this thought experiment, the string has no such strength and is torn apart. But, a strong enough string can hypothetically stay together. It becomes an engineering problem when dealing with extreme forces to find the right material that can stand up to the task.

This was surprisingly easy to follow. Relativity is like quantum mechanics in that it's the obstacle you face when looking at the universe on scales we never evolved to understand.

Feels kinda weird having a premiere for what i assume is a 5-10min video

If "[...] both rockets suddenly accelerate at the same amount at the same time..." how can the first one accelerate first? The 1:16 part, which is the core of the explanation, needs further detailing, since it has to break the firm assumptions that we have about our "reality".

Finally a new video! Where have you been, glad you're back :)

So when my mum said "you're tearing this family apart" she really meant "length contraction causes this family to accelerate at different times!"?

I love all of these physics questions and 'paradoxes', that only a few of us have thought about, but is still very interesting. It shows the imagination and creativity of scientists in creating science and physics questions!

Seeing there's a new vid, YAY! Seeing the vid is set to "Premiere" at some arbitrery later point, instead of just being available, BOO!

I actually just learned special relativity length contraction now cause of this thanks. It didn’t really explain how or why it happened it just said it happened in the video so I looked it up, very cool

See this also apply to all of us in our day to day lives as well. You can have the people tear you apart or you can tear yourselves apart. It is all the matter of perspective. Be strong and carry on !

I'm going to have to agree with other comments about the 'Premiere' feature in this usage. I imagine you're trying out various different features to see which improves engagement and sure, this generated a comment but also a dislike. It's not the same as changing a video's thumbnail or title, this seems like a move that actively alienates your existing subscribers by having them begin feeling negatively about a video that they've yet to even watch.

Using the premiere feature means I see the video show up now when I am interested in watching, but it's not there. That's already annoying, but the worst part (for you) is that I will forget about the video when it actually comes out. Nobody likes this horrible feature, please don't use it for normal videos

It's been so many years I've been thinking about this. Not with the rockets, but very similar example.

when i saw the video in my recommended the thumbnail was "Yes." with a broken string but when i clicked on it, the thumbnail preview while the video is loading changed to "Will it break?" or something

I think the most important lesson here, is that in GR, whatever happens, it must happen in every point of view in some way. So the string cannot snap from one point of view, but remain intact from another.

I feel like it's wrong. That length contraction WOULD tear an individual ship apart anyway, since the system of two ships and a string as a whole could be considered a single ship (replace the string with a strut, or simply a ship with two engines, and it's a matter of difference of material properties and the fraction of the speed of light). This would explain what happens when length contraction leads to tidal force tearing around a black hole (they say that bigger black holes are gravitationally weaker, but if you're near the event horizon, that's necessarily the area where you need to orbit the singularity center at C; you're already going a nearly C when you're near the event horizon of a giant black hole, and thus, experiencing length contraction at multiple different rates depending on how you're oriented.)

Minutephysics answering questions we didn't know we had and would have wanted answered

This is a great example of how in science questions lead to answers that in turn lead to more questions, like zooming in on a fractal.

For anyone waiting in the premiere, it's true because they're trying to keep the same distance in reference to the observer whilst the rope is going through length contraction itself. (For a more advanced way to explain, because leading clocks lag, in the spaceships' points of view, when the spaceships are accelerating at the same rate, to the observer it'll seem like the spaceship behind is catching up to the first one. But since the rule is that the distance between the spaceships are kept constant to the observer's point of view, the front spaceship will have to accelerate faster for the spaceships, causing the rope to break.) I only posted this comment because it seems like a lot of people are against the premiere feature and would want to know the answer now.

This thumbnail gives me salt lamp vibes

I was just thinking that regardless of both rockets accelerating the same the string itself would be pulled from the front most (the right one) rocket since it can not accelerate by itself (and as a string it is not an absolute rigid body). As such, depending on the degree of the acceleration the string would indeed snap.

I've been watching your videos for almost a decade now and I found it ironic that this video released the same day that I finally went back and finished the last physics class I need for my degree thanks for all that you do

MinutePhysics to veritasium: Can i copy your homework? *Derek*: o.k. you CAN copy my homework, just don't change it a bit this time 😂

It’s crazy how you can like and comment before you even see the video

I enjoyed the bass groove you used as bgm ❤️

I'm just thankful the macro scale allows us to ignore quantum phenomenon and special relativity for practically all normal problems, by virtue of their effects being far within tolerances.

does anybody know how to turn off notifications on premiers in the sub feed?

Please desist using the Premiere feature. It's wasted space in my subscription feed and by the second time I see it in there (after the premiere) I've got a mental 'you already know this one' stuck in my head.

"At the same time" "Aight Imma stop you right there"

Im on the verge of getting this I can tell. I’ll come back in a year and see if I can understand it better then

How does it work from the perspective of the back spaceship? From its perspective, it will accelerate first and get closer to the first ship, which would not snap the string. What about the perspective of the string? (in the middle, if you want to be precise) Both ships start simultaneously, accelerate together with the string but something happens and tears the string? This seems wrong. If you consider the Barn paradox with train and a tunnel does the answer suddenly change if the back has its own engine? (or depending on whether train is joined or free in the middle?)

Could we create a propulsion system based on this? If the rope is strong enough to pull the rear spaceship rather than snap, wouldn't it cause the rear spaceship to accelerate to a speed greater than the first, creating sort of a relativity slingshot?

As I understand it, it isn't the object that constricts on it's own, it's the space it occupies. Now since no events happen at 'the same time' since the speed of light and the bending of space imply that the idea that two things happen simultaneously is illusionairy, because they only happen at approximately the same time, correct for the speed of light over the distance that they are apart. Events don't occur 'at the same time' unless they also happen at the same space. the reason for this is a little complicated but this would imply that the paradox results from a faulty premise. If the rockets can't move at the same time, because they are apart from each other in space, then the time difference would be what snaps the string because one would leave at a different time from the other applying force to the string.

Finally the OG minute physics

You're tearing this family apart! With your simultaneous, but individual acceleration!

So basically, if one rocket pulls the rope, it doesn’t break, but if a second rocket attempts to help push the rope from the back it breaks the rope…

Note, your sponsor Brilliant is impossible to unsubscribe from. I had to have my bank step in. Yes I followed all the rules!

if we talk about intuition for me the whole is contracting because the space that encompasses the spacecraft is also contracting and this also includes the rope between the spacecraft (from the point of view of the astronauts the distance does not change because the rope and the two spacecraft are at the same speed) if we follow the analogy of the cat with the atoms it is more likely that an atom is detached because the acceleration is not experienced by all the atoms at the same time (the acceleration is transmitted from one atom to another in the structure of the material) ty for the video

Premiere, ditch it, never again

What about a space craft with multiple engines? Existing ones have them and come back in one piece, or does this only matter when traveling a significant fraction of the speed of slight? What about a larger space craft with multiple engines? What if you made those engines further apart? What if you thinned the members that connect them? At what point does a space craft with a large thrust surface become two thrust surfaces connected by a string that would break?

Great example of what Veritasium talked about in his video about titles. I didn't click on the video when the title was "Can length contraction tear you apart?" because the answer was obviously yes. But the video is actually a lot deeper than that, and the new title is a fairer description, even though, strictly speaking, there is no paradox. But then again, a self-contradictory statement is the only real paradox, and you don't get far with that.

I was going to ask why the rockets with string weren't considered as a whole, but the explanation of how it can work with there are multiple points of acceleration answered that.

if the string was weak enough it would break from the acceleration since part of the rope is "still at rest" even if there was zero length contraction and gravity did not break it first

My first thought was that the rope would simply pull the rocket in the back closer rather than snapping, but it seems like we're imagining ropes/strings of different strengths

15 seconds into this video and my brain already shit itself

Conceptually there is a flaw here though... There is no reason the rope should be torn apart if the vehicles accelerate at the same rate because they are all part of the same physical assembly, as though they were indeed one giant long spacecraft. There should be no reason for the rope to be broken apart because it is not the matter which is stretching or contracting but spacetime itself, which will affect all the actors in the puzzle relatively. The objects themselves are not stretched or contracted, rather the spacetime they occupy is, thus there should be no reason for the rope to break in the same way that the surface of a vessel of water would not be broken by transferring the water to a larger vessel. It would be the same volume of water but have a larger surface area in the larger vessel.

I like many of your videos, but the answer on this one is simply wrong, the string would not break. Check my assumptions below to make sure the match yours. Assuming that both rockets accelerate on a strait line with the exact same acceleration starting at the 'same time' in their inertial reference frame, an observer that is sitting on the lead rocket would see the rear rocket maintain the exact same distance; no measurable length or time dilation would occur between the rockets from his point of view. Thus the string would not break. The appearance of lenth dilation only occurs to an observer in a different inertial frame of reference. From this other frame or reference, in this case, the distance between the rockets would shrink exactly as much as the lenght of the string. So no breakage from his point of view either. (Ps in the real world a portion of the lead rockets plume would hit the rear rocket's nose and push him away, thus to maintain the exact same acceleration would require slightly more thrust from the rear rocket.)

Exactly the anti-clickbait Derek talked about

I think about the spaceship paradox often and now I'll think about it even more. thank you... ^_^

This was an interesting piece of information to put into my braincase today.

Wait, if length contractions occur due to a warping in space time itself (assuming speeds close to light), then won't the entire system contract uniformly i.e. the string won't break? Where am I going wrong?

This would be a really interesting thing to explore; Do they undergo contraction as one common "bubble" because all the atoms are accelerating together or do they have their own effects based on their mass that scales to that mass?

Been a while, keep it up bro.

Also man, I am loving the upright bass score!

"if both rockets accelerate the same amount at the same time" why does switching to the perspective of the moving object's nullify the "at the same time"

Please for the love of God stop encouraging this stupid premiere feature. I don't need a list of videos I can't watch yet. It literally adds nothing.

for some reason youtube does not recommand me ur videos anymore im triggered i need my minute physics

This sounds a lot like the pole-barn paradox... One of my first intros to relativity, and probably the one that stuck with me the most since then.

What would be the source of the rope break from the back rocket’s perspective? Wouldn’t it appear that the space between them and the front rocket is shorter and therefore the rope shouldn’t break?

"Do women know about length contraction?" - George Castanza

Brilliant! Thank you!

"In our universe it's not only space and time that are relative, in some cases it's also weather you are torn apart or weather you tear yourself apart". That took off from Physics to Physiology very quickly

Length contraction only happens from the point of view of a static observer, who does not accelerate. Such an observer would see the whole rocket-string-rocket system accelerate together as a single object. From the point of view of the string, which is moving and accelerating with the rockets, the rockets stay at exactly the same place and no contraction is happening. This is a common and frequently perpetuated misconception of how Lorenz transformation works and what effects it actually has in which reference points.

69 yay 12 nay Looks like premier mode is a no go unless content is interactive.

One detail missing from this superb video on SR length-tension is that there is also an SR time-tension or _age gradient_ alpha_m = -((beta)/c) times length. Front clocks in a 0.6 c 100 m spaceship thus show times 200 ns earlier than rear clocks. The rest frame version gets indefinitely large: alpha = -(gamma*beta)/c = -((beta)/(c*sqrt(1-(beta)^2)

Very happy to have guessed that the answer would have to do with relativity of simultaneity.

Wait a minute. Doesn't the whole universe contracts in the axis of the acceleration? That means if the two rockets accelerate the same amount at the same time the distance between them gets shorter with the string. Someone pls explain 😬

gotta appreciate anti-clickbait thumbnail. Thank you

In fact they are two inconsistencies in this video. The synchronization issue arises when you consider two objects in two different frames. The two rockets being in the same frame of reference they can be synchronized by setting the clock at the same distance from the two rockets or accounting for the speed of light if the clock is in one of the rocket. The second inconsistency is this idea of a rope contraction that is different from the distance separating the two rockets. According to me the two contract in the same way. If not, stopping the engines at a given instant and measuring the rope tension will give an information about your absolute velocity (if the tension has increased then your absolute speed must have increased, and if the tension has decreased then your absolute speed must have decreased), this is not allowed by the relativity principle.

Is like to add a different postulate for why the string snaps. Inertial reference. According to the string, both ships start moving simultaneously, with the forward ship tensioning the string and the rear one compressing the string. Because there is no work to be done with regard to the rear ship, the string begins bunching up in the rear while the front stretches beyond tensile limits. The rear of the string finally passes the center of mass of the string, tensioning it again and snapping it in a new spot. The same relativity is in play, the string years itself apart because it cannot catch up to the changing situation fast enough, and the ships tear it apart because they are accelerating faster than the string can change velocity on its own. Interestingly, from the rear ship's point of view, the front shop moves second, so the space between the ships appears to contract, meaning the string is bunched for longer in this frame and doesn't break until the rear ship catches the strings center of gravity and tensions the loop behind it.

good thumbnail, straight to the point

But how does the rocket at the behind observe the string snapping? I mean to itself it moved first and string should not be pulled but lose tension to the observer at the back, right?

Nice. John Bell wrote an excellent essay on this years ago.

I'm going to go with string having inertia - and when the rear end of the string is accelerated it doesn't 'push' the front of the string - because string deforms, and when the front end of the 'weak' string is pulled - the string snaps :)

Are you insinuating that intramolecular signals travel faster than light inside an object?

So, to take this to a sci-fi POV, the TOS Enterprise is good at sub-light speeds because it has a single point of thrust, but the NX-01 Enterprise, which has big impulse engines on the very aft of the ship and about half-way along at the aft of the saucer, might be causing itself some risky hull stresses?

This video completed an inherent gap in my understanding of length contraction. Thank u so much for this.

THIS! this video right here, the one we all just watched, is the reason i went with biology and not physics as my career

Shouldn't the whole system contract together since the ships are stationary relative to each other? Plus, the engines still have to be strong enough to break the rope. I don't see why this is a paradox.

This thumbnail and title is 100% inspired by Veritasiums latest video!

You've already made a so many videos on Relativity and every time it retrains my brain on thinking differently instead of relying on intuition and it helps me solve other problems I have at times. Thanks for the inspiration we can all enjoy. Still fascinates me how one man came up with all of this a hundred years ago revolutionized the way we see our world forever and especially considering he opposed most scientific theories of that era. EDIT: Narf Whals was right!

A space ship would shrink when it moves, as it pushes its forward pieces forward with the backparts at the start of the thrusting force. It doesn't shrink as much as the space between atoms being slightly squeezed. Like two magnets that repel each other, they can go closer if force is applied, and then will push the other way, causing potential other magnets to shrink their distance to it. As a constant motion and thrust, you'd imagine the magnets would neutralize their distance after a while, but the constant thrust force is greater than the outermost repelling force of the magnet, leaving them no choice but to stay closer to each other throughout the travel, as the closer they are the stronger and more capable they are of keeping themselves apart from the other magnet. Magnets work very similarily to atoms, so don't start thinking this is exclusive to magnets. Now, whether the rope snaps, it would be likely that a rope could snap from the movement alone, as suddenly moving on the back and the front would be irrelevant as there would be no push power applied, only drag. Drag extends the distance between the attracting magnet, or in this case the atoms, or rope fibers - which are mostly staying together using friction. Friction is caused by uneven surfaces kind of hooking together or hanging on to each other like rock climbers using the tips of their fingers on small rocks. With the drag from two ships, the rope would not have a heavy amount of weight to drag from just one end, but split it in two, leaving the potential for the rope to hold. If the rope is dragged on one side before the other, which is kind of the point of this theory, the rope would like a domino, be pulled by the first ship for probably up to 99% of the rope, as the other ship would not actually pull the rope at all except for the very part attached to it, as long as the rope was ahead of the ship. You can't push a rope. This could cause the rope to snap because of the weight pushing down being heavier when all the rope is hanging on one side. If we're thinking of a veeery long rope, it would cause a distortion effect in the first place, and not "look like because of the speed of light" that you were pulling the whole rope, but instead would give a sensible visual to the onlooker of the first spaceship that the rope was being 99% by your ship. Galaxies aren't spirals after all. If the back ship had a headstart, it could pull more of the rope as it caught up to the second ship. For a better example, something like a long pole would make more sense, as you can push a pole - but again, the pole would be repelling magnets at the start with the following ship while going away from attracting magnets at the end with the ship furthest away. *TL;DR: rope snap if rope weak and heavy, and leadig ship fast. Back ship do 1% work if rope is exact length and both ships same speed.*